# Shear Stress Calculator Calculate the maximum shear stress τ_max = V·Q/(I·b) at the neutral axis of a beam section. Supports rectangle (1.5V/A), solid circle (4V/3A), hollow tube, and I-beam (exact V·Q_web/(I·tw)). Also returns the average shear stress V/A for comparison. > Canonical page: https://elysiatools.com/en/tools/shear-stress-calculator - **Category:** Math & Numbers - **Keywords:** shear stress, transverse shear, tau = VQ/(Ib), neutral axis, rectangular beam, I-beam web, strength of materials, mechanics of materials, structural, civil engineering ## Overview The Shear Stress Calculator computes the maximum transverse shear stress at the neutral axis of a beam cross-section subjected to a shear force. It supports rectangular, solid circular, hollow circular, and I-beam profiles, providing both the peak shear stress and the average shear stress for comparison. ## Inputs - **Cross-Section Shape** (select) - **Shear Force V (N)** (number): e.g. 20000 - **Width b (mm)** (number): Section width (horizontal). Required for Rectangle. - **Height h (mm)** (number): Section height (vertical). Required for Rectangle. - **Diameter D (mm)** (number): Required for Solid Circle. - **Outer Diameter Do (mm)** (number): Required for Hollow Circle. - **Inner Diameter Di (mm)** (number): Required for Hollow Circle. Must be less than Do. - **Flange Width B (mm)** (number): Required for I-Beam. - **Total Height H (mm)** (number): Required for I-Beam. - **Web Thickness tw (mm)** (number): Required for I-Beam. - **Flange Thickness tf (mm)** (number): Required for I-Beam. - **Decimal Places** (number) ## When to use - When verifying that the maximum transverse shear stress in a beam does not exceed the allowable shear strength of the material. - When analyzing shear stress distribution across rectangular, circular, hollow, or I-beam cross-sections in structural design. - When comparing the average shear stress against the peak shear stress at the neutral axis to evaluate structural safety margins. ## How it works - Select the cross-section shape of the beam and input the shear force (V) in Newtons. - Provide the geometric dimensions of the selected shape, such as width, height, diameter, or flange and web thicknesses in millimeters. - The calculator computes the cross-sectional area, moment of inertia, first moment of area, and determines the maximum shear stress at the neutral axis. ## Use cases - Verifying the shear capacity of a rectangular timber joist under a concentrated load. - Calculating the peak shear stress in a hollow steel tube torque-arm or structural column. - Determining the maximum web shear stress of an I-beam to prevent shear failure or web buckling. ## Frequently asked questions ### What formula is used to calculate the maximum shear stress? The calculator uses the transverse shear formula τ = VQ/(Ib) at the neutral axis, which simplifies to 1.5V/A for rectangles and 4V/3A for solid circles. ### What units should I use for the inputs? Input the shear force in Newtons (N) and all dimensional measurements in millimeters (mm) to obtain the shear stress output in Megapascals (MPa). ### How does the calculator handle I-beams? It calculates the exact maximum shear stress in the web at the neutral axis using the I-beam's specific moment of inertia and first moment of area. ### Why is the maximum shear stress higher than the average shear stress? Average shear stress is simply force divided by area (V/A), whereas transverse shear stress varies across the depth of the beam and peaks at the neutral axis. ### Can this calculator compute shear stress at points other than the neutral axis? 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