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Axial Members under Loading

Typical axial members with tensile loading, P.

In a Nut Shell: Deformation of an Axial Member, δ

For an axial member, of constant cross-section, the deformation is δ = PL/AE .

Note it depends directly on the force and length of the member and inversely on

the cross-sectional area and material. Common units for deformation are in. or mm.

Key limitations are that the stress does not exceed the proportional limit, σ = Eε ,

and σ = P/A (constant cross-section).

Deformations for tapered, axial members (ε is a function of x and σ = Eε)

δ = ∫ ε dx = ∫ σ/E dx = ∫ (P/AE) dx where integration is over the length of the member

Deformations for axial with abrupt changes in section and perhaps material (and σ = Eε)

δ = Σ P_iL_i / A_i E_i

P_iis the force in section i, L_i is the length of section i,

A_i is the cross-sectional area of section i, and E_i is Young’s modulus for section i

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