# Hollow Rectangle

on . Posted in Plane Geometry

• A two-dimensional figure that is a quadrilateral with two pair of parallel edges.
• A hollow rectangle is a structural shape used in construction.
• Interior angles are 90°
• Exterior angles are 90°
• Angle $$\;A = B = C = D$$
• 2 diagonals
• 4 edges
• 4 vertexs

### Area of a Hollow Rectangle formula

$$A = b\;a - b_1\;a_1$$
Symbol English Metric
$$A$$ = area $$in^2$$ $$mm^2$$
$$a, b, a_1, b_1$$ = edge $$in$$ $$mm$$

### Distance from Centroid of a Hollow Rectangle formulas

$$C_x = \frac{ b }{ 2 }$$

$$C_y = \frac{ a }{ 2}$$

Symbol English Metric
$$C$$ = distance from centroid $$in$$ $$mm$$
$$a, b, a_1, b_1$$ = edge $$in$$ $$mm$$

### Elastic Section Modulus of a Hollow Rectangle formulas

$$S_x = \frac{ I_x }{ C_y }$$

$$S_y = \frac{ I_y }{ C_x }$$

Symbol English Metric
$$S$$ = elastic section modulus $$in^3$$ $$mm^3$$
$$C$$ = distance from centroid $$in$$ $$mm$$
$$I$$ = moment of inertia $$in^4$$ $$mm^4$$

### Perimeter of a Hollow Rectangle formulas

$$P_o = 2\; \left( a + b \right)$$     (outside)

$$P_i = 2\; \left( a_1 + b_2 \right)$$     (inside)

Symbol English Metric
$$P$$ = perimeter $$in$$ $$mm$$
$$a, b, a_1, b_1$$ = edge $$in$$ $$mm$$

### Polar Moment of Inertia of a Hollow Rectangle formulas

$$J_{z} = I_x + I_y$$

$$J_{z1} = I_{x1} + I_{y1}$$

Symbol English Metric
$$J$$ = torsional constant $$in^4$$ $$mm^4$$
$$I$$ = moment of inertia $$in^4$$ $$mm^4$$

### Radius of Gyration of a Hollow Rectangle formulas

$$k_{x} = \sqrt{ \frac{ b\;a^3 \;-\; b_1\; a_{1}{^3} }{ 12 \; \left( b\;a \;-\; b_1\; a_1 \right) } }$$

$$k_{y} = \sqrt{ \frac{ b^3 \;a \;-\; b_{1}{^3} \; a_1 }{ 12\; \left( b\;a \;-\; b_1\; a_1 \right) } }$$

$$k_{z} = \sqrt{ k_{x}{^2} + k_{y}{^2} }$$

$$k_{x1} = \sqrt{ \frac{ I_{x1} }{ A } }$$

$$k_{y1} = \sqrt{ \frac{ I_{y1} }{ A } }$$

$$k_{z1} = \sqrt{ k_{x1}{^2} + k_{y1}{^2} }$$

Symbol English Metric
$$k$$ = radius of gyration $$in$$ $$mm$$
$$A$$ = area $$in^2$$ $$mm^2$$
$$a, b, a_1, b_1$$ = edge $$in$$ $$mm$$
$$I$$ = moment of inertia $$in^4$$ $$mm^4$$

### Second Moment of Area of a Hollow Rectangle formulas

$$I_{x} = \frac{ b\;a^3 \;-\; b_1\; a_{1}{^3} }{12}$$

$$I_{y} = \frac{ b^3 \;a \;-\; b_{1}{^3}\; a_1 }{12}$$

$$I_{x1} = \frac{ b\;a^3 }{3} - \frac { b_1 \; a_1 \; \left( a_{1}{^2} \;+\; 3\;a^2 \right) }{12}$$

$$I_{y1} = \frac{ b^3 \;a }{3} - \frac { b_1 \; a_1 \; \left( b_{1}{^2} \;+\; 3\;b^2 \right) }{12}$$

Symbol English Metric
$$I$$ = moment of inertia $$in^4$$ $$mm^4$$
$$a, b, a_1, b_1$$ = edge $$in$$ $$mm$$

### Side of a Hollow Rectangle formulas

$$a = \frac{P}{2} - b$$

$$b = \frac{P}{2} - a$$

Symbol English Metric
$$a, b, a_1, b_1$$ = edge $$in$$ $$mm$$
$$P$$ = perimeter $$in$$ $$mm$$

Tags: Structural Steel