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 30 mm0.5 mP = 50 kN

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

P = 50 kNd = 30 mm
σ = MPa
2.Easy
250 kNØ25120 GPaØ120/50300 mmσr​ = ?

A steel rod (diameter 25 mm, E = 200 GPa) sits inside a tube made of copper (outer diameter 120 mm, inner diameter 50 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: Ø120/Ø50 mm, E = 120 GPaL = 300 mm
σr = MPa
3.Medium
Ø 10 mmSteel3 mP = 120 kN

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

P = 120 kNd = 10 mmL = 3 mE = 200 GPa
ε = µε
4.Medium
P = ?12500 mm300 mmØ40Ø30δ = 0.25 mm

A bar is made of a steel segment (diameter 40 mm, length 500 mm, E = 200 GPa) joined end to end with a segment made of brass (diameter 30 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 0.25 mm in total.

segment 1: steel, Ø40 mm, 500 mm, E = 200 GPasegment 2: brass, Ø30 mm, 300 mm, E = 100 GPaδ = 0.25 mm
P = kN
5.Hard
P = ?Ø25110 GPaØ80/60400 mm

A steel rod (diameter 25 mm, E = 200 GPa, allowable stress 150 MPa) sits inside a tube made of bronze (outer diameter 80 mm, inner diameter 60 mm, E = 110 GPa, allowable stress 70 MPa). They are compressed together between rigid plates. Find the largest load Pmax.

rod: Ø25 mm, E = 200 GPa, σallow = 150 MPatube: Ø80/Ø60 mm, E = 110 GPa, σallow = 70 MPa
Pmax = kN
6.Hard
Ø 30 mmAluminium2 mØ 20 mmSteel1 mP = 110 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 = 110 kNsegment 1: Ø30 mm, 2 m, aluminium (E = 70 GPa)segment 2: Ø20 mm, 1 m, steel (E = 200 GPa)
σmax = MPa

Answer key

  1. 1. σ = 70.74 MPa
  2. 2. σr = 40.99 MPa
  3. 3. ε = 7639 µε
  4. 4. P = 40.11 kN
  5. 5. Pmax = 216.4 kN
  6. 6. σmax = 350.1 MPa

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