Saint-Venant torsion of an elastic prismatic shaft

StaticPASS · 0%

Pure torsion of an elastic circular shaft fixed at one end and loaded by an axial torque at the free tip. Solved via Saint-Venant torsion theory where plane cross-sections remain planar (no out-of-plane warping for circular sections) and twist angle is linearl… show full text

Tolerance:: 5%

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Problem statement

Geometry: Solid circular shaft of radius R = 25 mm (diameter D = 50 mm), length L = 500 mm. Polar moment of inertia Jp = Jt = pi*R^4/2 = 613592.315 mm^4, cross-sectional area A = 1963.495 mm^2.
Material: Structural steel: Young's modulus E = 210000 MPa, Poisson's ratio nu = 0.3, shear modulus G = E / [2*(1+nu)] = 80769.23 MPa.
Boundary conditions: Root cross-section at x = 0 fully clamped (all 6 DOFs fixed). Free tip cross-section at x = L subjected to a twisting moment Mx = T = 500 N*m = 500000 N*mm.
Measured quantity: Free-end tip rotation theta_tip against closed-form Saint-Venant analytical solution: theta = T*L / (G*Jt) = 0.0050445 rad (0.28903 deg).

WebCAE Terminal

Paste these commands into the Terminal panel inside WebCAE. They use the same text DSL as the application; run one command per line:

units mm
frame up=z
material E=210000 nu=0.3
frame node at=0,0,0
frame node at=100,0,0
frame node at=200,0,0
frame node at=300,0,0
frame node at=400,0,0
frame node at=500,0,0
frame member 1 2 section=circle r=25
frame member 2 3 section=circle r=25
frame member 3 4 section=circle r=25
frame member 4 5 section=circle r=25
frame member 5 6 section=circle r=25
frame support node=1 dofs="all"
frame load node=6 moment=500000,0,0
frame solve static
frame probe rot node=6 comp=rx

Results comparison

Reference value	θ = 0.0050445 рад (0.28903°), τ_max = 20.37 МПа
Our result	θ = 0.0050445 рад (0.28903°)
Deviation	0%
Tolerance	5%
Status	PASS · 0%
Element family	Beam element
Mesh details	10 элементов, круглое сечение R=25 мм, L=500 мм, T=500 Н·м, G=80769.23 МПа, Jt=613592.32 мм⁴

Updated: 2026-10-19 · WebCAE solver