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 kNØ25120 GPaØ100/60300 mmσr​ = ?

A steel rod (diameter 25 mm, E = 200 GPa) sits inside a tube made of copper (outer diameter 100 mm, inner diameter 60 mm, E = 120 GPa). Both are 300 mm long and are compressed together between rigid plates by 250 kN. Find the compressive stress σr in the rod.

P = 250 kNrod: Ø25 mm, E = 200 GPatube: Ø100/Ø60 mm, E = 120 GPaL = 300 mm
σr = MPa
2.Easy
Ø 12 mm0.5 mP = 15 kN

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

P = 15 kNd = 12 mm
σ = MPa
3.Medium
50 kNØ25120 GPaØ80/50400 mmδ = ?

A steel rod (diameter 25 mm, E = 200 GPa) sits inside a tube made of copper (outer diameter 80 mm, inner diameter 50 mm, E = 120 GPa). Both are 400 mm long and are compressed together between rigid plates by 50 kN. Find the shortening δ.

P = 50 kNrod: Ø25 mm, E = 200 GPatube: Ø80/Ø50 mm, E = 120 GPaL = 400 mm
δ = mm
4.Medium
P = ?12400 mm300 mmØ30Ø40δ = 0.2 mm

A bar is made of a steel segment (diameter 30 mm, length 400 mm, E = 200 GPa) joined end to end with a segment made of aluminium (diameter 40 mm, length 300 mm, E = 70 GPa). It is fixed at one end and pulled at the other. Find the axial load P that stretches it by 0.2 mm in total.

segment 1: steel, Ø30 mm, 400 mm, E = 200 GPasegment 2: aluminium, Ø40 mm, 300 mm, E = 70 GPaδ = 0.2 mm
P = kN
5.Hard
P = ?Ø40110 GPaØ100/70400 mm

A steel rod (diameter 40 mm, E = 200 GPa, allowable stress 160 MPa) sits inside a tube made of bronze (outer diameter 100 mm, inner diameter 70 mm, E = 110 GPa, allowable stress 80 MPa). They are compressed together between rigid plates. Find the largest load Pmax.

rod: Ø40 mm, E = 200 GPa, σallow = 160 MPatube: Ø100/Ø70 mm, E = 110 GPa, σallow = 80 MPa
Pmax = kN
6.Hard
Ø 35 mmSteel1 mØ 16 mmCopper0.5 mP = 10 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 = 10 kNsegment 1: Ø35 mm, 1 m, steel (E = 200 GPa)segment 2: Ø16 mm, 0.5 m, copper (E = 117 GPa)
σmax = MPa

Answer key

  1. 1. σr = 71.29 MPa
  2. 2. σ = 132.6 MPa
  3. 3. δ = 0.04294 mm
  4. 4. P = 32.05 kN
  5. 5. Pmax = 503.2 kN
  6. 6. σmax = 49.74 MPa

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