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
250 kNØ30100 GPaØ100/70800 mmσr​ = ?

A steel rod (diameter 30 mm, E = 200 GPa) sits inside a tube made of brass (outer diameter 100 mm, inner diameter 70 mm, E = 100 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: Ø30 mm, E = 200 GPatube: Ø100/Ø70 mm, E = 100 GPaL = 800 mm
σr = MPa
2.Easy
Ø 25 mm1.5 mP = 20 kN

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

P = 20 kNd = 25 mm
σ = MPa
3.Medium
Ø 30 mmSteel2.5 mP = 105 kN

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

P = 105 kNd = 30 mmL = 2.5 mE = 200 GPa
ε = µε
4.Medium
Ø 12 mmAluminium0.5 mP = 25 kN

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

P = 25 kNd = 12 mmL = 0.5 mE = 70 GPa
δ = mm
5.Hard
20 kN12300 mm400 mmØ40Ø60σ2​ = ?

A steel segment (diameter 40 mm, length 300 mm, E = 200 GPa) and a segment made of brass (diameter 60 mm, length 400 mm, E = 100 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, 300 mm, E = 200 GPasegment 2: brass, Ø60 mm, 400 mm, E = 100 GPaP = 20 kN
σ2 = MPa
6.Hard
P = ?Ø3070 GPaØ80/50800 mm

A steel rod (diameter 30 mm, E = 200 GPa, allowable stress 160 MPa) sits inside a tube made of aluminium (outer diameter 80 mm, inner diameter 50 mm, E = 70 GPa, allowable stress 60 MPa). They are compressed together between rigid plates. Find the largest load Pmax.

rod: Ø30 mm, E = 200 GPa, σallow = 160 MPatube: Ø80/Ø50 mm, E = 70 GPa, σallow = 60 MPa
Pmax = kN

Answer key

  1. 1. σr = 92.26 MPa
  2. 2. σ = 40.74 MPa
  3. 3. ε = 742.7 µε
  4. 4. δ = 1.579 mm
  5. 5. σ2 = 3.237 MPa
  6. 6. Pmax = 284.6 kN

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