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The thickness of the connecting plate or gusset on the failure line.
Every area in this calculation is a length multiplied by this thickness, so it scales the whole answer linearly. Use the delivered thickness, not the nominal one, where a mill certificate is available and the plate is close to a limit. Where two plates sandwich the connected member, run each one separately at its own thickness rather than adding them: they are separate elements with separate edge distances.
Tools needed: Vernier caliper or ultrasonic thickness gauge, Mill certificate for the plate
The specified minimum yield strength of the plate steel.
ASTM A572 Grade 50 and A992 are 345 MPa (50,000 psi); the older A36 is 250 MPa (36,000 psi); S355 to EN 10025 is 355 MPa. Yield governs the two yielding limit states here — gross section tension and the Whitmore section — and it also sets the ceiling AISC places on block shear, so entering a grade the plate is not is an error in two directions at once.
The specified minimum tensile strength of the plate steel.
A572 Grade 50 and A992 are 450 MPa (65,000 psi); A36 is 400 MPa (58,000 psi); S355 is commonly 470 MPa. Tensile strength drives every rupture limit state, which is where a bolted plate usually fails, so it matters more here than yield does. A tensile strength entered below the yield strength describes no steel that exists, and the page says so rather than quietly answering.
The hole width to take out of the section, which is wider than the hole itself.
AISC 360 Section B4.3 requires the width deducted for net area to exceed the nominal hole dimension, to allow for the material damaged in punching. A 20 mm bolt runs in a 22 mm standard hole and is deducted at 24 mm; a 3/4 in bolt runs in a 13/16 in hole and is deducted at 7/8 in. Both add the same 2 mm (1/16 in) of punching damage to the hole — the earlier metric example gave 22 mm, which is the HOLE, and so left the damage allowance out on every metric detail. Oversized and slotted holes deduct more, and a slot deducts its width perpendicular to the failure line, not its length. This page asks for the figure directly instead of adding an allowance you cannot see, because the allowance differs between the hole types on one drawing.
Tools needed: Connection detail showing hole type and size
How many lines of bolts sit side by side across the plate, perpendicular to the force.
This is the count the tension plane of the block crosses, and the count of holes taken out of the section. Two is the fewest that gives a block with a tension side to it; a single line of bolts tears out rather than blocking out, and that is a bearing-and-tearout check at each hole rather than the block shear this page runs.
How many bolts sit one behind another in a single line, along the direction of the force.
This count sets the length of the two shear planes on the block, and it sets the length the thirty-degree spread has to open out over. Adding a bolt to each line lengthens both, which is why the guide's advice when the failure line looks thin is another bolt row rather than a bigger bolt.
The spacing between adjacent bolt lines, measured across the plate.
Gauge sets the width of the block's tension plane and, with the edge distance, the gross width of the plate. It is also the dimension a fitter is most likely to change on site to clear something, and the change moves three limit states at once.
The spacing between adjacent bolts within one line, along the force.
Pitch lengthens the shear planes of the block and widens the thirty-degree spread, so it helps two limit states and hurts none. It does not appear in the net section calculation at all, because a straight row of holes across the plate takes the same area out whatever the spacing behind it is.
From the centre of an outer bolt line to the nearer long edge of the plate.
Measured across the plate, perpendicular to the force. Two edge distances plus the gauges make the gross width used here, so trimming a plate to clear a duct removes gross area, net area and Whitmore width in one cut. This is the dimension the guide names as the single commonest thing that turns an adequate bolt group into a plate that unzips.
Tools needed: Steel rule or tape, Marked-up connection detail
From the centre of the end bolt to the free end of the plate, along the force.
This is the length that finishes each of the block's two shear planes, and it is where block shear is won or lost: a short end distance shortens both planes at once while leaving the tension plane untouched, so the block gets cheaper to tear out and nothing else on the plate changes.
Whether tension is spread evenly across the block's tension plane, or concentrated at one end.
AISC 360 Section J4.3 sets Ubs to 1.0 where the tension stress on the block is uniform, which covers a gusset or splice plate pulled along its own axis, and to 0.5 where it is not, the classic case being a coped beam web with a single line of bolts where the tension plane is loaded eccentrically. Choosing 1.0 for an eccentric case doubles the tension term of a limit state that already governs slender blocks.
Governing design strength
81.33 kips
The governing limit state is net section tension rupture. The thirty-degree spread reaches past both plate edges, so the Whitmore section has been truncated at the plate's own width — there is no material out there to yield.
- Net section tension rupture
- 81.33 kips
- Block shear rupture
- 162.65 kips
- Yielding on the Whitmore section
- 105.38 kips
- Gross section tension yielding
- 105.38 kips
- Nominal strength at the governing limit state
- 108.43 kips
- Allowable strength at the governing limit state
- 54.22 kips
- Whitmore effective width from the thirty-degree spread
- 9.93 in
- Gross plate width across the bolt group
- 6 in
- Area remaining on the rupture line
- 1.66 in²
- Area remaining on the two shear planes
- 4.15 in²
They open the calculator with your figures already in it
Steel Plate Block Shear and Net Section Calculator: 81.33 kips — shown in imperial, US market. The link sets both, so the result they see is the one on your screen.
