Connection Checks — Engineering Reference
AISC 360 demand-to-capacity checks for steel connections: bolt shear, bearing, block shear, weld throat, and tearout limit states explained.
Overview
Every steel connection must be checked against a series of limit states to confirm that the demand-to-capacity ratio (DCR) does not exceed 1.0 for any failure mode. A DCR = R_u / (phi x R_n), where R_u is the required strength (factored demand) and phi x R_n is the design strength (factored capacity). The connection is adequate when every DCR <= 1.0. The governing DCR (the highest ratio) identifies the controlling limit state and the remaining reserve in the connection.
AISC 360-22 Chapter J provides the limit state equations for bolts (J3), welds (J2), and connecting elements (J4). A typical bolted shear connection requires checking 6-10 limit states; a moment connection may require 12-15 checks including column-side verifications.
Complete limit state checklist
Bolted connection checks
| # |
Limit State |
AISC Section |
Equation |
phi |
| 1 |
Bolt shear |
J3.6, Table J3.2 |
R_n = F_nv x A_b x n_s |
0.75 |
| 2 |
Bolt bearing |
J3.10 |
R_n = 1.2 x L_c x t x F_u (per bolt) |
0.75 |
| 3 |
Bolt tearout |
J3.10 |
R_n = 1.5 x d x t x F_u (upper limit) |
0.75 |
| 4 |
Bolt tension |
J3.6, Table J3.2 |
R_n = F_nt x A_b |
0.75 |
| 5 |
Combined shear-tension |
J3.7 |
F'_nt = 1.3F_nt - (F_nt/(phi x F_nv)) x f_rv |
0.75 |
| 6 |
Slip resistance |
J3.8 |
R_n = mu x D_u x h_f x T_b x n_s |
1.00 or 0.85 |
Connecting element checks
| # |
Limit State |
AISC Section |
Equation |
phi |
| 7 |
Gross section yielding |
J4.1(a) |
R_n = F_y x A_g |
0.90 (tension), 1.00 (shear) |
| 8 |
Net section rupture |
J4.1(b) |
R_n = F_u x A_e |
0.75 |
| 9 |
Block shear rupture |
J4.3 |
R_n = 0.6F_u x A_nv + U_bs x F_u x A_nt |
0.75 |
| 10 |
Plate flexure |
F11 or J4 |
M_n = F_y x Z (compact) |
0.90 |
| 11 |
Plate buckling |
E3 (Thornton) |
P_n = F_cr x A_whitmore |
0.90 |
Weld checks
| # |
Limit State |
AISC Section |
Equation |
phi |
| 12 |
Fillet weld shear |
J2.4 |
R_n = 0.60 x F_EXX x t_e x L |
0.75 |
| 13 |
Base metal at weld |
J2.4 |
R_n = 0.60 x F_u x t x L (shear) |
0.75 |
| 14 |
CJP weld (tension) |
J2.3 |
Same as base metal |
per base metal |
Column-side checks (moment connections)
| # |
Limit State |
AISC Section |
Equation |
phi |
| 15 |
Column flange bending |
J10.1 |
Yield line / T-stub |
0.90 |
| 16 |
Web local yielding |
J10.2 |
R_n = F_yw x t_w x (5k + l_b) |
1.00 |
| 17 |
Web crippling |
J10.3 |
Per AISC Eq. J10-4 |
0.75 |
| 18 |
Web panel zone shear |
J10.6 |
R_v = 0.60 x F_y x d_c x t_w |
0.90 |
Worked example — DCR summary for a shear tab
Given: W21x44 beam, R_u = 55 kip, 3/8 in. x 9 in. A36 shear tab, three 3/4 in. A325-N bolts at 3 in. spacing, 5/16 in. fillet weld (E70XX) to W14x48 column.
| Check |
phi x R_n (kip) |
R_u (kip) |
DCR |
Status |
| Bolt shear (3 bolts) |
53.7 |
55 |
1.02 |
NG — need 4 bolts |
| Bearing on tab (3 bolts) |
58.2 |
55 |
0.94 |
OK |
| Block shear (beam web) |
112 |
55 |
0.49 |
OK |
| Block shear (tab) |
98 |
55 |
0.56 |
OK |
| Tab gross shear yielding |
72.9 |
55 |
0.75 |
OK |
| Tab net shear rupture |
66.7 |
55 |
0.82 |
OK |
| Weld (2 x 9 in. lines) |
111.5 |
55 |
0.49 |
OK |
| Column web yielding |
185 |
55 |
0.30 |
OK |
Revised with 4 bolts (12 in. tab): Bolt shear = 4 x 17.9 = 71.6 kip. DCR = 55/71.6 = 0.77. All checks pass. Governing limit state: bolt shear at DCR = 0.77.
Demand-to-capacity ratio interpretation
| DCR Range |
Interpretation |
| 0.00 - 0.50 |
Significantly over-designed — consider reducing plate/bolt size |
| 0.50 - 0.85 |
Efficient design — good balance of economy and reserve |
| 0.85 - 0.95 |
Tight design — acceptable but limited reserve for field changes |
| 0.95 - 1.00 |
Marginally adequate — reconsider if loading assumptions change |
| > 1.00 |
Fails — must revise connection |
Code comparison — connection check approach
| Feature |
AISC 360 |
AS 4100 |
EN 1993-1-8 |
CSA S16 |
| Bolt shear check |
Table J3.2 (F_nv tabulated) |
Clause 9.2.2 (V_f) |
Table 3.4 (alpha_v x f_ub x A) |
Clause 13.12.1 |
| Block shear model |
Combined shear + tension planes |
Clause 9.1.9 |
Not explicit (use Annex) |
Clause 13.11 |
| Bearing model |
1.2 L_c t F_u per bolt |
3.2 d t f_up |
k_1 x alpha_b x f_u x d x t |
3 x phi x n x t x d x F_u |
| Weld directional strength |
1.0 + 0.50 sin^1.5(theta) |
Not permitted |
k_w directional factor |
Not permitted |
| Base metal check required |
Yes (J2.4) |
Yes (implicitly) |
Yes (Table 4.1) |
Yes |
Common mistakes to avoid
- Checking bolt shear but skipping bearing/tearout — bearing on thin plates (shear tabs, gussets) with short edge distances frequently governs over bolt shear. This is the single most commonly missed check in practice.
- Not checking block shear on the beam web — at coped beams, the beam web block shear capacity can be 30-50% lower than the bolt group shear capacity. This check must be performed for every coped beam connection.
- Using gross area for net section rupture — the net area deducts bolt holes (nominal diameter + 1/16 in. per AISC B4.3). Forgetting hole deductions overestimates the rupture capacity.
- Ignoring base metal capacity at welds — the weld may be stronger than the base metal it connects to. Both the weld throat and the base metal at the weld must be checked. For thin plates with large welds, base metal shear rupture often governs.
- Not presenting a DCR summary — a well-organized DCR table is essential for peer review and building permit approval. Presenting only the governing check without showing all limit states makes it impossible for the reviewer to verify completeness.
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Disclaimer
This page is for educational and reference use only. It does not constitute professional engineering advice. All design values must be verified against the applicable standard and project specification before use. The site operator disclaims liability for any loss arising from the use of this information.