# Thin Wall Rectangle

on . Posted in Plane Geometry

• A two-dimensional figure that is a quadrilateral with two pair of parallel edges.
• A thin wall 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 Thin Wall Rectangle formula

$$A = 2\;t \; \left( b + a \right)$$
Symbol English Metric
$$A$$ = area $$in^2$$ $$mm^2$$
$$a, b$$ = edge $$in$$ $$mm$$
$$t$$ = thickness $$in$$ $$mm$$

### Distance from Centroid of a Thin Wall Rectangle formulas

$$C_x = b \;/\; 2$$

$$C_y = a \;/\; 2$$

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

### Elastic Section Modulus of a Thin Wall Rectangle formulas

$$S_x = 2\;a\;b\;t \;/\; 3$$

$$S_y = 2\;a\;b\;t \;/\; 3$$

Symbol English Metric
$$S$$ = elastic section modulus $$in^3$$ $$mm^3$$
$$a, b$$ = edge $$in$$ $$mm$$
$$t$$ = thickness $$in$$ $$mm$$

### Perimeter of a Thin Wall Rectangle formulas

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

$$P_i = 2\; \left( a + b - 4\;t \right)$$     (inside)

Symbol English Metric
$$P$$ = perimeter $$in$$ $$mm$$
$$a, b$$ = edge $$in$$ $$mm$$
$$t$$ = thickness $$in$$ $$mm$$

### Plastic Section Modulus of a Thin Wall Rectangle formulas

$$Z_x = 2 \; [ \; b\;t \; [\; (a\;/\;2) - (t\;/\;2 ) \;] + t \; [\; (a\;/\;2) - t \;]^2 \; ]$$

$$Z_y = 2\;t \; [ \; (a\;/\;2) - t \;] \; [ \;(b\;/\;2) - t\; ] + 2\;b\;t \; [ \;(b\;/\;2) - ( t\;/\;2) \;]$$

Symbol English Metric
$$Z$$ = elastic section modulus $$in^3$$ $$mm^3$$
$$a, b$$ = edge $$in$$ $$mm$$
$$t$$ = thickness $$in$$ $$mm$$

### Polar Moment of Inertia of a Thin Wall Rectangle formulas

$$J_{z} = ( a\;b\;t\;/\;3 ) \; ( a + b )$$

$$J_{z1} = [ \; \frac{1}{2} \; ( b^3 + a^3 ) + \frac{5}{6} \; b\;a \; ( b + a ) \;] \; t$$

Symbol English Metric
$$J$$ = tortional constant $$in^4$$ $$mm^4$$
$$a, b$$ = edge $$in$$ $$mm$$
$$t$$ = thickness $$in$$ $$mm$$

### Radius of Gyration of a Thin Wall Rectangle formulas

$$k_{x} = [\; \sqrt{ b\;/\;6 \; ( b + a ) }\; ] \; a$$

$$k_{y} = [\; \sqrt{ a\;/\;6 \; ( b + a ) } \;] \; b$$

$$k_{z} = \sqrt{ a\;b\;/\;6 }$$

$$k_{x1} = [\; \sqrt{ 5\;b + 3\;a \;/\;12 \; ( b + a ) }\; ] \; \;a$$

$$k_{y1} = [\; \sqrt{ 3\;b + 5\;a \;/\; 12 \; ( b + a ) }\; ] \; \;b$$

$$k_{z1} = \sqrt{ 3 \; ( b^3 + a^3 ) + 5\;b\;a \; ( b + a ) \;/\; 12 \; ( b + a ) }$$

Symbol English Metric
$$k$$ = radius of gyration $$in$$ $$mm$$
$$a, b$$ = edge $$in$$ $$mm$$

### Second Moment of Area of a Thin Wall Rectangle formulas

$$I_{x} = \frac{1}{3} \; b\;a^2\; t$$

$$I_{y} = \frac{1}{3} \; b^2\; a\;t$$

$$I_{x1} = ( \; \frac{5}{6} \; b + \frac{1}{2} \; a \; ) \; a^2\; t$$

$$I_{y1} = ( \; \frac{1}{2} \; b + \frac{5}{6} \; a \; ) \; b^2\; t$$

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

### Side of a Thin Wall Rectangle formulas

$$a = (P\;/\;2) - b$$

$$b = (P\;/\;2) - a$$

Symbol English Metric
$$a, b$$ = edge $$in$$ $$mm$$
$$\large{ P }$$ = perimeter $$in$$ $$mm$$

### Torsional Constant of a Thin Wall Rectangle formula

$$J = 2\;t^2 \; ( b - 2 )^2 \; ( a - t )^2 \;/\; a\;t + b\;t - 2\;t^2$$
Symbol English Metric
$$J$$ = tortional constant $$in^4$$ $$mm^4$$
$$a, b$$ = edge $$in$$ $$mm$$
$$t$$ = thickness $$in$$ $$mm$$