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 kNØ30110 GPaØ80/60300 mmσr​ = ?

A steel rod (diameter 30 mm, E = 200 GPa) sits inside a tube made of bronze (outer diameter 80 mm, inner diameter 60 mm, E = 110 GPa). Both are 300 mm long and are compressed together between rigid plates by 80 kN. Find the compressive stress σr in the rod.

P = 80 kNrod: Ø30 mm, E = 200 GPatube: Ø80/Ø60 mm, E = 110 GPaL = 300 mm
σr = MPa
2.Easy
300 kNØ20100 GPaØ120/70600 mmσr​ = ?

A steel rod (diameter 20 mm, E = 200 GPa) sits inside a tube made of brass (outer diameter 120 mm, inner diameter 70 mm, E = 100 GPa). Both are 600 mm long and are compressed together between rigid plates by 300 kN. Find the compressive stress σr in the rod.

P = 300 kNrod: Ø20 mm, E = 200 GPatube: Ø120/Ø70 mm, E = 100 GPaL = 600 mm
σr = MPa
3.Medium
P = ?12600 mm200 mmØ30Ø30δ = 0.4 mm

A bar is made of a steel segment (diameter 30 mm, length 600 mm, E = 200 GPa) joined end to end with a segment made of aluminium (diameter 30 mm, length 200 mm, E = 70 GPa). It is fixed at one end and pulled at the other. Find the axial load P that stretches it by 0.4 mm in total.

segment 1: steel, Ø30 mm, 600 mm, E = 200 GPasegment 2: aluminium, Ø30 mm, 200 mm, E = 70 GPaδ = 0.4 mm
P = kN
4.Medium
50 kNØ4070 GPaØ100/50300 mmδ = ?

A steel rod (diameter 40 mm, E = 200 GPa) sits inside a tube made of aluminium (outer diameter 100 mm, inner diameter 50 mm, E = 70 GPa). Both are 300 mm long and are compressed together between rigid plates by 50 kN. Find the shortening δ.

P = 50 kNrod: Ø40 mm, E = 200 GPatube: Ø100/Ø50 mm, E = 70 GPaL = 300 mm
δ = mm
5.Hard
P = ?Ø30110 GPaØ120/60300 mm

A steel rod (diameter 30 mm, E = 200 GPa, allowable stress 150 MPa) sits inside a tube made of bronze (outer diameter 120 mm, inner diameter 60 mm, E = 110 GPa, allowable stress 50 MPa). They are compressed together between rigid plates. Find the largest load Pmax.

rod: Ø30 mm, E = 200 GPa, σallow = 150 MPatube: Ø120/Ø60 mm, E = 110 GPa, σallow = 50 MPa
Pmax = kN
6.Hard
Ø 30 mmSteel2 mØ 20 mmBrass0.5 mP = 75 kN

The stepped bar is fixed at the wall and loaded at its free end. Find the largest normal stress σmax in the bar.

P = 75 kNsegment 1: Ø30 mm, 2 m, steel (E = 200 GPa)segment 2: Ø20 mm, 0.5 m, brass (E = 100 GPa)
σmax = MPa

Answer key

  1. 1. σr = 41.75 MPa
  2. 2. σr = 74.17 MPa
  3. 3. P = 48.27 kN
  4. 4. δ = 0.0226 mm
  5. 5. Pmax = 488.4 kN
  6. 6. σmax = 238.7 MPa

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