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
200 kNØ25110 GPaØ120/50600 mmσr​ = ?

A steel rod (diameter 25 mm, E = 200 GPa) sits inside a tube made of bronze (outer diameter 120 mm, inner diameter 50 mm, E = 110 GPa). Both are 600 mm long and are compressed together between rigid plates by 200 kN. Find the compressive stress σr in the rod.

P = 200 kNrod: Ø25 mm, E = 200 GPatube: Ø120/Ø50 mm, E = 110 GPaL = 600 mm
σr = MPa
2.Easy
200 kNØ30120 GPaØ100/50600 mmσr​ = ?

A steel rod (diameter 30 mm, E = 200 GPa) sits inside a tube made of copper (outer diameter 100 mm, inner diameter 50 mm, E = 120 GPa). Both are 600 mm long and are compressed together between rigid plates by 200 kN. Find the compressive stress σr in the rod.

P = 200 kNrod: Ø30 mm, E = 200 GPatube: Ø100/Ø50 mm, E = 120 GPaL = 600 mm
σr = MPa
3.Medium
P = ?12500 mm400 mmØ25Ø50δ = 0.5 mm

A bar is made of a steel segment (diameter 25 mm, length 500 mm, E = 200 GPa) joined end to end with a segment made of copper (diameter 50 mm, length 400 mm, E = 120 GPa). It is fixed at one end and pulled at the other. Find the axial load P that stretches it by 0.5 mm in total.

segment 1: steel, Ø25 mm, 500 mm, E = 200 GPasegment 2: copper, Ø50 mm, 400 mm, E = 120 GPaδ = 0.5 mm
P = kN
4.Medium
Ø 30 mmBrass2 mP = 10 kN

Find the axial strain ε in the brass bar, in microstrain (µε = 10⁻⁶).

P = 10 kNd = 30 mmL = 2 mE = 100 GPa
ε = µε
5.Hard
P = ?Ø40110 GPaØ100/50800 mm

A steel rod (diameter 40 mm, E = 200 GPa, allowable stress 200 MPa) sits inside a tube made of bronze (outer diameter 100 mm, inner diameter 50 mm, E = 110 GPa, allowable stress 60 MPa). They are compressed together between rigid plates. Find the largest load Pmax.

rod: Ø40 mm, E = 200 GPa, σallow = 200 MPatube: Ø100/Ø50 mm, E = 110 GPa, σallow = 60 MPa
Pmax = kN
6.Hard
P = ?Ø20100 GPaØ100/50500 mm

A steel rod (diameter 20 mm, E = 200 GPa, allowable stress 250 MPa) sits inside a tube made of brass (outer diameter 100 mm, inner diameter 50 mm, E = 100 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/Ø50 mm, E = 100 GPa, σallow = 70 MPa
Pmax = kN

Answer key

  1. 1. σr = 35.52 MPa
  2. 2. σr = 47.16 MPa
  3. 3. P = 73.63 kN
  4. 4. ε = 141.5 µε
  5. 5. Pmax = 490.5 kN
  6. 6. Pmax = 456.3 kN

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