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
300 kNØ30100 GPaØ100/70300 mmσr​ = ?

A steel rod (diameter 30 mm, E = 200 GPa) sits inside a tube made of brass (outer diameter 100 mm, inner diameter 70 mm, E = 100 GPa). Both are 300 mm long and are compressed together between rigid plates by 300 kN. Find the compressive stress σr in the rod.

P = 300 kNrod: Ø30 mm, E = 200 GPatube: Ø100/Ø70 mm, E = 100 GPaL = 300 mm
σr = MPa
2.Easy
Ø 20 mm0.5 mP = 40 kN

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

P = 40 kNd = 20 mm
σ = MPa
3.Medium
P = ?12300 mm300 mmØ20Ø60δ = 0.2 mm

A bar is made of a steel segment (diameter 20 mm, length 300 mm, E = 200 GPa) joined end to end with a segment made of bronze (diameter 60 mm, length 300 mm, E = 110 GPa). It is fixed at one end and pulled at the other. Find the axial load P that stretches it by 0.2 mm in total.

segment 1: steel, Ø20 mm, 300 mm, E = 200 GPasegment 2: bronze, Ø60 mm, 300 mm, E = 110 GPaδ = 0.2 mm
P = kN
4.Medium
50 kNØ30100 GPaØ120/60300 mmδ = ?

A steel rod (diameter 30 mm, E = 200 GPa) sits inside a tube made of brass (outer diameter 120 mm, inner diameter 60 mm, E = 100 GPa). Both are 300 mm long and are compressed together between rigid plates by 50 kN. Find the shortening δ.

P = 50 kNrod: Ø30 mm, E = 200 GPatube: Ø120/Ø60 mm, E = 100 GPaL = 300 mm
δ = mm
5.Hard
P = ?Ø30120 GPaØ100/70600 mm

A steel rod (diameter 30 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 50 MPa). They are compressed together between rigid plates. Find the largest load Pmax.

rod: Ø30 mm, E = 200 GPa, σallow = 250 MPatube: Ø100/Ø70 mm, E = 120 GPa, σallow = 50 MPa
Pmax = kN
6.Hard
Ø 40 mmBrass1 mØ 16 mmAluminium1.5 mP = 30 kN

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

P = 30 kNsegment 1: Ø40 mm, 1 m, brass (E = 100 GPa)segment 2: Ø16 mm, 1.5 m, aluminium (E = 70 GPa)
δ = mm

Answer key

  1. 1. σr = 110.7 MPa
  2. 2. σ = 127.3 MPa
  3. 3. P = 34.85 kN
  4. 4. δ = 0.01516 mm
  5. 5. Pmax = 259.2 kN
  6. 6. δ = 3.436 mm

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