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 kNØ20120 GPaØ80/50500 mmσr​ = ?

A steel rod (diameter 20 mm, E = 200 GPa) sits inside a tube made of copper (outer diameter 80 mm, inner diameter 50 mm, E = 120 GPa). Both are 500 mm long and are compressed together between rigid plates by 80 kN. Find the compressive stress σr in the rod.

P = 80 kNrod: Ø20 mm, E = 200 GPatube: Ø80/Ø50 mm, E = 120 GPaL = 500 mm
σr = MPa
2.Easy
50 kNØ40120 GPaØ100/70800 mmσr​ = ?

A steel rod (diameter 40 mm, E = 200 GPa) sits inside a tube made of copper (outer diameter 100 mm, inner diameter 70 mm, E = 120 GPa). Both are 800 mm long and are compressed together between rigid plates by 50 kN. Find the compressive stress σr in the rod.

P = 50 kNrod: Ø40 mm, E = 200 GPatube: Ø100/Ø70 mm, E = 120 GPaL = 800 mm
σr = MPa
3.Medium
Ø 25 mmSteel1 mP = 85 kN

Find the elongation δ of the steel bar under the axial load.

P = 85 kNd = 25 mmL = 1 mE = 200 GPa
δ = mm
4.Medium
50 kNØ40100 GPaØ100/70300 mmδ = ?

A steel rod (diameter 40 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 50 kN. Find the shortening δ.

P = 50 kNrod: Ø40 mm, E = 200 GPatube: Ø100/Ø70 mm, E = 100 GPaL = 300 mm
δ = mm
5.Hard
P = ?Ø30100 GPaØ100/70500 mm

A steel rod (diameter 30 mm, E = 200 GPa, allowable stress 250 MPa) sits inside a tube made of brass (outer diameter 100 mm, inner diameter 70 mm, E = 100 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: Ø100/Ø70 mm, E = 100 GPa, σallow = 70 MPa
Pmax = kN
6.Hard
Ø 40 mmSteel0.5 mØ 16 mmBrass1 mP = 95 kN

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

P = 95 kNsegment 1: Ø40 mm, 0.5 m, steel (E = 200 GPa)segment 2: Ø16 mm, 1 m, brass (E = 100 GPa)
δ = mm

Answer key

  1. 1. σr = 37.17 MPa
  2. 2. σr = 13.66 MPa
  3. 3. δ = 0.8658 mm
  4. 4. δ = 0.02301 mm
  5. 5. Pmax = 379.3 kN
  6. 6. δ = 4.914 mm

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