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 steel rod (diameter 25 mm, E = 200 GPa) sits inside a tube made of bronze (outer diameter 100 mm, inner diameter 50 mm, E = 110 GPa). Both are 300 mm long and are compressed together between rigid plates by 100 kN. Find the compressive stress σ_r in the rod.

P = 100 kNrod: Ø25 mm, E = 200 GPatube: Ø100/Ø50 mm, E = 110 GPaL = 300 mm

σ_r = MPa

2.Easy

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 800 mm long and are compressed together between rigid plates by 100 kN. Find the compressive stress σ_r in the rod.

P = 100 kNrod: Ø40 mm, E = 200 GPatube: Ø100/Ø50 mm, E = 100 GPaL = 800 mm

σ_r = MPa

3.Medium

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

P = 40 kNd = 30 mmL = 1 mE = 200 GPa

ε = µε

4.Medium

A bar is made of a steel segment (diameter 30 mm, length 600 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 0.5 mm in total.

segment 1: steel, Ø30 mm, 600 mm, E = 200 GPasegment 2: brass, Ø40 mm, 500 mm, E = 100 GPaδ = 0.5 mm

P = kN

5.Hard

A steel rod (diameter 20 mm, E = 200 GPa, allowable stress 120 MPa) sits inside a tube made of aluminium (outer diameter 80 mm, inner diameter 50 mm, E = 70 GPa, allowable stress 80 MPa). They are compressed together between rigid plates. Find the largest load P_max.

rod: Ø20 mm, E = 200 GPa, σ_allow = 120 MPatube: Ø80/Ø50 mm, E = 70 GPa, σ_allow = 80 MPa

P_max = kN

6.Hard

A steel segment (diameter 40 mm, length 300 mm, E = 200 GPa) and a segment made of copper (diameter 60 mm, length 500 mm, E = 120 GPa) are joined end to end and fixed between two rigid walls. An axial load of 30 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: copper, Ø60 mm, 500 mm, E = 120 GPaP = 30 kN

σ₂ = MPa

Answer key

1. σ_r = 26.81 MPa
2. σ_r = 23.8 MPa
3. ε = 282.9 µε
4. P = 60.81 kN
5. P_max = 166.3 kN
6. σ₂ = 4.748 MPa

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