Eccentric Load Stress

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

Variables

sigmaMax[σmax]maximum normal stress (Pa)

sigmaMin[σmin]minimum normal stress (Pa)

Peccentric axial load (N)

Across-sectional area (m²)

eeccentricity from centroid (m)

cdistance from centroidal axis to extreme fiber (m)

Isecond moment of area (m⁴)

Description

What is this formula?

Eccentric load stress calculates the normal stress produced when an axial load is applied away from the centroid of a structural member. The eccentricity creates an additional bending moment equal to P·e, causing the stress distribution to become non-uniform.

When to use it

Use this formula for columns, foundations, brackets, machine supports, retaining structures, and structural members subjected to loads that do not pass through the centroid.

Example

A steel column is subjected to:

P = 150000 N

A = 0.008 m²

e = 0.05 m

c = 0.10 m

I = 0.00008 m⁴

Formula:

σmax = P/A + (P·e·c)/I

Substitution:

σmax = 150000/0.008 + (150000×0.05×0.10)/0.00008

Result:

σmax = 28,125,000 Pa

Result:

σmax = 28.1 MPa

Applications

Columns, bearing walls, foundations, anchor systems, machine bases, steel structures, reinforced concrete members, and structural stability checks.