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 kNØ25120 GPaØ100/60300 mmσr​ = ?

A steel rod (diameter 25 mm, E = 200 GPa) sits inside a tube made of copper (outer diameter 100 mm, inner diameter 60 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: Ø25 mm, E = 200 GPatube: Ø100/Ø60 mm, E = 120 GPaL = 300 mm
σr = MPa
2.Easy
Ø 10 mm1.5 mP = 75 kN

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

P = 75 kNd = 10 mm
σ = MPa
3.Medium
Ø 20 mmSteel1.5 mP = 75 kN

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

P = 75 kNd = 20 mmL = 1.5 mE = 200 GPa
ε = µε
4.Medium
200 kNØ25100 GPaØ100/60500 mmδ = ?

A steel rod (diameter 25 mm, E = 200 GPa) sits inside a tube made of brass (outer diameter 100 mm, inner diameter 60 mm, E = 100 GPa). Both are 500 mm long and are compressed together between rigid plates by 200 kN. Find the shortening δ.

P = 200 kNrod: Ø25 mm, E = 200 GPatube: Ø100/Ø60 mm, E = 100 GPaL = 500 mm
δ = mm
5.Hard
80 kN12400 mm300 mmØ30Ø40σ2​ = ?

A steel segment (diameter 30 mm, length 400 mm, E = 200 GPa) and a segment made of copper (diameter 40 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, Ø30 mm, 400 mm, E = 200 GPasegment 2: copper, Ø40 mm, 300 mm, E = 120 GPaP = 80 kN
σ2 = MPa
6.Hard
Ø 25 mmBrass0.5 mØ 16 mmSteel1 mP = 120 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 = 120 kNsegment 1: Ø25 mm, 0.5 m, brass (E = 100 GPa)segment 2: Ø16 mm, 1 m, steel (E = 200 GPa)
σmax = MPa

Answer key

  1. 1. σr = 71.29 MPa
  2. 2. σ = 954.9 MPa
  3. 3. ε = 1194 µε
  4. 4. δ = 0.1664 mm
  5. 5. σ2 = 37.38 MPa
  6. 6. σmax = 596.8 MPa

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