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
200 kNØ2570 GPaØ100/70500 mmσr​ = ?

A steel rod (diameter 25 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: Ø25 mm, E = 200 GPatube: Ø100/Ø70 mm, E = 70 GPaL = 500 mm
σr = MPa
2.Easy
Ø 16 mm1.5 mP = 50 kN

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

P = 50 kNd = 16 mm
σ = MPa
3.Medium
P = ?12300 mm400 mmØ25Ø30δ = 0.4 mm

A bar is made of a steel segment (diameter 25 mm, length 300 mm, E = 200 GPa) joined end to end with a segment made of bronze (diameter 30 mm, length 400 mm, E = 110 GPa). It is fixed at one end and pulled at the other. Find the axial load P that stretches it by 0.4 mm in total.

segment 1: steel, Ø25 mm, 300 mm, E = 200 GPasegment 2: bronze, Ø30 mm, 400 mm, E = 110 GPaδ = 0.4 mm
P = kN
4.Medium
250 kNØ40120 GPaØ80/60400 mmδ = ?

A steel rod (diameter 40 mm, E = 200 GPa) sits inside a tube made of copper (outer diameter 80 mm, inner diameter 60 mm, E = 120 GPa). Both are 400 mm long and are compressed together between rigid plates by 250 kN. Find the shortening δ.

P = 250 kNrod: Ø40 mm, E = 200 GPatube: Ø80/Ø60 mm, E = 120 GPaL = 400 mm
δ = mm
5.Hard
Ø 40 mmSteel1.5 mØ 16 mmAluminium1 mP = 65 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 = 65 kNsegment 1: Ø40 mm, 1.5 m, steel (E = 200 GPa)segment 2: Ø16 mm, 1 m, aluminium (E = 70 GPa)
σmax = MPa
6.Hard
20 kN12400 mm300 mmØ20Ø40σ2​ = ?

A steel segment (diameter 20 mm, length 400 mm, E = 200 GPa) and a segment made of aluminium (diameter 40 mm, length 300 mm, E = 70 GPa) are joined end to end and fixed between two rigid walls. An axial load of 20 kN acts at the joint, towards segment 2. Find the magnitude of the stress σ2 in segment 2.

segment 1: steel, Ø20 mm, 400 mm, E = 200 GPasegment 2: aluminium, Ø40 mm, 300 mm, E = 70 GPaP = 20 kN
σ2 = MPa

Answer key

  1. 1. σr = 105.7 MPa
  2. 2. σ = 248.7 MPa
  3. 3. P = 48.78 kN
  4. 4. δ = 0.1941 mm
  5. 5. σmax = 323.3 MPa
  6. 6. σ2 = 10.36 MPa

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