Calculateur de Contrainte de Poutre Gratuit
Calculez la contrainte de flexion dans une poutre à partir du moment et du module de section.
Maximum Bending Stress
89.76 MPa
Maximum Bending Stress vs Bending Moment (M)
Formule
## Bending Stress in Beams The flexure formula relates the internal bending moment to the normal stress at any fibre of the cross-section. ### Formula **sigma = M c / I** M is the bending moment, c is the perpendicular distance from the neutral axis to the outermost fibre, and I is the second moment of area about the neutral axis. The result is the peak tensile or compressive stress at the extreme fibre.
Exemple Résolu
A steel beam with I = 8356 cm^4, depth 300 mm (c = 150 mm), under a moment of 50 kN-m.
- 01Convert moment: 50 kN-m = 50 x 10^6 N-mm
- 02Convert inertia: 8356 cm^4 = 8356 x 10^4 mm^4 = 8.356 x 10^7 mm^4
- 03sigma = (50 x 10^6 x 150) / (8.356 x 10^7)
- 04sigma = 7.5 x 10^9 / 8.356 x 10^7 = 89.76 MPa
Questions Fréquentes
What happens when stress exceeds yield strength?
The beam begins to yield plastically. For structural steel with yield strength around 250 MPa, the beam can still carry load through plastic redistribution, but permanent deformation occurs.
Is bending stress the same on both sides?
In magnitude yes, but the sign changes: one side is in tension and the other in compression. For symmetric sections, both extreme fibres have the same absolute stress.
How does section modulus relate to this formula?
Section modulus S = I / c, so the formula simplifies to sigma = M / S. This is a convenient shortcut when S is tabulated for standard sections.
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