AISC Design Example II.A-17A, walked through limit state by limit state

Example II.A-17A in the Companion to the AISC Steel Construction Manual, v16.0, Vol. 1: Design Examples is the published conventional single-plate shear connection example — and shearcheck's canonical verification case. This page lists the given configuration, then puts shearcheck's verified numbers side-by-side with the example's printed values for every limit state. Run this exact case live to see the full result page and download the .docx.

Given

Beam	W16×50, ASTM A992 (d = 16.3 in, t_w = 0.380 in), uncoped
Support	W14×90 column flange (t_f = 0.710 in)
Plate	PL 1/4 × 4 1/2 × 11 1/2, ASTM A572 Gr 50 (F_y = 50 ksi, F_u = 65 ksi)
Bolts	Four 3/4-in Group 120, threads in shear plane (N), standard holes, single vertical row
Geometry	s = 3 in, l_ev = 1 1/4 in, l_eh = 1 1/2 in, a = 3 in → e = a/2 = 1.50 in
Weld	3/16-in E70 fillets, both sides (= 5/8 · t_p)
Reactions	R_u = 49.6 kips (LRFD) / R_a = 33.0 kips (ASD)

One limit state in full: plate shear rupture

The governing state is worth seeing end-to-end. The net shear area uses the effective hole — the 13/16-in standard hole plus the 1/16-in net-area allowance of AISC 360-22 §B4.3b gives 7/8 in per hole:

A_{nv} = \left(11.5 - 4 \times \tfrac{7}{8}\right)(0.25) = 2.00\ \text{in}^2

R_n = 0.60\,F_u\,A_{nv} = 0.60(65)(2.00) = 78.0\ \text{kip}, \qquad \phi R_n = 0.75(78.0) = 58.5\ \text{kip}

Both witnesses, the engine, and the printed example land on φR_n = 58.5 kips for this state exactly.

Every limit state, side-by-side (available strengths, kips)

Quantity	DE printed	shearcheck	Δ	Note
Shear yield φR_n	86.4	86.25	0.17%	DE rounds A_gv to 2.88 in²
Shear rupture φR_n	58.5	58.5000	0.00%	exact
Block shear φR_n / R_n/Ω	65.3 / 43.6	65.508 / 43.672	0.32% / 0.17%	DE rounds areas (1.79 / 0.266)
Bolt shear φr_n	17.9	17.892	0.04%
Plate tearout, edge φr_n	12.4	12.340	0.49%	DE per-inch table rounding (49.4 k/in)
Plate bearing, interior φr_n	22.0	21.938	0.28%
Web bearing φr_n	33.4	33.345	0.16%
ICR coefficient C	3.54 (Table 7-6 interp.)	3.5564	0.46%	exact ICR vs table interpolation
Bolt group φR_n / R_n/Ω	58.5 / 38.9	58.695 / 39.130	0.33% / 0.59%	via exact C
Connection φR_n / R_n/Ω	58.5 / 38.9	58.5 / 39.0	0% / 0.26%

Every difference is within the committed ±1% tolerance and traces to the example's intermediate rounding, noted per row. The dimensional checks (plate thickness ≤ d_b/2 + 1/16, edge distances per Table J3.4, plate depth within the beam's workable flat) all pass, as in the example.

Governing limit state

The example concludes "shear transfer at the bolt holes" governs at φR_n = 58.5 kips — which at printed precision ties plate shear rupture (also 58.5 kips). With the exact ICR coefficient the bolt group rises to 58.7 kips, so shearcheck reports plate shear rupture (58.500 kips) as governing. The connection's available strength — and the PASS verdict against R_u = 49.6 / R_a = 33.0 — is identical either way. Full disclosure on the verification page.