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
250 kNØ20120 GPaØ80/50500 mmσr​ = ?

A steel rod (diameter 20 mm, E = 200 GPa) sits inside a tube made of copper (outer diameter 80 mm, inner diameter 50 mm, E = 120 GPa). Both are 500 mm long and are compressed together between rigid plates by 250 kN. Find the compressive stress σr in the rod.

P = 250 kNrod: Ø20 mm, E = 200 GPatube: Ø80/Ø50 mm, E = 120 GPaL = 500 mm
σr = MPa
2.Easy
100 kNØ20120 GPaØ80/50300 mmσr​ = ?

A steel rod (diameter 20 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: Ø20 mm, E = 200 GPatube: Ø80/Ø50 mm, E = 120 GPaL = 300 mm
σr = MPa
3.Medium
P = ?12500 mm500 mmØ40Ø40δ = 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 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 0.3 mm in total.

segment 1: steel, Ø40 mm, 500 mm, E = 200 GPasegment 2: brass, Ø40 mm, 500 mm, E = 100 GPaδ = 0.3 mm
P = kN
4.Medium
P = ?12300 mm400 mmØ25Ø60δ = 0.4 mm

A bar is made of a steel segment (diameter 25 mm, length 300 mm, E = 200 GPa) joined end to end with a segment made of bronze (diameter 60 mm, length 400 mm, E = 110 GPa). It is fixed at one end and pulled at the other. Find the axial load P that stretches it by 0.4 mm in total.

segment 1: steel, Ø25 mm, 300 mm, E = 200 GPasegment 2: bronze, Ø60 mm, 400 mm, E = 110 GPaδ = 0.4 mm
P = kN
5.Hard
P = ?Ø3070 GPaØ120/50300 mm

A steel rod (diameter 30 mm, E = 200 GPa, allowable stress 120 MPa) sits inside a tube made of aluminium (outer diameter 120 mm, inner diameter 50 mm, E = 70 GPa, allowable stress 50 MPa). They are compressed together between rigid plates. Find the largest load Pmax.

rod: Ø30 mm, E = 200 GPa, σallow = 120 MPatube: Ø120/Ø50 mm, E = 70 GPa, σallow = 50 MPa
Pmax = kN
6.Hard
Ø 30 mmBrass1 mØ 20 mmSteel1 mP = 90 kN

The stepped bar is fixed at the wall and loaded at its free end. Find the total elongation δ.

P = 90 kNsegment 1: Ø30 mm, 1 m, brass (E = 100 GPa)segment 2: Ø20 mm, 1 m, steel (E = 200 GPa)
δ = mm

Answer key

  1. 1. σr = 116.2 MPa
  2. 2. σr = 46.47 MPa
  3. 3. P = 50.27 kN
  4. 4. P = 92.13 kN
  5. 5. Pmax = 477.4 kN
  6. 6. δ = 2.706 mm

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