SLL 04: torsion on a stepped cantilever


Material Modulus of elasticity G=80 000 N/mm^2
Geometry Cross-section For bar AB ⌀ 80mm
For bar BC ⌀ 60mm
For bar CD ⌀ 40mm
Boundary conditions Point A Fixed support
Loads In point B M_x=3 kNm
In point C M_x=2 kNm
In point D M_x=0.8 kNm
Mesh No. of divisions 8



    \[I_{t.AB}=\frac{\pi \cdot D^4}{32}=\frac{\pi \cdot (80mm)^4}{32}=4.021 \cdot 10^6mm^4\]

    \[I_{t.BC}=\frac{\pi \cdot D^4}{32}=\frac{\pi \cdot (60mm)^4}{32}=1.272 \cdot 10^6mm^4\]

    \[I_{t.CD}=\frac{\pi \cdot D^4}{32}=\frac{\pi \cdot (40mm)^4}{32}=0.251 \cdot 10^6mm^4\]

    \[\varphi_{x.B}=\frac{L \cdot (M_{x.B}+M_{x.C}+M_{x.D})}{I_{t.AB} \cdot G}=\frac{0.5m \cdot (5.8kNm)}{4.021 \cdot 10^6mm^4 \cdot 80000N/mm^2}=0.000009rad\]

    \[\varphi_{x.C}=\varphi_{x.B}+\frac{L \cdot (M_{x.C}+M_{x.D})}{I_{t.BC} \cdot G}=0.000009rad+\frac{0.5m \cdot (3.8kNm)}{1.272 \cdot 10^6mm^4 \cdot 80000N/mm^2}=0.000023rad\]

    \[\varphi_{x.D}=\varphi_{x.B}+\varphi_{x.C}+\frac{L \cdot M_{x.D}}{I_{t.CD} \cdot G}=0.000009rad+0.000023rad+\frac{0.5m \cdot (3.8kNm)}{0.251 \cdot 10^6mm^4 \cdot 80000N/mm^2}=0.000043rad\]

Angle of twist \varphi_x in Diamonds

Point Which result Independent reference Diamonds Difference
B Angle of twist \varphi_x 0.000009rad 0.000009rad 0%
C Angle of twist \varphi_x 0.000023rad 0.000023rad 0%
D Angle of twist \varphi_x 0.000043rad 0.000043rad 0%


  • Hibbeler, R. (2006). Sterkteleer, 2/e. Pearson Education.

    Gere J. M., and Timoshenko, S. P., Mechanics of Materials, 2nd Edition, PWS Engineering, Page 171, Problem 3.3 – 1

  • Tested in Diamonds 2023r01.

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