Carpentry and Construction

Tools in this group

• Stair Calculator - Risers, runs, and headroom from total rise.
• Roof Pitch - Pitch as fraction, degrees, and percent.
• Rafter Length - Rafter length from span, pitch, overhang.
• Square Footage - Area for rectangle, triangle, trapezoid, circle.
• Lumber Board Footage - Total board feet from thickness, width, length, count.
• Concrete Volume - Cubic yards for slab, footing, column, footing-with-stem.
• Shotcrete / Gunite Order Quantity with Rebound - Cubic yards of shotcrete or gunite to order once rebound (the fraction that bounces off and never stays) is grossed up: shot = in-place / (1 - rebound). A 500 sf face at 4 in holds 6.17 cy but needs 7.72 cy shot at 20% rebound, 8.82 cy at 30%. The applicator's field rebound governs.
• Rebar Spacing and Quantity - Linear feet of rebar from slab dimensions and spacing.
• Lumber Spans - Maximum span from species, grade, size, load.
• Nail and Screw Pull-Out - Typical pull-out resistance by fastener and species.
• Beam Loading - Moment and deflection for simply supported beams.
• Material Quantity - Quantity for common assemblies with waste factor.
• Stair Stringer Length - Diagonal stringer length and 2x12 board feet from rise and run.
• Joist Mid-Span Deflection - Mid-span deflection with L/360 and L/240 checks.
• Footing Area for Soil Bearing - Required footing area and side dimension by soil class.
• Tile Count and Grout Volume - Tile count with waste and grout cubic-inch estimate.
• Paint Coverage - Gallons per coat by surface porosity and coats.
• Excavation Volume - Cubic yards of soil for a sloped excavation.
• Brick and CMU Count - Unit count from wall area, unit size, and mortar joint.
• Wind Velocity Pressure - q = 0.00256 * V^2 with windward and leeward Cp.
• Basic Wind Speed from Velocity Pressure - The inverse of the wind velocity-pressure tile: the equivalent basic wind speed behind a bare velocity pressure, V = sqrt(q / 0.00256). A 25-psf velocity pressure corresponds to a ~98.8 mph basic wind speed. Enter the bare q (not a Cp-loaded design surface pressure). A design aid; ASCE 7 and the engineer of record govern.
• Flat-Roof Snow Load - Pf = 0.7 * Ce * Ct * Is * Pg per public ASCE 7.
• Anchor Bolt Embedment - Required embedment depth from public bond strength formula.
• Drywall Sheet Count and Mud - Sheets, mud gallons, tape lf, and screws from wall and ceiling area.
• Roofing Squares and Bundles - Squares, bundles per shingle product, underlayment rolls, drip edge.
• Asphalt Tonnage - Tons of mix and truck loads at typical 20 tons per haul.
• Asphalt Paver Speed and Production Rate - Tons per hour and lane-feet per hour a paver lays at a given screed width, depth, and forward speed, with the daily output - the production the asphalt-tonnage takeoff assumes and that sizes the plant delivery and truck rotation.
• Asphalt Tack / Prime Coat Quantity - Emulsion gallons to order for a tack or prime coat: the DOT spec sets a residual (asphalt) rate but the truck meters emulsion, so the residue fraction grosses the order up. A 0.04 gal/sy residual over a 10,000 sf lane needs 74 gal of a 60%-residue emulsion, not the 44 the residual figure alone suggests.
• Aggregate / Gravel Cubic Yards - Cubic yards and tons from area, depth, and material density.
• Conical Stockpile Volume and Tonnage - Volume (cy) and tonnage of a free-standing conical stockpile from its base diameter, angle of repose, and bulk density: height = radius x tan(repose), volume = 1/3 pi r^2 h. A 60 ft pile of stone at 37 degrees stands 22.6 ft and holds ~789 cy (1,065 tons). A survey governs for payment.
• Mortar Mix and Yield - Bags of mortar mix from brick / CMU count and joint thickness.
• Concrete Mix Design (Simplified) - Water-to-cement ratio interpolated from ACI 211-style curves; cement, coarse, fine aggregate per cubic yard.
• Bolt Torque to Clamp Load - Short-form torque T = K * D * F with grade proof loads.
• Sheet Metal Bend Allowance - Bend allowance and flat blank length from K-factor and angle.
• Coil / Roll Stock Length - How much strip is left on the coil without unrolling it: the wound material is an annulus, so L = pi (OD^2 - ID^2) / (4 t) for coil outside diameter OD, core diameter ID, and thickness t. A 48 in coil on a 16 in core at 0.024 in (24 ga) holds 5,585 ft; halve the thickness and the same coil OD holds twice the length. Exact for a tight coil with no telescoping; the last wrap and core stub trim it slightly. A layout aid; weigh or measure-off before a critical cut.
• Bar / Tube Stock Cut List Yield - How many cut pieces come off a stick of bar, tube, or angle and how many sticks to buy, with the saw kerf counted: pieces per stick = floor( (stock + kerf) / (piece + kerf) ); drop = stock - [pieces x piece + (pieces - 1) x kerf]; sticks = ceil(pieces needed / pieces per stick). A 20 ft (240 in) stick cut into 14.5 in pieces with a 1/8 in kerf yields 16 per stick with a 6.13 in drop, so 100 pieces take 7 sticks at 86.3% yield; a 24 ft stick cut into 40 in pieces yields 7 with a 7.63 in drop, 8 sticks for 50 pieces. N pieces take N-1 internal saw cuts. Mixed-length nesting, end trim, and clamping loss are not modeled; the cut list and saw govern. A material-ordering estimate.
• Dished Tank / Vessel Head Volume - The liquid volume of one dished tank head (the bulge past the tangent line), plus any straight-flange skirt: 2:1 semi-elliptical = pi D^3/24; hemispherical = pi D^3/12; ASME flanged-and-dished (torispherical) ~ 0.0847 D^3; straight flange = pi/4 D^2 x length; gallons = in^3/231. A 48 in ID 2:1 elliptical head holds 62.7 gal (14,477 in^3); a hemispherical head of the same diameter holds 125.3 gal, an F&D head 40.5 gal. Two heads make a tank's end allowance beyond the straight-shell volume; the F&D figure is a standard-geometry approximation, the head maker's stamped crown and knuckle radii govern the exact volume. Complements the flat-end tank-volume gauging tile.
• Multi-Bend Flat Pattern (Developed Length) - The flat blank length for a sheet-metal part with several bends: flat = mold-line - n_bends x BD, the sum of the outside (mold-line) flange dimensions minus the bend deduction per bend (from bend-allowance). A U-channel of 2 + 4 + 2 = 8 in mold-line with 2 bends at 0.1355 in BD develops to 7.73 in; a hat section of 12 in mold-line over 4 bends develops to 11.46 in -- more bends pull more material out of the blank. A layout aid; confirm the first part against a test bend, since the real BD shifts with tooling, material, and grain.
• Shop Speeds and Feeds - Spindle RPM and feed rate from SFM and chipload by tool / material.
• Welding Rod and Wire Usage - Deposit weight, consumable weight, time, and shielding gas by process.
• Demolition Debris Weight - Tons of debris and recommended dumpster size by structure type.
• Formwork Pressure - Lateral form pressure (ACI 347 short form) capped at wet head.
• Concrete Pour Rate, Rate of Rise, and Delivery Cadence - The rate of rise (ft/hr) a placement rate produces in a given form footprint - the input formwork-pressure consumes - plus the pour duration and the ready-mix trucks-per-hour delivery cadence. Placing faster than the forms are designed for is how a blowout happens.
• Residential Framing Package - Stud + plate + joist + rafter rollup with board-feet totals from footprint, perimeter, wall height, joist span, rafter span, and pitch.
• Excavation Slope and Bench-Step Plan - OSHA Appendix B slope ratios A 0.75:1 / B 1:1 / C 1.5:1 turned into spoil volume (yd^3), surface footprint, and bench-step layout. Competent person on-site governs the final plan.
• Window / Door Header Sizing (IRC R602.7) - Smallest built-up dimension-lumber header (double / triple 2x6-2x12) from tributary load, span, snow, and species, with the AWC NDS bending / L-360 deflection check and IRC R602.7.5 jack-stud count.
• Wall Stud Notching and Boring Limits (IRC R602.6) - The 'can I drill or notch this stud' field check on the actual stud width: a notch may not exceed 25% of the width in a bearing or exterior wall, or 40% in a nonbearing wall; a bored hole may not exceed 40% (single stud) or 60% (doubled, up to two successive), with the hole edge at least 5/8 in from the stud edge and not in the same cross section as a notch. A 2x6 (5.5 in) bearing stud allows a 1.375 in notch and a 2.20 in single bore; a 2x4 (3.5 in) nonbearing stud allows a 1.40 in notch. Prescriptive IRC limits; a plumbing/mechanical wall, an engineered stud, or a shear wall may be tighter, and the AHJ-adopted code governs. A field check, not a stamped detail.
• Floor Joist Notching and Boring Limits (IRC R502.8.1) - The 'where can I notch or drill this floor joist' field check on the actual joist depth (sawn lumber): an end notch at the bearing may not exceed D/4; a top or bottom notch elsewhere is limited to D/6 deep and D/3 long and is not allowed in the middle third of the span; a bored hole may not exceed D/3 in diameter with its edge at least 2 in from the top and bottom and from any other hole or notch. A 2x10 (9.25 in) allows a 2.31 in end notch and a 3.08 in bore. ENGINEERED I-joists and trusses follow the manufacturer's hole chart only -- never field-notch a flange. Prescriptive IRC limits; a cantilever or heavily loaded joist may be tighter, and the AHJ-adopted code governs. A field check, not a stamped detail.
• Joist / Deck Cantilever Ratio Check (IRC R507.6) - The 1:4 cantilever rule: a joist may overhang its support by no more than a quarter of its backspan (the span back to the next support), per IRC R507.6 for decks and R502.3.3 for floors. A 10 ft backspan allows a 2.5 ft cantilever, so a 3 ft overhang EXCEEDS it and needs a 12 ft or longer backspan; a 12 ft backspan allows 3.0 ft. The prescriptive tables also cap the absolute overhang and require an uplift check, and a beam, wall, or roof bearing on the tip is a separate engineered case. This is the RATIO screen; the span tables, the tip load, the support connection, and the AHJ-adopted code govern. Distinct from the engineering cantilever-beam moment/deflection tile.
• Deck Beam and Post Sizing (IRC R507) - Deck beam ply and size, post size (4x4 / 6x6) from an NDS column check, footing size from soil bearing, and the IRC R507.9.1.3 ledger fastener spacing.
• Braced-Wall-Panel Length (IRC R602.10) - Required braced-panel length (bracing percent x wall-line length), provided vs. required, and a pass/fail. Per IRC R602.10; the required percent is user-supplied from the adopted table.
• Deck Ledger Fastener Spacing (IRC R507.9) - On-center spacing, fasteners for the ledger length, and a span/table check. Per IRC R507.9; the spacing is user-supplied from the adopted table for the fastener/span row.
• Stair Stringer Layout (with code check) - Riser count, exact rise, total run, stringer hypotenuse, throat depth, and pass/fail against your AHJ's max rise / min tread.
• Hip / Valley / Jack Rafter Schedule - Common-rafter and hip multipliers, jack-rafter shortening per OC, irregular-hip second pitch handling. Framing-square method.
• Rebar Bend and Weight Schedule - Cut length with bend allowance and total weight by bar size from the bundled #3-#11 unit weights.
• Welded-Wire Reinforcement (Mesh) Sheet Takeoff - Sheets of welded-wire reinforcement (mesh / WWF) for a slab once the side and end laps eat coverage: effective sheet = (width - side lap)(length - end lap); sheets = ceil(area x (1 + waste) / effective). A 2,000 sf slab with 5x10 sheets at 6 in laps needs 50 sheets, not the 42 a no-lap count suggests.
• Plywood and OSB Sheathing Span Rating - Allowable spacing / live load / total load from APA span-rating tables; pass/fail against user-supplied design loads.
• Helical Pile Torque-to-Capacity - Ultimate axial capacity from torque × Kt and allowable from factor of safety. Engineer of record governs.
• Helical Pile Acceptance Torque for a Target Capacity - The inverse of the helical-pile tile: the installation torque a pile must reach to confirm a target capacity, torque = (allowable × factor_of_safety) / Kt = ultimate / Kt. A 22,500 lb allowable at FS 2 on a 1.5 in solid shaft (Kt 10) needs 4,500 ft-lb; a lower-Kt 3.5 in pipe (Kt 5) needs 9,000 ft-lb for the same capacity. This is the field-acceptance torque the crew watches on the drive-head gauge. An installation check, not a load test; the engineer of record governs.
• Crane Lift Plan Quick-Math - Gross load, sling tension, percent of chart, and 75 / 90 percent flag. The crane manufacturer's load chart governs.
• Bearing Length on a Wood Plate - Required bearing length and actual compression-perpendicular-to-grain stress for a point load on a wood plate, with a pass/fail against the allowable Fc-perp.
• Wood Column Capacity (Slenderness) - Slenderness ratio, column stability factor Cp, allowable Fc-prime, and allowable axial capacity for a solid rectangular sawn-lumber column via the NDS Cp / Euler buckling basis.
• Simple-Span Beam Reactions and Max Moment - Left/right reactions, max shear, and max bending moment for a simple-span beam under a uniform load plus an optional point load, by superposition.
• Welding Heat Input - Heat input in kJ/in and kJ/mm from volts, amps, travel speed, and arc efficiency, with WPS pass/fail.
• Metal Weight by Shape and Alloy - Weight per piece and total by shape, dimensions, length, and alloy density.
• Layout Squaring (3-4-5) - Diagonal to pull and out-of-square diagnosis for a rectangular layout.
• Horizontal Curve Layout - Tangent, length, external, middle ordinate, chord, and PC/PT stations for a circular curve.
• Curve Deflection-Angle Stakeout - The field method horizontal-curve leaves out: to set a circular curve by deflection angles, an arc length l from the PC turns a deflection from the back tangent of delta = (l/2R)(180/pi) deg and pulls a sub-chord c = 2R sin(l/2R). On a 500 ft radius, 100 ft of arc is a 5.7296 deg deflection and a 99.83 ft chord (degree of curve 11.459). Enter radius or degree of curve. Simple circular curve, no spiral; the design of record governs.
• Vertical Curve Elevations - Equal-tangent parabolic elevations and the high or low point of a vertical curve.
• Earthwork Volume (End-Area) - Average-end-area and prismoidal earthwork volume in cubic feet and yards.
• Slope-Stake Cut and Fill - Cut or fill depth and the catch-point offset for a planar design slope.
• Superelevation / Min Curve Radius (AASHTO) - AASHTO point-mass e + f = V^2/(15 R): required superelevation for a radius, or the minimum radius at a maximum bank.
• Safe Curve Speed from Radius and Superelevation - The inverse of the superelevation tile: the maximum safe speed a curve supports from its radius, superelevation (bank), and side-friction factor, V = sqrt( 15 R (e + f) ) mph. A 1,500 ft radius at e 0.08 and f 0.12 supports about 67 mph. Use the AASHTO f for the resulting speed band (f decreases with speed; iterate once). Point-mass model; ignores grade and the transition. A design/check aid; the civil engineer governs.
• Crest Vertical Curve Length for SSD (AASHTO) - AASHTO minimum crest vertical-curve length L for a stopping sight distance, both S<=L and S>L branches, with the K rate.
• Sag Vertical Curve Length for Headlight SSD (AASHTO) - The sag (valley) companion the crest tile hands off: a sag curve is limited at night by headlight reach, so its minimum length comes from the AASHTO headlight criterion L = A S^2/(400 + 3.5 S) for S<=L, L = 2 S - (400 + 3.5 S)/A for S>L, with K = L/A (400 and 3.5 embed the 2.0 ft headlight height and 1-degree beam). A 4% grade break needing 400 ft SSD wants a 350 ft sag curve (K 87.5). Headlight-SSD control only; comfort (A V^2/46.5) and drainage (K<=167) are separate. A design aid, not a substitute for a licensed civil engineer's design.
• Sag Vertical Curve Comfort and Drainage (AASHTO) - The comfort and drainage sag-curve controls the headlight tile names as separate checks. The AASHTO comfort criterion L = A V^2/46.5 (A in %, V in mph) is the length that holds the vertical acceleration on the sag to about 1 ft/s^2, giving K = L/A = V^2/46.5; the drainage maximum K <= 167 (a 0.30% minimum grade within 50 ft of the low point, 50/0.30) caps the length at 167 A on curbed sections. A 4% break at 60 mph wants at least a 310 ft curve (K 77.4) for comfort and no more than 668 ft for drainage. Comfort is far less restrictive than headlight SSD; a licensed civil engineer's design governs.
• Horizontal Sightline Offset on a Curve (AASHTO) - AASHTO middle-ordinate clear-zone M = R(1 - cos(28.65 S/R)) an inside obstruction must clear for stopping sight distance.
• Fillet Weld Strength and Size - Throat, ASD/LRFD shear capacity, utilization, and the AISC J2.4/J2.2b min/max fillet size for a steel fillet weld (AWS D1.1 / AISC 360).
• Intermittent Fillet Weld Schedule (AISC J2 / AWS) - When a required continuous fillet is smaller than the practical minimum weld, sizes the intermittent (stitch) schedule that matches it: weld a fraction w_req/w of the length at the larger stitch size, pitch = increment / fraction, each increment at least the greater of 4 x the weld size or 1.5 in (AISC 360 J2.2b). A 3/16 in required weld done as 5/16 in stitches means welding 60% of the length; a 3 in increment gives a 5 in pitch (weld 3, skip 2) and clears the 1.5 in minimum. Maximum spacing and end returns are separate checks. A design aid, not a substitute for the engineer of record.
• Groove Weld Strength - CJP / PJP groove-weld shear capacity on the effective throat (ASD / LRFD), with the CJP base-metal note and utilization (AWS D1.1 / AISC 360 §J2).
• Groove Weld Length for an Applied Load - The inverse of the groove-weld-strength tile: the weld length an applied load needs at a given effective throat, L = load / (stress_ksi x 1000 x throat), with stress_ksi = 0.30 FEXX (ASD) or 0.75 x 0.60 FEXX (LRFD). A 100,000 lb LRFD load on a 0.25 in E70 PJP throat needs about 12.7 in. Round up, split between joint sides, and add for returns and minimum-length rules. AWS D1.1 / AISC 360 §J2; the WPS and engineer of record govern.
• Press-Brake Air-Bend Tonnage - Air-bend press-brake tonnage from thickness, bend length, V-die opening, and tensile strength: tons/ft = 575 x (UTS/60) x T^2 / V (the published mild-steel 575 constant), with the 8 x T die and minimum-flange advisories (empirical air-bend rule).
• Press-Brake Max Bendable Thickness - The inverse of the press-brake tonnage tile: the thickest material a press can air-bend, T = sqrt(tons x V / (575 x (UTS/60) x L)). A 100-ton press with a 0.5 in V-die over a 4 ft bend in mild steel tops out at ~0.147 in; stronger stainless drops to ~0.120 in. Air bending only - bottoming and coining need several times the tonnage. The die maker's chart governs.
• Welder Duty Cycle - Allowable welder duty cycle at a target amperage from the rated amperage and duty cycle: DC2 = DC1 x (A1/A2)^2 (capped at 100%), minutes on per 10-minute window, and the maximum continuous amperage A1 x sqrt(DC1/100) (first-principles I-squared heating, NEMA EW-1).
• Carbon Equivalent and Preheat Screen - IIW carbon equivalent CE = C + Mn/6 + (Cr + Mo + V)/5 + (Ni + Cu)/15 from the steel chemistry, with a plain-English weldability / preheat band (the formula adopted in AWS D1.1; a screen, not a welding procedure).
• Shielding-Gas Cylinder Runtime and Cost - Gas used, runtime per cylinder, cylinders needed, and the prorated gas cost from a flow setting and arc-on time. Compressed-gas and hot-work hazards govern; follow the maker's instructions and your hot-work permit.
• Oxy-Fuel Cutting Gas Consumption - Cut time, oxygen and fuel consumed, and runtime per cylinder for an oxy-fuel cut from the tip flows, cut length, and travel speed. The torch maker's tip chart sets the real flows; compressed-gas and flashback hazards govern.
• Weld Preheat Energy and Fuel - Heat needed, fuel energy after efficiency, and propane in pounds and gallons to bring a steel mass to a preheat temperature. The preheat temperature comes from carbon-equivalent or the WPS; hot-work hazards govern.
• All-In Welding Cost per Foot - Consumable per foot, filler cost, labor hours and cost, and the all-in cost per foot of weld -- where labor and the operating factor, not the filler, usually dominate. A real bid adds shop overhead, grinding, and power.
• Weld Deposit Weight, Filler, and Pass Count - Weld cross-section, deposit weight, filler purchased after deposition efficiency, and the pass count for a fillet (by leg) or groove (by area) weld from first-principles joint geometry and steel density (0.2836 lb/in3). The WPS and the shop's measured deposition efficiency govern.
