Combined Axial and Bending Stress
Combined Axial and Bending Stress
Many real members — columns with eccentric loads, beam-columns — carry axial force and bending together. The stresses simply add at the extreme fibre.
By superposition σ = P/A + M·c/I. where P is the axial load, A the area, M the moment, c the distance to the extreme fibre and I the second moment of area.
Inputs
P := 200 kN=200000 N
A := 6000 mm^2=6e-03 m^2
M := 18 kN·m=18000 Nm
c := 150 mm=150 mm
I := 90e6 mm^4=9e-05 m^4
Add the uniform axial stress to the peak bending stress at the same fibre.
sigma := P/A + M·c/I=63.33 MPa
Results
The combined stress must stay within the allowable. On the opposite fibre the bending term subtracts, so always check both faces — one may go into tension.
Assumptions & limitations
- Linear-elastic superposition applies.
- No second-order (P-δ) amplification included.
- Section remains fully effective (no buckling).