How is shear stress distributed in a beam?

Shear stress τ = VQ/(Ib) varies over the cross-section. In a rectangle, it is parabolic, with maximum at the neutral axis. In I-beams, most shear is carried by the web.

What is the first moment Q?

Q is the first moment of the area above (or below) the cut point about the neutral axis: Q = A' × ȳ' where A' is the partial area and ȳ' is its centroidal distance from the neutral axis.

When does shear stress govern beam design?

Shear typically governs for deep, short-span beams; bending governs for slender beams. In I-beams, shear in the web (where b is small) can be critical despite low shear force.

Shear Stress in Beams Calculator

Calculate transverse shear stress τ = VQ/(Ib) where V = shear force, Q = first moment of area above cut, I = moment of inertia, b = width. Max shear in rectangular beam at neutral axis: τ_max = 1.5V/A.

2D stress state at a point. All stresses in MPa.

σx — Normal Stress X (MPa)

σy — Normal Stress Y (MPa)

τxy — Shear Stress (MPa)

⚙ Mechanical Note: Results are based on standard textbook formulas and ISO/AASHTO references. Always verify critical designs with applicable codes (ISO 898, AASHTO 1993, AISC, Eurocode 3) and a qualified engineer.

How to Use

Enter the values for the patient or scenario you are assessing. Calculate transverse shear stress τ = VQ/(Ib) where V = shear force, Q = first moment of area above cut, I = moment of inertia, b = width. Max shear in rectangular beam at neutral axis: τ_max = 1.5V/A. Use the shear stress beam result to inform your clinical assessment.

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Frequently Asked Questions

How is shear stress distributed in a beam?

What is the first moment Q?

When does shear stress govern beam design?