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.
Example
You enter
- Vertical load P (kip) 30
- Eccentricity e (in) 6
- Number of bolt columns 2
- Number of bolt rows 3
- Column gage gx (in) 3
- Row pitch gy (in) 3
You get
- Polar moment Ip 49.5 in^2
- Direct shear P/n 5.00 kip
- Critical bolt force R 15.11 kip
Details, formula, and sources
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.
M = P x e; Ip = sum(x^2 + y^2) about the centroid; direct = P/n; tors_h = M ymax / Ip, tors_v = M xmax / Ip; R = sqrt(tors_h^2 + (direct + tors_v)^2).
The elastic (vector) method for an eccentric fastener group, the traditional conservative superposition; AISC Manual Part 7 gives the less-conservative instantaneous-center tables.
The elastic vector superposition (direct plus torsional shear distributed by the polar moment of inertia) is public structural mechanics; the instantaneous-center coefficients are in the AISC Manual.
Estimate. AHJ and licensed professional govern.
Field names used by the API: load_kip, ecc_in, ncols, nrows, gage_in, pitch_in, ip, direct_kip, resultant_kip
- Elastic vector method direct shear P/n plus torsional shear M r / Ip on the critical corner bolt; conservative vs the instantaneous-center methodAISC Manual Part 7
- Polar moment Ip = sum(x^2 + y^2) over all bolts about the group centroid (unit-area bolts)elastic mechanics
- Compare to per-bolt strength the resultant is the demand on the worst bolt; check it against bolt-shear-bearing (AISC J3)AISC 360-22 J3