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 mm1.5 mP = 70 kN

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

P = 70 kNd = 30 mm
σ = MPa
2.Easy
100 kNØ30100 GPaØ80/50600 mmσr​ = ?

A steel rod (diameter 30 mm, E = 200 GPa) sits inside a tube made of brass (outer diameter 80 mm, inner diameter 50 mm, E = 100 GPa). Both are 600 mm long and are compressed together between rigid plates by 100 kN. Find the compressive stress σr in the rod.

P = 100 kNrod: Ø30 mm, E = 200 GPatube: Ø80/Ø50 mm, E = 100 GPaL = 600 mm
σr = MPa
3.Medium
P = ?12600 mm200 mmØ40Ø40δ = 0.3 mm

A bar is made of a steel segment (diameter 40 mm, length 600 mm, E = 200 GPa) joined end to end with a segment made of brass (diameter 40 mm, length 200 mm, E = 100 GPa). It is fixed at one end and pulled at the other. Find the axial load P that stretches it by 0.3 mm in total.

segment 1: steel, Ø40 mm, 600 mm, E = 200 GPasegment 2: brass, Ø40 mm, 200 mm, E = 100 GPaδ = 0.3 mm
P = kN
4.Medium
Ø 30 mmSteel1 mP = 70 kN

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

P = 70 kNd = 30 mmL = 1 mE = 200 GPa
ε = µε
5.Hard
50 kN12500 mm400 mmØ30Ø60σ2​ = ?

A steel segment (diameter 30 mm, length 500 mm, E = 200 GPa) and a segment made of aluminium (diameter 60 mm, length 400 mm, E = 70 GPa) are joined end to end and fixed between two rigid walls. An axial load of 50 kN acts at the joint, towards segment 2. Find the magnitude of the stress σ2 in segment 2.

segment 1: steel, Ø30 mm, 500 mm, E = 200 GPasegment 2: aluminium, Ø60 mm, 400 mm, E = 70 GPaP = 50 kN
σ2 = MPa
6.Hard
P = ?Ø40100 GPaØ120/70600 mm

A steel rod (diameter 40 mm, E = 200 GPa, allowable stress 120 MPa) sits inside a tube made of brass (outer diameter 120 mm, inner diameter 70 mm, E = 100 GPa, allowable stress 70 MPa). They are compressed together between rigid plates. Find the largest load Pmax.

rod: Ø40 mm, E = 200 GPa, σallow = 120 MPatube: Ø120/Ø70 mm, E = 100 GPa, σallow = 70 MPa
Pmax = kN

Answer key

  1. 1. σ = 99.03 MPa
  2. 2. σr = 44.68 MPa
  3. 3. P = 75.4 kN
  4. 4. ε = 495.1 µε
  5. 5. σ2 = 11.25 MPa
  6. 6. Pmax = 598.5 kN

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