# TORSION IN SOLID RECTANGULAR SECTIONS AND BARS

Torsion calculator finds torsional stiffness constant, shear stress and angle of twist parameters of a solid rectangular cross section, which is under twisting moment. The calculator is only valid for solid rectangular cross sections and bars. The formulas used for calculations are given in the "List of Equations" section.

### Torsion Calculator:

 INPUT PARAMETERS Parameter Value Twisting Moment [T] N*m lbf*in lbf*ft Width [2a] mm cm m inch ft Height [2b] 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.

### List of Equations:

 Equation $$\theta =\frac { TL }{ KG }$$ $${ \tau }_{ max }=\frac { 3T }{ 8a{ b }^{ 2 } } \left[ 1+0.6095\frac { b }{ a } +0.8865{ (\frac { b }{ a } ) }^{ 2 }-1.8023{ (\frac { b }{ a } ) }^{ 3 }+0.9100{ (\frac { b }{ a } ) }^{ 4 } \right]$$ $$K=a{ b }^{ 3 }\left[ \frac { 16 }{ 3 } -3.36\frac { b }{ a } (1-\frac { { b }^{ 4 } }{ { 12a }^{ 4 } } ) \right] \quad for\quad a\ge b$$

 Symbol Parameter θ Angle of twist τmax Maximum shear stress T Twisting moment K Torsional stiffness constant 2a Longer edge length 2b Shorter edge length L Length of the beam G Modulus of rigidity