• Wire Feed Speed to Deposition Rate - Melt-off rate from wire feed speed and electrode diameter, and the deposition rate after spatter loss, from first-principles wire-volume geometry and steel density. Pairs with weld-metal-volume for arc time. The WPS and process (spray vs short-circuit, gas) govern the real efficiency.
• Wire Feed Speed for a Target Deposition Rate - The inverse of the wire-feed-deposition tile: the wire feed speed a target deposition rate needs, WFS = deposit / (60 x wire cross-section x 0.2836 x efficiency). A 6 lb/hr target on 0.035 in wire at 92% efficiency needs about 398 in/min; a smaller wire needs a much higher speed (rate goes as diameter squared). Answers 'what WFS to set' instead of the rate from a set speed. The WFS must be within the WPS-qualified range; the WPS and process govern.
• Weld Transverse Shrinkage and Pre-Set - Transverse shrinkage per weld and total pull from the Blodgett relation (0.2 x weld area / thickness), and the recommended pre-set to lay the parts apart so the assembly cools to size. A screen; restraint, sequence, and a mock-up govern, and longitudinal/angular distortion are out of scope.
• Eccentric Fillet Weld Group (Elastic Method) - Line polar moment, direct shear, torsional components, the resultant unit force at the critical corner, and the required fillet leg for two vertical welds under in-plane eccentric load by the AISC elastic (vector) method. The conservative elastic method, a screen; the engineer of record governs.
• Minimum Plate Bend Radius - Minimum inside bend radius and radius-to-thickness multiple to avoid cracking the outer fiber, from the published forming-limit relation R_min = T x (50 / %elongation - 1) and the mill-cert elongation. A screen; the mill cert, grain direction, and a test bend govern.
• Sheet-Metal Bend Springback - How much a sheet-metal bend springs OPEN when the tooling releases, by the Machinery's Handbook relation Ks = Ri/Rf = 4 x^3 - 3 x + 1 with x = Ri x yield / (E x thickness). Elastic recovery makes the released radius Rf = Ri/Ks LARGER than the die radius, and the angle opens too, so the operator must OVERBEND. A 1 in tool radius in 0.1 in, 50 ksi steel gives Ks 0.948 -> the radius springs from 1.0 to 1.05 in (~5%); a high-yield or aluminum part (higher yield/E) springs more, a thicker part less. The exact overbend depends on the tooling (air bend vs bottoming vs coining -- coining nearly eliminates it), grain direction, and press, so the first article is confirmed with a protractor and radius gauge. A screen; the material cert, tooling method, and a test bend govern.
• Weld Dilution Ratio - Weld dilution = melted base-metal area / total deposit area, the base-metal fraction of the deposit. A structural single-pass weld runs 30-40% (A_base 0.03, A_filler 0.05 -> 37.5%); a hardfacing overlay is kept low (16.7%) so the alloy stays near the filler. The WPS and filler data govern.
• Weld Passes and Arc Time to Fill a Groove - Passes = ceil(groove area / area per pass), deposited weight = area x length x density, arc time = weight / deposition rate, total = arc / operator factor. A 12 in, 0.15 in^2 groove at 8 lb/h -> 5 passes, 0.51 lb, 3.8 min arc (9.5 min at 40%). The WPS and shop rates govern.
• Weld Travel Speed for a Target Heat Input - Travel speed TS = (60 V I eta)/(1000 HI) to hold a target heat input; travel at or above it to stay at or under the limit. GMAW 24 V, 200 A, eta 0.8, 40 kJ/in -> 5.76 in/min; a 25 kJ/in ceiling forces 9.22 in/min. The qualified WPS governs.
• Compound Miter (Crown Molding) - Saw settings to cut crown molding flat on the table: miter (table) = atan(tan(corner/2) x sin(spring)) and bevel (blade tilt) = asin(cos(spring) x cos(corner/2)) from the molding spring angle (38 or 45 degrees) and the wall corner angle (90 for a square corner) (first-principles trigonometry; reproduces the standard compound-miter chart).
• Soil Swell / Shrinkage Volume Conversion - Convert bank (in-place) cubic yards to loose (truck) and compacted (placed) volume with the load factor and the borrow shortfall. The geotech report governs the percentages.
• RUSLE Annual Soil Loss - Tons per acre per year a disturbed site sheds by the USDA public-domain RUSLE method, A = R x K x LS x C x P, plus the site total - the driver that sizes every SWPPP BMP. A bare 5-acre site (R 150, K 0.32, LS 1.5) loses 72 tons/acre/yr; a blanket dropping C to 0.10 pulls it to 7.2. Every factor is user-entered; the permitting AHJ governs.
• Riprap Median Stone Size (Isbash) - Median stone size D50 to armor a channel or outlet against a scouring velocity by the public-domain Isbash equation, D50 = SF x V^2 / (2 g C^2 (Ss - 1)). An 8 ft/s flow in turbulent water (C 0.86) wants a 12 in stone; the same flow in a calm reach (C 1.20) needs only 6 in - turbulence, not just velocity, sets the rock. The hydraulic engineer governs.
• Riprap Layer Volume and Tonnage - Cubic yards and tons of stone to order for a riprap layer: volume = area x thickness / 27, tons = area x thickness x unit weight / 2000. A 500 sf outlet apron 2 ft thick is 37 cy and 82.5 tons at solid 165 pcf, but ordering to a placed 130 pcf (voids counted) drops it to 65 tons. The order-quantity companion to riprap-d50.
• Silt Fence Drainage-Area and Length Check - Whether a silt fence is long enough for the drainage area behind it (required length = tributary acres x 400, the quarter-acre-per-100-ft guideline) and whether the slope length stays under the AHJ limit. A 0.5-acre tributary needs 200 ft of fence; a 250 ft run catches up to 0.625 acre. Sheet flow only - a channel needs a check dam.
• Rock Check Dam Spacing - Spacing between rock check dams in a channel or swale, where the toe of each upper dam sits at the crest of the next: spacing = dam height / channel slope, dams = ceil(reach / spacing). A 2 ft dam in a 4% channel spaces at 50 ft (6 dams over 300 ft); on an 8% grade the spacing halves and the count doubles. Small channels only; the AHJ governs.
• Sediment Basin / Trap Storage Volume - Settling storage a construction general permit requires per disturbed acre: required volume = disturbed acres x per-acre rule (commonly ~3,600 cf/acre wet storage), surface = volume / depth. A 5-acre disturbance needs 18,000 cf (667 cy), a 6,000 sf pond at 3 ft. Sizes settling storage only; the spillways are designed separately. Distinct from flood-control detention.
• Erosion Blanket (RECP) Roll and Staple Takeoff - Rolls and staples to order for a slope erosion-control blanket (RECP), where the side/end overlap drives the roll count: rolls = ceil(area x (1 + overlap) / roll area), staples = ceil(area sy x staples per sy). An 18,000 sf slope at 10% overlap needs 22 rolls and ~3,000 staples. The manufacturer's guide sets the overlap and staple pattern.
• Hydroseed Slurry Mix and Tank Count - Seed, mulch, and tackifier solids for a hydroseed job and the tank loads to shoot it: solids = area x (seed + mulch + tackifier rates), tanks = ceil(solids / (tank gallons x loading limit)). A 3-acre stabilization at 2,000 lb/acre mulch is 6,165 lb of solids, 6 loads in a 3,000-gallon tank. The mulch rate (set by the slope) dominates; distinct from agricultural seed-rate.
• Stabilized Construction Entrance Stone - Cubic yards and tons of coarse stone for a stabilized construction entrance (track-out BMP): tons = length x width x depth x unit weight / 2000. The common 50 ft x 14 ft x 6 in pad is 13 cy (~17.5 tons) - the load on site before the first truck rolls out. The geotextile separator under the pad is taken off separately; the AHJ sets the size.
• Buried Pipe Flotation and Anti-Flotation Backfill - Flotation check for an empty large-diameter pipe in a flooded trench: uplift = water unit weight x pi/4 x OD^2; FS = (pipe + backfill weight) / uplift. A 48 in empty pipe sees 784 lb/ft of uplift, so 200 lb/ft of pipe plus 900 lb/ft of backfill gives only FS 1.40 - short of 1.5, needing ~976 lb/ft of backfill to hold it down. Submerged backfill counts only its buoyant weight; the design engineer governs.
• Restrained-Joint Length at a Pipe Bend - Run of restrained pipe each side of a bend that holds the thrust when a concrete block will not fit: thrust = 2 x pressure x area x sin(bend/2); length each side = thrust / soil resistance per foot. A 12 in main at 150 psi through a 90-degree bend throws 24,000 lb, so at 600 lb/ft the crew restrains ~40 ft each side; a 45-degree bend needs half that. The restraint manufacturer's tables (EBAA / AWWA M41) set the unit resistance.
• HDD Pullback Force First-Order Estimate - First-order force to draw a product pipe back through a horizontal directional bore (ASTM F1962 basis): pullback = friction x effective weight x length x bend factor + fluid drag. A floated 12 in HDPE at ~5 lb/ft over an 800 ft bore, at 0.3 friction and a 1.5 bend factor, pulls back at ~1,800 lb - checked against the pipe safe pull and the rig thrust. Omits the full F1962 capstan/bend and hydrokinetic drag terms; the drilling contractor governs.
• Dust-Control Watering Volume and Truck Trips - Gallons a water truck spreads on a haul road and the trips to keep the fugitive-dust permit satisfied: gallons = area/9 x rate (gal/sy); trips = ceil(gallons / truck capacity). A 2,000 ft x 20 ft road at 0.5 gal/sy is 2,222 gal an application (one 4,000-gal load); at six passes a day that is ~13,300 gal over six trips. The dust plan and AHJ air permit set the rate and frequency; frequency, not area, drives the water budget.
• Haul-Road Total Resistance and Required Rimpull - The resistance a loaded hauler fights and the rimpull to climb it: total resistance = grade + rolling resistance; rimpull = total x GVW (20 lb/ton per 1%). A 150,000 lb hauler on a 5% grade over a 4% rolling-resistance road fights 9% and needs 13,500 lb of rimpull (180 lb/ton). Downhill the resistance goes negative and the operator is on the retarder. Grading the road down cuts rolling resistance - the cheapest horsepower there is.
• Dump Truck Governing Payload and Load Count - Whether the box volume or the legal weight limit fills the truck first, and the load count: weight-limited volume = weight limit / density; payload = min(weight-limited, box); loads = ceil(total / payload). 625 loose cy in 12 cy boxes is 53 loads when the box governs, but haul wet 3,600 lb/cy material and the 40,000 lb limit caps each truck at 11 cy - 57 loads. Weight governs heavy material, volume governs light; pairs with haul-cycle-production.
• Earthwork Production Unit Cost - Joins the equipment hourly rate to the hourly production into the unit cost a bid needs: unit cost ($/cy) = (equipment + operator + support $/hr) / production (cy/hr). A dozer at $215/hr all-in moving 656 cy/hr costs $0.33/cy, but let production fall to 400 cy/hr on soft ground and it costs $0.54/cy - a 63% jump the rate alone never shows. Low production, not the rate, is what blows up the unit price.
• Soil Stabilization (Lime / Cement) Quantity - Lime or cement takeoff for subgrade stabilization from a percent-by-dry-weight mix design: spread (lb/sy) = percent/100 x density x depth/12 x 9; tons = spread x area / 2000. A 6% lime treatment 8 in deep in 110 pcf soil is 39.6 lb/sy, so a 10,000 sy pad needs 198 tons; a 4% cement treatment is 26.4 lb/sy and 132 tons. The geotech's mix design sets the percent - lime for plastic clays, cement for granular subgrades.
• Buried Flexible Pipe Deflection (Modified Iowa) - How much a plastic or thin-wall pipe ovals under its soil load, by the public-domain Modified Iowa formula: deflection % = DL x K x Wc / (0.149 PS + 0.061 E') x 100. A pipe under 12 ft of 120 pcf soil on good bedding (E' = 1,000) deflects 2.2% - fine - but drop the bedding support to E' = 200 and it jumps to 7.9%, past the 5% limit, on the same pipe. The compaction beside the pipe is the whole game; a mandrel test confirms it.
• Asphalt Spread Rate and Yield Check - The spread rate (lb/sy) a mat lays and the yield (sy/ton) a paving crew checks load by load: spread = thickness x density x 0.75; yield = 2000 / spread. A 2 in mat at 145 pcf lays 217.5 lb/sy and yields 9.2 sy/ton; a 3 in lift lays 326 lb/sy at 6.1 sy/ton. A low yield means the mat is running thick or the trucks are short. The mix design's compacted density governs.
• Cold-Planing (Milling) Production and RAP Tonnage - Square yards per hour a cold planer cuts and the reclaimed-asphalt (RAP) tonnage it makes, which sizes the haul fleet: sy/hr = drum width x speed x 60 x efficiency / 9; RAP tph = sy/hr x depth x density x 0.75 / 2000. A 7 ft drum at 30 ft/min covers 980 sy/hr, and a 4 in cut of 148 pcf pavement is ~218 tph of RAP - a truck every three minutes, or the mill stops. Field conditions govern the efficiency.
• Pavement Marking Paint and Glass Bead Quantity - Paint and glass beads for a pavement-marking run: stripe area = length x width / 12; gallons = area / coverage (sf/gal); beads = gallons x rate (lb/gal). A mile of 4-in line is 1,760 sf - 5.5 gal of paint and 33 lb of beads; a 6-in edge line takes 8.25 gal and 49.5 lb. The coverage follows the wet-mil thickness and the bead rate the retroreflectivity spec. Distinct from architectural paint-coverage.
• Work-Zone Merging Taper Length and Device Count (MUTCD) - MUTCD merging-taper length for a lane closure and the channelizing devices it takes: for 40 mph or less L = W x S^2 / 60, for 45 mph or more L = W x S; devices = ceil(L / spacing) + 1. Closing a 12 ft lane at 55 mph needs a 660 ft taper and 18 cones at 40 ft spacing; at 30 mph the taper shortens to 180 ft (6 devices) because the low-speed branch uses the speed squared. The low- and high-speed branches are a deliberate step. Shifting, shoulder, and downstream tapers use fractions of L.
• Lap / Panel Siding Squares and Linear Footage - Siding takeoff: net wall area after openings, the squares with waste, and the lap linear footage at a reveal. net = wall - openings; squares = net x (1 + waste/100) / 100; linear = net / (exposure/12). 2,000 sf of wall less 200 sf of openings at 12% waste is 20.16 squares, and at a 4 in exposure about 5,400 LF of lap board; a wider 6 in reveal cuts it to 3,600 LF at the same squares. A square is 100 sf. Starter strip, corners, J-channel, and trim are taken off separately. Distinct from fence-estimate and metal-roof-panels.
• Portland-Cement Plaster (Stucco) Material Takeoff - Bags of portland-cement plaster for a multi-coat thickness over an area: bags = ceil(area x thickness / bag yield x (1 + waste/100)). 1,000 sf of a three-coat 7/8 in system on an 80-lb bag yielding 10.1 square-foot-inches is about 96 bags with waste; a two-coat 5/8 in system drops to 69. The coats (scratch + brown + finish, ~3/8 + 3/8 + 1/8 in over metal lath) come from the spec; the sand and lime are batched per the mix design. Distinct from mortar-mix and thinset-coverage.
• Under-Slab Vapor Barrier Rolls and Seam Tape - Poly vapor-barrier rolls for a slab (with lap and waste) and the seam tape: rolls = ceil(area x (1 + overlap + waste) / roll coverage); seam tape = area / roll width. A 3,000 sf slab on 10-mil 1,000 sf rolls with 6 in laps and waste takes 4 rolls and about 300 LF of tape; a 6,000 sf slab takes 7 rolls and 600 LF. Under-slab retarders follow ASTM E1745 (a Class A membrane is common under conditioned slabs); penetrations and the perimeter seal are added separately.
• Concrete Control-Joint Saw-Cut Footage - Saw-cut linear feet for the control-joint grid a slab implies: panels each way = ceil(dimension / spacing); joint footage = (panels_L - 1) x width + (panels_W - 1) x length. A 60 x 40 ft slab on a 12 ft grid is a 5 x 4 panel layout and 340 LF of saw cut; a tighter 10 ft grid gives 380 LF. The cut is made early (a soft cut within hours or a conventional cut before shrinkage cracks) to about a quarter of the slab depth. Takes control-joint-spacing to the blade footage.
• Foundation Waterproofing / Dampproofing Takeoff - The fluid-applied waterproofing or dampproofing to coat a below-grade foundation wall: area = perimeter x average below-grade height; gallons = ceil(area x (1 + waste) / the product's coverage rate). A 150 ft perimeter, 8 ft below grade is 1,200 sf, so at 50 sf/gal spray-applied with 10% waste it takes 27 gallons (6 five-gallon pails). The coverage rate is the lever and varies widely: thin sprayed-asphalt DAMPPROOFing runs ~40-60 sf/gal (a moisture barrier, IRC R406.1), while a fluid-applied WATERPROOFing membrane built to a wet-mil thickness (for hydrostatic head, IRC R406.2) covers far fewer sf/gal per coat and often needs two coats plus reinforcing fabric -- read it off the data sheet, not a default. Sheet peel-and-stick membrane is ordered by the roll instead. A material-ordering estimate; the product data sheet, the assembly detail (drainage board, footing drain), and IRC R406 and the AHJ govern.
• Foundation Drainage Board (Dimple Mat) Takeoff - The dimpled drainage board (dimple mat / composite drainage sheet) to cover a below-grade foundation wall over the waterproofing, ordered by the roll -- it relieves hydrostatic pressure to the footing drain and protects the membrane during backfill. Area = perimeter x average below-grade height; rolls = ceil(area x (1 + waste) / roll coverage); plus a top-edge termination bar per perimeter. A 150 ft perimeter, 8 ft below grade is 1,200 sf, so at a 4 x 50 ft (200 sf) roll with 10% waste it takes 7 rolls plus ~150 lf of termination molding. The dimples face the WALL so the air gap sits against the membrane. Order the termination bar, corners, and butyl tape separately and lap per the maker's detail. A material-ordering estimate; the roll size and lap, the assembly detail (membrane below, footing drain per IRC R405), and the AHJ govern.
• Ballasted Roof Ballast Weight and Order - The weight and order quantity of loose ballast on a ballasted single-ply (EPDM / TPO) low-slope roof. Total dead load = roof area x ballast rate: 5,000 sf at 12 psf = 60,000 lb (30 tons). Stone is ordered by the yard, so volume = weight / bulk density (~90-105 pcf river gravel) / 27 = 22.2 cu yd, ~1.4 in deep. The BALLAST RATE is set by ANSI/SPRI RP-4 from the building height, roof-edge/parapet condition, and wind zone: often 10 psf (nominal 1,000 lb/square) of smooth #4 river gravel in the field, rising to ~13-15 psf or concrete pavers at the corners and perimeter and on taller/higher-wind buildings. A dead-load and ordering SCREEN, not a wind-uplift design; RP-4 and the structural engineer set the rate and zone layout, and the deck capacity governs.
• Concrete Curing Compound Coverage - Gallons of liquid membrane-forming curing compound (ASTM C309) for a slab: gallons = ceil(area x coats / coverage x (1 + waste)), coverage about 200 sf/gal but the product label governs. A 2,500 sf slab at one coat and 200 sf/gal takes 13 gal (3 five-gallon pails); a 3,200 sf slab at two coats with 10% overspray takes 36 gal. A rough broom or tined finish, vertical faces, and a second coat all cut the coverage. Apply right after the surface sheen leaves so the membrane seals in the mix water; a dissipating-resin (Type 1-D) or white-pigmented heat-reflecting (Type 2) is chosen per the job. A material-ordering estimate; the product data sheet and the spec govern the rate and type.
• Concrete Isolation-Joint Filler Takeoff - Pre-molded isolation-joint filler (usually 1/2 in fiber or foam) around a slab-on-grade where it abuts rigid elements so it can move independently: filler = 2 x (length + width) + columns x column-perimeter, strips = ceil(filler / strip length). A 40 x 30 ft slab around six 12 in columns is 164 LF (140 perimeter + 24 columns), 17 ten-foot strips; a 50 x 40 ft slab with no interior columns is 180 LF. This is distinct from the sawn CONTROL joints (concrete-sawcut-footage), which relieve shrinkage within the slab. The structural and slab-on-grade details (ACI 302 / ACI 360) govern where the isolation joints go and the filler type.
• Concrete Stair / Stoop Volume Takeoff - The ready-mix volume of a poured stair or stoop = the stepped wedge plus the raking waist slab: cross-section = n triangular steps (each 1/2 x riser x tread) + the throat slab (throat thickness x rake length sqrt((n x riser)^2 + (n x tread)^2)), times the width; cy = in^3 / 46656. A 4-riser stoop at 7 in rise, 11 in tread, 48 in wide on a 4 in throat is about 10.1 ft^3 (0.37 cy); a 6-riser flight at 7.5/10 in, 36 in wide, 5 in throat is 12.5 ft^3. Order a bit over -- this is the neat geometry and ignores the nosing overhang, a top landing or bottom footing, and the rebar displacement. A ready-mix ordering estimate; the structural stair detail and the finisher's forms govern the pour.
