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 mm1.5 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
200 kNØ25110 GPaØ80/60400 mmσr​ = ?

A steel rod (diameter 25 mm, E = 200 GPa) sits inside a tube made of bronze (outer diameter 80 mm, inner diameter 60 mm, E = 110 GPa). Both are 400 mm long and are compressed together between rigid plates by 200 kN. Find the compressive stress σr in the rod.

P = 200 kNrod: Ø25 mm, E = 200 GPatube: Ø80/Ø60 mm, E = 110 GPaL = 400 mm
σr = MPa
3.Medium
Ø 10 mmCopper0.5 mP = 35 kN

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

P = 35 kNd = 10 mmL = 0.5 mE = 117 GPa
ε = µε
4.Medium
P = ?12400 mm400 mmØ40Ø60δ = 0.4 mm

A bar is made of a steel segment (diameter 40 mm, length 400 mm, E = 200 GPa) joined end to end with a segment made of bronze (diameter 60 mm, length 400 mm, E = 110 GPa). It is fixed at one end and pulled at the other. Find the axial load P that stretches it by 0.4 mm in total.

segment 1: steel, Ø40 mm, 400 mm, E = 200 GPasegment 2: bronze, Ø60 mm, 400 mm, E = 110 GPaδ = 0.4 mm
P = kN
5.Hard
Ø 25 mmAluminium1 mØ 20 mmBrass0.5 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: Ø25 mm, 1 m, aluminium (E = 70 GPa)segment 2: Ø20 mm, 0.5 m, brass (E = 100 GPa)
σmax = MPa
6.Hard
P = ?Ø20110 GPaØ120/50800 mm

A steel rod (diameter 20 mm, E = 200 GPa, allowable stress 160 MPa) sits inside a tube made of bronze (outer diameter 120 mm, inner diameter 50 mm, E = 110 GPa, allowable stress 80 MPa). They are compressed together between rigid plates. Find the largest load Pmax.

rod: Ø20 mm, E = 200 GPa, σallow = 160 MPatube: Ø120/Ø50 mm, E = 110 GPa, σallow = 80 MPa
Pmax = kN

Answer key

  1. 1. σ = 152.8 MPa
  2. 2. σr = 117.6 MPa
  3. 3. ε = 3809 µε
  4. 4. P = 139 kN
  5. 5. σmax = 350.1 MPa
  6. 6. Pmax = 793.4 kN

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