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How this was calculated
Formula source(s)
- AISC 360, Specification for Structural Steel Buildings, Section J4.1 — tensile yielding on the gross area (Rn = Fy·Ag) and tensile rupture on the effective net area, with the effective net area of a connecting element capped at 0.85 times its gross area
- AISC 360, Specification for Structural Steel Buildings, Section J4.2 — shear yielding on the gross area at 0.60·Fy·Agv and shear rupture on the net area at 0.60·Fu·Anv
- AISC 360, Specification for Structural Steel Buildings, Section J4.3 — block shear rupture, Rn = 0.60·Fu·Anv + Ubs·Fu·Ant, not taken greater than 0.60·Fy·Agv + Ubs·Fu·Ant, with Ubs 1.0 for uniform tension stress and 0.5 where it is non-uniform
- R. E. Whitmore, Experimental Investigation of Stresses in Gusset Plates, University of Tennessee Engineering Experiment Station Bulletin No. 16 (1952) — the effective width taken as the thirty-degree spread from the outer fasteners of the first row to the last row, the convention the AISC Steel Construction Manual uses for gusset plate checks
- AISC 360 Section B4.3 — for net area, the width of a bolt hole is taken larger than the hole itself; this page asks for that deduction width directly rather than adding an allowance behind your back
Inputs used
- Plate Thickness
- 0.39 in
- Steel Yield Strength Fy
- 50038.02 psi
- Steel Tensile Strength Fu
- 65266.98 psi
- Hole Width Deducted for Net Area
- 0.87 in
- Bolt Lines Across the Plate (count)
- 2
- Bolts in Each Line, Along the Force (count)
- 3
- Gauge — Spacing Between Bolt Lines
- 3 in
- Pitch — Spacing Along Each Bolt Line
- 3 in
- Edge Distance, Outer Bolt Line to Plate Edge
- 1.5 in
- End Distance, Last Bolt to Plate End
- 1.5 in
- Tension Stress Distribution on the Block (Ubs)
- Uniform — a gusset or splice plate in axial tension (Ubs = 1.0)
Intermediate steps
- Net section tension rupture
- 81.33 kips
- Block shear rupture
- 162.65 kips
- Yielding on the Whitmore section
- 105.38 kips
- Gross section tension yielding
- 105.38 kips
- Nominal strength at the governing limit state
- 108.43 kips
- Allowable strength at the governing limit state
- 54.22 kips
- Whitmore effective width from the thirty-degree spread
- 9.93 in
- Gross plate width across the bolt group
- 6 in
- Area remaining on the rupture line
- 1.66 in²
- Area remaining on the two shear planes
- 4.15 in²
Confidence note: The governing limit state is net section tension rupture. The thirty-degree spread reaches past both plate edges, so the Whitmore section has been truncated at the plate's own width — there is no material out there to yield.
What this calculation does not cover
- Checks the PLATE only. Bolt shear, bearing and tearout at each hole are Section J3 checks that frequently govern before any of the four run here, and a plate that passes on this page can still fail at the first bolt.
- Does not check the gusset in compression. Buckling on the Whitmore section needs an unbraced length and an effective length factor taken from the detail geometry, and both are outside what a bolt pattern alone can tell you.
- Assumes holes in line, not staggered. A staggered pattern earns back net width through the s²/4g term in AISC 360 Section B4.3, which is not applied here.
- Assumes a flat plate carrying axial force. An angle leg, a tee stem or a coped beam web has different geometry, and the coped web also belongs at Ubs = 0.5.
Add the equipment this sizes
This result is a specification — 81.33 kips — not a quantity. Put the thing it sizes into your project: how many, what you call it, and your supplier’s price.
Computed in your browser — nothing you enter is uploaded. Presented in US customary units and US trade terminology. Where a formula follows a published standard, that standard and its edition are cited beside it on this page; where none governs, the page says so. Local amendments override model codes — verify against the code in force where you build.
Sources checked 2026-09-06 · in the site-wide review of 2026-09-06 · v1.0.1
Regulatory standards & verification citations5
- AISC 360, Specification for Structural Steel Buildings, Section J4.1 — tensile yielding on the gross area (Rn = Fy·Ag) and tensile rupture on the effective net area, with the effective net area of a connecting element capped at 0.85 times its gross area
- AISC 360, Specification for Structural Steel Buildings, Section J4.2 — shear yielding on the gross area at 0.60·Fy·Agv and shear rupture on the net area at 0.60·Fu·Anv
- AISC 360, Specification for Structural Steel Buildings, Section J4.3 — block shear rupture, Rn = 0.60·Fu·Anv + Ubs·Fu·Ant, not taken greater than 0.60·Fy·Agv + Ubs·Fu·Ant, with Ubs 1.0 for uniform tension stress and 0.5 where it is non-uniform
- R. E. Whitmore, Experimental Investigation of Stresses in Gusset Plates, University of Tennessee Engineering Experiment Station Bulletin No. 16 (1952) — the effective width taken as the thirty-degree spread from the outer fasteners of the first row to the last row, the convention the AISC Steel Construction Manual uses for gusset plate checks
- AISC 360 Section B4.3 — for net area, the width of a bolt hole is taken larger than the hole itself; this page asks for that deduction width directly rather than adding an allowance behind your back
Which documents these citations point at
Standards referenced: AISC 360 (American Institute of Steel Construction, United States).
Cite this page
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Most jobs need more than one number. Add the calculators you need next and they open right here, underneath this one — your figures stay on screen and nothing is lost to a page change.
The pattern entered holds 6 bolts, in 2 lines of 3, and which of the four failure lines arrives first is named in the note beside the result. That one is the only one worth spending steel on. Widening the gauge or the edge distance buys net section and gross section together; lengthening the pitch or the end distance buys block shear and the Whitmore width together, and buys the net section nothing at all. Where the remaining area looks thin, that is the whole choice — and it is why another bolt row usually answers better than a bigger bolt.