• Slab Load-Transfer Dowel Schedule (ACI 302) - The smooth, GREASED load-transfer dowels for a jointed slab-on-grade, per ACI 302 detailing -- round bond-broken dowels that make two panels deflect together under wheel loads while still free to shrink and slide (distinct from the deformed bonded bars of rc-shear-friction). One dowel every spacing (commonly 12 in o.c.) along the joint, inset from each edge: dowels per joint = floor((joint length x 12 - 2 x edge clearance) / spacing) + 1. A 40 ft joint at 12 in o.c. with 6 in edge clearance takes 40 dowels; five such joints need 200. Dowel diameter ~ slab thickness / 8 (about 3/4 in for a 6 in slab), ~18 in long, ONE end greased so the joint can open -- but ACI 302.1R gives the actual size/length/spacing by thickness in a table, which governs. Dowels must be aligned parallel (a basket), or a locked joint cracks the slab. A takeoff/detailing aid; the structural drawings, ACI 302/360, and the engineer of record govern.
• Joist Hanger and Connector-Nail Count - Joist hangers and the connector nails that fill them: joists = ceil(width x 12 / spacing) + 1; hangers = joists x hung ends; nails = hangers x nails per hanger. A 16 ft-wide floor at 16 in on center is 13 joists, hung both ends, so 26 hangers and about 260 connector nails; if one end bears on a beam (ends = 1) it is 13 hangers and 130 nails. Every hanger hole is filled with the specified structural connector nails (not roofing nails); the manufacturer sets the model. Distinct from deck-ledger-fasteners.
• Drywall Screw Fastener Takeoff - Drywall screws from the framing spacing and the field pattern: studs per sheet = floor(width x 12 / stud spacing) + 1; screws per stud = floor(length x 12 / field spacing) + 1; total = sheets x studs per sheet x screws per stud. 100 sheets on 16 in framing at a 12 in field pattern is 36 screws a sheet (3,600 screws); a tighter 8 in pattern on a fire-rated or ceiling assembly runs it to 5,200. Counts fasteners only -- the sheets and mud are in the drywall tile.
• Glass Weight and Suction-Cup Lifter Count - Glass weight and the suction-cup lifter count it takes: weight = area x thickness x density (~13 lb/ft^2 per in for soda-lime); cups = ceil(weight x safety factor / cup working load). A 4 x 8 ft insulated unit with a half-inch of total glass weighs 208 lb and at a 4:1 safety factor on 150-lb cups needs 6 cups; a monolithic 1/4 in lite of the same size is 104 lb and 3 cups. The safety factor and cup WLL come from the lifter manufacturer; a competent person and the rated lifter govern the pick.
• Polymeric Paver Joint Sand Bag Count - Bags of polymeric joint sand for a paver area, with waste: bags = ceil(area x (1 + waste/100) / coverage per bag). A 400 sf patio at 75 sf per bag is 6 bags, but wide joints around large-format pavers cut the coverage to about 45 sf/bag and push it to 10. The coverage per bag comes from the product chart and drops sharply with wider joints and larger pavers; the sand is swept in, compacted, and misted. Distinct from the paver and base takeoff in paver-patio.
• Rigid / Continuous Insulation Board Count - Rigid continuous-insulation boards (XPS, polyiso, EPS) for an area, with waste and layers: boards = ceil(area x (1 + waste/100) / board area) x layers. A 1,600 sf wall in 4 x 8 boards at 8% waste is 54 boards a layer, so a two-layer continuous-insulation assembly with offset seams is 108 boards; a single layer is 54. The layer count, set by the required continuous-insulation R, is the multiplier; fasteners, plates, and tape are taken off separately. Distinct from spray-foam-board-feet and insulation-batt-coverage.
• Roof Board Fastener and Plate Count by Zone - Fasteners and plates for mechanically-attached roof insulation, by wind-uplift zone: fasteners = field boards x field rate + perimeter boards x perimeter rate + corner boards x corner rate; plates = fasteners (one each). 100 field boards at 8, 20 perimeter at 12, and 5 corner at 16 is 1,120 fasteners and plates; a high-wind field pattern of 12 raises it to 1,520. The zone densities come from the manufacturer's FM or UL uplift design. Distinct from the shingle and panel fastener tiles.
• Housewrap (WRB) Rolls, Cap Fasteners, and Seam Tape - Housewrap (weather-resistive barrier) takeoff: rolls = ceil(area x (1 + overlap + waste) / roll coverage); cap fasteners = ceil(area x fasteners per sf); seam tape = area / roll width. 4,000 sf of wall on 9 x 150 ft rolls (1,350 sf) at 10% is 4 rolls, 2,000 cap fasteners, and 444 LF of tape; an 8,000 sf job is 7 rolls, 4,000 fasteners, and 889 LF. The WRB is the drainage plane behind the cladding; the cap spacing and flashing tape follow the manufacturer. Distinct from the under-slab vapor-barrier-rolls.
• Chain-Link Fabric, Post, and Tension-Band Takeoff - Chain-link-specific parts list: fabric = perimeter - gates; total posts = ceil(perimeter / spacing); terminals = corners + gate jambs; line posts = total - terminals; tension bands = terminals x (height - 1). A 200 ft run of 4 ft fence with one gate is 196 LF of fabric, 20 posts (14 line, 6 terminal), 200 LF each of top rail and tension wire, and 18 tension bands; a taller 6 ft fence raises the bands to 30. Height drives the bands, the run drives the posts. Distinct from the generic fence-estimate.
• Curb-and-Gutter Concrete Volume - Concrete for a curb-and-gutter run, a linear per-station pour of a fixed cross-section: volume = cross-section x length / 27 x (1 + waste); cy per 100 LF = cross-section x 100 / 27. A 2.0 ft^2 section over 300 LF is 24 cy with waste (7.4 cy per 100 LF); a heavier 2.5 ft^2 section is 30 cy (9.3 cy/100 LF). The cross-section comes from the DOT or municipal standard curb-and-gutter detail; the cy per 100 LF is the ordering rule of thumb. Distinct from the shape presets in concrete.
• Rebar Chair / Bar-Support Count - Bar supports (chairs and bolsters) that hold rebar or mesh at the design cover: chairs = ceil(slab area / support spacing^2 x (1 + waste)). A 1,000 sf mat on a 4 ft support grid is 66 chairs with waste; a tighter 3 ft grid under heavier bars is 117 (the spacing enters squared, so a foot tighter nearly doubles the count). The support spacing (~3 to 4 ft each way) comes from the spec and CRSI practice. Distinct from the ties (rebar-tie-wire) and the bars (rebar-weight-takeoff).
• Gutter LF and Downspout Count Takeoff - Gutter footage, downspout count, pipe, and hangers: gutter = eave; downspouts = ceil(roof area / max area per downspout); pipe = downspouts x wall height; hangers = ceil(eave / spacing). 140 LF of eave on a 2,400 sf roof at 800 sf per downspout is 3 downspouts, 30 LF of downspout pipe, and about 70 hangers; a bigger 4,000 sf roof needs 5 downspouts and 50 LF of pipe. The roof area drives the downspouts, the eave drives the gutter and hangers. Distinct from the cross-section sizing in gutter-downspout.
• Soffit Vent and Ridge-Vent Count from Required NFA - Soffit vents and ridge-vent feet from the required net free area, split balanced intake / exhaust: total NFA = attic area / ratio x 144; intake = exhaust = total / 2; soffit vents = ceil(intake / per-vent NFA); ridge = ceil(exhaust / ridge NFA per ft). A 1,500 sf attic at 1/300 needs 720 in^2 of NFA (360 each way), so 14 soffit vents at 26 in^2 and 20 LF of ridge at 18 in^2/ft; without a vapor retarder the 1/150 ratio doubles it to 28 vents and 40 LF. The ratio comes from the IRC (attic-ventilation gives the NFA); the product NFA comes from the manufacturer.
• Internal Vibrator Spacing (ACI 309) - Spaces the internal-vibrator insertions that consolidate fresh concrete (ACI 309): max spacing = 1.5 x radius of action; edge distance <= 0.75 R; insertions = ceil(lift length x 12 / spacing). A 12 in radius head spaces at 18 in, stays within 9 in of the form, and a 20 ft lift takes 14 stabs; a smaller 8 in head tightens to 12 in and 20 stabs. The head's radius of action, not the wall, sets the count. ACI 309 governs.
• Formwork Tie Load and Spacing - Sizes the wall-form ties that take the lateral concrete pressure in tension: tie load = pressure x horizontal spacing x vertical spacing; max tributary = SWL / pressure. At 600 psf on a 24 x 24 in grid, each tie carries 2,400 lb - inside a 3,000 lb tie (5 sf max tributary). Pour faster (900 psf) and the tie hits 3,600 lb, over - tighten to 18 in and it drops to 2,025 lb. A tie failure is a form blowout; the tie manufacturer and ACI 347 govern.
• Mass Concrete Adiabatic Temperature Rise Screen (ACI 207) - Screens mass-concrete heat: rise = cementitious x coefficient / 100; peak = placing + rise. A rich 600 lb/cy mix at 12 degF/100lb gains 72 degF and, placed at 70 degF, peaks near 142 degF - past the ~35 degF differential that governs cracking, so it needs cooling. A leaner 400 lb/cy slag mix at 8 degF/100lb gains only 32 degF. A screen, not a thermal analysis; the mix data sets the coefficient and the EOR governs.
• Concrete Washout Containment Volume - Sizes the lined pit or container that catches chute and pump rinse so high-pH slurry never reaches the ground or a storm drain (required by the CGP): required volume = trucks x washout / 7.48 x (1 + freeboard); pit side = sqrt(volume / depth). 20 trucks at 50 gal each is 1,000 gal - 154 cf (5.7 cy), a ~9 ft square pit at 2 ft deep. Built for the whole day's washouts, not one truck; the CGP governs containment.
• Roofing Nail Count by Wind Zone - Field fasteners for an asphalt-shingle roof, where the wind zone drives the nailing pattern: nails = squares x shingles-per-square x nails-per-shingle; weight = nails / nails-per-pound. A 30-square roof at 80 shingles per square, six-nailed for high wind, takes 14,400 nails - about 103 lb of 1-1/4 in roofing nails, half again the standard four-nail pattern (9,600 nails, 69 lb). The manufacturer and wind zone set the pattern; eaves and rakes get six regardless.
• Roof Underlayment Roll Count - Field underlayment rolls over the whole deck: rolls = ceil(area x (1 + lap + waste) / roll coverage). A 2,500 sf deck with 10% laps and waste, on 10-square synthetic rolls (1,000 sf), takes 3 rolls; on 15-lb felt (4 squares, 400 sf) the same deck takes 7 - the roll coverage, set by the product, drives the count. Distinct from the eave/valley ice-barrier-coverage; the code and manufacturer set the underlayment and lap requirements.
• Single-Ply Membrane Roof Rolls and Seam Length - Rolls and seam length for a single-ply membrane (TPO/EPDM/PVC), where the side lap eats the usable width: usable = roll width - side lap; rolls = ceil(area x (1 + waste) / (usable x roll length)); seam = area / usable. An 8,000 sf roof on 10 ft x 100 ft rolls with a 6 in side lap takes 9 rolls and ~842 LF of seam; a wider 12 ft roll cuts it to 8 rolls and 696 LF - a wider sheet cuts both the rolls and the welding. Fasteners and cover tape are separate.
• Tapered Roof Insulation Average Thickness and Quantity - Average thickness, board-feet, and average R for a slope-to-drain tapered layout: avg = start + slope x run / 2; board-feet = area x avg; avg R = avg x R-per-inch. A 40 ft run at 1/4 in per foot off a 1/2 in start averages 5.5 in, so a 2,000 sf field is 11,000 board-feet at ~R-31; a shallower 1/8 in/ft taper averages 3.0 in - 6,000 bf and only R-17. The slope has to serve both drainage (>= 1/4 in/ft) and the code R. Distinct from flat assembly-r-value.
• Wall / Roof Sheathing Panel and Nail Takeoff - Sheathing panels and nails for a wall or roof: sheets = ceil(area x (1 + waste) / sheet area); nails = sheets x nails-per-sheet. A 1,600 sf wall at 8% waste is 54 sheets, and at a 6-in edge / 12-in field pattern (~60 nails a sheet) that is 3,240 nails; a tight shear-panel schedule (~104 nails) roughly doubles it to 5,616 on the same 54 sheets. The nailing schedule, not the area, drives the fastener order. Distinct from the plywood-span rating.
• Construction Adhesive Tube Count - Adhesive tubes for a subfloor or panel job, where the bead size sets the coverage: length per tube = tube volume / (pi/4 x bead dia^2) / 12; tubes = ceil(total / length per tube). A 28 oz tube run as a 3/8 in bead covers 38 ft, so 1,200 LF of joist tops takes 32 tubes; a 1/2 in bead cuts coverage to 21.5 ft and takes 56 tubes - the bead diameter enters squared, so a step up dominates. The spec sets the bead.
• Sill-Plate Anchor Bolt Count (IRC R403.1.6) - Lays out sill-plate anchor bolts at the IRC max spacing with a bolt near each end: bolts = max(2, ceil((wall - 2 x end distance) / max spacing) + 1). A 40 ft wall at 6 ft spacing with 9 in end distances takes 8 bolts; a short 8 ft wall still needs 3 because the 6.5 ft between end bolts exceeds the 6 ft spacing - a mid bolt the two-bolt minimum alone would miss. IRC R403.1.6 caps spacing at 6 ft; the code and engineered plan govern. Distinct from anchor-embedment capacity.
• Light-Gauge Steel Stud and Track Takeoff - Light-gauge steel studs and track for a partition: studs = ceil(wall / spacing) + 1 + openings x extra; track = 2 x wall (top and bottom runners). A 50 ft partition at 16 in on center with two door openings is 43 studs and 100 LF of track; at 24 in on center the field studs drop and it is 30 studs on the same 100 LF. The spacing sets the field count, the openings add on top. Distinct from the wood residential-framing.
• Suspended Acoustical Ceiling Grid Takeoff - Panels, tees, wall angle, and hanger wires for a lay-in acoustical ceiling (2x4 grid): panels = area/8; main tee = area/4; cross tee = area/2; wall angle = perimeter; hangers = area/16. A 24 x 40 ft room (960 sf) is 120 panels, 240 LF of main tee, 480 LF of cross tee, 128 LF of wall angle, and 60 hanger wires. Every quantity but the wall angle tracks the area; seismic areas add bracing and clips per code. Distinct from floor tile-count.
• Masonry Control-Joint Layout - Lays out masonry control joints by the NCMA empirical rule: max spacing = min(1.5 x wall height, project cap); panels = ceil(length / max spacing); joints = panels - 1. An 80 ft CMU wall 16 ft tall caps at 24 ft, so 4 panels of 20 ft with 3 control joints; a 120 ft wall at the same spacing is 5 panels and 4 joints - the height sets the spacing, the length sets the count. Keeps shrinkage cracking in the joints, not the field. Distinct from the concrete-slab control-joint-spacing.
• Roll-Off Dumpster / Haul Count - Turns a demolition debris volume and weight into a haul count, where either the box volume or the weight cap governs: by volume = ceil(cy / (box x fill)); by weight = ceil(tons / cap); hauls = max. 60 cy of debris fills 3 boxes by volume, but at 45 tons the 8-ton cap forces 6 hauls - for heavy concrete debris the weight always wins. Lighter 12-ton debris governs by volume at 3. The hauler's container size and weight cap govern; overweight boxes are a haul-back.
• Caulk / Sealant Cartridge Yield from Joint Size - How many linear feet a sealant cartridge does for a joint size, and the cartridges for a run: length per cartridge = cartridge volume / (width x depth) / 12; cartridges = ceil(joint / length per cartridge). A 10.1 oz cartridge on a 3/8 x 1/4 in joint does 18 ft, so 500 LF takes 28 cartridges; a big 1/2 x 1/2 in joint burns them at more than double the rate (74). The joint cross-section is the lever; the manufacturer's joint design governs.
• Self-Leveling Underlayment Bag Count - Self-leveling underlayment (SLU) bags, where the yield depends on the average pour thickness: neat bags = area x thickness / bag yield (square-foot-inches); bags = ceil(neat x (1 + waste)). 500 sf poured at 1/4 in average, on a 6.25 sf-in bag yield, is 20 bags neat - 21 with waste; a deeper 1/2 in average doubles it to 42. The average thickness drives the order, so a low floor with deep spots eats material. SLU sets fast - stage bags first.
• Carpet Square-Yard and Linear-Foot Takeoff - Carpet in the units it is bought (square yards off a 12 ft roll), with higher waste for seam layout and pattern: gross = area x (1 + waste); SY = gross / 9; linear feet = gross / roll width. A 900 sf room at 10% waste is 110 SY, or 82.5 linear feet off a 12 ft roll; a 15 ft roll cuts it to 66 LF at the same 110 SY - a wider roll cuts the length and often the seams, not the yards. Distinct from the square-foot flooring-takeoff.
• Spray Fireproofing (SFRM) Material Takeoff - Spray-applied fire-resistive material - the volume, weight, and bags at the design thickness: volume = area x thickness / 12; weight = volume x density; bags = ceil(weight / bag x (1 + waste)). 5,000 sf of steel at a 1.5 in design thickness in 15 pcf material is 625 ft^3 and 9,375 lb - about 246 44-lb bags with the high SFRM rebound waste; a 2 in design takes 327 bags. The design thickness, set by the UL assembly and fire rating, drives the order.
• Spray Foam Board-Feet and Set Count - Sizes spray foam in the board-feet and sets it is ordered by (a board-foot is one square foot one inch thick): board-feet = area x thickness; sets = ceil(bd-ft x (1 + waste) / set yield). 2,000 sf at 3 in of closed-cell is 6,000 board-feet, which on a 4,800 bd-ft set (with waste) is 2 sets; open-cell at a thicker 5.5 in still fits in 1 set because it yields far more. Temperature and substrate cut the field yield; the product set yield governs.
• Steel Roof / Floor Deck Sheet Takeoff - Structural steel deck - sheets by net cover, and the side-lap run that sizes the fastening: cover area = cover width x sheet length; sheets = ceil(area x (1 + waste) / cover area); side lap = area / cover width. 10,000 sf on a 36 in cover, 30 ft deck at 5% waste is 117 sheets and ~3,333 LF of side lap; a narrower 24 in cover is 175 sheets and 5,000 LF - more sheets and more button-punch/weld fastening. Distinct from exposed metal-roof-panels; the SDI and drawings set the fastening.
• Rebar Tie-Wire Count and Weight - Tie wire for a rebar mat - the intersections tied and the wire consumed: bars each way = floor(span / spacing) + 1; intersections = product; ties = round(intersections x fraction); weight = ties x tie length / 12 x wire per foot. A 30 x 20 ft mat of #4 at 12 in each way has 651 intersections; tying half with 8 in ties is ~3.9 lb of wire, and a full-tie spec nearly doubles it to 7.9 lb. The spec sets the tie fraction; distinct from the bar rebar-weight-takeoff.
• Adhesive-Anchor Epoxy Cartridge Volume - The epoxy to set adhesive anchors - the annular volume per hole and the cartridges: per hole = pi/4 x (hole^2 - bar^2) x embedment; cartridges = ceil(holes x per hole x (1 + waste) / cartridge volume). 40 holes of a 5/8 in bar in a 3/4 in hole at 6 in embedment is 0.81 in^3 each - about 3 cartridges with waste; a deeper 9 in embedment runs it to 4. The hole diameter comes from the adhesive manufacturer's instructions; distinct from the concrete-anchor capacity calcs.
• Non-Shrink Grout Volume Under a Base Plate - Non-shrink grout under a column base plate - the gap volume minus the steel footprint, and the bags: grout = (plate length x plate width - column area) x thickness; bags = ceil(grout / bag yield). An 18 x 18 in plate over an 8 x 8 in column on a 1.5 in grout bed is 390 in^3 - 1 bag with waste; a big 24 x 24 in plate at 2 in takes 2. Plate area and bed thickness both drive it. Distinct from the pipe-casing annular-grout-volume.
• Guard Baluster / Picket Count (4-in Sphere Rule) - Balusters on a guard or fence spaced so a 4 in sphere cannot pass: pickets = ceil((clear span - max gap) / (picket width + max gap)); actual gap = (clear span - pickets x width) / (pickets + 1). A 96 in span with 1.5 in pickets holds 17 pickets at a 3.92 in gap; 3.5 in wide pickets take 13 at 3.61 in. The clear span and picket width both drive the count. The guard height and load are checked by guard-handrail-check.
