Pick your Beam Cross-Section shape, enter the Bending Moment (M), and fill in your beam's dimensions — Width, Height, and Wall Thickness where applicable — and the Distance from Neutral Axis (c) to get the Maximum Bending Stress, along with the Moment of Inertia, Section Modulus, and Stress at a Specified Point.
Maximum Bending Stress
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Moment of Inertia
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Section Modulus
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Stress at Specified Point
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Bending stress is the normal stress that develops in a beam when it bends under load. It varies linearly across the cross-section, with maximum values at the extreme fibers and zero at the neutral axis.
The maximum bending stress formula is σ = M×c/I, where σ is bending stress, M is bending moment, c is the distance from neutral axis to extreme fiber, and I is the moment of inertia of the cross-section.
For a square beam with side 'a', the moment of inertia I = a⁴/12, and c = a/2. The maximum bending stress is σ = 6M/a³, where M is the bending moment.
For a 200mm × 300mm rectangular beam, I = (200×300³)/12 = 450×10⁶ mm⁴, c = 150mm. With these values, you can calculate bending stress using σ = M×c/I.
Bending stress is normal stress that acts perpendicular to the cross-section due to bending moment, while shear stress acts parallel to the cross-section due to shear force. Bending stress varies linearly across the section, shear stress varies parabolically.
Cross-section shape determines the moment of inertia (I) and section modulus. Shapes with more material away from the neutral axis (like I-beams) have higher moment of inertia and lower bending stress for the same moment.
Bending stress is typically expressed in MPa or N/mm². Bending moment should be in N⋅mm if dimensions are in mm, or N⋅m with dimensions in meters. Always ensure consistent units throughout the calculation.
Bending stress analysis is crucial for beam design in structures, ensuring the material's allowable stress is not exceeded. It's essential for preventing failure in beams, bridges, and any structural member subjected to bending loads.