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 mm1 mP = 20 kN

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

P = 20 kNd = 20 mm
σ = MPa
2.Easy
150 kNØ25110 GPaØ120/70600 mmσr​ = ?

A steel rod (diameter 25 mm, E = 200 GPa) sits inside a tube made of bronze (outer diameter 120 mm, inner diameter 70 mm, E = 110 GPa). Both are 600 mm long and are compressed together between rigid plates by 150 kN. Find the compressive stress σr in the rod.

P = 150 kNrod: Ø25 mm, E = 200 GPatube: Ø120/Ø70 mm, E = 110 GPaL = 600 mm
σr = MPa
3.Medium
200 kNØ30110 GPaØ80/60300 mmδ = ?

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 200 kN. Find the shortening δ.

P = 200 kNrod: Ø30 mm, E = 200 GPatube: Ø80/Ø60 mm, E = 110 GPaL = 300 mm
δ = mm
4.Medium
250 kNØ20110 GPaØ120/60400 mmδ = ?

A steel rod (diameter 20 mm, E = 200 GPa) sits inside a tube made of bronze (outer diameter 120 mm, inner diameter 60 mm, E = 110 GPa). Both are 400 mm long and are compressed together between rigid plates by 250 kN. Find the shortening δ.

P = 250 kNrod: Ø20 mm, E = 200 GPatube: Ø120/Ø60 mm, E = 110 GPaL = 400 mm
δ = mm
5.Hard
Ø 40 mmSteel1 mØ 12 mmBrass0.5 mP = 15 kN

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

P = 15 kNsegment 1: Ø40 mm, 1 m, steel (E = 200 GPa)segment 2: Ø12 mm, 0.5 m, brass (E = 100 GPa)
δ = mm
6.Hard
P = ?Ø20120 GPaØ100/60800 mm

A steel rod (diameter 20 mm, E = 200 GPa, allowable stress 250 MPa) sits inside a tube made of copper (outer diameter 100 mm, inner diameter 60 mm, E = 120 GPa, allowable stress 80 MPa). They are compressed together between rigid plates. Find the largest load Pmax.

rod: Ø20 mm, E = 200 GPa, σallow = 250 MPatube: Ø100/Ø60 mm, E = 120 GPa, σallow = 80 MPa
Pmax = kN

Answer key

  1. 1. σ = 63.66 MPa
  2. 2. σr = 32.65 MPa
  3. 3. δ = 0.1565 mm
  4. 4. δ = 0.1004 mm
  5. 5. δ = 0.7228 mm
  6. 6. Pmax = 444 kN

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