• Galvanized Duct Sheet-Metal Weight Takeoff - Duct sheet-metal weight from the perimeter, run, and gauge - the number that sizes the coil order and the hangers: perimeter = 2 x (width + height); weight = perimeter x length x sheet weight x seam factor. A 24 x 12 in run, 100 ft long in 24-gauge galvanized, is about 798 lb once the SMACNA seam-and-reinforcement allowance is counted; a heavier 20-gauge run is over 1,140 lb. The gauge schedule is the lever; fittings are taken off separately.
• Electrical Duct-Bank Concrete Encasement Volume - Concrete for an electrical duct bank - the encasement around a bundle of conduits: net area = bank width x height - conduits x pi/4 x OD^2; volume = net area x length / 27. A 24 x 18 in bank around six 4.5 in-OD conduits over 100 ft is 8.66 cy (9.1 cy with 5% waste); a bigger 30 x 24 in bank is 16 cy - the envelope, not the conduits, drives the pour. Order right so it finishes in one continuous lift with no cold joint; the engineer sets the encasement.
• Duct Wrap / Liner Material Takeoff - External duct-wrap insulation area and rolls, where the overlap and corner compression add to the bare surface: perimeter = 2 x (width + height); wrap = perimeter x length x overlap/waste factor; rolls = ceil(wrap / roll coverage). A 20 x 12 in duct, 40 ft long, needs 245 sf of wrap (3 rolls of 100 sf); a larger 30 x 20 in duct needs 383 sf (4 rolls) - the perimeter, not the length, drives the wrap. The factor (~1.15) covers the taped overlap; internal liner is taken off on the interior perimeter.
• Duct Hanger Load and Count - The weight each duct hanger carries at a chosen spacing and the count a run needs: load = per-foot weight x spacing; count = ceil(run / spacing) + 1. A duct at 5.5 lb/ft on 8 ft centers puts 44 lb on each hanger, and a 40 ft run takes 6 hangers; a heavier lined duct at 9 lb/ft on 10 ft centers is 90 lb/hanger over 5 hangers - wider spacing means fewer hangers but more load on each. SMACNA sets the max spacing (~8-10 ft rectangular); large duct goes on a trapeze.
• Haul-Cycle Production and Fleet Match - Truck cycle time, loads per hour, single-truck and matched-fleet production, and the number of trucks that keep the loader working.
• Wheel-Loader / Excavator Bucket Production Rate - Loose-yards-per-hour a wheel loader or excavator digs and dumps from the rated bucket capacity, fill factor, and cycle time, plus the daily output - the load-side production the haul-cycle fleet match assumes.
• Dozer Slot / Blade Production Rate - Loose-yards-per-hour a dozer pushes from the blade capacity, push distance, and push/return speeds. Production falls off fast as the push lengthens - the reason dozing is a short-haul tool.
• Roller Compaction Production Rate - Surface coverage (sf/hr, sy/hr) and compacted cubic yards per hour a roller turns out from the drum width, speed, lift thickness, and passes - the production that sizes the fill schedule and the number of rollers. The test strip sets the passes.
• Dozer Ripper Loosening Production Rate - Bank cubic yards per hour a dozer ripper loosens in place from the shank spacing, penetration, and speed - the loosening step that feeds the push, load, and haul spread. Ripping fractures rock and hardpan; it does not move it. The operator judges rippability.
• Excavation Dewatering Pump Rate - Pump rate to draw an open excavation down in a target time and hold it against a steady inflow, with a safety-margined selection rate. Defers head to pump-tdh.
• Trench Spoil Pile Setback and Surcharge - Required spoil-pile setback (the larger of the OSHA 2 ft minimum and the depth-based surcharge), the pile toe spread, and the total clear distance from the trench edge.
• Trench Pipe Bedding and Backfill Take-Off - Bedding stone (cy and tons), pipe-zone embedment aggregate, and backfill volume for a pipe trench from the trench and pipe dimensions per ASTM D2321.
• Coating Coverage from Volume-Solids and DFT - Theoretical and practical coverage, gallons, and the wet-film thickness from a coating's volume-solids and a target dry-film thickness (SSPC/AMPP PA 2; 1604 constant).
• Abrasive Blast Air and Abrasive Consumption - Nozzle air-flow (cfm), compressor horsepower, abrasive consumption (lb/hr), and total abrasive for an area from the nozzle bore and blast pressure.
• Fence Material Takeoff - Section, post, rail, and picket counts for a straight fence run from the run length, post spacing, rails per section, and picket width. Corner/end/gate posts are field-judgment extras.
• Concrete per Post Hole - The concrete a batch of post holes needs: the cylinder volume of each hole less the post's displacement, totaled and divided into bags. For a fence, deck, sign, or mailbox.
• Thin-Set Mortar Coverage - The bags of thin-set a tile job needs, sized off the trowel notch the way a setter buys it -- a 1/4 in notch covers about twice the area of a 1/2 in notch. tile-count gives the tile and grout.
• Cement Board (Tile Backer) Sheet and Screw Takeoff - Cement-board tile-backer sheets and fasteners for a tub surround, wall, or floor: sheets = ceil(area x (1 + waste) / sheet area), a 3x5 board being 15 sf; screws = sheets x per-sheet, roughly 30 to 40 corrosion-resistant backer screws at 8 in on center. A 120 sf tub surround at 10% waste is 9 sheets and about 315 screws; a 200 sf floor is 15 sheets. Add alkali-resistant mesh tape and thin-set at the joints (not counted) and set the board over a moisture barrier per the wet-area detail. Distinct from the gypsum drywall takeoff. A material-ordering estimate; ANSI A108 / the TCNA Handbook and the board manufacturer govern the fastener schedule and the wet-area assembly.
• Roof Step-Flashing Piece Count - The step-flashing pieces for a roof-to-wall or chimney sidewall: one piece is woven into EACH shingle course as the roof rises along the wall, plus one to start, so pieces = ceil(sloped wall run x 12 / shingle exposure) + 1. A 20 ft run against a wall at a 5 in exposure takes ceil(240/5) + 1 = 49 pieces; a longer exposure means fewer courses and fewer pieces. Order a few extra for waste. Each L-shaped piece laps the one below by the exposure and tucks under the siding/counterflashing -- step flashing is woven course-by-course, NOT a single continuous strip (a leak-prone mistake). A takeoff estimate; the shingle exposure, the flashing size, and IRC R905.2.8.3 and the manufacturer's details govern the install.
• Resilient / LVP Flooring Takeoff - Boxes of plank or tile to order at the waste allowance for the install pattern (straight / diagonal / herringbone), with the last-row balance that tells you whether to rip the first course.
• Concrete Control Joint Spacing - Where to cut contraction (control) joints in a slab: the spacing in feet (about 2-3 times the slab thickness, capped), the saw-cut depth (a quarter of the slab), and the panel grid with an aspect-ratio check.
• Rebar Lap-Splice Length - The tension lap-splice length as a multiple of the bar diameter (the jobsite 40-48 bar-diameter rule), with a 12 in floor and a feet-and-inches readout. The engineer of record and the drawings govern.
• Paver Patio Takeoff - Pavers to order with a cut allowance from the patio area and paver face, plus the compacted base-aggregate and bedding-sand volumes underneath, in cubic yards.
• Segmental Retaining Wall Takeoff - Blocks per course and number of courses (with the buried first course), total and cap blocks, and base-trench and drainage gravel for a segmental wall. Over 4 ft needs an engineered design with geogrid.
• Attic Ventilation Net Free Area - The net free vent area an attic needs (the IRC 1/150 rule, or 1/300 balanced with a vapor retarder), the 50/50 intake/exhaust split, and the soffit-vent count and ridge-vent length.
• Powered Attic Ventilator Sizing - The fan size and matching intake for a powered attic ventilator: fan CFM = attic floor area x ~0.7 CFM/ft^2 (about 10 air changes/hr), with a ~15% increase for a dark roof, and the required intake (soffit) net free area of about 1 ft^2 per 300 CFM so the fan pulls outdoor air rather than starving. A 1,500 ft^2 attic needs a 1,050 CFM fan and 3.5 ft^2 (504 in^2) of intake; a dark roof pushes the fan to 1,208 CFM. Balanced passive ridge-and-soffit ventilation is often preferred and some codes restrict powered fans. A sizing aid; the fan manufacturer's data and the local code govern.
• Gutter and Downspout Sizing - The gutter size and number of downspouts a roof needs: the adjusted (design) roof area from the plan area, the roof pitch, and the local rainfall intensity, then the gutter and downspout count.
• Deck Board and Fastener Takeoff - The decking surface takeoff a deck builder orders from: boards run the length, so the count across the width is ceil((width_in + gap) / (board face + gap)) -- the gap falls between boards, not after the last. A 12 x 16 ft deck of 5.5" boards at a 0.25" gap needs 26 boards, 458 lineal feet at 10% waste, 13 joists (ceil(length x 12 / 16" OC) + 1), and 676 deck screws at 2 per board per joist. Sizes the surface and fasteners only, not the joists, beam, posts, or footings, which come from the span tables and the load. A takeoff estimate; the deck plan governs.
• Flat Glass Lite Weight - The weight of a glass lite for a safe lift: soda-lime float glass runs about 13.0 lb per square foot per inch of thickness (specific gravity 2.50), so weight = 13.0 x thickness(in) x area(ft^2). A 60 x 40 in lite of 1/4" glass is 16.7 ft^2 and 54 lb -- past the ~50 lb one-person limit, so a two-person or vacuum-cup lift. Tempering does not change the weight; an insulating unit (IGU) is the sum of its lites. Sizes the lift and checks it against a suction lifter's rating. A handling estimate; the glass type, the lifter's rating, and safe-lifting practice govern.
• Steel Beam Lateral-Torsional Buckling (AISC 360 F2) - The moment the actual bracing allows - the check steel-beam-flexure defers: an unbraced compression flange buckles sideways below the plastic moment. AISC F2 grades the unbraced length against Lp = 1.76 ry sqrt(E/Fy) and the F2-6 Lr; between them Mn falls linearly, beyond Lr the elastic Fcr governs. A W18x50 braced every 10 ft drops from 421 to 360 kip-ft, and at 20 ft to 200 - less than half the braced number, the cliff that forces a brace or a heavier shape. Doubly-symmetric compact I-shapes, entered Cb. A design aid, not the engineer of record's stamped design.
• Steel Block Shear Rupture (AISC 360 J4.3) - The tear-out failure that pulls a tab of steel out of a bolted end or coped web along a combined tension-and-shear path - the separate check steel-beam-shear names, and the one that frequently governs over the bolts. Rn = 0.6 Fu Anv + Ubs Fu Ant, capped by yielding on the gross shear plane; three 3/4 in bolts in a 1/2 in A36 plate give 111.8 kip nominal (ASD 55.9), and tightening the end distance drops it - why the detail sheet holds the edges. One row, standard holes. A design aid, not the engineer of record's stamped design.
• Steel Tension Member: Yield and Rupture with Shear Lag (AISC 360 D2/D3) - The missing axial-tension leg beside the flexure, shear, and column tiles: a brace, hanger, or truss diagonal is the lower of gross yielding Fy Ag and net rupture Fu U An, where the shear-lag factor U = 1 - xbar/L punishes a member connected through only some of its elements. An L4x4x1/2 bolted through one leg draws U = 0.80 and flips the governing limit from yielding to rupture - the penalty a straight Fy Ag estimate misses; weld the full section and it flips back. Single hole line, no stagger. A design aid, not the engineer of record's stamped design.
• RC Tied Column Axial Capacity (ACI 318-19 22.4) - The column the RC beam tiles never supplied: a concentrically loaded short tied column carries Po = 0.85 f'c (Ag - Ast) + fy Ast, capped at 0.80 phi Po (phi = 0.65) for the accidental eccentricity a concentric load never truly avoids. A 16 in square 4,000 psi column with eight #8 Grade 60 bars gives Po = 1,228 kip and a 639 kip design capacity, with the longitudinal ratio checked against the ACI 1-8% band. No P-M interaction or slenderness - short, tied, concentric only. A design aid, not the engineer of record's stamped design.
• RC Column Longitudinal Steel for a Target Load - The inverse of the rc-column-axial tile: the longitudinal steel a target factored axial load needs for a given tied column, Ast = (phi Pn / 0.52 - 0.85 f'c Ag) / (fy - 0.85 f'c). A 16 in square 4,000 psi column carrying a 639 kip design load needs about 6.33 in^2 (2.47%). Reports the larger of the strength requirement and the ACI 1% minimum, and flags a load that needs more than 8% (section too small). Concentric short tied column; no P-M interaction. A design aid; the engineer of record governs.
• Two-Way Slab Punching Shear at a Column (ACI 318-19 22.6) - The limit state that sets flat-plate thickness and footing depth: the column punches a truncated cone through the slab on the critical perimeter d/2 from its face. The stress is the least of 4, (2 + 4/beta), and (2 + alpha_s d/bo) times lambda sqrt(f'c) (alpha_s 40/30/20 interior/edge/corner), and phi Vc = 0.75 vc bo d. An interior 20 in column on a d = 6 in slab holds 118.4 kip; grow the column to 36 in and the large-column term takes over - the case a drop panel fixes. No moment transfer or shear reinforcement. A design aid, not the engineer of record's stamped design.
• Standard Hook Development Length (ACI 318-19 25.4.3) - Where a straight bar cannot fit - a beam bar anchoring into a column - the detailer hooks it, and the hook develops in ldh = (fy psi_e psi_r psi_o psi_c / (55 lambda sqrt(f'c))) db^1.5, never less than max(8 db, 6 in). A #8 Grade 60 bar in 4,000 psi concrete needs 14.9 in; a #5 only 7.4 - the db^1.5 scaling a hook = multiple-of-db rule of thumb gets wrong. Companion to the straight-bar rc-development-length. Standard 90/180 hooks; headed bars separate. A design aid, not the engineer of record's stamped detailing.
• Shallow Foundation Elastic (Immediate) Settlement - The serviceability check soil-bearing-capacity calls separate: a footing can be far below its bearing strength yet settle too much. The theory-of-elasticity immediate settlement Se = q B (1 - nu^2) Is / Es (Is ~0.82 rigid square) gives a 6 ft footing at 3 ksf on medium sand 0.64 in - under the customary 1 in limit - but halve the modulus and the same footing fails at 1.29 in. Sizes the footing against movement, not strength; consolidation and embedment are separate. A design aid, not the geotechnical engineer's report.
• Allowable Bearing Pressure for a Settlement Limit - The inverse of the elastic-settlement tile: the largest net contact pressure that keeps immediate settlement within a limit, q = Se Es / (B (1 - nu^2) Is). A 6 ft footing on Es = 250 ksf soil holds ~4.65 ksf at a 1 in limit; a 12 ft footing only ~2.33 ksf, since a wider footing settles more. A settlement (serviceability) pressure, not the bearing-capacity strength limit. A design aid, not the geotechnical engineer's report.
• Deep Pile Axial Capacity in Clay (Alpha Method) - The analytical pile capacity beside helical-pile's torque correlation: in clay the alpha method takes Qult = alpha cu (pi D L) skin friction plus 9 cu (pi D^2/4) end bearing. A 16 in pile 40 ft into cu = 1 ksf clay carries 105 kip ultimate (88% in skin friction) and 35 kip allowable at FS 3 - and doubling the length nearly doubles it while the tip term stays put, which is why a friction pile is lengthened, not fattened. Single pile, uniform clay, total-stress method. A design aid; the geotechnical engineer and a load test govern.
• Pile Embedment Length for a Target Capacity (Alpha Method) - The inverse of the pile-axial-capacity tile: the embedded length that carries a target allowable load, L = (Qall x FS - Qp) / (alpha cu pi D), since the tip Qp is fixed by the diameter and the skin friction must supply the rest. A 16 in pile in cu = 1 ksf clay carrying 50 kip at FS 3 needs ~60 ft. Single pile, uniform clay. A design aid; the geotechnical engineer and a load test govern.
• Infinite Slope Stability Factor of Safety - The screen a site engineer runs before benching a hillside cut: for a shallow slide parallel to a long uniform slope, FS = (c' + gamma H cos^2 beta tan phi') / (gamma H sin beta cos beta). A 25 degree cut in c' = 200 psf, phi' = 30 soil holds at FS 1.78; strip the cohesion and the elegant tan phi'/tan beta remains - depth-independent, why dry sand stands exactly at its angle of repose. Translational only, no seepage - a circular Bishop analysis and pore pressure are the geotech's work. A screening aid, not a stability analysis.
• Infinite Slope Critical Depth for a Target FS - The inverse of the infinite-slope tile: the critical failure-plane depth at which the FS drops to a target, H = c' / (gamma cos beta (FS sin beta - cos beta tan phi')). A 25 degree cut in c' 200 psf, phi' 30, gamma 120 soil reaches FS 1.5 at about 16.6 ft deep. FS is high at the surface (cohesion helps) and falls with depth toward the cohesionless limit tan phi'/tan beta - a target below that is met at any depth. Needs c' > 0. Translational, no seepage; a screening aid, the geotech governs.
• Infinite Slope Stability with Seepage - Why a slope that stood dry all summer slides in the spring: with steady seepage parallel to the slope and the water table at the surface, FS = (c' + (gamma_sat - 62.4) H cos^2 beta tan phi') / (gamma_sat H sin beta cos beta). The pore pressure cuts the friction term to the buoyant weight while the driving weight stays saturated, so a cohesionless factor of safety drops to (gamma_sat - 62.4)/gamma_sat -- about half. A phi = 32 sand at 18 degrees is a safe 1.92 dry but a failing 0.96 wet; the tile shows both so a subdrain's value is obvious. Translational, drained, no seismic. A screening aid, not a stability analysis.
• Wood Bearing Perpendicular to Grain (NDS 3.10) - The crushing check a framer skips until the beam sinks into the plate: where a joist or beam lands across the grain, fc_perp = R/(b x lb) must clear Fc_perp x Cb, where the NDS 3.10.4 bearing-area factor Cb = (lb + 0.375)/lb rewards a short interior bearing. An 800 lb joist on 1.5 in of DF-L plate runs at DCR 0.46 and needs only 0.85 in; put a 6,000 lb beam reaction on the same footprint and it fails at 3.4x, demanding 6.4 in or a bearing plate. Fc_perp takes no load-duration factor. A design aid, not the engineer of record's stamped design.
• Wood Tension Member Parallel to Grain (NDS 3.8) - The tie beside the strut: a truss bottom chord or collector checks ft = T/An against Ft x CD x CF, where the net area deducts the bolt holes a gross-area estimate misses. A 2x6 DF-L chord carrying 3,000 lb through one 3/4 in bolt loses 14% of its section at the hole and runs at DCR 0.56; snow-duration CD 1.15 and a clean section relax it to 0.42 - the two levers the code gives a tension member. Single hole line, no stagger; the bolt itself is the wood-bolt-connection tile. A design aid, not the engineer of record's stamped design.
• Wood Beam-Column Interaction (NDS 3.9.2) - A stud carrying wind on a bearing wall is a beam and a column at once: NDS 3.9.2 combines them as (fc/Fc')^2 + fb/[Fb'(1 - fc/FcE)] <= 1.0, where FcE = 0.822 Emin'/(le/d)^2 and the 1 - fc/FcE denominator is the P-delta magnifier. A 4x4 stud at 3,000 lb + 3,000 in-lb passes at 0.55 with the bending term already amplified 1.6x; double the axial load and the amplifier nearly quadruples it to a 1.55 fail - the effect a designer must not drop. Enter Fc' with Cp and Fb' with CL from the companion tiles. A design aid, not the engineer of record's stamped design.
• Steel Web Local Yielding and Crippling (AISC 360 J10) - Where a column bears on a beam or a beam lands on a plate, the web itself can fail before the member does: J10.2 web local yielding Rn = Fy tw (5k + lb) interior or (2.5k + lb) at an end, and J10.3 web crippling with its sqrt(E Fy tf/tw) term. Because their safety factors differ (1.50 vs 2.00), the governing limit can flip - a W18x50 on a 4 in interior bearing is crippling-governed at 102.1 kip ASD, but move the same bearing to the end and yielding takes over at 84.3 kip. The check that decides a bearing stiffener. A design aid, not the engineer of record's stamped design.
• Slip-Critical Bolt Design Strength (AISC 360 J3.8) - Where slip cannot be tolerated - oversized holes, fatigue, load reversal - the joint is governed by friction, not shear: Rn = mu Du hf Tb ns with mu 0.30 (Class A) or 0.50 (Class B blast-cleaned), Du 1.13, and the Table J3.1 pretension. A 3/4 in A325 on a Class A surface resists 9.49 kip per bolt (6.33 ASD); go Class B in double shear and one bolt jumps 3.3x to 31.6 kip - surface prep and a second plane are the levers. The strength-level bolt-shear-bearing check must also pass. A design aid, not the engineer of record's stamped design.
