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.
Formula and source
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.
Audience
This tile is built for trades and the adjacent professions in the Carpentry and Construction group. The interactive calculator runs entirely in your browser. No account, no fee, no advertising, no tracking.
Related tools
Posture
Rough Logic answers the math question the working professional asks on the job. The site is a calm, fast, ad-free, account-free, ever-free reference. It does not interpret code. It does not replace the licensed professional. It does not store your inputs. The Authority Having Jurisdiction governs all installations and inspections.