Combined Axial and Bending Stress

\[\sigma=\frac{P}{A}\pm\frac{Mc}{I}\]

Variables

sigmaMax[σmax]maximum combined normal stress (Pa)

sigmaMin[σmin]minimum combined normal stress (Pa)

Paxial load (N)

Across-sectional area (m²)

Mbending moment (N·m)

cdistance from neutral axis to extreme fiber (m)

Isecond moment of area (m⁴)

Description

What is this formula?

Combined axial and bending stress calculates the normal stress in a structural member subjected to both an axial load and a bending moment. The axial stress is uniform over the cross-section, while the bending stress varies linearly from one side of the section to the other.

When to use it

Use this formula for columns, beams, frames, brackets, and structural members where axial force and bending moment act at the same time. It is especially useful for checking the maximum tensile or compressive stress at the extreme fibers.

Example

A steel member has:

P = 120000 N

A = 0.006 m²

M = 8500 N·m

c = 0.08 m

I = 0.000045 m⁴

Formula:

σmax = P/A + M*c/I

Substitution:

σmax = 120000/0.006 + (8500*0.08)/0.000045

Result:

σmax = 35,111,111 Pa

Result:

σmax = 35.1 MPa

Applications

Steel columns, reinforced concrete members, structural frames, bridge components, machine supports, crane structures, and combined load checks.