Eccentric Groups

Eccentric Bolt and Weld Groups

Instantaneous centre of rotation — the method behind AISC Manual Tables 7-6 to 7-13 and 8-4 to 8-11, solved for the geometry you actually have instead of interpolated off a printed grid. Load–deformation from Manual Eq. 7-1 (bolts) and Eqs. 8-3 to 8-7 (welds).
Given eccentric shear in the plane of the faying surface — Manual Part 7

Bolt group

low → bolt force, fraction of rn instantaneous centre applied Pr

Available strength

Solution

    Coefficient C — Manual Table 7-6 arrangement

    Bolt by bolt

    How this is worked out

    1. Both groups rotate about a point, not a centroid. An eccentric load is a rotation plus a translation, and the two combine into pure rotation about the instantaneous centre. Where that point sits depends on the geometry and on where and how the load is applied, so it has to be solved for, not looked up.Manual pp. 7-7, 8-13
    2. Deformation is proportional to distance from that centre. The element furthest from the IC is taken to its rupture deformation; every other element gets a share in proportion to its own distance, and its force follows from the load–deformation curve at that deformation.
    3. Bolts follow R = Rult(1 − e−10Δ)0.55 calibrated on \xbe-in. Grade A325 bolts in double shear, with Δmax = 0.34 in. Eq. 7-1
    4. Welds follow Fnwi = 0.60FEXX(1.0 + 0.50 sin1.5θi)[pi(1.9 − 0.9pi)]0.3 where a weld element's strength depends on the angle its force makes with its own axis — a transverse fillet is half again as strong as a longitudinal one, but it also ruptures at roughly a third of the deformation, which is exactly why the two cannot both be counted at peak. Eqs. 8-3 to 8-7
    5. Equilibrium closes it. The IC is moved until the element forces balance the applied load in both directions and in moment. The coefficient is then C = Rn/rn for bolts and Rn = C C1Dl for welds — the same numbers the Manual prints.
    6. Concentric load is a special case. With the load through the centroid the IC is at infinity and the group simply translates, so Specification Section J2.4 governs the weld group directly: J2.4(a) where every element makes the same angle with the load, and the greater of Eqs. J2-10a and J2-10b where the group has both longitudinal and transverse elements.