# TORSION IN SOLID SQUARE SECTIONS

Torsion calculator for solid square section under twisting moment.

### Torsion of Square Tube Calculator: INPUT PARAMETERS Parameter Value Twisting Moment [T] N*m lbf*in lbf*ft Width [2a] mm cm m inch ft Section length [L] Modulus of rigidity [G] GPa psi*10^6

Note: Use dot "." as decimal separator.

 RESULTS Parameter Value Maximum shear stress [τmax]* --- MPa psi Angle of twist [θ] --- Radian Degree Torsional stiffness constant [K] --- mm^4 cm^4 inch^4 ft^4

Note: *Maximum shear stress is at the midpoint of each longer side for a≥b.

### Definitions:

Angle of Twist: The angle through which a part of an object such as a shaft is rotated from its normal position when a torque is applied.

Modulus of rigidity (modulus of elasticity in shear): The rate of change of unit shear stress with respect to unit shear strain for the condition of pure shear within the proportional limit. Typical values Aluminum 6061-T6: 24 GPa, Structural Steel: 79.3 GPa.

### Formulas:

 Parameter Equation Angle of twist [θ] $$\theta =\frac { TL }{ KG }$$ Maximum shear stress [τ] $${ \tau }_{ max }=\frac { 0.601T }{ { a }^{ 3 } }$$ Torsional stiffness constant [K ] $$K=2.25{ a }^{ 4 }$$

T: Twisting moment, K: Torsional stiffness constant, 2a: Edge length, L: Length of the beam, G: Modulus of rigidity

### Reference:

• Young, W. C., Budynas, R. G.(2002). Roark's Formulas for Stress and Strain . 7nd Edition, McGraw-Hill, Chapter 10 , pp 401