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 mm1 mP = 40 kN

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

P = 40 kNd = 30 mm
σ = MPa
2.Easy
50 kNØ20110 GPaØ120/50400 mmσr​ = ?

A steel rod (diameter 20 mm, E = 200 GPa) sits inside a tube made of bronze (outer diameter 120 mm, inner diameter 50 mm, E = 110 GPa). Both are 400 mm long and are compressed together between rigid plates by 50 kN. Find the compressive stress σr in the rod.

P = 50 kNrod: Ø20 mm, E = 200 GPatube: Ø120/Ø50 mm, E = 110 GPaL = 400 mm
σr = MPa
3.Medium
Ø 16 mmBrass1.5 mP = 35 kN

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

P = 35 kNd = 16 mmL = 1.5 mE = 100 GPa
ε = µε
4.Medium
P = ?12500 mm500 mmØ20Ø40δ = 0.3 mm

A bar is made of a steel segment (diameter 20 mm, length 500 mm, E = 200 GPa) joined end to end with a segment made of bronze (diameter 40 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, Ø20 mm, 500 mm, E = 200 GPasegment 2: bronze, Ø40 mm, 500 mm, E = 110 GPaδ = 0.3 mm
P = kN
5.Hard
Ø 25 mmBrass0.5 mØ 16 mmBrass1 mP = 50 kN

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

P = 50 kNsegment 1: Ø25 mm, 0.5 m, brass (E = 100 GPa)segment 2: Ø16 mm, 1 m, brass (E = 100 GPa)
δ = mm
6.Hard
30 kN12600 mm200 mmØ30Ø50σ2​ = ?

A steel segment (diameter 30 mm, length 600 mm, E = 200 GPa) and a segment made of copper (diameter 50 mm, length 200 mm, E = 120 GPa) are joined end to end and fixed between two rigid walls. An axial load of 30 kN acts at the joint, towards segment 2. Find the magnitude of the stress σ2 in segment 2.

segment 1: steel, Ø30 mm, 600 mm, E = 200 GPasegment 2: copper, Ø50 mm, 200 mm, E = 120 GPaP = 30 kN
σ2 = MPa

Answer key

  1. 1. σ = 56.59 MPa
  2. 2. σr = 9.167 MPa
  3. 3. ε = 1741 µε
  4. 4. P = 25.92 kN
  5. 5. δ = 2.996 mm
  6. 6. σ2 = 12.73 MPa

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