Shear Flow and Connector Spacing (Built-Up Beam)
The horizontal shear flow at a connected interface of a built-up beam and the fastener/weld spacing that carries it.
Example
You enter
- Transverse shear V at the section (kip) 50
- Connected element area A (in²) 6
- Connected element centroid distance from NA, y_bar (in) 8
- Moment of inertia of whole section I (in⁴) 800
- Capacity per connector R (kip) 10
- Connectors per row n (2 = a pair of lines) 2
You get
- First moment Q = A y_bar 48.0 in^3
- Shear flow q = V Q / I 3.000 kip/in
- Maximum connector spacing s 6.67 in
Checked against published worked examples from: FAMU-FSU College of Engineering (W. Oates).
Details, formula, and sources
ScopeShear flow q = V Q / I, with V the transverse shear, I the moment of inertia of the whole built-up section, and Q = A y_bar the first moment of the connected element about the neutral axis; the maximum connector spacing is s = n R / q for n connectors per row of capacity R each. A 6 in^2 cover plate at y_bar 8 in on a section with I 800 in^4 under a 50 kip shear carries q = 3.0 kip/in, so two 10 kip bolts per row space at 6.7 in. The spacing tightens where the shear is largest (near supports), which is why fabricators step the bolt pattern along the span. First-principles mechanics of materials (Hibbeler / Gere); the connector capacity R is from AISC and entered here. A design aid; the engineer of record governs.
Formula or tableQ = A y_bar (first moment of the connected element about the neutral axis); q = V Q / I (shear flow); s = n R / q (max connector spacing).
Source and editionFirst-principles mechanics of materials (shear flow in a built-up beam), as in Hibbeler Mechanics of Materials and Gere; the connector capacity R is from AISC and entered.
Free accessThe shear-flow relation q = VQ/I and the connector-spacing s = nR/q are standard published mechanics-of-materials results (Hibbeler, Gere, Roark), reproduced in every strength-of-materials text.
What governsEstimate. AHJ and licensed professional govern.
API field namesshear_kip, area_in2, ybar_in, inertia_in4, connector_kip, connectors_per_row, first_moment_in3, q_kip_in, spacing_in
- Shear flow q = V Q / I, Q = A y_bar of the connected element about the section neutral axismechanics of materials (Hibbeler / Gere)
- Connector spacing s = n R / q; the connector capacity R is entered (from AISC bolt/weld strength)built-up-member connection design