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 kNØ20100 GPaØ80/60800 mmσr​ = ?

A steel rod (diameter 20 mm, E = 200 GPa) sits inside a tube made of brass (outer diameter 80 mm, inner diameter 60 mm, E = 100 GPa). Both are 800 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/Ø60 mm, E = 100 GPaL = 800 mm
σr = MPa
2.Easy
200 kNØ4070 GPaØ100/70500 mmσr​ = ?

A steel rod (diameter 40 mm, E = 200 GPa) sits inside a tube made of aluminium (outer diameter 100 mm, inner diameter 70 mm, E = 70 GPa). Both are 500 mm long and are compressed together between rigid plates by 200 kN. Find the compressive stress σr in the rod.

P = 200 kNrod: Ø40 mm, E = 200 GPatube: Ø100/Ø70 mm, E = 70 GPaL = 500 mm
σr = MPa
3.Medium
Ø 10 mmAluminium0.5 mP = 50 kN

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

P = 50 kNd = 10 mmL = 0.5 mE = 70 GPa
δ = mm
4.Medium
50 kNØ2570 GPaØ100/50600 mmδ = ?

A steel rod (diameter 25 mm, E = 200 GPa) sits inside a tube made of aluminium (outer diameter 100 mm, inner diameter 50 mm, E = 70 GPa). Both are 600 mm long and are compressed together between rigid plates by 50 kN. Find the shortening δ.

P = 50 kNrod: Ø25 mm, E = 200 GPatube: Ø100/Ø50 mm, E = 70 GPaL = 600 mm
δ = mm
5.Hard
80 kN12400 mm200 mmØ40Ø50σ2​ = ?

A steel segment (diameter 40 mm, length 400 mm, E = 200 GPa) and a segment made of copper (diameter 50 mm, length 200 mm, E = 120 GPa) are joined end to end and fixed between two rigid walls. An axial load of 80 kN acts at the joint, towards segment 2. Find the magnitude of the stress σ2 in segment 2.

segment 1: steel, Ø40 mm, 400 mm, E = 200 GPasegment 2: copper, Ø50 mm, 200 mm, E = 120 GPaP = 80 kN
σ2 = MPa
6.Hard
Ø 30 mmSteel1 mØ 16 mmCopper1.5 mP = 120 kN

The stepped bar is fixed at the wall and loaded at its free end. Find the largest normal stress σmax in the bar.

P = 120 kNsegment 1: Ø30 mm, 1 m, steel (E = 200 GPa)segment 2: Ø16 mm, 1.5 m, copper (E = 117 GPa)
σmax = MPa

Answer key

  1. 1. σr = 176.8 MPa
  2. 2. σr = 75.23 MPa
  3. 3. δ = 4.547 mm
  4. 4. δ = 0.05876 mm
  5. 5. σ2 = 26.57 MPa
  6. 6. σmax = 596.8 MPa

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