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 kNØ2070 GPaØ80/50600 mmσr​ = ?

A steel rod (diameter 20 mm, E = 200 GPa) sits inside a tube made of aluminium (outer diameter 80 mm, inner diameter 50 mm, E = 70 GPa). Both are 600 mm long and are compressed together between rigid plates by 100 kN. Find the compressive stress σr in the rod.

P = 100 kNrod: Ø20 mm, E = 200 GPatube: Ø80/Ø50 mm, E = 70 GPaL = 600 mm
σr = MPa
2.Easy
Ø 30 mm1.5 mP = 40 kN

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

P = 40 kNd = 30 mm
σ = MPa
3.Medium
300 kNØ40110 GPaØ80/60500 mmδ = ?

A steel rod (diameter 40 mm, E = 200 GPa) sits inside a tube made of bronze (outer diameter 80 mm, inner diameter 60 mm, E = 110 GPa). Both are 500 mm long and are compressed together between rigid plates by 300 kN. Find the shortening δ.

P = 300 kNrod: Ø40 mm, E = 200 GPatube: Ø80/Ø60 mm, E = 110 GPaL = 500 mm
δ = mm
4.Medium
P = ?12600 mm400 mmØ25Ø40δ = 0.2 mm

A bar is made of a steel segment (diameter 25 mm, length 600 mm, E = 200 GPa) joined end to end with a segment made of bronze (diameter 40 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 0.2 mm in total.

segment 1: steel, Ø25 mm, 600 mm, E = 200 GPasegment 2: bronze, Ø40 mm, 400 mm, E = 110 GPaδ = 0.2 mm
P = kN
5.Hard
100 kN12300 mm400 mmØ40Ø50σ2​ = ?

A steel segment (diameter 40 mm, length 300 mm, E = 200 GPa) and a segment made of brass (diameter 50 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, Ø40 mm, 300 mm, E = 200 GPasegment 2: brass, Ø50 mm, 400 mm, E = 100 GPaP = 100 kN
σ2 = MPa
6.Hard
20 kN12500 mm300 mmØ30Ø30σ2​ = ?

A steel segment (diameter 30 mm, length 500 mm, E = 200 GPa) and a segment made of brass (diameter 30 mm, length 300 mm, E = 100 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, Ø30 mm, 500 mm, E = 200 GPasegment 2: brass, Ø30 mm, 300 mm, E = 100 GPaP = 20 kN
σ2 = MPa

Answer key

  1. 1. σr = 72.14 MPa
  2. 2. σ = 56.59 MPa
  3. 3. δ = 0.3041 mm
  4. 4. P = 22.21 kN
  5. 5. σ2 = 18.82 MPa
  6. 6. σ2 = 12.86 MPa

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