Combined Axial and Bending Stress (P/A +/- Mc/I)
Extreme-fiber stresses for a short member under axial load plus bending.
Example
You enter
- Axial force P (lb, + compression) 20000
- Bending moment M (lb-in) 30000
- Area A (in²) 30.25
- Extreme-fiber distance c (in) 2.75
- Moment of inertia I (in⁴) 76.3
You get
- Axial stress P/A 661 psi
- Max fiber (compression) 1,742 psi
- Min fiber -420 psi (net tension)
Checked against published worked examples from: Pytel & Singer (via MATHalino).
Details, formula, and sources
ScopeExtreme-fiber stresses sigma = P/A +/- M c/I for a short member under axial force plus bending (or a moment from an eccentricity e). Reports whether the far face stays in compression (the kern threshold e <= r^2/c). Short member, no P-delta. A design aid, not the engineer of record.
Formula or tablesigma_axial = P/A; sigma_bend = M c/I; sigma_max = P/A + |M c/I|; sigma_min = P/A - |M c/I|; optional M = P e; no tension while M c/I <= P/A (kern e <= r^2/c).
Source and editionThe standard combined axial-plus-bending stress superposition (mechanics of materials), by name.
Free accessThe combined-stress superposition is published free in any mechanics-of-materials reference. The engineer of record governs the design.
What governsEstimate. AHJ and licensed professional govern.
API field namesP_lb, M_lbin, A_in2, c_in, I_in4, sigma_axial, sigma_max, sigma_min
- Superposition sigma = P/A +/- M c/I, extreme fibers; M from a moment or an eccentricity M = P emechanics of materials
- Kern / no-tension the far face stays in compression while e <= r^2/c (the kern)mechanics of materials
- Short member no P-delta amplification; not a slender-column beam-column checkscope of this tile