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 20 mm0.5 mP = 55 kN

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

P = 55 kNd = 20 mm
σ = MPa
2.Easy
150 kNØ40110 GPaØ100/60800 mmσr​ = ?

A steel rod (diameter 40 mm, E = 200 GPa) sits inside a tube made of bronze (outer diameter 100 mm, inner diameter 60 mm, E = 110 GPa). Both are 800 mm long and are compressed together between rigid plates by 150 kN. Find the compressive stress σr in the rod.

P = 150 kNrod: Ø40 mm, E = 200 GPatube: Ø100/Ø60 mm, E = 110 GPaL = 800 mm
σr = MPa
3.Medium
P = ?12500 mm400 mmØ20Ø60δ = 0.25 mm

A bar is made of a steel segment (diameter 20 mm, length 500 mm, E = 200 GPa) joined end to end with a segment made of copper (diameter 60 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 0.25 mm in total.

segment 1: steel, Ø20 mm, 500 mm, E = 200 GPasegment 2: copper, Ø60 mm, 400 mm, E = 120 GPaδ = 0.25 mm
P = kN
4.Medium
P = ?12500 mm400 mmØ20Ø40δ = 0.4 mm

A bar is made of a steel segment (diameter 20 mm, length 500 mm, E = 200 GPa) joined end to end with a segment made of brass (diameter 40 mm, length 400 mm, E = 100 GPa). It is fixed at one end and pulled at the other. Find the axial load P that stretches it by 0.4 mm in total.

segment 1: steel, Ø20 mm, 500 mm, E = 200 GPasegment 2: brass, Ø40 mm, 400 mm, E = 100 GPaδ = 0.4 mm
P = kN
5.Hard
Ø 35 mmCopper1 mØ 16 mmCopper2 mP = 55 kN

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

P = 55 kNsegment 1: Ø35 mm, 1 m, copper (E = 117 GPa)segment 2: Ø16 mm, 2 m, copper (E = 117 GPa)
δ = mm
6.Hard
P = ?Ø3070 GPaØ80/60300 mm

A steel rod (diameter 30 mm, E = 200 GPa, allowable stress 250 MPa) sits inside a tube made of aluminium (outer diameter 80 mm, inner diameter 60 mm, E = 70 GPa, allowable stress 70 MPa). They are compressed together between rigid plates. Find the largest load Pmax.

rod: Ø30 mm, E = 200 GPa, σallow = 250 MPatube: Ø80/Ø60 mm, E = 70 GPa, σallow = 70 MPa
Pmax = kN

Answer key

  1. 1. σ = 175.1 MPa
  2. 2. σr = 37.3 MPa
  3. 3. P = 27.36 kN
  4. 4. P = 35.9 kN
  5. 5. δ = 5.165 mm
  6. 6. Pmax = 295.3 kN

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