Axial stress & strain worksheet with answers

Free printable Axial stress & strain worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

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1.Easy
250 kNØ20110 GPaØ80/50400 mmσr​ = ?

A steel rod (diameter 20 mm, E = 200 GPa) sits inside a tube made of bronze (outer diameter 80 mm, inner diameter 50 mm, E = 110 GPa). Both are 400 mm long and are compressed together between rigid plates by 250 kN. Find the compressive stress σr in the rod.

P = 250 kNrod: Ø20 mm, E = 200 GPatube: Ø80/Ø50 mm, E = 110 GPaL = 400 mm
σr = MPa
2.Easy
Ø 20 mm1.5 mP = 10 kN

A solid round bar carries an axial tensile load P. Find the normal stress σ in the bar.

P = 10 kNd = 20 mm
σ = MPa
3.Medium
Ø 12 mmCopper1 mP = 75 kN

Find the axial strain ε in the copper bar, in microstrain (µε = 10⁻⁶).

P = 75 kNd = 12 mmL = 1 mE = 117 GPa
ε = µε
4.Medium
P = ?12400 mm400 mmØ20Ø30δ = 0.5 mm

A bar is made of a steel segment (diameter 20 mm, length 400 mm, E = 200 GPa) joined end to end with a segment made of aluminium (diameter 30 mm, length 400 mm, E = 70 GPa). It is fixed at one end and pulled at the other. Find the axial load P that stretches it by 0.5 mm in total.

segment 1: steel, Ø20 mm, 400 mm, E = 200 GPasegment 2: aluminium, Ø30 mm, 400 mm, E = 70 GPaδ = 0.5 mm
P = kN
5.Hard
Ø 40 mmAluminium2 mØ 12 mmCopper1.5 mP = 115 kN

The stepped bar is fixed at the wall and loaded at its free end. Find the total elongation δ.

P = 115 kNsegment 1: Ø40 mm, 2 m, aluminium (E = 70 GPa)segment 2: Ø12 mm, 1.5 m, copper (E = 117 GPa)
δ = mm
6.Hard
40 kN12300 mm200 mmØ40Ø50σ2​ = ?

A steel segment (diameter 40 mm, length 300 mm, E = 200 GPa) and a segment made of brass (diameter 50 mm, length 200 mm, E = 100 GPa) are joined end to end and fixed between two rigid walls. An axial load of 40 kN acts at the joint, towards segment 2. Find the magnitude of the stress σ2 in segment 2.

segment 1: steel, Ø40 mm, 300 mm, E = 200 GPasegment 2: brass, Ø50 mm, 200 mm, E = 100 GPaP = 40 kN
σ2 = MPa

Answer key

  1. 1. σr = 125.1 MPa
  2. 2. σ = 31.83 MPa
  3. 3. ε = 5668 µε
  4. 4. P = 34.6 kN
  5. 5. δ = 15.65 mm
  6. 6. σ2 = 10.99 MPa

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