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V1.6 — Torsion and bending of a shaft with an offset load

A circular shaft with a transverse load applied through a rigid offset arm, producing combined bending and torsion in the shaft — a check that a frame member's torsional and flexural stiffness are both correct and act independently.

Time
About 5 minutes
Level
All levels
You'll need
None — this is a reference document
You're done when
You can see how V1.6 compares to its reference
On this page
  1. Description
  2. Reference
  3. Model
  4. Comparison
  5. Conclusion

← Verification — Linear (Frames & Trusses)

V1.6 — Torsion and bending of a shaft with an offset load

Exact

Description

A circular shaft with a transverse load applied through a rigid offset arm, producing combined bending and torsion in the shaft — a check that a frame member's torsional and flexural stiffness are both correct and act independently.

Reference

Combined bending + torsion of a circular shaft (closed form): w = FL³/(3EI) + Fa²L/(GJ), T = Fa.

Model

An elastic circular-section frame member (the shaft), fixed at its base, with a rigid arm offset from the shaft axis. A transverse load applied at the end of the arm produces both a bending moment and a torque on the shaft at the same time.

Load, F10 kip
Shaft length, L120 in
Arm offset, a24 in
Shaft diameter, D12 in
Elastic modulus, E29,000 ksi
Poisson's ratio, ν0.3
Shear modulus, G11,153.8 ksi

Comparison

QuantityReferencevfopro% diffStatus
Arm-end vertical displacement (in)-0.2256-0.2256-0.00%Exact
Shaft torque, end i (kip-in)2402400.00%Exact
Base vertical reaction (kip)10100.00%Exact
Base bending moment (kip-in)-1,200-1,2000.00%Exact

Conclusion

Every reported quantity matched the closed-form value to at least 6 significant figures.

Last updated September 22, 2026 · applies to vfopro 20260922.0.0 or later