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
Ø 25 mm1 mP = 75 kN

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

P = 75 kNd = 25 mm
σ = MPa
2.Easy
80 kNØ25120 GPaØ120/60500 mmσr​ = ?

A steel rod (diameter 25 mm, E = 200 GPa) sits inside a tube made of copper (outer diameter 120 mm, inner diameter 60 mm, E = 120 GPa). Both are 500 mm long and are compressed together between rigid plates by 80 kN. Find the compressive stress σr in the rod.

P = 80 kNrod: Ø25 mm, E = 200 GPatube: Ø120/Ø60 mm, E = 120 GPaL = 500 mm
σr = MPa
3.Medium
Ø 16 mmBrass1.5 mP = 105 kN

Find the axial strain ε in the brass bar, in microstrain (µε = 10⁻⁶).

P = 105 kNd = 16 mmL = 1.5 mE = 100 GPa
ε = µε
4.Medium
P = ?12600 mm300 mmØ20Ø30δ = 0.3 mm

A bar is made of a steel segment (diameter 20 mm, length 600 mm, E = 200 GPa) joined end to end with a segment made of copper (diameter 30 mm, length 300 mm, E = 120 GPa). It is fixed at one end and pulled at the other. Find the axial load P that stretches it by 0.3 mm in total.

segment 1: steel, Ø20 mm, 600 mm, E = 200 GPasegment 2: copper, Ø30 mm, 300 mm, E = 120 GPaδ = 0.3 mm
P = kN
5.Hard
20 kN12300 mm400 mmØ20Ø50σ2​ = ?

A steel segment (diameter 20 mm, length 300 mm, E = 200 GPa) and a segment made of bronze (diameter 50 mm, length 400 mm, E = 110 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, 300 mm, E = 200 GPasegment 2: bronze, Ø50 mm, 400 mm, E = 110 GPaP = 20 kN
σ2 = MPa
6.Hard
P = ?Ø4070 GPaØ80/50600 mm

A steel rod (diameter 40 mm, E = 200 GPa, allowable stress 150 MPa) sits inside a tube made of aluminium (outer diameter 80 mm, inner diameter 50 mm, E = 70 GPa, allowable stress 80 MPa). They are compressed together between rigid plates. Find the largest load Pmax.

rod: Ø40 mm, E = 200 GPa, σallow = 150 MPatube: Ø80/Ø50 mm, E = 70 GPa, σallow = 80 MPa
Pmax = kN

Answer key

  1. 1. σ = 152.8 MPa
  2. 2. σr = 14.34 MPa
  3. 3. ε = 5222 µε
  4. 4. P = 22.93 kN
  5. 5. σ2 = 7.339 MPa
  6. 6. Pmax = 349.3 kN

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