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
100 kNØ40100 GPaØ100/50300 mmσr​ = ?

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

P = 100 kNrod: Ø40 mm, E = 200 GPatube: Ø100/Ø50 mm, E = 100 GPaL = 300 mm
σr = MPa
2.Easy
250 kNØ30110 GPaØ120/60600 mmσr​ = ?

A steel rod (diameter 30 mm, E = 200 GPa) sits inside a tube made of bronze (outer diameter 120 mm, inner diameter 60 mm, E = 110 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: Ø30 mm, E = 200 GPatube: Ø120/Ø60 mm, E = 110 GPaL = 600 mm
σr = MPa
3.Medium
150 kNØ25100 GPaØ80/60600 mmδ = ?

A steel rod (diameter 25 mm, E = 200 GPa) sits inside a tube made of brass (outer diameter 80 mm, inner diameter 60 mm, E = 100 GPa). Both are 600 mm long and are compressed together between rigid plates by 150 kN. Find the shortening δ.

P = 150 kNrod: Ø25 mm, E = 200 GPatube: Ø80/Ø60 mm, E = 100 GPaL = 600 mm
δ = mm
4.Medium
Ø 25 mmCopper1.5 mP = 45 kN

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

P = 45 kNd = 25 mmL = 1.5 mE = 117 GPa
ε = µε
5.Hard
20 kN12500 mm300 mmØ40Ø60σ2​ = ?

A steel segment (diameter 40 mm, length 500 mm, E = 200 GPa) and a segment made of bronze (diameter 60 mm, length 300 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, Ø40 mm, 500 mm, E = 200 GPasegment 2: bronze, Ø60 mm, 300 mm, E = 110 GPaP = 20 kN
σ2 = MPa
6.Hard
P = ?Ø25100 GPaØ120/70800 mm

A steel rod (diameter 25 mm, E = 200 GPa, allowable stress 250 MPa) sits inside a tube made of brass (outer diameter 120 mm, inner diameter 70 mm, E = 100 GPa, allowable stress 60 MPa). They are compressed together between rigid plates. Find the largest load Pmax.

rod: Ø25 mm, E = 200 GPa, σallow = 250 MPatube: Ø120/Ø70 mm, E = 100 GPa, σallow = 60 MPa
Pmax = kN

Answer key

  1. 1. σr = 23.8 MPa
  2. 2. σr = 46.54 MPa
  3. 3. δ = 0.2829 mm
  4. 4. ε = 783.5 µε
  5. 5. σ2 = 4.764 MPa
  6. 6. Pmax = 506.6 kN

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