Staggered-Hole Net Width (AISC 360 B4.3b)
The net width of a tension member across a STAGGERED (zigzag) bolt chain.
Example
You enter
- Gross plate width (in) 12
- Plate thickness (in) 0.5
- Bolt diameter (in) 0.75
- Hole allowance over the bolt diameter (in) 0.125
- Gage, transverse spacing between gage lines (in) 3
- Pitch, longitudinal spacing between staggered holes (in) 2
- Holes crossed by the straight chain 2
- Holes crossed by the zigzag chain 3
- Gage spaces crossed by the zigzag chain 2
You get
- Hole deducted 0.875
- Straight chain 10.250 in net width
- Net width zigzag (in) 10.0417
- Stagger credit (in) 0.666667
- Net area (in²) 5.02083
- Pitch where straight governs (in) 2.29129
Checked against published worked examples from: American Institute of Steel Construction.
Details, formula, and sources
ScopeB4.3b deducts the diameters of ALL holes in a diagonal chain and then ADDS s^2/4g for each gage space it crosses, and every possible chain has to be checked with the SMALLEST net width governing. Two things get missed: the hole comes off at the bolt diameter plus 1/8 in, not the bolt diameter, which overstates the area on every hole in the chain; and staggering has a CEILING -- past a computable pitch the straight chain governs and further stagger buys nothing at all. It reports that pitch, the number worth having before the pattern gets redrawn.
Formula or tablehole diameter deducted = bolt diameter + allowance (1/8 in default). Straight chain net width = W - n_straight x hole. Zigzag chain net width = W - n_zigzag x hole + k x s^2/(4g), k gage spaces crossed. The smaller governs; An = governing net width x thickness. The pitch at which the two chains are equal is s = sqrt(4 g (n_zigzag - n_straight) x hole / k).
Source and editionAISC 360 Section B4.3b (Net Area).
Free accessAISC 360 is published as a free PDF download by the American Institute of Steel Construction.
What governsEstimate. AHJ and licensed professional govern.
API field namesplate_width_in, thickness_in, bolt_dia_in, hole_allowance_in, gage_in, pitch_in, holes_straight, holes_zigzag, gage_spaces_zigzag, hole_dia_in, net_width_straight_in, net_width_zigzag_in, stagger_credit_in, net_area_in2, pitch_where_straight_governs_in
- Zigzag credit s^2/4g added for each gage space in the chainAISC 360 B4.3b
- Hole deduction bolt diameter + 1/8 in by default; editable for oversized and slotted holesAISC 360 B4.3b and Commentary
- Governing chain the smallest net width of all possible chains; only the two entered are evaluatedAISC 360 B4.3b
- Stagger ceiling pitch = sqrt(4 g (n_zigzag - n_straight) x hole / k), past which the straight chain governsderived from B4.3b
- Shape rectangular plate; angles use the developed flat width and are not coveredstated scope limit