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
80 kNØ4070 GPaØ80/60800 mmσr​ = ?

A steel rod (diameter 40 mm, E = 200 GPa) sits inside a tube made of aluminium (outer diameter 80 mm, inner diameter 60 mm, E = 70 GPa). Both are 800 mm long and are compressed together between rigid plates by 80 kN. Find the compressive stress σr in the rod.

P = 80 kNrod: Ø40 mm, E = 200 GPatube: Ø80/Ø60 mm, E = 70 GPaL = 800 mm
σr = MPa
2.Easy
50 kNØ2570 GPaØ80/60600 mmσr​ = ?

A steel rod (diameter 25 mm, E = 200 GPa) sits inside a tube made of aluminium (outer diameter 80 mm, inner diameter 60 mm, E = 70 GPa). Both are 600 mm long and are compressed together between rigid plates by 50 kN. Find the compressive stress σr in the rod.

P = 50 kNrod: Ø25 mm, E = 200 GPatube: Ø80/Ø60 mm, E = 70 GPaL = 600 mm
σr = MPa
3.Medium
Ø 30 mmBrass2 mP = 40 kN

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

P = 40 kNd = 30 mmL = 2 mE = 100 GPa
ε = µε
4.Medium
Ø 12 mmSteel1 mP = 80 kN

Find the elongation δ of the steel bar under the axial load.

P = 80 kNd = 12 mmL = 1 mE = 200 GPa
δ = mm
5.Hard
Ø 35 mmBrass0.5 mØ 16 mmBrass0.5 mP = 110 kN

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

P = 110 kNsegment 1: Ø35 mm, 0.5 m, brass (E = 100 GPa)segment 2: Ø16 mm, 0.5 m, brass (E = 100 GPa)
δ = mm
6.Hard
100 kN12300 mm400 mmØ30Ø30σ2​ = ?

A steel segment (diameter 30 mm, length 300 mm, E = 200 GPa) and a segment made of brass (diameter 30 mm, length 400 mm, E = 100 GPa) are joined end to end and fixed between two rigid walls. An axial load of 100 kN acts at the joint, towards segment 2. Find the magnitude of the stress σ2 in segment 2.

segment 1: steel, Ø30 mm, 300 mm, E = 200 GPasegment 2: brass, Ø30 mm, 400 mm, E = 100 GPaP = 100 kN
σ2 = MPa

Answer key

  1. 1. σr = 39.48 MPa
  2. 2. σr = 39.66 MPa
  3. 3. ε = 565.9 µε
  4. 4. δ = 3.537 mm
  5. 5. δ = 3.307 mm
  6. 6. σ2 = 38.58 MPa

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