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 12 mm1.5 mP = 35 kN

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

P = 35 kNd = 12 mm
σ = MPa
2.Easy
250 kNØ20110 GPaØ100/60600 mmσr​ = ?

A steel rod (diameter 20 mm, E = 200 GPa) sits inside a tube made of bronze (outer diameter 100 mm, inner diameter 60 mm, E = 110 GPa). Both are 600 mm long and are compressed together between rigid plates by 250 kN. Find the compressive stress σr in the rod.

P = 250 kNrod: Ø20 mm, E = 200 GPatube: Ø100/Ø60 mm, E = 110 GPaL = 600 mm
σr = MPa
3.Medium
P = ?12600 mm500 mmØ25Ø60δ = 0.3 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 60 mm, length 500 mm, E = 110 GPa). It is fixed at one end and pulled at the other. Find the axial load P that stretches it by 0.3 mm in total.

segment 1: steel, Ø25 mm, 600 mm, E = 200 GPasegment 2: bronze, Ø60 mm, 500 mm, E = 110 GPaδ = 0.3 mm
P = kN
4.Medium
Ø 20 mmSteel1.5 mP = 100 kN

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

P = 100 kNd = 20 mmL = 1.5 mE = 200 GPa
ε = µε
5.Hard
Ø 30 mmAluminium1 mØ 12 mmSteel1 mP = 55 kN

The stepped bar is fixed at the wall and loaded at its free end. Find the total elongation δ.

P = 55 kNsegment 1: Ø30 mm, 1 m, aluminium (E = 70 GPa)segment 2: Ø12 mm, 1 m, steel (E = 200 GPa)
δ = mm
6.Hard
100 kN12600 mm400 mmØ20Ø40σ2​ = ?

A steel segment (diameter 20 mm, length 600 mm, E = 200 GPa) and a segment made of bronze (diameter 40 mm, length 400 mm, E = 110 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, Ø20 mm, 600 mm, E = 200 GPasegment 2: bronze, Ø40 mm, 400 mm, E = 110 GPaP = 100 kN
σ2 = MPa

Answer key

  1. 1. σ = 309.5 MPa
  2. 2. σr = 81.2 MPa
  3. 3. P = 38.86 kN
  4. 4. ε = 1592 µε
  5. 5. δ = 3.543 mm
  6. 6. σ2 = 61.07 MPa

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