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 30 mm1.5 mP = 20 kN

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

P = 20 kNd = 30 mm
σ = MPa
2.Easy
250 kNØ2570 GPaØ120/60300 mmσr​ = ?

A steel rod (diameter 25 mm, E = 200 GPa) sits inside a tube made of aluminium (outer diameter 120 mm, inner diameter 60 mm, E = 70 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: Ø25 mm, E = 200 GPatube: Ø120/Ø60 mm, E = 70 GPaL = 300 mm
σr = MPa
3.Medium
Ø 16 mmSteel3 mP = 75 kN

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

P = 75 kNd = 16 mmL = 3 mE = 200 GPa
ε = µε
4.Medium
P = ?12600 mm500 mmØ25Ø60δ = 0.5 mm

A bar is made of a steel segment (diameter 25 mm, length 600 mm, E = 200 GPa) joined end to end with a segment made of bronze (diameter 60 mm, length 500 mm, E = 110 GPa). It is fixed at one end and pulled at the other. Find the axial load P that stretches it by 0.5 mm in total.

segment 1: steel, Ø25 mm, 600 mm, E = 200 GPasegment 2: bronze, Ø60 mm, 500 mm, E = 110 GPaδ = 0.5 mm
P = kN
5.Hard
P = ?Ø40100 GPaØ120/60400 mm

A steel rod (diameter 40 mm, E = 200 GPa, allowable stress 200 MPa) sits inside a tube made of brass (outer diameter 120 mm, inner diameter 60 mm, E = 100 GPa, allowable stress 70 MPa). They are compressed together between rigid plates. Find the largest load Pmax.

rod: Ø40 mm, E = 200 GPa, σallow = 200 MPatube: Ø120/Ø60 mm, E = 100 GPa, σallow = 70 MPa
Pmax = kN
6.Hard
P = ?Ø40110 GPaØ100/50300 mm

A steel rod (diameter 40 mm, E = 200 GPa, allowable stress 200 MPa) sits inside a tube made of bronze (outer diameter 100 mm, inner diameter 50 mm, E = 110 GPa, allowable stress 70 MPa). They are compressed together between rigid plates. Find the largest load Pmax.

rod: Ø40 mm, E = 200 GPa, σallow = 200 MPatube: Ø100/Ø50 mm, E = 110 GPa, σallow = 70 MPa
Pmax = kN

Answer key

  1. 1. σ = 28.29 MPa
  2. 2. σr = 72.26 MPa
  3. 3. ε = 1865 µε
  4. 4. P = 64.77 kN
  5. 5. Pmax = 769.7 kN
  6. 6. Pmax = 572.3 kN

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