# TORSION IN SOLID RECTANGULAR SECTIONS AND BARS

Torsion calculator for 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.

### Torsion in Solid Rectangular Sections 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.

### Formulas:

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

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