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 mP = 90 kN

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

P = 90 kNd = 30 mm
σ = MPa
2.Easy
300 kNØ40100 GPaØ120/50300 mmσr​ = ?

A steel rod (diameter 40 mm, E = 200 GPa) sits inside a tube made of brass (outer diameter 120 mm, inner diameter 50 mm, E = 100 GPa). Both are 300 mm long and are compressed together between rigid plates by 300 kN. Find the compressive stress σr in the rod.

P = 300 kNrod: Ø40 mm, E = 200 GPatube: Ø120/Ø50 mm, E = 100 GPaL = 300 mm
σr = MPa
3.Medium
Ø 16 mmSteel1.5 mP = 60 kN

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

P = 60 kNd = 16 mmL = 1.5 mE = 200 GPa
ε = µε
4.Medium
P = ?12500 mm400 mmØ30Ø50δ = 0.5 mm

A bar is made of a steel segment (diameter 30 mm, length 500 mm, E = 200 GPa) joined end to end with a segment made of copper (diameter 50 mm, length 400 mm, E = 120 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, Ø30 mm, 500 mm, E = 200 GPasegment 2: copper, Ø50 mm, 400 mm, E = 120 GPaδ = 0.5 mm
P = kN
5.Hard
Ø 25 mmBrass1 mØ 16 mmSteel0.5 mP = 25 kN

The stepped bar is fixed at the wall and loaded at its free end. Find the largest normal stress σmax in the bar.

P = 25 kNsegment 1: Ø25 mm, 1 m, brass (E = 100 GPa)segment 2: Ø16 mm, 0.5 m, steel (E = 200 GPa)
σmax = MPa
6.Hard
60 kN12300 mm400 mmØ30Ø30σ2​ = ?

A steel segment (diameter 30 mm, length 300 mm, E = 200 GPa) and a segment made of bronze (diameter 30 mm, length 400 mm, E = 110 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, Ø30 mm, 300 mm, E = 200 GPasegment 2: bronze, Ø30 mm, 400 mm, E = 110 GPaP = 60 kN
σ2 = MPa

Answer key

  1. 1. σ = 127.3 MPa
  2. 2. σr = 50.59 MPa
  3. 3. ε = 1492 µε
  4. 4. P = 95.52 kN
  5. 5. σmax = 124.3 MPa
  6. 6. σ2 = 24.79 MPa

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