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
200 kNØ40110 GPaØ80/50600 mmσr​ = ?

A steel rod (diameter 40 mm, E = 200 GPa) sits inside a tube made of bronze (outer diameter 80 mm, inner diameter 50 mm, E = 110 GPa). Both are 600 mm long and are compressed together between rigid plates by 200 kN. Find the compressive stress σr in the rod.

P = 200 kNrod: Ø40 mm, E = 200 GPatube: Ø80/Ø50 mm, E = 110 GPaL = 600 mm
σr = MPa
2.Easy
Ø 30 mm1.5 mP = 85 kN

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

P = 85 kNd = 30 mm
σ = MPa
3.Medium
Ø 30 mmBrass3 mP = 110 kN

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

P = 110 kNd = 30 mmL = 3 mE = 100 GPa
ε = µε
4.Medium
Ø 10 mmSteel0.5 mP = 95 kN

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

P = 95 kNd = 10 mmL = 0.5 mE = 200 GPa
δ = mm
5.Hard
P = ?Ø25110 GPaØ120/60400 mm

A steel rod (diameter 25 mm, E = 200 GPa, allowable stress 150 MPa) sits inside a tube made of bronze (outer diameter 120 mm, inner diameter 60 mm, E = 110 GPa, allowable stress 100 MPa). They are compressed together between rigid plates. Find the largest load Pmax.

rod: Ø25 mm, E = 200 GPa, σallow = 150 MPatube: Ø120/Ø60 mm, E = 110 GPa, σallow = 100 MPa
Pmax = kN
6.Hard
80 kN12400 mm400 mmØ20Ø60σ2​ = ?

A steel segment (diameter 20 mm, length 400 mm, E = 200 GPa) and a segment made of bronze (diameter 60 mm, length 400 mm, E = 110 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, Ø20 mm, 400 mm, E = 200 GPasegment 2: bronze, Ø60 mm, 400 mm, E = 110 GPaP = 80 kN
σ2 = MPa

Answer key

  1. 1. σr = 68 MPa
  2. 2. σ = 120.3 MPa
  3. 3. ε = 1556 µε
  4. 4. δ = 3.024 mm
  5. 5. Pmax = 773.4 kN
  6. 6. σ2 = 23.54 MPa

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