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

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Related references

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.