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Axial Members under Loading

Typical axial members with tensile loading, P.

In a Nut Shell: Normal Stress in an Axial Member

The average normal stress. σ, in an axial member is the force, P, in the member divided

by its cross-sectional area, A. σ = P / A

Common units for stress are psi, ksi, MPa, N/mm² (English/Metric)

Normal Stress at a Point, P, in an axial member

It’s possible that the axial force might vary over the cross-section of a structural member.

In that case let the element of force be ΔF over an element of area ΔA for the cross-

-section. Then the normal stress, σ, at a given point P in the cross-section of the axial

member is

σ_p = lim ΔF / ΔA

ΔA→ 0

assuming the limit exists. If the cross-section lies in the y-z plane then the axial stress may be

a function of both y and z so that σ = σ(y,z) and the total axial force, P, acts through the

centroid at any given cross-section is simply the integral of σ over the cross-section.

P = ∫ σ(y,z) dA

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