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
80 kNØ20110 GPaØ100/50600 mmσr​ = ?

A steel rod (diameter 20 mm, E = 200 GPa) sits inside a tube made of bronze (outer diameter 100 mm, inner diameter 50 mm, E = 110 GPa). Both are 600 mm long and are compressed together between rigid plates by 80 kN. Find the compressive stress σr in the rod.

P = 80 kNrod: Ø20 mm, E = 200 GPatube: Ø100/Ø50 mm, E = 110 GPaL = 600 mm
σr = MPa
2.Easy
Ø 10 mm1 mP = 15 kN

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

P = 15 kNd = 10 mm
σ = MPa
3.Medium
100 kNØ20110 GPaØ80/60600 mmδ = ?

A steel rod (diameter 20 mm, E = 200 GPa) sits inside a tube made of bronze (outer diameter 80 mm, inner diameter 60 mm, E = 110 GPa). Both are 600 mm long and are compressed together between rigid plates by 100 kN. Find the shortening δ.

P = 100 kNrod: Ø20 mm, E = 200 GPatube: Ø80/Ø60 mm, E = 110 GPaL = 600 mm
δ = mm
4.Medium
Ø 16 mmSteel1.5 mP = 10 kN

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

P = 10 kNd = 16 mmL = 1.5 mE = 200 GPa
δ = mm
5.Hard
60 kN12500 mm400 mmØ30Ø40σ2​ = ?

A steel segment (diameter 30 mm, length 500 mm, E = 200 GPa) and a segment made of aluminium (diameter 40 mm, length 400 mm, E = 70 GPa) are joined end to end and fixed between two rigid walls. An axial load of 60 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, Ø40 mm, 400 mm, E = 70 GPaP = 60 kN
σ2 = MPa
6.Hard
P = ?Ø30120 GPaØ100/50800 mm

A steel rod (diameter 30 mm, E = 200 GPa, allowable stress 150 MPa) sits inside a tube made of copper (outer diameter 100 mm, inner diameter 50 mm, E = 120 GPa, allowable stress 80 MPa). They are compressed together between rigid plates. Find the largest load Pmax.

rod: Ø30 mm, E = 200 GPa, σallow = 150 MPatube: Ø100/Ø50 mm, E = 120 GPa, σallow = 80 MPa
Pmax = kN

Answer key

  1. 1. σr = 22.51 MPa
  2. 2. σ = 191 MPa
  3. 3. δ = 0.1969 mm
  4. 4. δ = 0.373 mm
  5. 5. σ2 = 20.89 MPa
  6. 6. Pmax = 565.5 kN

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