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

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

P = 50 kNd = 12 mm

σ = MPa

2.Easy

A steel rod (diameter 20 mm, E = 200 GPa) sits inside a tube made of aluminium (outer diameter 120 mm, inner diameter 50 mm, E = 70 GPa). Both are 400 mm long and are compressed together between rigid plates by 50 kN. Find the compressive stress σ_r in the rod.

P = 50 kNrod: Ø20 mm, E = 200 GPatube: Ø120/Ø50 mm, E = 70 GPaL = 400 mm

σ_r = MPa

3.Medium

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

P = 50 kNd = 16 mmL = 1 mE = 117 GPa

δ = mm

4.Medium

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

P = 45 kNd = 12 mmL = 0.5 mE = 100 GPa

ε = µε

5.Hard

The stepped bar is fixed at the wall and loaded at its free end. Find the total elongation δ.

P = 25 kNsegment 1: Ø40 mm, 1 m, copper (E = 117 GPa)segment 2: Ø20 mm, 2 m, steel (E = 200 GPa)

δ = mm

6.Hard

A steel segment (diameter 25 mm, length 400 mm, E = 200 GPa) and a segment made of bronze (diameter 50 mm, length 500 mm, E = 110 GPa) are joined end to end and fixed between two rigid walls. An axial load of 100 kN acts at the joint, towards segment 2. Find the magnitude of the stress σ₂ in segment 2.

segment 1: steel, Ø25 mm, 400 mm, E = 200 GPasegment 2: bronze, Ø50 mm, 500 mm, E = 110 GPaP = 100 kN

σ₂ = MPa

Answer key

1. σ = 442.1 MPa
2. σ_r = 13.95 MPa
3. δ = 2.125 mm
4. ε = 3979 µε
5. δ = 0.9658 mm
6. σ₂ = 32.48 MPa

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