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 kNØ4070 GPaØ100/70800 mmσr​ = ?

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

P = 200 kNrod: Ø40 mm, E = 200 GPatube: Ø100/Ø70 mm, E = 70 GPaL = 800 mm
σr = MPa
2.Easy
300 kNØ30110 GPaØ80/50600 mmσr​ = ?

A steel rod (diameter 30 mm, E = 200 GPa) sits inside a tube made of bronze (outer diameter 80 mm, inner diameter 50 mm, E = 110 GPa). Both are 600 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: Ø80/Ø50 mm, E = 110 GPaL = 600 mm
σr = MPa
3.Medium
Ø 30 mmSteel2 mP = 50 kN

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

P = 50 kNd = 30 mmL = 2 mE = 200 GPa
δ = mm
4.Medium
Ø 12 mmCopper1.5 mP = 70 kN

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

P = 70 kNd = 12 mmL = 1.5 mE = 117 GPa
δ = mm
5.Hard
20 kN12400 mm500 mmØ40Ø40σ2​ = ?

A steel segment (diameter 40 mm, length 400 mm, E = 200 GPa) and a segment made of brass (diameter 40 mm, length 500 mm, E = 100 GPa) are joined end to end and fixed between two rigid walls. An axial load of 20 kN acts at the joint, towards segment 2. Find the magnitude of the stress σ2 in segment 2.

segment 1: steel, Ø40 mm, 400 mm, E = 200 GPasegment 2: brass, Ø40 mm, 500 mm, E = 100 GPaP = 20 kN
σ2 = MPa
6.Hard
P = ?Ø20100 GPaØ120/60300 mm

A steel rod (diameter 20 mm, E = 200 GPa, allowable stress 160 MPa) sits inside a tube made of brass (outer diameter 120 mm, inner diameter 60 mm, E = 100 GPa, allowable stress 60 MPa). They are compressed together between rigid plates. Find the largest load Pmax.

rod: Ø20 mm, E = 200 GPa, σallow = 160 MPatube: Ø120/Ø60 mm, E = 100 GPa, σallow = 60 MPa
Pmax = kN

Answer key

  1. 1. σr = 75.23 MPa
  2. 2. σr = 125.4 MPa
  3. 3. δ = 0.7074 mm
  4. 4. δ = 7.935 mm
  5. 5. σ2 = 4.547 MPa
  6. 6. Pmax = 546.6 kN

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