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
250 kNØ30120 GPaØ120/70300 mmσr​ = ?

A steel rod (diameter 30 mm, E = 200 GPa) sits inside a tube made of copper (outer diameter 120 mm, inner diameter 70 mm, E = 120 GPa). Both are 300 mm long and are compressed together between rigid plates by 250 kN. Find the compressive stress σr in the rod.

P = 250 kNrod: Ø30 mm, E = 200 GPatube: Ø120/Ø70 mm, E = 120 GPaL = 300 mm
σr = MPa
2.Easy
80 kNØ4070 GPaØ80/60600 mmσr​ = ?

A steel rod (diameter 40 mm, E = 200 GPa) sits inside a tube made of aluminium (outer diameter 80 mm, inner diameter 60 mm, E = 70 GPa). Both are 600 mm long and are compressed together between rigid plates by 80 kN. Find the compressive stress σr in the rod.

P = 80 kNrod: Ø40 mm, E = 200 GPatube: Ø80/Ø60 mm, E = 70 GPaL = 600 mm
σr = MPa
3.Medium
150 kNØ30100 GPaØ100/50300 mmδ = ?

A steel rod (diameter 30 mm, E = 200 GPa) sits inside a tube made of brass (outer diameter 100 mm, inner diameter 50 mm, E = 100 GPa). Both are 300 mm long and are compressed together between rigid plates by 150 kN. Find the shortening δ.

P = 150 kNrod: Ø30 mm, E = 200 GPatube: Ø100/Ø50 mm, E = 100 GPaL = 300 mm
δ = mm
4.Medium
Ø 12 mmAluminium2.5 mP = 50 kN

Find the axial strain ε in the aluminium bar, in microstrain (µε = 10⁻⁶).

P = 50 kNd = 12 mmL = 2.5 mE = 70 GPa
ε = µε
5.Hard
P = ?Ø4070 GPaØ120/50400 mm

A steel rod (diameter 40 mm, E = 200 GPa, allowable stress 120 MPa) sits inside a tube made of aluminium (outer diameter 120 mm, inner diameter 50 mm, E = 70 GPa, allowable stress 60 MPa). They are compressed together between rigid plates. Find the largest load Pmax.

rod: Ø40 mm, E = 200 GPa, σallow = 120 MPatube: Ø120/Ø50 mm, E = 70 GPa, σallow = 60 MPa
Pmax = kN
6.Hard
80 kN12300 mm300 mmØ25Ø50σ2​ = ?

A steel segment (diameter 25 mm, length 300 mm, E = 200 GPa) and a segment made of copper (diameter 50 mm, length 300 mm, E = 120 GPa) are joined end to end and fixed between two rigid walls. An axial load of 80 kN acts at the joint, towards segment 2. Find the magnitude of the stress σ2 in segment 2.

segment 1: steel, Ø25 mm, 300 mm, E = 200 GPasegment 2: copper, Ø50 mm, 300 mm, E = 120 GPaP = 80 kN
σ2 = MPa

Answer key

  1. 1. σr = 48.23 MPa
  2. 2. σr = 39.48 MPa
  3. 3. δ = 0.06161 mm
  4. 4. ε = 6316 µε
  5. 5. Pmax = 543.3 kN
  6. 6. σ2 = 28.76 MPa

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