shearcheck AISC 360-22
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Shear tab eccentricity: why e = a/2, and how the ICR method handles it

A single-plate shear connection carries the beam reaction through a bolt group that does not sit at the support face — the bolt line stands a distance a away from the weld line. The reaction therefore reaches the bolt group with a lever arm, and the group resists a small moment on top of the direct shear. That lever arm is the eccentricity e, and it is why a shear tab's bolt group is checked as an eccentrically loaded group rather than n bolts in pure shear.

The conventional configuration and e = a/2

In the conventional configuration — single vertical bolt row, plate fillet-welded both sides to a rigid support — the true point of inflection lies somewhere between the weld line and the bolt line, depending on the relative rigidity of the plate and the support. The design convention, as illustrated in AISC Design Examples v16.0, Example II.A-17A, places the effective eccentricity at half the weld-to-bolt-line distance:

$$e = \frac{a}{2}$$

shearcheck applies e = a/2 as illustrated in that published example, and surfaces the computed e on every result page so the assumption is never hidden. For the demo case, a = 3 in gives e = 1.50 in.

The ICR method

An eccentrically loaded bolt group rotates about an instantaneous center of rotation (ICR): each bolt's force acts perpendicular to its radius from that center, with a magnitude set by how far the bolt has deformed. The method uses the experimentally derived load-deformation relationship (Crawford & Kulak 1971, cited via Brandt):

$$R = R_{ult}\left(1 - e^{-10\Delta}\right)^{0.55}$$
$$\Delta_{max} = 0.34\ \text{in},\qquad \Delta_i = 0.34\,\frac{d_i}{d_{max}}$$

where Δ is the bolt deformation, capped at 0.34 in at the bolt farthest from the instantaneous center. The solver iterates the center's position until the bolt forces balance the applied load; the result is the group coefficient C — the number of "effective" bolts, always fewer than n because eccentricity costs capacity. The group's nominal strength is then C times the single-bolt strength. The iterative procedure shearcheck implements is the one published in Brandt, "Rapid Determination of Ultimate Strength of Eccentrically Loaded Bolt Groups," AISC Engineering Journal, Q2 1982 (open access).

Worked numbers: the verified demo case

For the AISC Design Example II.A-17A configuration — four bolts in a single row at s = 3 in, vertical reaction, e = a/2 = 1.50 in — the exact ICR iteration converges to C = 3.5564: the four-bolt group works like 3.56 bolts. The Design Example reads the same case from the AISC Manual's interpolated table as C = 3.54 (0.46% apart — interpolation vs exact iteration). shearcheck's solver also reproduces both fully-worked examples published in Brandt (1982); the verification page tabulates all three checks.

You can see this exact computation live: the demo result reports C, e, and the converged iteration count, or run your own connection — free, no signup.

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