• Fillet Weld Size Limits and Effective Throat (AISC 360 J2.2b) - What size the code allows before the strength calc even applies: the Table J2.4 minimum leg from the THINNER part joined (so the weld cools slowly enough not to crack), the J2.2b maximum along an edge (full thickness under 1/4 in, thickness minus 1/16 at or over - so the edge is not melted away), the equal-leg throat 0.707 w, and the 4w minimum length. A 1/2 to 3/8 in joint takes a 3/16-to-5/16 window, and a chosen 1/4 in weld carries a 0.177 in throat. The numbers a WPS is written to; fillet-weld-strength assumes you already picked them. A fabrication aid; AWS D1.1 and the engineer govern.
• Wind Components and Cladding Pressure (ASCE 7 Ch. 30) - The local envelope pressure wind-pressure cannot make: ASCE 7 Chapter 30 C&C design pressure p = qh [(GCp) - (GCpi)], where qh = 0.00256 Kz Kzt Kd Ke V^2 and GCpi = +/-0.18 (enclosed). A 115 mph Exposure C building draws qh 25.9 psf, and a roof corner (Zone 3, GCp = -1.8) sees -51.3 psf of suction - roughly double the field, the number a corner fastener and its spacing are designed for. GCp comes from the Ch. 30 zone figures (enter it). Local cladding pressure, not the whole-building MWFRS. A design aid, not the engineer of record's stamped design.
• Live Load Reduction (ASCE 7 Ch. 4) - The reduction a big tributary area earns, which sizing to the full tabulated live load misses: ASCE 7 §4.7 L = L0 (0.25 + 15/sqrt(KLL x AT)), where L0 is the unreduced live load, AT the tributary area, and KLL the element factor from Table 4.7-1 (interior/exterior columns 4, beams and cantilever-slab edge columns 2-3, other members 1). It applies only where KLL x AT >= 400 ft^2 and cannot drop below 0.50 L0 (one floor) or 0.40 L0 (two or more). A 50 psf office load on an interior column (KLL 4) with 400 ft^2 tributary reduces 37.5% to 31.25 psf; a 1,000 ft^2 area hits the 0.50 floor at 25 psf. Loads over 100 psf, garages, and assembly spaces are generally not reducible. A design aid; the adopted code and the engineer of record govern.
• Snow Drift Surcharge at a Roof Step or Parapet (ASCE 7 Ch. 7) - The triangular surcharge that collapses lower roofs, which the flat-roof snow-load never adds: ASCE 7 Chapter 7 leeward drift height hd = 0.43 (lu)^(1/3) (pg + 10)^(1/4) - 1.5, density gamma = 0.13 pg + 14 (capped 30 pcf), peak pd = hd gamma over a 4 hd width. A 100 ft upwind roof at pg 30 psf piles 63 psf at the wall on top of the balanced load; a heavier 50 psf snow zone drives it to 83 psf. Leeward form, on top of snow-load's balanced number. A design aid, not the engineer of record's stamped design.
• Rain-on-Snow Surcharge (ASCE 7-22 7.10) - The rain-on-snow surcharge added to the balanced flat-roof snow load where the ground snow Pg is 20 psf or less and the roof slope (deg) is less than W/50 (W the eave-to-ridge distance). ASCE 7-22 raised this to 5-8 psf (commonly 8) from the older flat 5, because a low-slope roof in wet-snow climates holds rain a steeper roof would shed. A Pf of 15 psf at Pg 18 low-slope becomes 23 psf; a deep-snow region (Pg 25) takes no surcharge, staying 15 psf. Balanced case only, both triggers required. A design aid, not a substitute for the engineer of record.
• Sliding Snow Load on a Lower Roof (ASCE 7 7.9) - The surcharge from snow sliding off a slippery upper roof onto a lower roof: total = 0.4 x the upper roof's flat snow load Pf x its eave-to-ridge length W (lb/ft), distributed over the lesser of 15 ft or the lower-roof width. A 20 psf / 40 ft upper roof drops 320 lb/ft, which over 15 ft is a 21.3 psf surcharge; a narrow 10 ft catch roof concentrates the same total into 32 psf. Adds to the lower roof's own balanced load. A design aid, not a substitute for the engineer of record.
• Minimum Roof Snow Load (ASCE 7 7.3.4) - The floor a low-slope roof's design snow load cannot fall below: Pm = Is x Pg where the ground snow Pg is 20 psf or less, or 20 x Is where Pg is over 20 (Is the snow importance factor). The design flat-roof snow is the greater of this minimum and the computed Pf, so the exposure/thermal/slope reductions cannot drop a low-slope roof below a single heavy snowfall. Pg 15 / Is 1.0 gives 15 psf; Pg 30 caps at 20 psf; Pg 25 with an essential-facility Is 1.1 gives 22 psf. Balanced case only. A design aid, not a substitute for the engineer of record.
• ADA Ramp Slope, Runs, and Landings (IBC 1012 / ADA) - The full layout of an accessible ramp, not just the slope: run = rise x the slope ratio (max 1:12 / 8.33%), the number of runs = ceil(rise / 30 in) because a single run may rise only 30 in before a >=60 in landing, the landings that adds, and the total ramp length; handrails are required where the rise exceeds 6 in. A 24 in rise at 1:12 is one 24 ft run with handrails; a 40 in rise needs 2 runs and a 60 in landing for 45 ft of total ramp. A layout aid; the adopted code and ADA/ANSI A117.1 govern slope, width, and handrail details.
• MWFRS Wall Pressure (ASCE 7 Ch. 27) - The lateral pressure the whole building resists, feeding the diaphragm and shear walls: ASCE 7 Chapter 27 MWFRS p = q G Cp - qi (GCpi), G = 0.85 rigid, Cp +0.8 windward / -0.5 leeward. A 25.9 psf building carries +22.3 psf on the windward wall (pushing in) and -15.7 psf on the leeward (suction), for a 28.6 psf net horizontal design pressure - the internal pressure cancels in the net, so the story force is insensitive to enclosure while the walls are not. Enter qz/qh from wind-pressure. Walls only. A design aid, not the engineer of record's stamped design.
• Wind Force on Solid Freestanding Wall / Sign - Design wind force and Case B eccentric (torsion) moment on a solid freestanding wall, monument sign, or pylon: ASCE 7-22 Section 29.3, F = qh G Cf As with a net two-face Cf from Fig 29.3-1 (~1.2-2.0, not a building-wall +/- GCp). The 0.2B eccentricity, not the straight force, sizes the post and footing.
• Unbalanced Snow Load on Gable Roof (ASCE 7 7.6.1) - The ASCE 7-22 7.6.1 unbalanced gable case: windward slope drops to 0.3 ps while the leeward carries ps plus a wind-blown ridge drift surcharge (hd gamma/sqrt(S)). Applies only in the ~1/2:12 to 7:12 slope band with W > 20 ft; sizes the leeward rafter and ridge the balanced case misses.
• One-Way Slab / Beam Minimum Thickness for Deflection (ACI 318-19) - The depth that lets a designer skip a deflection calculation entirely: ACI 318-19 Table 7.3.1.1 / 9.3.1.1 gives l/20 simply supported, l/24 one end continuous, l/28 both continuous, l/10 cantilever, times (0.4 + fy/100,000) for non-Grade-60 steel and a lightweight factor. A simply supported 12 ft one-way slab needs 7.2 in; a both-ends-continuous Grade 40 slab only 4.1 in. The serviceability depth the strength tiles assume, for members not supporting damageable partitions. A design aid, not the engineer of record's stamped design.
• Max One-Way Slab / Beam Span for a Given Depth (ACI 318-19) - The inverse of the minimum-thickness tile: with the slab or beam depth fixed, the longest span that still waives a deflection calculation, max_span = h x denom / (12 kfy klw). A 10 in both-ends-continuous Grade 60 member spans up to 23.3 ft without a deflection check; a longer span needs a deeper member or an explicit calculation. A design aid, not the engineer of record's stamped design.
• Doubly-Reinforced Concrete Beam Flexural Capacity (ACI 318-19) - When a beam's depth is limited and the tension steel outruns a singly-reinforced section, the designer adds compression steel and the capacity gains a second couple A's fy (d - d'). ACI equilibrium gives a = (As - A's) fy / (0.85 f'c b) and Mn = the singly-reinforced couple plus the steel-to-steel couple. A 14x24 beam with As 8, A's 3 in^2 reaches 771 kip-ft (694 design) - above what the section could singly - and the compression steel both raises capacity and shrinks the stress block. Both layers assumed to yield (flagged if not). A design aid, not the engineer of record's stamped design.
• Shear Friction Across an Interface (ACI 318-19 22.9) - The mechanism that carries shear across a cold joint, a corbel interface, or a wall-to-footing plane - not the beam-web diagonal-tension of rc-beam-shear: Vn = mu Avf fy, with mu 1.4 monolithic / 1.0 roughened / 0.6 unroughened / 0.7 to steel, capped by the concrete interface. 2.0 in^2 of Grade 60 dowels across a roughened joint carry 120 kip (90 design); add more dowels past the 153.6 kip cap and nothing changes because the concrete itself limits the transfer. Perpendicular (no net tension) case. A design aid, not the engineer of record's stamped design.
• Concrete Modulus of Elasticity Ec (ACI 318-19 19.2.2) - Ec = wc^1.5 x 33 x sqrt(f'c) psi (ACI 19.2.2.1), the stiffness behind every deflection, drift, and short-column calculation; the normalweight shortcut is 57000 x sqrt(f'c). 4000 psi at 145 pcf -> 3,644,000 psi (3644 ksi); a 115 pcf lightweight deck is only ~70% as stiff. A design aid; the engineer of record's stamped design governs.
• Concrete f'c from Modulus of Elasticity (ACI 318-19 19.2.2) - The inverse of the elastic-modulus tile: back out the equivalent in-place f'c from a measured or specified stiffness, f'c = (Ec / (wc^1.5 x 33))^2. An Ec of 3,644,000 psi at 145 pcf implies ~4,000 psi. Useful from a resonance / sonic-modulus test; not a cylinder-break value. A design aid; the engineer of record's stamped design governs.
• Concrete Modulus of Rupture fr (ACI 318-19 19.2.3) - fr = 7.5 x lambda x sqrt(f'c) psi (ACI 19.2.3.1), the tensile stress at which plain concrete first cracks, setting the cracking moment behind deflection and minimum-reinforcement checks. 4000 psi normalweight -> 474 psi (~0.119 f'c); all-lightweight (lambda 0.75) -> 356 psi. A design aid; the engineer of record's stamped design governs.
• Concrete f'c from Modulus of Rupture (ACI 318-19 19.2.3) - The inverse of the modulus-of-rupture tile: back out the equivalent f'c from a flexural-beam (modulus-of-rupture) test, f'c = (fr / (7.5 x lambda))^2. A 474 psi normalweight rupture strength implies ~4,000 psi. The code fr is a conservative lower bound, so the implied f'c is a lower-bound equivalent, not a cylinder-break value. A design aid; the engineer of record's stamped design governs.
• Concrete Cracking Moment Mcr (ACI 318-19) - The bending moment at which a plain concrete section first cracks - the value the modulus-of-rupture tile names as its purpose but does not compute: Mcr = fr Ig/yt = fr b h^2/6, with fr = 7.5 lambda sqrt(f'c). A 12 x 20 in section at 4000 psi normalweight (fr 474 psi, S 800 in^3) cracks at 31.6 kip-ft. This is the value behind the effective-moment-of-inertia (Ie) deflection analysis and the minimum-reinforcement check (design strength >= 1.2 Mcr). Gross rectangular section; a T-beam uses the transformed Ig. A design aid; the engineer of record governs.
• Concrete Section Depth for a Target Cracking Moment - The inverse of the concrete-cracking-moment tile: the total section depth that reaches a target cracking moment for a given width, h = sqrt( 6 Mcr / (fr b) ) with fr = 7.5 lambda sqrt(f'c). A 12 in wide section at 4000 psi needs about a 20 in depth to crack at 31.6 kip-ft. A common use is to enter 1.2 Mcr for the minimum-reinforcement check. Gross rectangular section; the flexure/shear/deflection design still governs the final depth. A design aid; the engineer of record governs.
• Shrinkage and Temperature Reinforcement (ACI 318-19 24.4) - Minimum shrinkage/temperature steel perpendicular to the main bars in a one-way slab: ratio 0.0018 (Grade 60) or 0.0020 (Grade 40/50), As,min = ratio x b x h, spacing <= min(5h, 18 in). A 6 in slab, Grade 60 -> 0.130 in^2/ft, 18 in max (about #4 at 18). A design aid; the engineer of record's stamped design governs.
• T-Beam Effective Flange Width (ACI 318-19 6.3.2) - The slab width acting with a T-beam web: overhang = smallest of 8 hf, sw/2, ln/8 (interior; both sides) or 6 hf, sw/2, ln/12 (edge; one side). 12 in web, 4 in slab, ln 240, sw 48 -> be 60 in interior (sw/2 governs), 32 in edge (ln/12 governs). A design aid; the engineer of record governs.
• Minimum Flexural Reinforcement As,min (ACI 318-19 9.6.1.2) - As,min = max(3 sqrt(f'c)/fy, 200/fy) x bw x d, so the beam does not fail suddenly at first cracking. 4000 psi, Grade 60, 12x20 -> 0.80 in^2 (200/fy floor governs); at 5000 psi the sqrt term governs, 0.85 in^2. A design aid; the engineer of record's stamped design governs.
• Crack-Control Bar Spacing (ACI 318-19 24.3.2) - Max tension-bar spacing s = min(15(40000/fs) - 2.5 cc, 12(40000/fs)) for flexural crack control, fs = 2/3 fy typical. fs 40000, cover 2 in -> 10 in; more cover (3 in) tightens it to 7.5 in. A serviceability limit, not a strength check. A design aid; the engineer of record governs.
• Concrete Bearing Strength (ACI 318-19 22.8) - The concrete-on-concrete bearing check that forgets the confinement bonus: Bn is not just 0.85 f'c x A1 -- when the supporting surface is wider than the loaded patch, the surrounding concrete confines it and the strength is multiplied by sqrt(A2/A1), capped at 2.0. A 12x12 in column (144 in^2) on a 36x36 in footing earns the full 2x -> phiBn = 636.5 kip (phi = 0.65); a pad flush to its support edge (A2 = A1) earns none -> 318.2 kip, exactly half. The tile returns the capped factor, nominal and design strengths, and the demand-capacity ratio. A design aid, not the engineer of record's stamped design.
• Rebar Compression Development Length (ACI 318-19 25.4.9) - How deep compression dowels really go, which the tension development and hook tiles never answered: ldc = max(fy x psi_r / (50 lambda sqrt(f'c)) x db, 0.0003 fy psi_r db, 8 in). Compression development is SHORTER than tension because the bar end bears on concrete. A #8 Grade 60 dowel at 4,000 psi needs 19.0 in (the fy/sqrt(f'c) term governs); raise f'c to 8,000 psi and it stops falling at 18.0 in because the 0.0003 fy db floor takes over -- doubling the concrete strength did not shorten the dowel. Confining ties (psi_r = 0.75) drop it to 14.2 in. A design aid; the engineer of record's detailing governs.
• Long-Term Deflection Multiplier (ACI 318-19 24.2.4) - Why bottom-only beams sag and doubly-reinforced ones hold: a concrete beam keeps deflecting for years from creep and shrinkage. ACI 24.2.4.1.1 multiplier lambda = xi / (1 + 50 rho'), where xi is 2.0 at 5+ years and rho' is the compression-steel ratio. A bottom-only beam (rho' = 0) with a 0.4 in immediate deflection gets the full lambda = 2.0 -> 0.80 in additional -> 1.20 in total, sagging triple its snapshot value; add compression bars so rho' = 0.01 and lambda drops to 1.33 -> 0.93 in total, 22% less. This long-term total is what the L/240 and L/480 limits are actually checked against. A design aid; the engineer of record governs.
• Cast-In Anchor Tension Concrete Breakout (ACI 318-19 Ch. 17) - Concrete breakout capacity of a headed anchor in tension by the ACI 318-19 CCD method: Nb = kc lambda sqrt(f'c) hef^1.5 (kc 24 cast-in / 17 post-installed), edge-modified to Ncb and design phiNcb. The hef^1.5 cone and near-edge knockdown that anchor-embedment never checks; a near edge can cut capacity 25% before the steel yields.
• Concrete Headed-Anchor Pullout (ACI 318-19 17.6.3) - The other tension failure mode concrete-anchor-breakout named as its companion: the head crushing through the concrete. Np = 8 x Abrg x f'c; Npn = psi_cP x Np (1.4 uncracked, 1.0 cracked); phiNpn = 0.70 x Npn. A 3/4-in headed bolt (0.654-in^2 head) in 4,000-psi cracked concrete pulls out at a factored 14.6 kip - and unlike breakout it does not depend on embedment, so deepening the anchor does not raise it. Headed anchors only (not adhesive or expansion). A design check, not a stamped anchor design.
• Concrete Anchor Side-Face Blowout (ACI 318-19 17.6.4) - The third headed-anchor tension failure mode, the one deep anchors near an edge actually hit: Nsb = 160 x c_a1 x sqrt(Abrg) x lambda_a x sqrt(f'c), cut by (1 + c_a2/c_a1)/4 at a corner, phiNsb = 0.70 x Nsb. Governs when hef > 2.5 c_a1 - past that, deepening stops helping and the edge distance is the only knob. The v612 example anchor at a 3 in edge checks 17.2 kip design, and only 10.0 kip in a corner with a 4 in second edge. A design check, not a stamped anchor design.
• Slender Column Moment Magnifier, Nonsway (ACI 318-19 6.6.4) - The ACI 318-19 6.6.4.5 nonsway P-delta moment magnifier delta_ns = Cm/(1 - Pu/(0.75 Pc)) and the magnified design moment Mc a slender braced reinforced-concrete column picks up. A column just over the slenderness limit gains a 1.3-1.7x amplifier the flexure check never applies; floored at M2,min.
• Concrete Corbel / Bracket Design (ACI 318-19 16.5) - The primary tension steel of a concrete corbel or bracket by ACI 318-19 16.5: the mandatory 0.2 Vu horizontal tension, the greater of the flexure-plus-tension and shear-friction-plus-tension steel paths (which governs flips with the shear span), and the min-of-three shear cap. The corbel checks a bare shear-friction check misses.
• Primary Consolidation Settlement (NC Clay) - The slow settlement that governs a foundation on clay, which soil-settlement-elastic names as separate: Sc = (Cc H/(1 + e0)) log10((sigma'0 + d_sigma)/sigma'0). A 10 ft NC clay (Cc 0.25, e0 0.90) under a 1,000 psf footing load settles 2.8 in - several times the immediate elastic dip, over years as water squeezes out. Because it grows with the LOG of the stress ratio, doubling the load increment only lifts it to 4.75 in - the first increment is the costly one. Single NC layer, no time rate. A design aid; the geotechnical engineer of record governs.
• Allowable Load for a Settlement Limit (NC Clay) - The inverse of the primary-consolidation tile: the maximum load-induced stress increase that keeps a clay's settlement within an allowable limit - d_sigma = sigma'0 (10^(Sc(1 + e0)/(Cc H)) - 1). To hold a 10 ft NC clay (Cc 0.25, e0 0.90, sigma'0 2,000 psf) to a 2 in settlement, the added stress can be at most 677 psf; tighten the limit to 1 in and only 314 psf is allowed - because settlement grows with the log of the stress ratio, a tighter limit allows disproportionately less load. Single NC layer, no time rate. A design aid; the geotechnical engineer of record governs.
• Eccentric Footing Bearing Pressure and Kern Check - The trapezoidal-or-triangular bearing pressure under a column with axial load plus moment, generalizing the wall check to any footing: while e = M/P stays in the middle-third kern (e <= B/6) the pressure is q = (P/BL)(1 +/- 6e/B); past it the heel lifts to a triangle over the front 3(B/2 - e). A 60 kip load on an 8 ft footing at e 1 ft runs 0.23 to 1.64 ksf full-bearing; push e to 2 ft and the toe spikes to 2.5 ksf with a third of the footing in no contact - the reason columns are kept concentric. Uniaxial, rigid footing. A design aid; the engineer of record governs.
• Surcharge Lateral Pressure on a Wall from a Line Load (Boussinesq) - The bulge of lateral pressure a concentrated surface load (a footing, wheel line, or crane outrigger set back from a wall) puts on it - which the uniform Ka q surcharge never captures: the NAVFAC DM-7.2 modified-Boussinesq sigma_h = (0.203 qL/H) n/(0.16 + n^2)^2 for m <= 0.4, doubled for a rigid non-deflecting wall (m = x/H, n = z/H). A 1,000 lb/ft line 4 ft back from a 10 ft wall peaks near 97 psf at shallow depth; set it farther back and it pushes less and deeper. Line load, single depth. A design aid; the geotechnical engineer of record governs.
