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
250 kNØ30120 GPaØ80/50400 mmσr​ = ?

A steel rod (diameter 30 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 250 kN. Find the compressive stress σr in the rod.

P = 250 kNrod: Ø30 mm, E = 200 GPatube: Ø80/Ø50 mm, E = 120 GPaL = 400 mm
σr = MPa
3.Medium
100 kNØ4070 GPaØ100/60300 mmδ = ?

A steel rod (diameter 40 mm, E = 200 GPa) sits inside a tube made of aluminium (outer diameter 100 mm, inner diameter 60 mm, E = 70 GPa). Both are 300 mm long and are compressed together between rigid plates by 100 kN. Find the shortening δ.

P = 100 kNrod: Ø40 mm, E = 200 GPatube: Ø100/Ø60 mm, E = 70 GPaL = 300 mm
δ = mm
4.Medium
Ø 12 mmSteel2.5 mP = 105 kN

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

P = 105 kNd = 12 mmL = 2.5 mE = 200 GPa
ε = µε
5.Hard
Ø 35 mmSteel0.5 mØ 16 mmSteel1 mP = 65 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 = 65 kNsegment 1: Ø35 mm, 0.5 m, steel (E = 200 GPa)segment 2: Ø16 mm, 1 m, steel (E = 200 GPa)
σmax = MPa
6.Hard
P = ?Ø30110 GPaØ80/60500 mm

A steel rod (diameter 30 mm, E = 200 GPa, allowable stress 200 MPa) sits inside a tube made of bronze (outer diameter 80 mm, inner diameter 60 mm, E = 110 GPa, allowable stress 100 MPa). They are compressed together between rigid plates. Find the largest load Pmax.

rod: Ø30 mm, E = 200 GPa, σallow = 200 MPatube: Ø80/Ø60 mm, E = 110 GPa, σallow = 100 MPa
Pmax = kN

Answer key

  1. 1. σ = 152.8 MPa
  2. 2. σr = 98.24 MPa
  3. 3. δ = 0.04974 mm
  4. 4. ε = 4642 µε
  5. 5. σmax = 323.3 MPa
  6. 6. Pmax = 348.4 kN

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