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 20 mm1.5 mP = 25 kN

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

P = 25 kNd = 20 mm
σ = MPa
2.Easy
50 kNØ2570 GPaØ100/50800 mmσr​ = ?

A steel rod (diameter 25 mm, E = 200 GPa) sits inside a tube made of aluminium (outer diameter 100 mm, inner diameter 50 mm, E = 70 GPa). Both are 800 mm long and are compressed together between rigid plates by 50 kN. Find the compressive stress σr in the rod.

P = 50 kNrod: Ø25 mm, E = 200 GPatube: Ø100/Ø50 mm, E = 70 GPaL = 800 mm
σr = MPa
3.Medium
Ø 16 mmCopper1.5 mP = 40 kN

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

P = 40 kNd = 16 mmL = 1.5 mE = 117 GPa
ε = µε
4.Medium
P = ?12400 mm300 mmØ30Ø60δ = 0.4 mm

A bar is made of a steel segment (diameter 30 mm, length 400 mm, E = 200 GPa) joined end to end with a segment made of brass (diameter 60 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 0.4 mm in total.

segment 1: steel, Ø30 mm, 400 mm, E = 200 GPasegment 2: brass, Ø60 mm, 300 mm, E = 100 GPaδ = 0.4 mm
P = kN
5.Hard
Ø 40 mmSteel0.5 mØ 20 mmAluminium1.5 mP = 60 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 = 60 kNsegment 1: Ø40 mm, 0.5 m, steel (E = 200 GPa)segment 2: Ø20 mm, 1.5 m, aluminium (E = 70 GPa)
σmax = MPa
6.Hard
40 kN12400 mm200 mmØ30Ø30σ2​ = ?

A steel segment (diameter 30 mm, length 400 mm, E = 200 GPa) and a segment made of bronze (diameter 30 mm, length 200 mm, E = 110 GPa) are joined end to end and fixed between two rigid walls. An axial load of 40 kN acts at the joint, towards segment 2. Find the magnitude of the stress σ2 in segment 2.

segment 1: steel, Ø30 mm, 400 mm, E = 200 GPasegment 2: bronze, Ø30 mm, 200 mm, E = 110 GPaP = 40 kN
σ2 = MPa

Answer key

  1. 1. σ = 79.58 MPa
  2. 2. σr = 19.59 MPa
  3. 3. ε = 1700 µε
  4. 4. P = 102.8 kN
  5. 5. σmax = 191 MPa
  6. 6. σ2 = 29.64 MPa

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