• Steel Beam-Column Combined Axial and Flexure (AISC 360 H1.1) - The single number that decides a beam-column, which no single-action tile produces: AISC H1.1 combines axial and bending in a bilinear interaction - Pr/Pc + (8/9)(Mrx/Mcx + Mry/Mcy) for Pr/Pc >= 0.2, Pr/(2Pc) + (sum Mr/Mc) below. Pr 100 / Pc 400 with Mrx 80 / Mcx 200 passes at 0.61; drop the axial and the low-axial branch gives it a lighter half-weight, so a beam with only incidental axial is governed by its moment. Pc/Mc from the member tiles, in the same ASD or LRFD basis; second-order Mr assumed. A design aid, not the engineer of record's stamped design.
• Column Effective Length Factor K (Alignment Chart) - The K that steel-column-capacity consumes but never computes: from the joint stiffness ratios G = sum(EI/L)_columns / sum(EI/L)_beams, the Dumonteil closed-form fits to the AISC alignment charts give sway K = sqrt((1.6 GA GB + 4(GA+GB) + 7.5)/(GA+GB+7.5)) and a braced form. GA 1, GB 2 gives K 1.47 sway but 0.82 braced - a factor of 3.2 in buckling capacity, why bracing a frame is the cheapest way to shorten a column. Enter G (or 10 pinned / 1 fixed); within ~2% of the nomograph, no tau_b. A design aid, not the engineer of record's stamped design.
• Bolt Combined Tension and Shear (AISC 360 J3.7) - The tension a bracket, hanger, or moment end-plate bolt has left after its shear: AISC J3.7 reduces the nominal tensile stress F'nt = 1.3 Fnt - (Fnt/(phi Fnv)) frv, capped at Fnt. A 3/4 in A325 at 20 ksi required shear drops from 29.8 kip pure tension to 24.1 kip; a fully-sheared bolt floors at zero tension - the reduction a straight tension check misses. Bearing-type interaction (slip-critical is J3.9); the shear/bearing is the separate bolt-shear-bearing tile. A design aid, not the engineer of record's stamped design.
• Relative Compaction from Field Density and Proctor Maximum - The pass/fail an earthwork inspector reads at every test point: RC = (field dry density / Proctor max) x 100, with the field dry density backed out of the nuclear-gauge wet density and moisture, gamma_d = gamma_wet/(1 + w). 128 pcf wet at 12% against a 120 pcf Proctor gives 114.3 pcf dry -> 95.2%, passing a 95% structural-fill spec; the same wet density at 16% moisture fails at 91.9% - the moisture reading is as important as the density, why over-wet fill is rejected. Enter the Proctor maximum (D698 / D1557). A QC aid; the geotechnical spec governs.
• Water to Reach Optimum Moisture for Compaction - Gallons of water to bring a dry lift up to the Proctor's optimum moisture before rolling: water = (optimum - field)/100 x dry soil weight, gallons = lb / 8.34. A 100 bcy lift at 105 pcf dry, sitting at 9% when optimum is 14%, needs ~1,700 gal (one water truck); a lift wetter than optimum signals aerate, not water.
• Frost Penetration Depth (Stefan / Modified Berggren) - How deep frost drives into the ground, by the Stefan / modified-Berggren heat-of-fusion method. Stefan X = sqrt(48 kf FI / L) balances the cold the air delivers against the latent heat of freezing the soil moisture: kf = frozen conductivity (BTU/hr-ft-F), FI = air-freezing index (F-days), L = 144 x dry density x water content/100 (144 BTU/lb is the heat of fusion). A soil at kf 1.0, 100 pcf, 15% water in a 2,000 F-day climate has L 2,160 and a Stefan depth of ~6.7 ft. Stefan over-predicts (it ignores soil heat capacity); the modified-Berggren lambda (~0.6-0.9, off the nomograph) cuts it to ~5.3 ft. CRITICAL: computes the PHYSICS, not the code frost line -- the footing depth is set by the locally adopted frost depth (IRC Table R301.2 / amendment), which this does not replace. A drier soil freezes deeper. A screen; the adopted requirement, the geotech report, and the AHJ govern.
• Soil Phase Relations (Void Ratio, Porosity, Saturation) - The three-phase makeup behind every settlement and bearing calc, made explicit: from the total unit weight, water content, and specific gravity Gs, the dry unit weight gamma_d = gamma/(1 + w), void ratio e = Gs gamma_w/gamma_d - 1, porosity n = e/(1 + e), and saturation S = w Gs/e. A 120 pcf soil at 15% and Gs 2.70 gives gamma_d 104.3 pcf, e 0.62, n 0.38, S 66% - the void ratio a consolidation needs, the saturation that says how much air is left to squeeze out. gamma_w = 62.4 pcf; enter Gs. An engineering aid; the soil test data govern.
• Atterberg Plasticity Indices and A-Line Classification - The consistency numbers a geotech report leads with, and an earthwork spec screens fill against: the plasticity index PI = LL - PL, the liquidity index LI = (w - PL)/PI, and the USCS A-line PI = 0.73(LL - 20) that separates clay from silt. LL 45 / PL 22 gives PI 23 above the A-line 18.3 at LL < 50 -> CL lean clay, LI 0.35 (plastic/workable); a low-PI silt (LL 30, PI 5) plots below the A-line -> ML, the distinction that changes a fill's suitability. A-line chart classification, ASTM D4318. An engineering aid; the soil test data govern.
• Aggregate Fineness Modulus (ASTM C136) - The single number that captures how coarse a sand is, for concrete mix proportioning: FM = the sum of the cumulative percent retained on the #4, #8, #16, #30, #50, and #100 sieves, divided by 100. Cumulative retained of 2/12/32/57/82/95 sums to 280 -> FM 2.80, within the ASTM C33 concrete-sand band of 2.3-3.1. A higher FM is coarser (needs less paste); a finer sand needs more water for the same slump, and a mix's sand should not drift more than 0.20 FM without a mix adjustment. A gradation summary, not the full sieve check -- two different gradations can share an FM. A QC / mix-proportioning aid; the sieve analysis and mix design govern.
• Nail Withdrawal Design Value (NDS 12.2.3) - The design number behind the framer's 'nails don't hold in withdrawal' instinct, which fastener-pullout only tabulates: NDS W = 1,380 G^(5/2) D lb/in, times the penetration. A 16d common nail (D 0.162) in DF-L (G 0.50) gives 39.5 lb/in, so a 1.5 in bite holds 59 lb; toenailed at wind duration the 0.67 Ctn nearly cancels the 1.6 CD bump - the reason toenailed uplift is weak and framing hardware replaces it. Side grain only (no end-grain withdrawal). A design aid, not the engineer of record's stamped design.
• Lag Screw Withdrawal Design Value (NDS 12.2.1) - The lag's axial capacity from the NDS equation, not a table: W = 1,800 G^(3/2) D^(3/4) lb/in of thread penetration. A 1/2 in lag in DF-L over 4 in of thread holds 1,514 lb; step to a 5/8 in lag and it rises only 18% (the D^(3/4) law) - more or deeper lags beat one fat lag. Withdrawal (axial) value only, not the lateral yield-limit connection or the head bearing; end-grain installs take a 0.75 factor. A design aid, not the engineer of record's stamped design.
• Wood Screw Withdrawal Design Value (NDS 12.2.2) - Why a screw that holds in fir strips in spruce: NDS W = 2,850 G^2 D lb/in scales with the SQUARE of specific gravity. A #10 screw (D 0.190) in DF-L (G 0.50) gives 135 lb/in; the same screw in softer SPF (G 0.42) drops 30% to 95.5 lb/in. Times the penetration for the withdrawal capacity. Axial withdrawal only, not the lateral connection or the head pull-through. A design aid, not the engineer of record's stamped design.
• Cantilever Beam Moment, Shear, and Deflection - Max moment (P L + w L^2/2), max shear (P + w L), and tip deflection (P L^3/3EI + w L^4/8EI) of a cantilever from a tip point load, a uniform load, or both. Elastic small-deflection prismatic member. A design aid, not the engineer of record.
• Cross-Section Properties (A, I, S, r) - Area, moment of inertia (I = b h^3/12 etc.), section modulus S = I/c, and radius of gyration r = sqrt(I/A) for a rectangle, solid round, pipe, or hollow tube. I scales with the cube of the depth, so orientation dominates. A design aid, not the engineer of record.
• Combined Axial and Bending Stress (P/A +/- Mc/I) - Extreme-fiber stresses sigma = P/A +/- M c/I for a short member under axial force plus bending (or a moment from an eccentricity e). Reports whether the far face stays in compression (the kern threshold e <= r^2/c). Short member, no P-delta. A design aid, not the engineer of record.
• Shaft Torsional Shear Stress and Angle of Twist - Polar moment J = pi(d^4-di^4)/32, max shear tau = T r/J, and twist theta = T L/(J G) for a solid or hollow circular shaft. A 1.5 in steel shaft at 1,000 lb-ft over 24 in -> 18,100 psi, 2.9 deg; a 2 in shaft cuts both far (the d^3/d^4 leverage). A design aid, not the engineer of record.
• Solid Shaft Diameter for an Allowable Torsion - The inverse of the shaft-torsion tile: the minimum SOLID-shaft diameter that keeps the max surface shear stress within an allowable, d = (16 T / (pi tau_allow))^(1/3). A 12,000 lb-in torque at an 8,000 psi allowable needs about a 1.97 in shaft (round up to stock). Sizes for stress only; check the angle of twist (shown with a length and G) against the service limit. Pure torsion, no keyway concentration. A design aid, not the engineer of record.
• Restrained Thermal Stress and Force - A blocked member develops sigma = E alpha dT x restraint (independent of length) and force F = sigma A; the free expansion alpha L dT is what the restraint blocks. Steel +100 F fully restrained -> 18,850 psi; aluminum nets less. Heating = compression, cooling = tension. A design aid, not the engineer of record.
• Max Temperature Change for a Stress Limit - The inverse of the thermal-stress-restrained tile: the largest temperature change a restrained member can take before its thermal stress reaches the allowable, dT_max = sigma_allow / (E x alpha x restraint). Fully restrained steel at an 18,850 psi allowable can swing 100 F; aluminum tolerates 145 F for the same stress (lower modulus), and half restraint doubles the swing. Answers 'how big a temperature swing can this take' instead of the stress at one swing. Heating is compression, cooling is tension. A design aid, not the engineer of record.
• Thin-Wall Pressure Vessel Hoop and Longitudinal Stress - Hoop stress sigma_h = P D/(2t) and longitudinal sigma_l = P D/(4t) = half the hoop (why cylinders split lengthwise), valid for D/t >= 20. A 12 in tank, 0.25 in wall, 150 psi -> 3,600/1,800 psi. Not a substitute for the ASME BPVC or the engineer of record.
• Thin-Wall Vessel Max Allowable Working Pressure - The inverse of the hoop-stress-thin-wall tile: the maximum allowable working pressure of a thin-wall cylinder from its wall, diameter, and allowable stress, P_max = 2 t S_allow/D (hoop-governed; the longitudinal limit is double). A 12 in vessel with a 0.25 in wall at 15,000 psi allowable holds 625 psi. To size the wall for a known design pressure instead, rearrange to t_min = P D/(2 S_allow). Valid for D/t >= 20. Not a substitute for the ASME BPVC or the engineer of record.
• Design Spectral Response Accelerations SDS / SD1 (ASCE 7-22 11.4) - Site-adjust the mapped MCER accelerations (SMS = Fa Ss, SM1 = Fv S1) then take two-thirds for design (SDS = 2/3 SMS, SD1 = 2/3 SM1). Ss 1.0, S1 0.4, Site Class D (Fa 1.1, Fv 1.6) -> SDS 0.733g, SD1 0.427g, the exact inputs seismic-base-shear consumes. A design aid; the engineer of record governs.
• Seismic Design Story Drift and Allowable Limit (ASCE 7-22 12.8.6 / 12.12) - Amplified drift delta_x = Cd delta_xe / Ie against the allowable delta_a = drift coefficient x story height (commonly 0.020 hsx). Cd 5.5, delta_xe 0.5 in, 144 in story -> 2.75 in vs 2.88 in allowable, OK at 0.955 utilization; a softer frame at 0.6 in fails. A design aid; the engineer of record governs.
• Seismic P-Delta Stability Coefficient (ASCE 7-22 12.8.7) - theta = Px delta Ie / (Vx hsx Cd): below 0.10 neglect P-delta, up to theta_max = min(0.5/(beta Cd), 0.25) amplify by 1/(1-theta), above it the story is potentially unstable. Px 400 kip, Delta 2.75 in, Vx 80 kip -> theta 0.017, neglect; a soft story at theta 0.19 must be redesigned. A design aid; the engineer of record governs.
• Guard and Handrail Code Check - Whether a guard and handrail meet the dimensional code: a guard is required where the walking surface is over 30 in above the floor below, with a 36 in (residential) or 42 in (commercial) minimum height, a 4 in sphere infill limit (4-3/8 in on the stair triangle), and a 34-38 in stair handrail. IRC R312 / R311.7.8 / IBC 1015; the assembly must also carry a 200 lb load and the AHJ governs.
• Stair Geometry Code Check (IBC 1011 / IRC R311) - Whether a stair's riser, tread, and clear width meet the adopted code, the check every stair permit turns on: IBC (commercial) caps the riser at 7 in, floors the tread at 11 in, and needs 44 in of width; IRC (residential) allows a 7-3/4 in riser and a 10 in tread at 36 in. A 7-1/2 in riser is a legal residential stair and an illegal commercial one - the single most common tenant-improvement stair red-tag. Reports each dimension pass/fail against the selected code plus the 2R + T comfort read (24-25 in). Uniformity, nosing, landings, and winders are separate checks; the egress width from occupant load is the egress-capacity tile. A design aid, not a code-official determination; the AHJ governs.
• CMU Grout Volume (Partial and Full Grout) - The grout volume for a reinforced CMU wall: grouted cores at the rebar spacing (cores = floor(len x 12 / spacing) + 1) plus a continuous bond-beam course, in ft^3 and cubic yards. Core and bond cross-sections come from the unit data; the spacing comes from the structural drawings and the engineer of record governs the reinforcement - a material takeoff, not a structural design.
• Annular Grout Volume for Cased Bore / Pipe-in-Casing - The grout volume in the ring between a bored casing and the carrier pipe: annular area = pi/4 (bore^2 - carrier^2), volume = area x length grossed for waste. A 24 in bore around a 16 in carrier over 100 ft is a 6.46 cy ring (1,306 gal), ~6.79 cy ordered. The field always overruns the neat annulus.
• Masonry Coursing and Course-Out Check - How many courses reach a height and whether that height lands on a module: course = unit + bed joint (CMU 8 in, three brick courses 8 in), courses = round(target / course), and a course-out flag when the wall top or opening is off-module and forces a cut course or fattened joints. Nominal dimensions; the product and the mason's joint govern - a layout aid, not a stamped elevation.
• Wallcovering Roll Takeoff With Pattern Repeat - The rolls of wallcovering from the wall perimeter, height, and pattern repeat: full-height strips across the perimeter, one repeat wasted per strip to match the run, strips per roll, and rolls. A large repeat can nearly double the order for the same area. Roll size is the product's bolt size and openings are a manual credit - a material takeoff, not a hang plan.
• Eave Ice-Barrier Membrane Courses and Rolls - The self-adhering ice-and-water membrane the eave actually needs: the up-slope coverage from the overhang and pitch (IRC R905.1.2 runs it 24 in inside the exterior wall line, measured on the slope), the courses when that exceeds one roll width, and the rolls. A deep overhang or a low pitch quietly pushes the coverage past a single 36 in course, so a one-roll-per-eave guess shorts the order. Required only where the AHJ has adopted it; valley and low-slope coverage is a separate add. A material takeoff, not a flashing plan.
• Metal Roof Panels, Linear Feet, and Fasteners - Panels, linear feet, and through-fasteners (or clips) for one metal roof plane: the panel count from the product's net coverage width (not the sheet width), the total linear feet, the slope-area squares, and the fasteners from the wind-zone pattern. A 36 in exposed-fastener panel and a 16 in standing-seam panel covering the same plane differ by nearly a factor of two in panel count - which is why net coverage width, not square footage, sets a metal order. Per roof plane (double for a symmetric gable). A material takeoff, not a wind-uplift design.
• Hip / Ridge Cap Bundles and Roofing Nails by the Pound - The two accessories the shingle field takeoff leaves open: the hip-and-ridge cap bundles from the ridge and hip linear feet, and the roofing nails by the pound. IRC R905.2.6 steps the field pattern from four nails to six in the high-wind / steep rows, which moves the order by half again, and a pre-formed hip/ridge product covers far less per bundle than field-cut 3-tab caps. Cap pattern and nail density come from the product wrapper and the adopted wind zone. A material takeoff, not a nailing schedule.
• Roof Rain Load and Secondary-Drainage Flow (ASCE 7 Ch. 8) - The load that collapses flat roofs: standing water at the blocked-primary case. ASCE 7 Ch. 8 puts the rain load at 5.2 psf per inch of head - R = 5.2 x (static head to the secondary inlet + hydraulic head above it at design flow) - and the optional IPC design flow Q = 0.0104 x area x rainfall sizes the secondary drainage. Doubling the head to the overflow doubles the load, which makes the secondary inlet height a structural decision, not just a plumbing one. A flat roof must also pass the §8.4 ponding-instability check. A load and flow aid, not a stamped roof-drainage design.
• ASCE 7 ASD Load Combinations: Governing Demand and Net Uplift - Combines dead, live, roof (snow/rain), and signed wind into the seven ASCE 7 §2.4.1 basic ASD combinations and returns the two cases the trades design to: the largest gravity demand (which sizes the beam, joist, or footing) and the most negative case (which, when 0.6D + 0.6W goes below zero, is the net uplift the roof-to-wall hold-down must resist). A member is never designed for one load at a time - the governing combination is, which is why the design starts here, not at the largest single load. A load-combination aid, not a member design.
• Seismic Base Shear (ASCE 7 §12.8 Equivalent Lateral Force) - The earthquake demand on a regular building reduced to one equivalent static base shear: Cs = SDS / (R / Ie), capped at SD1 / (T x (R / Ie)) for T <= TL and floored at the code minimum, times the seismic weight. In much of the western US the seismic demand, not the wind, governs the lateral system - the shear walls, braced frames, hold-downs, and anchor bolts. A taller, more flexible building draws a smaller base shear because the period cap recognizes it rides the short-period spectral peak less. SDS / SD1 are from the USGS maps; R is from Table 12.2-1. A lateral-demand estimate, not a stamped seismic design.
• Vertical Distribution of Seismic Forces (ASCE 7 §12.8.3) - The standard hand calc after the base shear: distribute V up the height as Fx = Cvx x V with Cvx = wx hx^k / Sum(wi hi^k), then take the story shears Vx by summing the forces at and above each level (§12.8.4). The exponent k (1 at T <= 0.5 s, 2 at T >= 2.5 s, interpolated between) is the whole story - softening a 3-story from T = 0.4 to 1.06 s shifts nearly 10 of 200 kips up to the roof. Levels enter one per line, bottom-up, as weight and height from the base; the base story carries the full V as the built-in check. Feeds the story shear the drift and P-delta tiles consume. A design aid; the engineer of record governs.
• Seismic Overturning Moment (ASCE 7 §12.8.5) - The overturning the footing and the hold-downs resist, the next number after the vertical distribution: from the story forces Fx = Cvx x V, the base overturning moment M0 = Sum(Fi hi), the moment about each floor level (Sum of the forces above it times their height above it), and the 25% reduced foundation moment §12.13.4 permits at the soil interface. A 3-story with Fx = 37 / 74 / 89 kips at 12 / 24 / 36 ft carries 5,422 kip-ft at the base, 4,067 reduced. Levels enter one per line, bottom-up, as weight and height from the base; V and T come from seismic-base-shear. The resisting dead load, the foundation stability ratio, and the shear-wall hold-downs are separate checks. A design aid; the engineer of record governs.
• Building Occupant Load from Area and Use (IBC Table 1004.5) - The one number the whole life-safety chain hangs on: the occupant load = sum over spaces of ceil(area / occupant-load factor). The factor is set by how the space is used, not its label - a 3,000 ft^2 office at 150 ft^2/occ is 20 people; the same floor as a standing bar at 5 ft^2/occ is 600. Bundled representative factors (business, assembly, mercantile, classroom, kitchen, industrial, storage, residential) are editable defaults; the factor and its net-vs-gross basis come from the AHJ-adopted code edition. A design aid, not a code-official determination.
• Egress Exit Count and Required Width (IBC 1005.3 / 1006.2) - Turns the occupant load into the two egress demands: the number of separate exits (1 up to 49, 2 to 500, 3 to 1,000, 4 beyond) and the clear width per exit (occupant load x a capacity factor of 0.15 in/occ level or 0.2 in/occ stair when sprinklered, 0.2 / 0.3 without), divided among the exits and floored at the 32 in door-leaf minimum. For a modest load the exit count and the leaf minimum control, not the raw width. A design aid, not a code-official determination.
