------------------------- | -------- | --------------------- | ------------------ | --------------------------------------- | | 2 bolt lines, 3 rows at 3" c/c | 5.5" | 6" | 12.4" | Typical HSS brace connection | | 2 bolt lines, 4 rows at 3" c/c | 5.5" | 9" | 15.9" | Longer connection, wider Whitmore | | 2 bolt lines, 5 rows at 3" c/c | 5.5" | 12" | 19.3" | Heavy brace, many bolts | | Single bolt line, 4 bolts at 3" | N/A | 9" | 290.577 = 10.4" | Single line — s=0, spread from one line | | Welded connection, 10" length | N/A | 10" | 2100.577 = 11.5" | Spread from weld start to weld end |

Block shear per AISC J4.3 — detailed procedure

Block shear is a limit state where a block of material tears out of the gusset plate along a path combining shear and tension failure surfaces. AISC 360 Section J4.3 provides the block shear resistance equations.

Block shear resistance equations

phi*Rn = 0.75 * (0.60 * Fu * A_nv + Ubs * Fu * A_nt)         [rupture governs]
phi*Rn = 0.75 * (0.60 * Fy * A_gv + Ubs * Fu * A_nt)         [yielding governs]

Use the lesser of the two expressions.

Where:

Shear and tension areas for a typical gusset bolt pattern

For a gusset with n_bolt_rows rows of bolts at spacing s, edge distance L_ev (vertical), and n_bolt_cols columns at spacing g, edge distance L_eh (horizontal):

Shear area (along two vertical lines of bolts):

A_gv = 2 * t_p * (n_bolt_rows * s + L_ev - d_hole/2)   ... wait, let me correct
A_gv = 2 * t_p * (n_bolt_rows * s + L_ev)
A_nv = A_gv - n_bolt_rows * d_hole * t_p * 2             ... subtract holes in both lines

Actually, more precisely:

A_gv = 2 * t_p * [ (n_bolt_rows - 1) * s + L_ev ]
A_nv = A_gv - 2 * n_bolt_rows * (d_hole + 1/16) * t_p

Tension area (across the top between the two bolt lines):

A_nt = t_p * ( g - d_hole )    ... for one bolt hole in the tension path
A_gt = t_p * g                  ... gross tension area

Worked example — HSS6x6 brace gusset with full UFM procedure

Given: A diagonal brace connection in a braced frame. HSS6x6x3/8 brace (Fy = 46 ksi, Fu = 58 ksi) at 45 degrees from horizontal, carrying a factored compression force P = 180 kips. The gusset plate is 5/8" thick A36 (Fy = 36 ksi, Fu = 58 ksi). The brace is bolted to the gusset with 4 rows of 3/4" A325-N bolts at 3" spacing, 5.5" gage between outer bolt lines.

The gusset is welded to a W18x50 beam (d = 17.99", tf = 0.570", tw = 0.355") and a W14x68 column (d = 14.04", tf = 0.720", tw = 0.415"). Beam e_b = 17.99/2 = 9.0 in. Column e_c = 14.04/2 = 7.0 in. Selected alpha = 12.0 in., beta = 9.0 in.

Step 1 — Whitmore section

Connection length Lconn = 3 * 3 = 9 in. Lw = 5.5 + 2 * 9 * tan(30) = 5.5 + 10.39 = 15.89 in.

Step 2 — Compression buckling (Thornton)

Measured distances from Whitmore corners to nearest free gusset edge: L1 = 7.5 in., L2 = 9.0 in., L3 = 7.5 in. Lavg = (7.5 + 9.0 + 7.5) / 3 = 8.0 in. r = t_p / sqrt(12) = 0.625 / 3.464 = 0.1804 in. KL/r = 0.65 * 8.0 / 0.1804 = 28.8 (using K = 0.65, edges connected) Fe = pi^2 _ 29000 / 28.8^2 = 345 ksi Fcr = 0.658^(36/345) _ 36 = 0.658^0.104 _ 36 = 0.959 * 36 = 34.5 ksi phiRn (compression) = 0.90 _ 34.5 _ 15.89 * 0.625 = 308 kips > 180 kips. OK.

