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 mm2 mP = 60 kN

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

P = 60 kNd = 10 mm
σ = MPa
2.Easy
300 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 300 kN. Find the compressive stress σr in the rod.

P = 300 kNrod: Ø25 mm, E = 200 GPatube: Ø100/Ø50 mm, E = 70 GPaL = 800 mm
σr = MPa
3.Medium
250 kNØ30110 GPaØ80/60300 mmδ = ?

A steel rod (diameter 30 mm, E = 200 GPa) sits inside a tube made of bronze (outer diameter 80 mm, inner diameter 60 mm, E = 110 GPa). Both are 300 mm long and are compressed together between rigid plates by 250 kN. Find the shortening δ.

P = 250 kNrod: Ø30 mm, E = 200 GPatube: Ø80/Ø60 mm, E = 110 GPaL = 300 mm
δ = mm
4.Medium
Ø 20 mmSteel3 mP = 20 kN

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

P = 20 kNd = 20 mmL = 3 mE = 200 GPa
δ = mm
5.Hard
Ø 40 mmCopper1 mØ 20 mmSteel2 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: Ø40 mm, 1 m, copper (E = 117 GPa)segment 2: Ø20 mm, 2 m, steel (E = 200 GPa)
σmax = MPa
6.Hard
40 kN12300 mm400 mmØ20Ø50σ2​ = ?

A steel segment (diameter 20 mm, length 300 mm, E = 200 GPa) and a segment made of copper (diameter 50 mm, length 400 mm, E = 120 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, Ø20 mm, 300 mm, E = 200 GPasegment 2: copper, Ø50 mm, 400 mm, E = 120 GPaP = 40 kN
σ2 = MPa

Answer key

  1. 1. σ = 763.9 MPa
  2. 2. σr = 117.5 MPa
  3. 3. δ = 0.1957 mm
  4. 4. δ = 0.9549 mm
  5. 5. σmax = 350.1 MPa
  6. 6. σ2 = 15.03 MPa

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