Direct Shear Stress, Strain and Deflection Calculator
A force across a block of material: the shear stress, the shear strain, the sideways movement and the stiffness.
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Calculated from standard textbook formulas, with every step shown. The formulas are fixed, so the working does not need checking: what matters is the numbers you type in. Use these calculators only if you are competent to choose the inputs (loads, material strength, dimensions, supports) and check your units and assumptions. For learning and checking your own working: design and sign-off are for a qualified engineer. Drafting Central does not store the numbers you type.
How this calculator works
The shear stress is the force divided by the area it acts across. The shear strain is the stress divided by the shear modulus. The sideways movement is the strain times the thickness of the block, so the deflection is force times thickness over area times modulus.
This suits rubber mounts, bonded pads, keys, and any block loaded across its faces.
Formulas used
- \tau = V/A
- \gamma = \tau/G
- \delta_s = \dfrac{V L}{A G}
Worked example
With the default numbers in the calculator above:
- Shear stress: 0.8 MPa
- Shear strain: 0.000010127 rad (0.00058021°)
- Sideways movement of one face over the other: 0.00025316 mm
- Shear stiffness: 7900000 N/mm
Change the numbers in the calculator to see the full working, every step, for your own case.
Common questions
What is the shear modulus of steel?
About 79 000 MPa. Aluminium is about 26 000 MPa and rubber is a thousand times lower, between 0.3 and 1.5 MPa.
Is the shear stress in a beam the same?
No. In a beam the shear stress is not uniform across the section. This is for direct shear with a uniform stress.
Related calculators
Further reading: Standard strength of materials texts (direct shear stress and strain).
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