Step 3 — Block shear

Bolt hole diameter d_h = 3/4 + 1/8 = 7/8" = 0.875 in.

Shear paths (two lines, 4 bolt holes each): Agv = 2 * 0.625 _ (33 + 1.5) = 2 * 0.625 _ 10.5 = 13.13 in^2 A*nv = 13.13 - 2 * 4 _ 0.875 _ 0.625 = 13.13 - 4.38 = 8.75 in^2

Tension path (between outer bolt lines, single bolt hole): A*nt = 0.625 * (5.5 - 0.875) = 0.625 _ 4.625 = 2.89 in^2 Ubs = 1.0 (symmetric pattern)

Rupture expression: 0.75 _ (0.60 _ 58 _ 8.75 + 1.0 _ 58 _ 2.89) = 0.75 _ (304.5 + 167.6) = 0.75 _ 472.1 = 354 kips Yielding expression: 0.75 _ (0.60 _ 36 _ 13.13 + 1.0 _ 58 _ 2.89) = 0.75 _ (283.6 + 167.6) = 0.75 _ 451.2 = 338 kips

Block shear capacity = 338 kips (yielding expression governs) > 180 kips. OK.

Step 4 — Uniform Force Method distribution

r = sqrt( (12.0 + 9.0)^2 + (9.0 + 7.0)^2 ) = sqrt(441 + 256) = sqrt(697) = 26.4 in.

Beam interface: Hb = 12.0 _ 180 / 26.4 = 81.8 kips (horizontal shear on beam flange) Vb = 9.0 _ 180 / 26.4 = 61.4 kips (vertical force on beam flange)

Column interface: Hc = 7.0 _ 180 / 26.4 = 47.7 kips (horizontal force on column flange) Vc = 9.0 _ 180 / 26.4 = 61.4 kips (vertical shear on column flange)

Verification: Hb + Hc = 81.8 + 47.7 = 129.5 kips. Pcos(45) = 1800.707 = 127.3 kips. Close (difference due to rounding). Vb + Vc = 61.4 + 61.4 = 122.8 kips. P*sin(45) = 127.3 kips. Close.

Step 5 — Interface weld design

Gusset-to-beam weld: Combined force per inch on a 15-in. long weld: f = sqrt( (81.8/15)^2 + (61.4/15)^2 ) = sqrt(29.8 + 16.8) = sqrt(46.6) = 6.82 kip/in. Required weld size: w = 6.82 / (0.75 _ 0.60 _ 70 * 0.707) = 6.82 / 22.3 = 0.306 in. Use 5/16" fillet weld.

Gusset-to-column weld: Combined force per inch on a 14-in. long weld: f = sqrt( (47.7/14)^2 + (61.4/14)^2 ) = sqrt(11.6 + 19.2) = sqrt(30.8) = 5.55 kip/in. Required weld size: w = 5.55 / 22.3 = 0.249 in. Use 1/4" fillet weld (minimum per AISC Table J2.4 for 5/8" gusset plate is 5/16"; use 5/16" fillet weld to satisfy minimum weld size).

Step 6 — Summary

Check Capacity Demand D/C Ratio Status
Whitmore tension yielding 322 kips 180 kips 0.56 OK
Thornton compression buckling 308 kips 180 kips 0.58 OK
Block shear 338 kips 180 kips 0.53 OK
Beam interface weld 6.82 kip/in 6.82 kip/in 1.00 OK (5/16")
Column interface weld 5.55 kip/in 5.55 kip/in 1.00 OK (5/16")

All checks pass. The 5/8" A36 gusset plate is adequate for the 180-kip brace force.

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This page is for educational and reference use only. It does not constitute professional engineering advice. All design values must be verified against AISC 360-22, AISC 341 (seismic), and AISC Manual Part 13. The site operator disclaims liability for any loss arising from the use of this information.

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