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 12 mm1 mP = 55 kN

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

P = 55 kNd = 12 mm
σ = MPa
2.Easy
250 kNØ40120 GPaØ100/50600 mmσr​ = ?

A steel rod (diameter 40 mm, E = 200 GPa) sits inside a tube made of copper (outer diameter 100 mm, inner diameter 50 mm, E = 120 GPa). Both are 600 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 = 120 GPaL = 600 mm
σr = MPa
3.Medium
Ø 16 mmSteel3 mP = 45 kN

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

P = 45 kNd = 16 mmL = 3 mE = 200 GPa
δ = mm
4.Medium
50 kNØ25100 GPaØ120/50300 mmδ = ?

A steel rod (diameter 25 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 50 kN. Find the shortening δ.

P = 50 kNrod: Ø25 mm, E = 200 GPatube: Ø120/Ø50 mm, E = 100 GPaL = 300 mm
δ = mm
5.Hard
Ø 35 mmAluminium1.5 mØ 12 mmSteel1.5 mP = 10 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 = 10 kNsegment 1: Ø35 mm, 1.5 m, aluminium (E = 70 GPa)segment 2: Ø12 mm, 1.5 m, steel (E = 200 GPa)
σmax = MPa
6.Hard
40 kN12500 mm200 mmØ30Ø30σ2​ = ?

A steel segment (diameter 30 mm, length 500 mm, E = 200 GPa) and a segment made of copper (diameter 30 mm, length 200 mm, E = 120 GPa) are joined end to end and fixed between two rigid walls. An axial load of 40 kN acts at the joint, towards segment 2. Find the magnitude of the stress σ2 in segment 2.

segment 1: steel, Ø30 mm, 500 mm, E = 200 GPasegment 2: copper, Ø30 mm, 200 mm, E = 120 GPaP = 40 kN
σ2 = MPa

Answer key

  1. 1. σ = 486.3 MPa
  2. 2. σr = 52.18 MPa
  3. 3. δ = 3.357 mm
  4. 4. δ = 0.01452 mm
  5. 5. σmax = 88.42 MPa
  6. 6. σ2 = 33.95 MPa

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