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 mP = 105 kN

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

P = 105 kNd = 30 mm
σ = MPa
2.Easy
150 kNØ30110 GPaØ100/50500 mmσr​ = ?

A steel rod (diameter 30 mm, E = 200 GPa) sits inside a tube made of bronze (outer diameter 100 mm, inner diameter 50 mm, E = 110 GPa). Both are 500 mm long and are compressed together between rigid plates by 150 kN. Find the compressive stress σr in the rod.

P = 150 kNrod: Ø30 mm, E = 200 GPatube: Ø100/Ø50 mm, E = 110 GPaL = 500 mm
σr = MPa
3.Medium
80 kNØ4070 GPaØ100/60800 mmδ = ?

A steel rod (diameter 40 mm, E = 200 GPa) sits inside a tube made of aluminium (outer diameter 100 mm, inner diameter 60 mm, E = 70 GPa). Both are 800 mm long and are compressed together between rigid plates by 80 kN. Find the shortening δ.

P = 80 kNrod: Ø40 mm, E = 200 GPatube: Ø100/Ø60 mm, E = 70 GPaL = 800 mm
δ = mm
4.Medium
P = ?12500 mm500 mmØ40Ø60δ = 0.3 mm

A bar is made of a steel segment (diameter 40 mm, length 500 mm, E = 200 GPa) joined end to end with a segment made of brass (diameter 60 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 0.3 mm in total.

segment 1: steel, Ø40 mm, 500 mm, E = 200 GPasegment 2: brass, Ø60 mm, 500 mm, E = 100 GPaδ = 0.3 mm
P = kN
5.Hard
P = ?Ø2070 GPaØ120/70500 mm

A steel rod (diameter 20 mm, E = 200 GPa, allowable stress 150 MPa) sits inside a tube made of aluminium (outer diameter 120 mm, inner diameter 70 mm, E = 70 GPa, allowable stress 50 MPa). They are compressed together between rigid plates. Find the largest load Pmax.

rod: Ø20 mm, E = 200 GPa, σallow = 150 MPatube: Ø120/Ø70 mm, E = 70 GPa, σallow = 50 MPa
Pmax = kN
6.Hard
20 kN12400 mm200 mmØ40Ø40σ2​ = ?

A steel segment (diameter 40 mm, length 400 mm, E = 200 GPa) and a segment made of bronze (diameter 40 mm, length 200 mm, E = 110 GPa) are joined end to end and fixed between two rigid walls. An axial load of 20 kN acts at the joint, towards segment 2. Find the magnitude of the stress σ2 in segment 2.

segment 1: steel, Ø40 mm, 400 mm, E = 200 GPasegment 2: bronze, Ø40 mm, 200 mm, E = 110 GPaP = 20 kN
σ2 = MPa

Answer key

  1. 1. σ = 148.5 MPa
  2. 2. σr = 38.01 MPa
  3. 3. δ = 0.1061 mm
  4. 4. P = 79.83 kN
  5. 5. Pmax = 417.9 kN
  6. 6. σ2 = 8.337 MPa

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