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 mm1.5 mP = 30 kN

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

P = 30 kNd = 30 mm
σ = MPa
2.Easy
250 kNØ2070 GPaØ120/70800 mmσr​ = ?

A steel rod (diameter 20 mm, E = 200 GPa) sits inside a tube made of aluminium (outer diameter 120 mm, inner diameter 70 mm, E = 70 GPa). Both are 800 mm long and are compressed together between rigid plates by 250 kN. Find the compressive stress σr in the rod.

P = 250 kNrod: Ø20 mm, E = 200 GPatube: Ø120/Ø70 mm, E = 70 GPaL = 800 mm
σr = MPa
3.Medium
Ø 30 mmBrass2.5 mP = 55 kN

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

P = 55 kNd = 30 mmL = 2.5 mE = 100 GPa
ε = µε
4.Medium
P = ?12500 mm500 mmØ20Ø40δ = 0.25 mm

A bar is made of a steel segment (diameter 20 mm, length 500 mm, E = 200 GPa) joined end to end with a segment made of brass (diameter 40 mm, length 500 mm, E = 100 GPa). It is fixed at one end and pulled at the other. Find the axial load P that stretches it by 0.25 mm in total.

segment 1: steel, Ø20 mm, 500 mm, E = 200 GPasegment 2: brass, Ø40 mm, 500 mm, E = 100 GPaδ = 0.25 mm
P = kN
5.Hard
P = ?Ø30110 GPaØ120/60400 mm

A steel rod (diameter 30 mm, E = 200 GPa, allowable stress 250 MPa) sits inside a tube made of bronze (outer diameter 120 mm, inner diameter 60 mm, E = 110 GPa, allowable stress 50 MPa). They are compressed together between rigid plates. Find the largest load Pmax.

rod: Ø30 mm, E = 200 GPa, σallow = 250 MPatube: Ø120/Ø60 mm, E = 110 GPa, σallow = 50 MPa
Pmax = kN
6.Hard
20 kN12300 mm400 mmØ30Ø50σ2​ = ?

A steel segment (diameter 30 mm, length 300 mm, E = 200 GPa) and a segment made of bronze (diameter 50 mm, length 400 mm, E = 110 GPa) are joined end to end and fixed between two rigid walls. An axial load of 20 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, Ø50 mm, 400 mm, E = 110 GPaP = 20 kN
σ2 = MPa

Answer key

  1. 1. σ = 42.44 MPa
  2. 2. σr = 85.45 MPa
  3. 3. ε = 778.1 µε
  4. 4. P = 20.94 kN
  5. 5. Pmax = 488.4 kN
  6. 6. σ2 = 5.439 MPa

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