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 10 mm1.5 mP = 20 kN

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

P = 20 kNd = 10 mm
σ = MPa
2.Easy
250 kNØ4070 GPaØ120/50500 mmσr​ = ?

A steel rod (diameter 40 mm, E = 200 GPa) sits inside a tube made of aluminium (outer diameter 120 mm, inner diameter 50 mm, E = 70 GPa). Both are 500 mm long and are compressed together between rigid plates by 250 kN. Find the compressive stress σr in the rod.

P = 250 kNrod: Ø40 mm, E = 200 GPatube: Ø120/Ø50 mm, E = 70 GPaL = 500 mm
σr = MPa
3.Medium
Ø 30 mmCopper1.5 mP = 65 kN

Find the elongation δ of the copper bar under the axial load.

P = 65 kNd = 30 mmL = 1.5 mE = 117 GPa
δ = mm
4.Medium
Ø 10 mmAluminium2.5 mP = 20 kN

Find the elongation δ of the aluminium bar under the axial load.

P = 20 kNd = 10 mmL = 2.5 mE = 70 GPa
δ = mm
5.Hard
P = ?Ø30110 GPaØ120/50600 mm

A steel rod (diameter 30 mm, E = 200 GPa, allowable stress 150 MPa) sits inside a tube made of bronze (outer diameter 120 mm, inner diameter 50 mm, E = 110 GPa, allowable stress 60 MPa). They are compressed together between rigid plates. Find the largest load Pmax.

rod: Ø30 mm, E = 200 GPa, σallow = 150 MPatube: Ø120/Ø50 mm, E = 110 GPa, σallow = 60 MPa
Pmax = kN
6.Hard
40 kN12500 mm500 mmØ30Ø30σ2​ = ?

A steel segment (diameter 30 mm, length 500 mm, E = 200 GPa) and a segment made of brass (diameter 30 mm, length 500 mm, E = 100 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, 500 mm, E = 200 GPasegment 2: brass, Ø30 mm, 500 mm, E = 100 GPaP = 40 kN
σ2 = MPa

Answer key

  1. 1. σ = 254.6 MPa
  2. 2. σr = 55.21 MPa
  3. 3. δ = 1.179 mm
  4. 4. δ = 9.095 mm
  5. 5. Pmax = 637.9 kN
  6. 6. σ2 = 18.86 MPa

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