110/3337–11FE Reference Handbook 10.4 · Mechanics of Materials · Axial

Handbook formula

Axial Deformation

Elastic change in length of a prismatic bar. P is the internal axial force, L the original length, A the cross-sectional area, and E the modulus of elasticity. Stiffer members (larger AE) deform less.

(m)
Axial elongation (or shortening)
(N)
Internal axial force
(m)
Original length
()
Cross-sectional area
(Pa)
Modulus of elasticity

Step-by-step solved example

P = 120 kN, L = 1.5 m, A = 600 mm², E = 200 GPa. Find δ.

Lbar
δ = PL/AE along the bar length.
  1. 1. SI units

    A = 600×10⁻⁶ m² = 6.00×10⁻⁴ m². P = 1.20×10⁵ N.

  2. 2. Elongation

    δ = PL/AE = (1.20×10⁵)(1.5)/[(6.00×10⁻⁴)(2.00×10¹¹)] = 1.50 mm.

Answer: 1.50 mm

10 practice questions

0/10 correct

1.P = 50 kN, L = 2 m, A = 500 mm², E = 200 GPa. δ =

2.Doubling A (same P, L, E) will

3.Same P, L, A: aluminum (E ≈ 70 GPa) vs steel (200 GPa)

4.δ = 3.0 mm over L = 2.0 m. Axial strain ε =

5.The product AE has units of

6.A statically determinate bar uses P from

7.P = 40 kN, L = 4 m, A = 200 mm², E = 200 GPa. δ =

8.If P = 0, the mechanical δ is

9.A stiffer member means

10.L doubled, P, A, E unchanged: δ