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Solid rectangular section

Solid rectangular section 2b 2a
Solid rectangular section

Values for calculation

$T$ $\mathrm{Nm}$
$a$ $\mathrm{mm}$
$b$ $\mathrm{mm}$
$L$ $\mathrm{mm}$
$G$ $\mathrm{MPa}$

Calculation

Polar moment of inertia

$$K=a\cdot b^3\cdot\left[\cfrac{16}{3}-3.36\cdot\cfrac{b}{a}\cdot\left(1-\cfrac{b^4}{12\cdot a^4}\right)\right]$$
$K=a\cdot b^3\cdot\left[\cfrac{16}{3}-3.36\cdot\cfrac{b}{a}\cdot\left(1-\cfrac{b^4}{12\cdot a^4}\right)\right]$
Equations in LaTeX code
K=a\cdot b^3\cdot\left[\cfrac{16}{3}-3.36\cdot\cfrac{b}{a}\cdot\left(1-\cfrac{b^4}{12\cdot a^4}\right)\right]

Angle of twist

$$θ=\cfrac{T\cdot 10^3\cdot L}{K\cdot G}$$
$θ=\cfrac{T\cdot 10^3\cdot L}{K\cdot G}$
Equations in LaTeX code
θ=\cfrac{T\cdot 10^3\cdot L}{K\cdot G}

Torsion stress

$$τ_{max}=\cfrac{3\cdot10^3\cdot T}{8\cdot a\cdot b^2}\cdot\left[1+0.6095\cdot\cfrac{b}{a}+0.8865\cdot\left(\cfrac{b}{a}\right)^2-1.8023\cdot\left(\cfrac{b}{a}\right)^3+0.91\cdot\left(\cfrac{b}{a}\right)^4\right]$$
$τ_{max}=\cfrac{3\cdot10^3\cdot T}{8\cdot a\cdot b^2}\cdot\left[1+0.6095\cdot\cfrac{b}{a}+0.8865\cdot\left(\cfrac{b}{a}\right)^2-1.8023\cdot\left(\cfrac{b}{a}\right)^3+0.91\cdot\left(\cfrac{b}{a}\right)^4\right]$
Equations in LaTeX code
τ_{max}=\cfrac{3\cdot10^3\cdot T}{8\cdot a\cdot b^2}\cdot\left[1+0.6095\cdot\cfrac{b}{a}+0.8865\cdot\left(\cfrac{b}{a}\right)^2-1.8023\cdot\left(\cfrac{b}{a}\right)^3+0.91\cdot\left(\cfrac{b}{a}\right)^4\right]

Requirements

$$b\le a$$
$b\le a$
Equations in LaTeX code
b\le a
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