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 16 mm1.5 mP = 35 kN

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

P = 35 kNd = 16 mm
σ = MPa
2.Easy
250 kNØ4070 GPaØ100/50500 mmσr​ = ?

A steel rod (diameter 40 mm, E = 200 GPa) sits inside a tube made of aluminium (outer diameter 100 mm, inner diameter 50 mm, E = 70 GPa). Both are 500 mm long and are compressed together between rigid plates by 250 kN. Find the compressive stress σr in the rod.

P = 250 kNrod: Ø40 mm, E = 200 GPatube: Ø100/Ø50 mm, E = 70 GPaL = 500 mm
σr = MPa
3.Medium
Ø 20 mmCopper3 mP = 110 kN

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

P = 110 kNd = 20 mmL = 3 mE = 117 GPa
δ = mm
4.Medium
Ø 30 mmBrass2 mP = 120 kN

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

P = 120 kNd = 30 mmL = 2 mE = 100 GPa
ε = µε
5.Hard
P = ?Ø40120 GPaØ120/50500 mm

A steel rod (diameter 40 mm, E = 200 GPa, allowable stress 250 MPa) sits inside a tube made of copper (outer diameter 120 mm, inner diameter 50 mm, E = 120 GPa, allowable stress 80 MPa). They are compressed together between rigid plates. Find the largest load Pmax.

rod: Ø40 mm, E = 200 GPa, σallow = 250 MPatube: Ø120/Ø50 mm, E = 120 GPa, σallow = 80 MPa
Pmax = kN
6.Hard
60 kN12400 mm300 mmØ40Ø30σ2​ = ?

A steel segment (diameter 40 mm, length 400 mm, E = 200 GPa) and a segment made of brass (diameter 30 mm, length 300 mm, E = 100 GPa) are joined end to end and fixed between two rigid walls. An axial load of 60 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, Ø30 mm, 300 mm, E = 100 GPaP = 60 kN
σ2 = MPa

Answer key

  1. 1. σ = 174.1 MPa
  2. 2. σr = 75.34 MPa
  3. 3. δ = 8.978 mm
  4. 4. ε = 1698 µε
  5. 5. Pmax = 915.3 kN
  6. 6. σ2 = 23.15 MPa

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