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Half Circle

See Article - Geometric Properties of Structural Shapes

Arc Length of a Half Circle formula
$l \;=\; \dfrac{ 2 \cdot \pi \cdot r }{ 2 }$
Symbol	English	Metric
$\large{ l }$ = length	$in$	$mm$
$\large{ \pi }$ = Pi	$3.141 592 653 ...$	$3.141 592 653 ...$
$\large{ r }$ = radius	$in$	$mm$

Area of a Half Circle formula
$A_{area} \;=\; \dfrac{ \pi \cdot r^2 }{ 2 }$
Symbol	English	Metric
$\large{ A }$ = area	$in^2$	$mm^2$
$\large{ \pi }$ = Pi	$3.141 592 653 ...$	$3.141 592 653 ...$
$\large{ r }$ = radius	$in$	$mm$

Half of the interior of a circle having a straight chord and an arc.

Center of a circle having all points on the line circumference are at equal distance from the center point.

A half circle is a structural shape used in construction.

Perimeter of a Half Circle formula
$P \;=\; \dfrac{ 2 \cdot \pi \cdot r}{ 2 } + (2 \cdot r)$
Symbol	English	Metric
$\large{ P }$ = perimeter	$in$	$mm$
$\large{ \pi }$ = Pi	$3.141 592 653 ...$	$3.141 592 653 ...$
$\large{ r }$ = radius	$in$	$mm$

Radius of a Half Circle formula
$r \;=\; \sqrt{ \dfrac{ 2 \cdot A_{area} }{ \pi } }$
Symbol	English	Metric
$\large{ A }$ = area	$in^2$	$mm^2$
$\large{ \pi }$ = Pi	$3.141 592 653 ...$	$3.141 592 653 ...$
$\large{ r }$ = radius	$in$	$mm$

Distance from Centroid of a Half Circle formulas
$C_x \;=\; 0$ $C_y \;=\; \dfrac{ 4 \cdot r }{ 3 \cdot \pi }$
Symbol	English	Metric
$\large{ C_x, C_y }$ = distance from centroid	$in$	$mm$
$\large{ \pi }$ = Pi	$3.141 592 653 ...$	$3.141 592 653 ...$
$\large{ r }$ = radius	$in$	$mm$

Elastic Section Modulus of a Half Circle formula
$S \;=\; \dfrac{ I_x }{ C_y }$
Symbol	English	Metric
$\large{ S }$ = elastic section modulus	$in^3$	$mm^3$
$\large{ C_x, C_y }$ = distance from centroid	$in$	$mm$

Polar Moment of Inertia of a Circle formulas
$J_{z} \;=\; \left( \dfrac{ \pi}{ 4 } - \dfrac{ 8 }{ 9 \cdot \pi } \right) \cdot r^4$ $J_{z1} \;=\; \dfrac{ \pi \cdot r^4 }{ 4 }$
Symbol	English	Metric
$\large{ J }$ = torsional constant	$in^4$	$mm^4$
$\large{ \pi }$ = Pi	$3.141 592 653 ...$	$3.141 592 653 ...$
$\large{ r }$ = radius	$in$	$mm$

Radius of Gyration of a Half Circle formulas
$k_{x} \;=\; r \cdot \sqrt{ \dfrac{1 }{ 4 } - \dfrac{ 16 }{ 9 \cdot \pi^2 } }$ $k_{y} \;=\; \dfrac{ r }{ 2 }$ $k_{z} \;=\; r \cdot \sqrt{ \dfrac{ 1 }{ 2 } - \dfrac{ 16 }{ 9 \cdot \pi^2 } }$ $k_{x1} \;=\; \dfrac{ r }{ 2 }$ $k_{y1} \;=\; \dfrac{ r }{ 2 }$ $k_{z1} \;=\; \dfrac{ \sqrt {2} }{ 2 } \cdot r$
Symbol	English	Metric
$\large{ k }$ = radius of gyration	$in$	$mm$
$\large{ \pi }$ = Pi	$3.141 592 653 ...$	$3.141 592 653 ...$
$\large{ r }$ = radius	$in$	$mm$

Second Moment of Area of a Half circle formulas
$I_{x} \;=\; \left( \dfrac{ \pi }{ 8 } - \dfrac{ 8 }{ 9 \cdot \pi } \right) \cdot r^4$ $I_{y} \;=\; \dfrac{ \pi \cdot r^4}{ 8 }$ $I_{x1} \;=\; \dfrac{ \pi \cdot r^4}{ 8 }$ $I_{y1} \;=\; \dfrac{ \pi \cdot r^4}{ 8 }$
Symbol	English	Metric
$\large{ I }$ = moment of inertia	$in^4$	$mm^4$
$\large{ \pi }$ = Pi	$3.141 592 653 ...$	$3.141 592 653 ...$
$\large{ r }$ = radius	$in$	$mm$

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