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
100 kNØ25120 GPaØ80/50300 mmσr​ = ?

A steel rod (diameter 25 mm, E = 200 GPa) sits inside a tube made of copper (outer diameter 80 mm, inner diameter 50 mm, E = 120 GPa). Both are 300 mm long and are compressed together between rigid plates by 100 kN. Find the compressive stress σr in the rod.

P = 100 kNrod: Ø25 mm, E = 200 GPatube: Ø80/Ø50 mm, E = 120 GPaL = 300 mm
σr = MPa
2.Easy
Ø 12 mm1 mP = 65 kN

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

P = 65 kNd = 12 mm
σ = MPa
3.Medium
P = ?12500 mm500 mmØ25Ø40δ = 0.25 mm

A bar is made of a steel segment (diameter 25 mm, length 500 mm, E = 200 GPa) joined end to end with a segment made of brass (diameter 40 mm, length 500 mm, E = 100 GPa). It is fixed at one end and pulled at the other. Find the axial load P that stretches it by 0.25 mm in total.

segment 1: steel, Ø25 mm, 500 mm, E = 200 GPasegment 2: brass, Ø40 mm, 500 mm, E = 100 GPaδ = 0.25 mm
P = kN
4.Medium
P = ?12400 mm300 mmØ20Ø40δ = 0.3 mm

A bar is made of a steel segment (diameter 20 mm, length 400 mm, E = 200 GPa) joined end to end with a segment made of aluminium (diameter 40 mm, length 300 mm, E = 70 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, 400 mm, E = 200 GPasegment 2: aluminium, Ø40 mm, 300 mm, E = 70 GPaδ = 0.3 mm
P = kN
5.Hard
100 kN12500 mm200 mmØ25Ø50σ2​ = ?

A steel segment (diameter 25 mm, length 500 mm, E = 200 GPa) and a segment made of bronze (diameter 50 mm, length 200 mm, E = 110 GPa) are joined end to end and fixed between two rigid walls. An axial load of 100 kN acts at the joint, towards segment 2. Find the magnitude of the stress σ2 in segment 2.

segment 1: steel, Ø25 mm, 500 mm, E = 200 GPasegment 2: bronze, Ø50 mm, 200 mm, E = 110 GPaP = 100 kN
σ2 = MPa
6.Hard
P = ?Ø20110 GPaØ80/50800 mm

A steel rod (diameter 20 mm, E = 200 GPa, allowable stress 160 MPa) sits inside a tube made of bronze (outer diameter 80 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: Ø80/Ø50 mm, E = 110 GPa, σallow = 80 MPa
Pmax = kN

Answer key

  1. 1. σr = 42.94 MPa
  2. 2. σ = 574.7 MPa
  3. 3. P = 27.56 kN
  4. 4. P = 30.69 kN
  5. 5. σ2 = 43.09 MPa
  6. 6. Pmax = 290.7 kN

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