Shear Stress Calculator

A shear stress calculator divides the shear force on a part by the cross-sectional area that resists it. The formula is τ = V ÷ A. A 3,000 lb shear force on a 14 in² section gives 3,000 ÷ 14 = 214.29 psi.

The formula in plain words

Think of a deck of cards on a table, pushed sideways on the top card. The cards slide over each other. The sliding push is the shear force. The area where the cards touch is what resists it.

Spread the same push over a bigger touching area and each square inch carries less. Shear stress is the push divided by that area. Double the area and the stress is halved.

The result is an average. It assumes the load spreads evenly over the section, which is close to true for a small bolt or pin and less true for a deep beam.

Worked examples

Example 1, the default: 3,000 lb on 14 in².

• τ = 3,000 ÷ 14 = 214.29 psi

Example 2, a bolt in single shear: a 3/4 inch bolt carrying 1,200 lb.

• Area: 3.1416 × (0.375)² = 0.4418 in²
• τ = 1,200 ÷ 0.4418 = 2,716 psi

Example 3, the same bolt in double shear. The load goes through two cut planes, so the resisting area doubles to 0.8836 in².

• τ = 1,200 ÷ 0.8836 = 1,358 psi

Average shear stress for different loads

Shear force	Area	Stress
500 lb	0.1963 in² (1/2 inch bolt)	2,547 psi
1,200 lb	0.4418 in² (3/4 inch bolt)	2,716 psi
3,000 lb	14 in²	214 psi
5,000 lb	2 in²	2,500 psi
8,000 lb	10 in²	800 psi
10,000 lb	3 in²	3,333 psi

How to find the area

For a round bolt or pin, the area is π × (diameter ÷ 2)². For a rectangle, it is width times depth. For a weld, it is the throat area, which is smaller than the leg size and is covered by the weld strength calculator.

Count the number of shear planes. A bolt joining two plates passes one cut plane (single shear). A bolt through a plate sandwiched between two others has two (double shear), and the area doubles.

Beam shear is different

In a rectangular beam, shear stress is zero at the top and bottom faces and highest at the middle. For a solid rectangle the peak equals 1.5 times the average, so 214.29 psi of average becomes about 321 psi at the middle. For I-beams and other shapes the factor changes, and engineers use the VQ/Ib formula.

For that reason, use this calculator as a quick check for fasteners and simple sections, and leave beam design to a licensed structural engineer.

Common mistakes

• Using the wrong area. The area that resists shear is the cut plane, not the face you can see.
• Forgetting to count shear planes. Double shear halves the stress.
• Comparing to the wrong limit. Shear allowables are lower than tension allowables for the same material.
• Mixing units, such as pounds with square millimeters.
• Applying the average to a thin web or a short, deep member, where the real stress is higher.

A pin in double shear

A clevis pin of 1/2 inch diameter has an area of 0.1963 in². Loaded in double shear, it has two cut planes, so the resisting area is 0.3927 in². Under a 2,000 lb load, the average shear stress is 2,000 ÷ 0.3927 = 5,093 psi. Compare that with the allowable shear for the pin’s material and grade, which comes from its specification.

Reading the answer

The result is a stress in psi. To judge it, compare with the allowable shear stress for the material and the code or specification that governs the design. If the calculated stress is below the allowable value with a suitable safety factor, the part passes this simple check. If it is close, use a bigger part or more fasteners, and ask an engineer to look at the details.

Related calculators

The bolt shear calculator applies allowable stresses to a bolt, the stress calculator handles direct axial stress, and the bending stress calculator checks a beam in bending. When shear and bending act together, the von Mises stress calculator combines them.