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
100 kNØ40110 GPaØ100/60300 mmσr​ = ?

A steel rod (diameter 40 mm, E = 200 GPa) sits inside a tube made of bronze (outer diameter 100 mm, inner diameter 60 mm, E = 110 GPa). Both are 300 mm long and are compressed together between rigid plates by 100 kN. Find the compressive stress σr in the rod.

P = 100 kNrod: Ø40 mm, E = 200 GPatube: Ø100/Ø60 mm, E = 110 GPaL = 300 mm
σr = MPa
2.Easy
Ø 16 mm1 mP = 100 kN

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

P = 100 kNd = 16 mm
σ = MPa
3.Medium
P = ?12500 mm300 mmØ20Ø60δ = 0.2 mm

A bar is made of a steel segment (diameter 20 mm, length 500 mm, E = 200 GPa) joined end to end with a segment made of brass (diameter 60 mm, length 300 mm, E = 100 GPa). It is fixed at one end and pulled at the other. Find the axial load P that stretches it by 0.2 mm in total.

segment 1: steel, Ø20 mm, 500 mm, E = 200 GPasegment 2: brass, Ø60 mm, 300 mm, E = 100 GPaδ = 0.2 mm
P = kN
4.Medium
50 kNØ2070 GPaØ100/50400 mmδ = ?

A steel rod (diameter 20 mm, E = 200 GPa) sits inside a tube made of aluminium (outer diameter 100 mm, inner diameter 50 mm, E = 70 GPa). Both are 400 mm long and are compressed together between rigid plates by 50 kN. Find the shortening δ.

P = 50 kNrod: Ø20 mm, E = 200 GPatube: Ø100/Ø50 mm, E = 70 GPaL = 400 mm
δ = mm
5.Hard
Ø 35 mmCopper0.5 mØ 20 mmBrass0.5 mP = 25 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 = 25 kNsegment 1: Ø35 mm, 0.5 m, copper (E = 117 GPa)segment 2: Ø20 mm, 0.5 m, brass (E = 100 GPa)
σmax = MPa
6.Hard
P = ?Ø30100 GPaØ100/70500 mm

A steel rod (diameter 30 mm, E = 200 GPa, allowable stress 160 MPa) sits inside a tube made of brass (outer diameter 100 mm, inner diameter 70 mm, E = 100 GPa, allowable stress 50 MPa). They are compressed together between rigid plates. Find the largest load Pmax.

rod: Ø30 mm, E = 200 GPa, σallow = 160 MPatube: Ø100/Ø70 mm, E = 100 GPa, σallow = 50 MPa
Pmax = kN

Answer key

  1. 1. σr = 24.87 MPa
  2. 2. σ = 497.4 MPa
  3. 3. P = 22.18 kN
  4. 4. δ = 0.04209 mm
  5. 5. σmax = 79.58 MPa
  6. 6. Pmax = 271 kN

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