How to use this calculator
- Measure the group. w = width of the bolt/weld group at the first row (perpendicular to the load); L = connection length from first to last row along the load.
- Enter the plate. Plate thickness t and yield strength Fy, and pick LRFD or ASD.
- Read b_eff and A_w. b_eff = w + 2·L·tan(30°) is the effective width; A_w = b_eff·t is the area. Cap b_eff at the physical plate width if the 30° fan runs off the edge.
- Check tension, then compression. The tool returns the tension-yield capacity. For a compression gusset, run the separate Thornton buckling check on the same Whitmore area.
How it works
A gusset plate gets a concentrated force from a brace or member, but the whole plate width does not resist it — only the part the force can spread into. The Whitmore section models that spread as a 30° fan from the first fastener row out to the last:
b_eff = w + 2·L·tan(30°) · A_w = b_eff·t
w is the group width at the first row, L the
connection length, and the two 30° spreads add 2·L·tan(30°)
to the width. The resulting effective area A_w is what you
check for tensile yielding (φ·Fy·A_w, φ = 0.90) — and, in a
compression gusset, for buckling. The
calculator returns the width,
area and tension capacity.
The Whitmore tension check is one of several on a gusset. Net-section tear-out is the block shear capacity calculator; the member feeding the gusset is the tension member capacity calculator; and the compression/buckling side borrows the column logic of the column buckling calculator applied to the Whitmore area.
Worked example
Verified against the live calculator
A bolt group w = 150 mm wide at the first row, connection
length L = 200 mm, on a 12 mm A572-50 plate
(Fy = 345 MPa), LRFD:
b_eff = 150 + 2·200·tan(30°) = 150 + 230.9 = 380.9 mm · A_w = 380.9·12 = 4571 mm²
φPₙY = 0.90·345·4571 = 1419 kN
The 30° spread nearly triples the resisting width over the 150 mm group,
to 380.9 mm, giving a tension-yield capacity of about
1419 kN (LRFD). Switch to ASD and the same section
allows Fy·A_w/1.67 = 944 kN. If this gusset were in
compression, that 380.9 mm × 12 mm strip would now be checked as a short
column for buckling — usually the controlling case for brace gussets.
Frequently asked questions
What is the Whitmore section?
It is the effective width of a gusset or splice plate that actually resists a concentrated bolt- or weld-group force. The force is assumed to fan out at 30° on each side from the first fastener row over the length of the connection, giving an effective width b_eff = w + 2·L·tan(30°). The resisting area is A_w = b_eff·t.
How do you calculate the Whitmore width?
b_eff = w + 2·L·tan(30°), where w is the group width at the first row and L is the connection length to the last row. For w = 150 mm, L = 200 mm: b_eff = 150 + 2·200·0.5774 = 380.9 mm. With a 12 mm plate that is A_w = 4571 mm², and at Fy = 345 MPa the LRFD tension-yield capacity is φ·Fy·A_w = 0.90·345·4571 = 1419 kN.
Does the Whitmore section cover gusset buckling?
No — this is the tension-yield check on the Whitmore area. A gusset loaded in compression (a brace gusset, say) can buckle on the same section, which is a separate analysis: the Thornton effective-length method applies a column check (K·L over the average unbraced length, radius of gyration r = t/√12) to the Whitmore area. That needs the brace and edge geometry, so it is not computed here.
What if the 30° spread runs off the edge of the plate?
Then the Whitmore width is limited by the plate. If the dispersion fan reaches the last row wider than the physical plate at that point, cap b_eff at the available plate width — the effective section cannot be wider than the steel that is there. This calculator computes the geometric 30° width; you check it against your plate outline.
Method & assumptions
- Whitmore (1952) effective width: a 30° dispersion on each side from the first fastener row, b_eff = w + 2·L·tan(30°); Whitmore area A_w = b_eff·t. Widely used in AISC gusset design practice.
- Returns tensile yielding on the Whitmore section (Pn = Fy·A_w; LRFD φ = 0.90, ASD Ω = 1.67). Compression buckling of the same section is a SEPARATE check (Thornton average-length method, r = t/√12) that depends on brace/edge geometry and is not computed here.
- Cap b_eff at the physical plate width if the 30° fan runs past the plate edge at the last row — the tool computes the geometric width, not your plate outline.
- Also verify net-section rupture, block shear and bolt shear/bearing on the same plate. The governing capacity is the smallest, and a licensed engineer owns the final design.