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 = 55 kN

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

P = 55 kNd = 30 mm
σ = MPa
2.Easy
150 kNØ30110 GPaØ80/50400 mmσr​ = ?

A steel rod (diameter 30 mm, E = 200 GPa) sits inside a tube made of bronze (outer diameter 80 mm, inner diameter 50 mm, E = 110 GPa). Both are 400 mm long and are compressed together between rigid plates by 150 kN. Find the compressive stress σr in the rod.

P = 150 kNrod: Ø30 mm, E = 200 GPatube: Ø80/Ø50 mm, E = 110 GPaL = 400 mm
σr = MPa
3.Medium
P = ?12400 mm400 mmØ30Ø60δ = 0.5 mm

A bar is made of a steel segment (diameter 30 mm, length 400 mm, E = 200 GPa) joined end to end with a segment made of aluminium (diameter 60 mm, length 400 mm, E = 70 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, 400 mm, E = 200 GPasegment 2: aluminium, Ø60 mm, 400 mm, E = 70 GPaδ = 0.5 mm
P = kN
4.Medium
Ø 30 mmAluminium0.5 mP = 60 kN

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

P = 60 kNd = 30 mmL = 0.5 mE = 70 GPa
δ = mm
5.Hard
P = ?Ø4070 GPaØ80/50500 mm

A steel rod (diameter 40 mm, E = 200 GPa, allowable stress 120 MPa) sits inside a tube made of aluminium (outer diameter 80 mm, inner diameter 50 mm, E = 70 GPa, allowable stress 80 MPa). They are compressed together between rigid plates. Find the largest load Pmax.

rod: Ø40 mm, E = 200 GPa, σallow = 120 MPatube: Ø80/Ø50 mm, E = 70 GPa, σallow = 80 MPa
Pmax = kN
6.Hard
P = ?Ø4070 GPaØ120/70400 mm

A steel rod (diameter 40 mm, E = 200 GPa, allowable stress 160 MPa) sits inside a tube made of aluminium (outer diameter 120 mm, inner diameter 70 mm, E = 70 GPa, allowable stress 100 MPa). They are compressed together between rigid plates. Find the largest load Pmax.

rod: Ø40 mm, E = 200 GPa, σallow = 160 MPatube: Ø120/Ø70 mm, E = 70 GPa, σallow = 100 MPa
Pmax = kN

Answer key

  1. 1. σ = 77.81 MPa
  2. 2. σr = 62.72 MPa
  3. 3. P = 103.1 kN
  4. 4. δ = 0.6063 mm
  5. 5. Pmax = 279.4 kN
  6. 6. Pmax = 618.9 kN

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