• Minimum Plumbing Fixtures by Occupancy (IBC Table 2902.1) - The minimum water closets, lavatories, drinking fountains, and service sink a building must provide from its occupant load and occupancy class: fixtures = ceil(occupants-per-sex / ratio), each rounded up, load split evenly between the sexes. A 100-occupant office needs four water closets (the 1:25 first-tier ratio and the round-up push it past the naive per-50 read), where a 160-occupant restaurant on the 1:75 ratio needs far fewer. The occupancy class, not the head count alone, sets the fixtures. A design aid, not a code-official determination.
• Formwork Shore Post Load and Spacing (ACI 347) - The vertical load path of an elevated pour: design pressure = max(slab_in/12 x unit weight + form load + construction live load, 100 psf floor), and the load on any one shore is that pressure times its tributary area. An 8 in slab on a 4 ft grid carries over 2,500 lb per post. Motorized buggies raise the live load to 75 psf and the floor to 125 psf. The rated capacity is the manufacturer's allowable for the extended height and bracing; reshoring and the slab below are separate analyses. A design aid, not a stamped shoring plan.
• Scaffold Mudsill Bearing Pressure and Sill Length - The soil pressure a scaffold leg presses through its mudsill (leg load / plank area), whether it clears the allowable soil bearing, and the sill length needed if it does not. OSHA 1926.451(c)(2) requires base plates on sound, rigid mudsills. A first-check estimator, not the engineered design.
• Scaffold Per-Leg Load and OSHA 4:1 Check - The load on each scaffold leg and whether it clears the OSHA 4:1 safe working load: total = platform dead + workers x 250 lb + material; leg load = total / legs; SWL = component rating / 4. A bay with two workers, 500 lb of material, and a 100 lb platform puts 275 lb on each of four legs - fine against a frame rated 2,500 lb, but load it heavier and it crosses the 4:1 line. Feeds scaffold-mudsill-bearing; a competent person verifies.
• Frame Scaffold Material Takeoff - Frames, cross braces, planks, and base plates for a frame-scaffold run off the bay layout and lifts: bays = ceil(run / bay length); frames = (bays+1) x lifts; braces = 2 x bays x lifts; base plates = (bays+1) x 2. A 40 ft run on 7 ft bays, three lifts high, is 6 bays - 21 frames, 36 braces, 24 planks, and 14 base plates. Guardrails, ties, screw jacks, and access are taken off separately; a competent person designs the erection.
• Concrete Surface Evaporation Rate and Plastic-Shrinkage Risk (ACI 305) - The finisher's go / no-go on plastic-shrinkage precautions, read off the day's weather: the ACI 305 / Menzel evaporation rate from the concrete and air temperatures, the humidity, and the wind. Above about 0.2 lb/ft^2/hr the surface cracks before it sets unless you fog, screen, retard, or cover. A 90 F, 40% RH, 15 mph pour evaporates several times faster than a calm humid one; the concrete temperature, not the air, drives it. A field screen, not a curing specification (curing follows ACI 308).
• Fresh Concrete Temperature (ACI 305.1) - The batch temperature concrete-evaporation-rate takes as a given, from the ACI 305.1 ingredient heat balance: T = [0.22(Ta Wa + Tc Wc) + Tw Ww + Twa Wwa] / [0.22(Wa + Wc) + Ww + Wwa], solids weighted by their ~0.22 specific heat and water by 1.0. Aggregate 3000 lb at 80 F, cement 564 lb at 150 F, 240 lb of 70 F water, and 60 lb of aggregate moisture batch to 85.8 F. Water's heat capacity is four times the solids', so chilling the mix water or adding ice is the cheapest way to beat the ~90 F hot-weather ceiling. A batching aid; the mix design governs.
• Concrete Age-Strength Gain for Form Stripping (ACI 209) - How much of its specified 28-day strength a slab has reached at a given age, the ACI 209R fraction t / (a + b t) times f'c - about 46% at 3 days, 70% at 7, 88% at 14 for Type I moist-cured - plus the inverse solve for the age to hit a target percent (commonly 75% to pull shores). The schedule decision behind every form-strip and shore-removal. An estimate of the mean trend, not a substitute for field-cured cylinder breaks; the engineer of record and the spec govern the actual strip strength.
• Concrete Maturity and Equivalent Age (ASTM C1074) - The temperature-honest cure schedule: the Nurse-Saul time-temperature factor (Ta - T0) x hours in deg C-hr, the Arrhenius equivalent age at a 68 F reference, and the hours remaining to the mix's lab-calibrated TTF target. A 50 F week accrues 1,680 C-hr and reads as only 3.8 equivalent days - the cold slab is not '7 days old' - while three days at 90 F carry nearly six days of equivalent age. Datum 0 C and Q = 5000 K for Type I without admixtures, both editable. The strength a TTF represents comes only from the C1074 lab calibration of the actual mix; supplements, not replaces, acceptance cylinders.
• Rebar Weight Takeoff - ASTM A615 nominal bar weight per foot x total linear feet, to tons and cost. A #5 bar (1.043 lb/ft) x 500 ft -> 522 lb (0.26 ton); a #8 (2.670) at the same length weighs 1,335 lb (0.67 ton), more than double for the #5-to-#8 jump. Rebar is bought by weight. Add lap and waste before the takeoff. The shop drawings and mill weights govern.
• Ready-Mix Concrete Order (Trucks, Waste, Short Load) - Ordered = in-place volume x (1 + waste%), trucks = ceil(ordered/capacity), short-load fee below the plant minimum. 42 yd^3 at 8% waste, 10 yd^3 trucks -> 45.4 yd^3, 5 trucks, 5.4 yd^3 last load, no fee; a small 6 yd^3 pour trips the sub-10 yd^3 short-load fee. Ordering a little long beats a second delivery. The supplier's terms govern.
• Concrete Yield and Relative Yield (ASTM C138) - Whether a load delivered the yards ordered, from the batch weights and the measured fresh unit weight: yield = total batch mass / unit weight, relative yield = yield / design volume, and actual cement content = cement batched / yield. A 3,993 lb batch at 148 lb/ft^3 makes 26.98 ft^3 (0.999 yd^3) -- a full yard, 564 lb/yd^3 cement. A relative yield below 1.0 is a SHORT load (denser than designed, more cement per yard); above 1.0 is over-yield (lighter or high-air, cement diluted, strength at risk). The unit weight must be measured per ASTM C138, not estimated. Checks volume and cement content, not air or strength. A QC check; the mix design and measurement govern.
• Water-Cementitious Ratio and Exposure Cap (ACI 318) - The single strongest lever on concrete strength and durability: w/cm = mixing water / total cementitious (cement + fly ash + slag + pozzolans). 282 lb water over 470 lb cement + 94 lb fly ash (564 cementitious) is 0.50 -- which EXCEEDS the ACI 318 Table 19.3.2.1 cap of 0.45 for severe freeze-thaw or sulfate exposure. Lower w/cm means lower permeability, so ACI caps it by exposure class (0.55 F1 down to 0.40 F3/C2). Count the aggregate free-moisture and admixture water, not just plant batch water, or the real ratio is higher than the ticket. Checks the durability cap only; strength, minimum cementitious, and air are separate. A durability screen; the spec and mix design govern.
• Insulation Batt Coverage and Count - Batts and bags from the net cavity area / coverage per batt and per bag, at a waste allowance. 500 ft^2, R-13 batt (10.67 ft^2), 88 ft^2/bag -> 47 batts, 6 bags; a deeper R-21 bag covering 67 ft^2 raises it to 8 bags for the same wall. Count the batts to confirm a full fill. The label coverage governs.
• Trim Linear Footage and Miters - Trim = (perimeter - door openings) x (1 + waste%), pieces = ceil(net/stock); corners are 45-deg miters (base/casing) or a crown compound cut. 70 ft perimeter, 6 ft openings, 10% waste, 16 ft stock -> 70.4 ft, 5 sticks; a 38-deg crown corner is ~31.6 miter / 33.9 bevel cut flat. Verify on a scrap.
• Allowable Building Area per Story (IBC Chapter 5) - The first feasibility number on a commercial project: how many square feet per floor the building may be, Aa = At + NS x If, where the frontage increase If = [F/P - 0.25] x W/30 rewards perimeter on open space and floors at zero below a quarter of the perimeter. The tabular areas come from Table 506.2 in the correct sprinkler column, and adding a sprinkler system can triple the area for a single-story building - the first lever a developer reaches for when the area is tight. A feasibility aid, not a code-official determination.
• Egress Travel Distance, Common Path, and Dead-End Check (IBC Chapter 10) - The three distances a plans examiner checks against the floor plan: the exit-access travel distance to the nearest exit (Table 1017.2), the common path of egress travel before two independent paths are available (1006.2.1), and the longest dead-end corridor (1020.5). Each has its own editable limit that depends on the occupancy and whether the building is sprinklered; a single fail (e.g. travel over the limit) fails the floor, and a sprinkler system often clears it at once. A design aid, not a code-official determination.
• Exterior Wall Opening Limit by Fire Separation Distance (IBC Table 705.8) - How much of an exterior wall may be windows and doors, capped as a percentage of the wall area by the fire separation distance and by whether the openings are protected or the building sprinklered. A wall under 3 ft from the line gets none; at 5 to 10 ft a sprinklered wall may be 25% glass; at 30 ft or more there is no limit. The distance to the lot line, not the facade design, sets the glass - one of the strongest arguments for a sprinkler system on a wall tight to the property line. A design aid, not a code-official determination.
• Wood Bending Member (NDS Beam Stability Factor CL and Adjusted Fb') - Whether a wood beam bends without buckling its unbraced compression edge sideways, the flexural twin of the wood column check. Form the beam slenderness RB = sqrt(le x d / b^2), the critical buckling value FbE = 1.20 Emin' / RB^2, and the NDS 3.3.3 beam stability factor CL, then the adjusted bending value Fb' = Fb* x CL and the allowable moment M' = Fb' x S. A stocky, nearly-braced 4x12 keeps CL near 1.0; leaving the same beam tall and unbraced drops it off a cliff. A design aid, not a substitute for the engineer of record.
• Glulam Volume Factor Cv (NDS 5.3.6) - The volume factor that reduces a glued-laminated beam's bending strength -- the glulam-specific penalty that the sawn-lumber CL check never applies. Cv = KL x (21/L)^(1/x) x (12/d)^(1/x) x (5.125/b)^(1/x), capped at 1.0, with L the span (ft), d and b the depth and width (in), x = 10 for softwoods (20 for Southern Pine), because a larger stressed volume is more likely to contain a strength-limiting defect. A 5-1/8 x 18 in glulam over 20 ft gives Cv = 0.965 (a 3.5% cut); a 6-3/4 x 24 in girder over 32 ft gives 0.870 (13%). The allowable bending uses the lesser of Cv and the beam-stability factor CL. A design aid, not a substitute for the engineer of record.
• Wood Bending Member Shear (fv and the NDS Tension-Side End-Notch Reduction) - The end shear a wood beam carries, and how much a tension-side notch at the support takes away: the un-notched allowable Vr = (2/3) Fv' b d, the notched allowable V' = (2/3) Fv' b dn (dn/d)^2, and the actual stress fv = 3V / (2 b dn) on the net section. A single 2 in notch in a 4x12 cuts the allowable end reaction nearly in half - the reason the NDS penalizes notches on the tension side so hard. A design aid, not a substitute for the engineer of record.
• Single-Shear Bolted / Dowel Lateral Design Value (NDS Yield-Limit Z) - How much lateral load one bolt through two wood members carries, from the NDS European yield model: all six single-shear yield modes (Im, Is, II, IIIm, IIIs, IV) computed from the dowel bearing strengths, the bolt bending yield, and the geometry, with the governing Z the smallest. A 1/2 in bolt into a thin side member almost always governs in mode IIIs. The reference value before the CD / CM / Cg / geometry adjustment factors, which the user applies. A design aid, not a substitute for the engineer of record.
• Steel Beam Flexural Capacity (AISC 360 Ch. F, Compact + Braced) - Whether a compact, laterally-braced steel W-shape carries the moment: Mn = Mp = Fy x Zx, with the ASD allowable Mn/1.67 and the LRFD design 0.90 Mn. A W18x50 in A992 reaches 421 kip-ft nominal, 252 allowable, 379 design - the numbers a detailer reads off AISC Manual Table 3-2. The shape (Zx), not the grade, sizes the beam: the same steel in a section a fifth the weight carries barely a third of the moment. Compact + braced plastic plateau only (no LTB or slender-element reductions). A design aid, not a substitute for the engineer of record.
• Required Plastic Section Modulus for a Steel Beam - The design inverse of the flexural-capacity check: enter the demand moment and Fy, get the plastic section modulus Zx to pick a W-shape. LRFD Zx >= 12 Mu/(0.90 Fy); ASD Zx >= 12(1.67)Ma/Fy (AISC 360 Ch. F, Mp = Fy Zx, inverted). A 200 kip-ft LRFD demand on 50 ksi steel needs Zx 53.3 in^3 (a W16x31 works); design it by ASD and the required Zx jumps to 80.2. Feeds straight back into the flexural-capacity tile. Compact, fully braced (Lb <= Lp); the shape lookup and the engineer of record govern.
• Steel Beam Web Shear Capacity (AISC 360 Ch. G) - The web shear a steel beam carries at its ends, where the reaction is highest and the moment is zero: Vn = 0.6 x Fy x Aw x Cv1 with Aw = d x tw. For a rolled I-shape with a stocky web (h/tw under ~53.9 at Fy 50), Cv1 = 1.0 and the factors are Omega 1.50 / phi 1.00. A W18x50 carries 192 kips nominal, 128 allowable. Short heavily-loaded spans and coped ends are governed by the web, not the flange. Block shear at a coped end is a separate check. A design aid, not a substitute for the engineer of record.
• Steel Column Compressive Capacity (AISC 360 Ch. E, Flexural Buckling) - The axial load a steel column carries, set by its slenderness not its area: KL/r, the elastic buckling stress Fe = pi^2 E / (KL/r)^2, and Fcr from the inelastic 0.658^(Fy/Fe) Fy or the elastic 0.877 Fe branch at the 4.71 sqrt(E/Fy) transition. A 14 ft W10x45 carries 239 kips allowable; stretch it to 24 ft and slenderness alone cuts it to 97 kips. The unbraced length is the number to watch. Flexural buckling only. A design aid, not a substitute for the engineer of record.
• Eccentric Bolt Group in Shear (Elastic Vector Method) - The force on the worst bolt in a bracket or shear-tab group loaded off its centroid: the direct shear P/n superposed with the torsional shear from M = P x e, distributed by the group polar moment Ip = sum(x^2 + y^2). A 2x3 group at 3 in spacing under 30 kips at 6 in eccentricity puts 15.1 kips on the corner bolt; walk the load out to 12 in and torsion drives it to 27 kips. The conservative traditional method (not the instantaneous-center). Compare the resultant to the per-bolt strength. A design aid, not a substitute for the engineer of record.
• Bolt Shear + Bearing / Tearout Strength (AISC 360 J3) - The design strength of one bolt through a plate, the smaller of shear rupture (Rn = ns x Fnv x Ab) and bearing/tearout at the hole (1.2 lc t Fu, capped at 2.4 d t Fu). A 3/4 in A325-N bolt in single shear through 1/2 in A36 gives 17.9 kip design (LRFD) / 11.9 kip allowable - bolt-shear-governed. Thin the plate to 1/4 in and tearout takes over at 14.3 kip: the flip this tile exists to catch. Standard holes, one bolt at one hole. A design aid, not a substitute for the engineer of record.
• Column Base Plate under Axial Load (AISC Design Guide 1) - The plan size and thickness of a concentrically-loaded column base plate: the required concrete bearing area A1_req = Pu / (0.65 x 0.85 x f'c), the cantilever dimensions m, n, and n', and the thickness tp = l x sqrt(2 Pu / (0.90 Fy B N)). A W10x49 at 400 kips on a 14 in square A36 plate over 4 ksi concrete needs a 1-1/8 in plate; raise the load to 700 kips and the tile flags the plate as too small in bearing. Concentric axial only; anchor rods and shear transfer are separate. A design aid, not a substitute for the engineer of record.
• Composite Shear Stud Strength and Count (AISC 360-22 I8) - Qn = 0.5 Asc sqrt(f'c Ec) <= Rg Rp Asc Fu, studs each side = V'/Qn. A 3/4 in stud, f'c 4000, Ec 3.64e6, Fu 65, Rg 1.0, Rp 0.75 -> Qn_calc 26.7, cap 21.6 kip governs; V' 400 -> 19 studs; a weak-position Rp 0.6 raises it to 24. Deck orientation and stud position matter. The engineer of record governs.
• Composite Beam Flexural Strength (AISC 360-22 I3) - PNA-in-slab composite moment: C = As Fy, a = C/(0.85 f'c be), Mn = C(d/2 + tslab - a/2), phi Mn = 0.90 Mn. As 8.0, Fy 50, d 16, slab 4, be 90, f'c 4 -> C 400 kip, a 1.31 in, phi Mn 340 kip-ft; a narrow be 24 pushes a past the slab and flags PNA-in-steel. The engineer of record governs.
• Steel Beam Camber from Dead-Load Deflection - Camber = a fraction (75-80%) of the dead-load deflection 5 w L^4 / (384 E I), rounded to 1/4 in. 1.0 kip/ft, 40 ft, I 2100 -> 0.95 in deflection, 3/4 in camber; a stiff 20 ft beam deflecting 0.05 in is left flat (below the ~3/4 in practical minimum). The structural drawings govern.
• Required Moment of Inertia for a Deflection Limit - The inverse of the steel-camber tile: the moment of inertia a simple-span beam needs to hold the uniform-load midspan deflection to a limit, I = 5 w L^4 / (384 E delta_allow). A 1.0 kip/ft, 40 ft beam held to 1.0 in needs Ix about 1,986 in^4; pick a rolled shape with at least that Ix, then verify strength. Common limits are span/360 (LL) and span/240 (total). Sizes for stiffness only; the entered load is the service load. A design aid; the structural drawings govern.
• Steel Floor Walking Vibration (AISC DG11) - AISC Design Guide 11 walking-vibration check: peak acceleration ap/g = P0 e^(-0.35 fn) / (beta W) against the occupancy limit (0.5% office/residence, 1.5% mall). Stiffer is not automatically better -- low-frequency floors (4-8 Hz) resonate with the walking harmonic. The serviceability check strength alone misses.
• Column Web Panel-Zone Shear (AISC 360 J10.6) - The AISC 360-16 J10.6 panel-zone shear strength of a moment-connection column web, both branches: basic Rn = 0.60 Fy dc tw (J10-9) and the flange-stiffened bonus (J10-11, allowed only when panel-zone deformation is in the analysis), against the joint demand, with a doubler-plate flag. The moment-frame joint often fails here first.
• Panel-Zone Shear Under High Column Axial (AISC 360 J10-10/J10-12) - The axial reduction steel-panel-zone-shear flags but does not carry: past Pr = 0.4 Pc the basic panel-zone strength takes (1.4 - Pr/Pc) (Eq. J10-10), past 0.75 Pc the deformation-modeled strength takes (1.9 - 1.2 Pr/Pc) (Eq. J10-12), Pc = Py = Fy Ag. A W14-class column at 45% of axial yield loses 5% of its panel zone; at 83% it is losing 1.2% per additional percent of axial. Below the thresholds it matches the sibling exactly. A design aid, not a connection design.
• Panel-Zone Doubler-Plate Thickness (AISC 360 J10.6) - The how-thick that steel-panel-zone-shear leaves open: when the panel-zone check fails, the doubler plate is sized by two limits. Strength t = (Vu - phiRn_bare) / (0.90 x 0.60 Fy dc); stability (Eq. J10-12) t >= (dz + wz)/90 for a plate not plug-welded to the web. On a stocky column with a small shortfall the stability minimum governs (a strength-only calc would spec a plate too thin to be stable); on a deep beam the strength governs. Reports the governing thickness rounded up to the next 1/16-in plate. A detailing aid, not a stamped connection design.
• Reinforced Concrete Beam Flexural Capacity (ACI 318-19) - The design moment of a singly-reinforced, tension-controlled rectangular concrete beam: the equivalent stress-block depth a = As x fy / (0.85 x f'c x b), the nominal moment Mn = As x fy x (d - a/2), and phi Mn with phi = 0.90, plus the demand/capacity ratio against an entered required moment. A 12 x 24 in beam with three #9 Grade 60 bars on 4,000 psi concrete develops 260 kip-ft -- the textbook value -- and carries a 200 kip-ft demand at 77% utilization. Singly-reinforced and assumed tension-controlled (confirm epsilon_t >= 0.005); compression steel, T-beam action, and minimum steel are separate checks. A design aid, not a substitute for a licensed engineer's design.
