TORSION IN SOLID RECTANGULAR SECTIONS

Torsional stiffness constant, shear stress and angle of twist parameters of a solid rectangular section, which is under twisting moment, can be calculated with the following calculator. The calculator is only valid for solid rectangular sections. The formulas used for calculations are given in the "List of Equations" section.



Calculator:

Torsion in Rectangular Section
 INPUT PARAMETERS
Parameter Symbol Value Unit
Twisting Moment T
Width 2a
Height 2b
Section length L
Modulus of rigidity G

Note: Use dot "." as decimal separator.

 


 RESULTS
Parameter Symbol Value Unit
Maximum shear stress* τmax ---
Angle of twist θ ---
Torsional stiffness constant K ---

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.

List of Equations:

Step Parameter/Condition Symbol Equation
1 Angle of twist θ Equation for angle of twist for solid rectangle torsion
2 Maximum shear stress τmax Equation for maximum shear stress for solid rectangle torsion
3 Torsional stiffness constant Equation for torsional stiffness constant of solid rectangle

Symbol Parameter
T Twisting moment
K Torsional stiffness constant
2a Longer edge length
2b Shorter edge length
L Length of the beam
G Modulus of rigidity

Reference: