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 16 mm2 mP = 35 kN

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

P = 35 kNd = 16 mm
σ = MPa
2.Easy
250 kNØ40110 GPaØ120/50300 mmσr​ = ?

A steel rod (diameter 40 mm, E = 200 GPa) sits inside a tube made of bronze (outer diameter 120 mm, inner diameter 50 mm, E = 110 GPa). Both are 300 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 = 110 GPaL = 300 mm
σr = MPa
3.Medium
P = ?12400 mm300 mmØ30Ø40δ = 0.25 mm

A bar is made of a steel segment (diameter 30 mm, length 400 mm, E = 200 GPa) joined end to end with a segment made of brass (diameter 40 mm, length 300 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, Ø30 mm, 400 mm, E = 200 GPasegment 2: brass, Ø40 mm, 300 mm, E = 100 GPaδ = 0.25 mm
P = kN
4.Medium
100 kNØ25100 GPaØ120/70400 mmδ = ?

A steel rod (diameter 25 mm, E = 200 GPa) sits inside a tube made of brass (outer diameter 120 mm, inner diameter 70 mm, E = 100 GPa). Both are 400 mm long and are compressed together between rigid plates by 100 kN. Find the shortening δ.

P = 100 kNrod: Ø25 mm, E = 200 GPatube: Ø120/Ø70 mm, E = 100 GPaL = 400 mm
δ = mm
5.Hard
P = ?Ø20120 GPaØ100/70400 mm

A steel rod (diameter 20 mm, E = 200 GPa, allowable stress 250 MPa) sits inside a tube made of copper (outer diameter 100 mm, inner diameter 70 mm, E = 120 GPa, allowable stress 70 MPa). They are compressed together between rigid plates. Find the largest load Pmax.

rod: Ø20 mm, E = 200 GPa, σallow = 250 MPatube: Ø100/Ø70 mm, E = 120 GPa, σallow = 70 MPa
Pmax = kN
6.Hard
100 kN12500 mm500 mmØ25Ø50σ2​ = ?

A steel segment (diameter 25 mm, length 500 mm, E = 200 GPa) and a segment made of brass (diameter 50 mm, length 500 mm, E = 100 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: brass, Ø50 mm, 500 mm, E = 100 GPaP = 100 kN
σ2 = MPa

Answer key

  1. 1. σ = 174.1 MPa
  2. 2. σr = 39.08 MPa
  3. 3. P = 47.92 kN
  4. 4. δ = 0.04738 mm
  5. 5. Pmax = 317 kN
  6. 6. σ2 = 33.95 MPa

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