MachineCalcs

Whitmore Section Calculator

Gusset/splice plate Whitmore effective width b_eff = w + 2·L·tan(30°), the Whitmore area and the tension-yield capacity (LRFD φ = 0.90 / ASD Ω = 1.67). Compression buckling is a separate check.

Structural 5 inputs 3 results

Calculator

LRFD applies φ = 0.90 to the nominal tensile-yield strength (compare to the factored force); ASD divides by Ω = 1.67 (compare to the service force).
Width of the bolt or weld group perpendicular to the load, measured at the first (nearest) fastener row — the starting width the 30° spread fans out from.
mm
Length of the connection along the load, from the first to the last fastener row (for a weld, the weld length). The 30° dispersion acts over this length.
mm
Gusset / splice plate thickness.
mm
Specified minimum yield strength of the plate. A36 ≈ 250 MPa (36 ksi); A572-50 ≈ 345 MPa (50 ksi).
MPa

Results

Default result
Edit inputs
Whitmore effective width(b_eff)
380.9mm

b_eff = w + 2·L·tan(30°) — the width that actually resists the concentrated force.

Also computed

Whitmore area(A_w)4,571mm²

A_w = b_eff · t.

Tension-yield capacity(Pₙ)1,419,000N

1,419 kN · 319,100 lbf

Tensile yielding on the Whitmore section (LRFD). Check compression buckling and the connection limit states separately.

φ·Fy·A_w (φ = 0.90) or Fy·A_w/Ω (Ω = 1.67) — gross-section tensile yielding on the Whitmore section.

Method notes 4 notes
  • The Whitmore section is the effective width of a gusset/splice plate that carries a concentrated bolt- or weld-group force: the force fans out at 30° on each side from the first fastener row over the connection length, b_eff = w + 2·L·tan(30°). The resisting area is A_w = b_eff·t.
  • This screen returns the tension-yield capacity (Pn = Fy·A_w; LRFD φ = 0.90, ASD Ω = 1.67). For a gusset in COMPRESSION the same Whitmore section can buckle — that is a separate check (Thornton effective-length method: K·L on the average unbraced length, with r = t/√12), which depends on the brace and edge geometry and is not computed here.
  • Also verify the other gusset limit states on the same plate: net-section rupture, block shear at the bolt group, and the bolt shear/bearing. The governing capacity is the smallest. A licensed engineer owns the final connection design.
  • If the 30° spread runs off the edge of the plate (b_eff wider than the available plate at the last row), cap b_eff at the physical plate width — the calculator does not know your plate outline.

The Whitmore section is the effective width of a gusset or splice plate that resists a concentrated bolt/weld-group force: the force spreads at 30 degrees from the first fastener row over the connection length, so b_eff = w + 2*L*tan(30) and the Whitmore area A_w = b_eff*t. This calculator returns the effective width, area and tension-yield capacity (LRFD phi = 0.90, ASD Omega = 1.67); compression buckling of the same section is a separate Thornton check.

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All Structural

How to use this calculator

  1. 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.
  2. Enter the plate. Plate thickness t and yield strength Fy, and pick LRFD or ASD.
  3. 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.
  4. 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.
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