• Reinforced Concrete Beam Shear and Stirrup Spacing (ACI 318-19) - Whether a rectangular concrete beam carries its shear and what stirrup spacing it needs: the simplified concrete contribution Vc = 2 x lambda x sqrt(f'c) x bw x d, the design phi Vc at phi = 0.75, the stirrup demand Vs = Vu/phi - Vc when the demand exceeds phi Vc, the required spacing s = Av x fyt x d / Vs, and the d/2 code maximum. A 12 x 21.5 in beam on 4,000 psi concrete carries 24.5 kip on concrete alone; a 40 kip demand needs #3 stirrups at 10 in (the d/2 cap governs over the computed 13.7 in). Uses the simplified Vc for a member without axial load; the section upper limit and minimum-reinforcement triggers are separate checks. A design aid, not a substitute for a licensed engineer's design.
• Concrete Threshold and Cracking Torsion (ACI 318-19 22.7) - The two torsion thresholds every spandrel and edge beam is checked against: torsion may be neglected when the factored torque is below phi x Tth, where the threshold torsion Tth = lambda x sqrt(f'c) x (Acp^2/pcp) with Acp = b x h the outside area and pcp = 2(b+h) the outside perimeter; the section cracks in torsion at Tcr = 4 x Tth (phi = 0.75). A 12 x 20 in beam on 4,000 psi concrete has Tth = 4.74 ft-kip, so torsion is ignored below 3.56 ft-kip and the section cracks at 18.97 ft-kip; an 18 x 24 in beam raises the threshold to 11.7 ft-kip -- torsion capacity grows fast with section size. Above phi x Tth closed stirrups and longitudinal steel must be designed. A design aid, not a substitute for a licensed engineer's design.
• Rebar Tension Development Length (ACI 318-19) - The straight-bar tension development length from the ACI 318-19 general equation: ld = (3/40) x fy x psi_t x psi_e x psi_s x psi_g / (lambda x sqrt(f'c) x (cb + Ktr)/db) x db, with the confinement term capped at 2.5, the psi_t x psi_e product capped at 1.7, and the 12 in floor. A #8 Grade 60 bottom bar in 4,000 psi concrete, well confined, develops in 28.5 in; cast as a top bar the 1.3 casting-position factor stretches it to 37 in -- the trap the 40-bar-diameter rule of thumb papers over. Straight-bar tension only; hooks, compression bars, and lap splices are separate checks. A design aid, not a substitute for a licensed engineer's detailing.
• Shallow Foundation Bearing Capacity (Vesic) - The gross ultimate and allowable bearing pressure of a shallow footing from the soil's own strength: qu = c x Nc + q x Nq + 0.5 x gamma x B x Ngamma with the Vesic bearing-capacity factors from the friction angle, De Beer / Vesic shape factors for square and circular footings, and the customary factor of safety of 3. A 6 ft strip footing 4 ft deep on a phi = 32 medium-dense sand carries 22 ksf ultimate, 7.3 ksf allowable -- the number the footing-area tile has always needed handed to it; a phi = 0 stiff clay pins the Prandtl Nc = 5.14 branch. General shear on a level, concentric footing with deep groundwater; settlement usually governs on sand and is separate. A design aid, not a substitute for a geotechnical engineer's report.
• Lateral Earth Pressure and Thrust (Rankine) - The push of retained soil: the Rankine active coefficient Ka = tan^2(45 - phi/2) and passive Kp = 1/Ka, the triangular active thrust Pa = 0.5 x Ka x gamma x H^2 at H/3, the rectangular surcharge term Ka x q x H at H/2, the combined resultant and its height, and the passive resistance. A 10 ft wall of phi = 30 sand carries exactly 2,000 lb/ft active against 18,000 lb/ft passive -- the 9:1 ratio that is why passive is never counted on lightly; a 250 psf parking surcharge grows the thrust 42% and lifts its arm. Cohesionless, vertical, frictionless, dry Rankine case only. A design aid, not a substitute for a geotechnical engineer's report.
• At-Rest Earth Pressure on a Braced Wall (Jaky K0) - The push of retained soil on a wall that cannot yield -- a basement wall, a braced excavation, a rigid box culvert -- where the Rankine active pressure does not apply because the soil never relaxes to its active limit: Jaky's K0 = 1 - sin phi, the triangular at-rest thrust P0 = 0.5 x K0 x gamma x H^2 at H/3, the uniform-surcharge term K0 x q x H at H/2, the combined resultant and its height. A 10 ft wall of phi = 30 sand carries 3,000 lb/ft at rest against only 2,000 lb/ft active -- exactly 1.5x more, the error a designer makes reaching for the active tile on a braced wall. Normally-consolidated cohesionless, dry; an overconsolidated or submerged case needs its own analysis. A design aid, not a substitute for a geotechnical engineer's report.
• Submerged-Backfill Earth Pressure (Buoyant + Hydrostatic) - The push of a backfill below the water table, where the dry Rankine tile no longer applies: the soil skeleton pushes with its buoyant weight (gamma_sat - 62.4) at the Ka reduction, but the water pushes with the full hydrostatic pressure at no reduction. Pa' = 0.5 x Ka x gamma_buoy x H^2, Pw = 0.5 x 62.4 x H^2, plus the Ka q H surcharge. A 10 ft phi = 30, 125 pcf sand pushes 2,083 lb/ft dry but 4,163 lb/ft submerged -- almost exactly 2x, and three-quarters of it is water, which is why a working drain is the cheapest structural element on the wall. Fully-submerged active case. A design aid, not a substitute for a geotechnical engineer's report.
• Sloped-Backfill Earth Pressure (Rankine Inclined Surface) - The push of a backfill that rises behind the wall at a slope beta, which the level Ka under-predicts: the Rankine inclined-surface coefficient Ka = cos b (cos b - sqrt(cos^2 b - cos^2 phi)) / (cos b + sqrt(cos^2 b - cos^2 phi)), the thrust Pa = 0.5 x Ka x gamma x H^2 acting parallel to the slope, and its horizontal (overturning) and vertical (heel) components. A 15 deg backfill on a phi = 30 sand raises Ka from 0.333 to 0.373 -- a 12% heavier thrust that also tilts and adds an uplift the level analysis never sees; beta must stay below phi or the slope cannot be retained on Rankine terms. Cohesionless, vertical wall face. A design aid, not a substitute for a geotechnical engineer's report.
• Coulomb Active Earth Pressure (Wall Friction and Batter) - The active thrust Rankine leaves on the table: Coulomb credits wall friction delta, a battered face theta, and a sloped backfill alpha, Ka = cos^2(phi - theta) / [cos^2(theta) cos(delta + theta) (1 + sqrt(sin(phi + delta) sin(phi - alpha) / (cos(delta + theta) cos(theta - alpha))))^2]. A rough vertical wall on a phi = 30 level backfill carries only 1,676 lb/ft of horizontal thrust once two-thirds-phi wall friction is credited, versus 2,000 lb/ft by Rankine -- a 16% cut in the overturning force plus a downward drag that resists sliding. Reduces exactly to Rankine when the wall is smooth, vertical, and the fill level. Cohesionless, active limit. A design aid, not a substitute for a geotechnical engineer's report.
• Cantilever Retaining Wall Stability (Overturning / Sliding / Bearing) - The three global-stability checks of a cast-in-place cantilever retaining wall: the restoring moments of the stem, base, and heel soil about the toe against the Rankine thrust's overturning moment, the base friction against sliding (both against the IBC 1807.2.3 minimum of 1.5), and the eccentricity-based toe / heel bearing pressures with a middle-third check. A 10 ft wall on a 6 ft base passes dry at 3.37 / 1.69 / 1,731 psf toe -- and the same wall fails sliding at 1.31 under a 300 psf surcharge, the case that most often governs. Internal member design, passive toe credit, and seismic pressure are separate. A design aid, not a substitute for a licensed engineer's design.
• Consolidation Time Rate (Terzaghi) - Terzaghi 1-D consolidation: Tv = (pi/4)(U/100)^2 for U <= 60% else 1.781 - 0.933 log10(100-U), time t = Tv Hdr^2/cv. U 90%, cv 0.1 ft^2/day, Hdr 10 ft -> Tv 0.848, 848 days; U 50% -> 196 days (the decelerating curve). Hdr is half the layer for double drainage (a 4x time swing). The engineer of record governs.
• Consolidation Degree from Elapsed Time (Terzaghi) - The inverse of the consolidation-time tile: how far a surcharge or fill has consolidated after a given time - Tv = cv t / Hdr^2, then U = 100 sqrt(4 Tv/pi) for Tv <= 0.283 else 100 - 10^((1.781-Tv)/0.933). cv 0.1 ft^2/day, Hdr 10 ft, 848 days -> Tv 0.848, U 90%; at 196 days U is only 50% (the decelerating curve, U approaches 100% asymptotically). Hdr is half the layer for double drainage (a 4x time swing). The engineer of record governs.
• SPT Allowable Bearing on Sand (Meyerhof) - Meyerhof settlement-controlled allowable from the SPT N60: qa = N60/4 ksf for B <= 4 ft else (N60/6)((B+1)/B)^2, times Kd = min(1 + 0.33 D/B, 1.33). N60 20, B 6, D 2 -> 4.54 base, Kd 1.11, 5.04 ksf; a 3 ft footing gives 5.00 ksf. A 1 in settlement allowable, not the ultimate; N60 energy-corrected. The geotechnical report governs.
• Required SPT N60 for a Target Bearing (Meyerhof) - The inverse of the SPT-bearing tile: the energy-corrected N60 the sand must show to carry a target allowable pressure at a 1 in settlement, N60 = qa_target / qa(N60=1). A 6 ft footing 2 ft deep needing 5 ksf wants N60 ~20 (round up for design). A serviceability check against the boring's N-value, not the ultimate bearing. A design aid; the geotechnical report governs.
• Liquefaction Triggering Screening (Seed-Idriss CSR) - Seed-Idriss screen: rd = 1 - 0.00233172 z (z <= 30.02 ft; per-meter 0.00765/0.0267 scaled by 0.3048), CSR = 0.65 amax (sv/s'v) rd, FS = (CRR/CSR) MSF, liquefiable if FS < 1. amax 0.30g, sv 2000, s'v 1200 psf, z 16.4 ft, CRR 0.20 -> CSR 0.313, FS 0.64, liquefiable; denser sand (CRR 0.40) -> FS 1.28. A level-ground screen; the geotechnical engineer of record governs.
• Pile Group Efficiency (Converse-Labarre) - Why a pile group carries less than the sum of its piles: the stress bulbs of adjacent piles overlap, so the Converse-Labarre efficiency Eg = 1 - theta((n-1)m + (m-1)n)/(90 m n) with theta = atan(d/s) discounts the group. A 3x3 group of 12 in piles at 3d = 36 in spacing (100 kip each) runs Eg = 0.727 -> 654 kip, not the 900 kip the naive sum implies; squeeze to 2d = 24 in and Eg falls to 0.606 -> 546 kip, losing another 108 kip for zero added piles. Below about 3d, efficiency drops under 0.7, so close-spaced piles give diminishing returns. An empirical friction-pile hand check; block failure and settlement are separate. A design aid; the geotechnical engineer of record governs.
• Pile Group Spacing for a Target Efficiency - The inverse of the pile-group-efficiency tile: the center-to-center spacing that reaches a target Converse-Labarre efficiency, theta = (1 - Eg) x 90 m n / ((n-1)m + (m-1)n), then s = d / tan(theta). A 3x3 group of 12 in piles targeting Eg 0.75 needs about a 39.6 in (3.3d) spacing. Answers 'how far apart for this efficiency' instead of the efficiency from a set spacing. Spacing must be at least one diameter. An empirical hand check; block failure and settlement are separate; the geotechnical engineer of record governs.
• Reinforced CMU Wall Out-of-Plane Flexure (TMS 402 ASD) - The allowable out-of-plane bending moment of a reinforced, fully grouted CMU wall by the working-stress cracked transformed-section method: the modular ratio n = Es/(900 f'm), the neutral-axis and lever-arm coefficients k and j, the steel-governed Ms = As Fs j d against the masonry-governed Mm = 0.5 Fb k j b d^2, and whichever is less governs. An 8 in wall with #5 bars at 24 in on 2,000 psi masonry carries 1,428 lb-ft per foot, steel-governed -- the textbook lightly-reinforced outcome; tighten the bars to 16 in and the masonry compression block takes over at 1,924. Cracked section, pure flexure, no axial interaction or one-third increase. A design aid, not a substitute for the engineer of record's stamped design.
• Masonry Headed Anchor Bolt Tension (TMS 402 ASD) - The allowable tension of a headed anchor bolt in grouted masonry -- the anchor that fastens a ledger or sill to a CMU wall, which the wall-design tiles never check. TMS 402 allowable-stress design takes the lesser of masonry breakout Bab = 1.25 x Apt x sqrt(f'm), with Apt = pi x lbe^2 the projected breakout cone, and steel Bas = 0.6 x Ab x fy. A 3/4 in anchor (Ab = 0.442 in^2, Fy 36 ksi) embedded 4 in in 1,500 psi masonry gives Bab = 2,433 lb and Bas = 9,547 lb, so masonry breakout governs at 2,433 lb; double the embedment to 8 in and Bab rises to 9,733 lb, so now the 9,547 lb steel governs. Edge distance reduces Apt; shear (pryout) is a separate check. A design aid, not a substitute for the engineer of record's stamped design.
• Reinforced CMU Shear Wall In-Plane Shear (TMS 402 ASD) - The allowable in-plane shear of a reinforced, fully grouted masonry shear wall: the masonry term Fvm = 0.5 x ((4.0 - 1.75 M/(V dv)) sqrt(f'm)) + 0.25 P/An that grows with axial compression and shrinks with slenderness, the horizontal-steel term Fvs = 0.5 Av Fs dv/(An s), and the combined stress against the shear-span-graded 3-to-2 sqrt(f'm) cap, times the net area for the allowable force. An 8 in by 8 ft wall under 20 kip of axial with #4 horizontals at 48 in carries 76 psi and 55.7 kip -- the capacity the seismic-base-shear demand is checked against. Sustained axial only; special-reinforced detailing is separate. A design aid, not a substitute for the engineer of record's stamped lateral design.
• Reinforced CMU Wall Axial Compression (TMS 402 ASD) - The allowable concentric axial load of a reinforced masonry wall or column: the material capacity 0.25 f'm An + 0.65 Ast Fs (the steel term for laterally tied bars) times the slenderness factor -- 1 - (h/140r)^2 up to h/r = 99 and the Euler-type (70r/h)^2 beyond, the two branches meeting continuously. A one-foot strip of a 12 ft, 8 in grouted wall with #5 verticals at 24 in carries 38.3 kip; stretch it to 24 ft and the slender branch cuts it to 14.0 kip, the buckling penalty that forces thickness or a brace. Pure axial; the moment interaction pairs with the flexure tile. A design aid, not a substitute for the engineer of record's stamped design.
• Masonry Anchor Embedment for a Tension (TMS 402 ASD) - The inverse of the masonry-anchor-bolt tile: the effective embedment that makes the TMS 402 masonry-breakout capacity equal a required tension, lbe = sqrt(T / (1.25 pi sqrt(f'm))). 5,000 lb in 1,500 psi masonry needs ~5.7 in of embedment; the steel branch Bas = 0.6 Ab fy is a separate ceiling (a bolt too small yields no matter how deep). Edge distance reduces the cone. A design aid; the engineer of record's stamped design governs.
• Masonry Compressive Strength f'm, Unit-Strength Method (TMS 602 Table 2) - The net-area masonry compressive strength f'm every CMU wall tile consumes but none derives -- from the net-area unit strength and the mortar type by the TMS 602-16 Table 2 unit-strength method, no prism test. f'm is not the unit strength: a 2,000 psi (net) concrete unit gives f'm 2,000 psi in Type M or S mortar but only 1,750 in Type N, a 12.5% cut from the mortar alone; a 3,250 psi unit in Type M/S gives 2,500 (77% of the block). Linear interpolation between Table 2 rows; 2,000 psi is the ASTM C90 net-area minimum and the table caps f'm (a higher value needs a prism test). Feeds cmu-wall-axial, cmu-wall-flexure, cmu-shear-wall, and masonry-anchor-bolt. A specification aid, not a substitute for TMS 602 and the engineer of record.
• Masonry Wall Dead Load - Wall dead load = hollow (NCMA) weight + grout adder prorated by grout spacing (capped at full). 8 in CMU, grouted 48 in o.c. -> 59.8 psf (598 lb/ft at 10 ft); fully grouted -> 84 psf, a 40% heavier wall. Line load and total from height/area. The NCMA tables and engineer of record govern.
• Brick Veneer Anchor Spacing and Count (TMS 402 / IBC 1405) - Anchor count = ceil(area / area-per-anchor) with the 32 in horizontal / 24 in vertical spacing caps, per TMS 402 / IBC 1405. A 200 ft^2 veneer at 2.67 ft^2/anchor -> 75 ties; a high-wind 2.0 ft^2 limit -> 100. TMS 402 / IBC and the engineer of record govern.
• Brick Veneer Weep-Hole Count (IRC R703.8.6) - Weep holes to drain the veneer air space at each through-wall flashing line: weeps per line = ceil(wall length in / max spacing) + 1, so both ends get a weep. IRC R703.8.6 and TMS 402 cap the spacing at 33 in on center (a common tighter spec is 24 in), at least 3/16 in diameter, immediately above the flashing. A 30 ft wall at 33 in is 12 weeps per line; the base course plus every shelf angle and lintel flashing above openings each need their own line. The weeps must sit directly on the flashing over a clear, un-mortar-clogged air space; the AHJ-adopted code and the wall detail govern. Distinct from the veneer ANCHOR count (brick-veneer-anchor-spacing).
• Masonry Horizontal Joint-Reinforcement Takeoff (IRC R606.12.2) - Ladder or truss wire laid in the bed joints of a masonry wall: reinforced courses = ceil(height in / vertical spacing), pieces per course = ceil(length / piece length), total = courses x pieces. IRC R606.12.2 / TMS 402 cap the vertical spacing at 16 in (every other 8 in course); some specs tighten it to 8 in or add wire at bond beams and above and below openings. A 40 x 12 ft CMU wall at 16 in and 10 ft pieces is 9 courses x 4 = 36 pieces; a 30 x 10 ft wall is 24. Wire laps at least 6 in (the lap is not added here). A material count; the spacing, the lap, and the extra wire at openings come from the structural spec and the adopted code.
• Masonry Lintel Arching Load (Triangular Load Over an Opening) - The triangular dead load a lintel carries within a 45-degree triangle (height span/2) when the wall above >= span/2, else the full rectangle. A 6 ft opening, 60 psf, 5 ft above -> 540 lb (90 lb/ft); only 2 ft above -> the full 720 lb. Dead load only; the engineer of record governs.
• Wood Diaphragm Unit Shear and Chord Force (SDPWS) - The flexible wood diaphragm as a deep horizontal beam: the end reaction V = wL/2, the maximum unit shear v = wL/(2b) the sheathing nailing must carry, the moment wL^2/8, and the chord force T = C = M/b the perimeter members resolve it into. A 192 x 120 ft roof at 516 plf runs 413 plf of unit shear -- the published WoodWorks value -- and 19.8 kip of chord force; narrow the diaphragm to 60 ft and both exactly double. Simple-span flexible (tributary) distribution; collectors, deflection, and openings are separate. A design aid, not a substitute for the engineer of record's stamped lateral design.
• Wood Shear Wall Unit Shear and Holdown (SDPWS / ASD) - The two numbers a wood shear wall is detailed for: the unit shear v = V/b checked against the SDPWS nailing schedule, and the net holdown tension T = (V h - 0.6 W b/2)/b once the story shear tries to overturn the wall and only 0.6 times the tributary dead load resists it (the ASD combination). An 8 ft wall taking 8 kip at 10 ft with 3,000 lb of dead load runs 1,000 plf and a 9.1 kip holdown; load the wall to 20,000 lb and gravity cuts the holdown to 4.0 kip, and past the balance point the tile clamps to zero. Segmented wall; sill anchorage and chord bearing are separate. A design aid, not a substitute for the engineer of record's stamped lateral design.
• Wood Shear Wall Deflection (SDPWS Eq 4.3-1) - How far the top of a wood shear wall drifts, from the SDPWS three-term equation: end-post bending 8vh^3/(EAb), panel shear plus nail slip vh/(1000 Ga) with the tabulated apparent stiffness, and anchorage rotation h da/b from the holdown slack -- in the equation's own calibrated units. A 10 x 8 ft wall at 400 plf on 4x4 posts deflects 0.47 in (0.40% drift), the shear and anchorage terms carrying nearly all of it; double the height and the h^3 bending term wakes up. Checked against the ASCE 7 story-drift limit -- the reason a tall narrow wall can pass strength and fail stiffness. A design aid, not a substitute for the engineer of record's stamped lateral design.
• Collector / Drag Strut Axial Force (ASCE 7 12.10) - The accumulated axial force in a collector (drag strut) that gathers diaphragm shear across an opening and drags it back to the shear wall: collector_force = unit_shear x collector_length, plus the ASCE 7 12.10.2.1 Omega0 overstrength demand the diaphragm chord never carries. The separate load path diaphragm-shear leaves out.