Simple Beam - Uniform Load Partially Distributed at Each End
- See Article Link - Beam Design Formulas
- Tags: Beam Support
diagram Symbols
- Bending moment diagram (BMD) - Used to determine the bending moment at a given point of a structural element. The diagram can help determine the type, size, and material of a member in a structure so that a given set of loads can be supported without structural failure.
- Free body diagram (FBD) - Used to visualize the applied forces, moments, and resulting reactions on a structure in a given condition.
- Shear force diagram (SFD) - Used to determine the shear force at a given point of a structural element. The diagram can help determine the type, size, and material of a member in a structure so that a given set of loads can be supported without structural failure.
- Uniformly distributed load (UDL) - A load that is distributed evenly across the entire length of the support area.
Simple Beam - Uniform Load Partially Distributed at Each End formulas |
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\( R_1 = V_1 \;=\; [\;w_1 \;a \; ( 2\;L - a ) \;] + (w_2 \;c^2 \;/\; 2\;L) \) \( R_2 = V_2 \;=\; [\;w_2 \;c \; ( 2\;L - c ) \;] + ( w_1\; a^2 \;/\; 2\;L) \) \( V_x \; ( x < a ) \;=\; R_1 - w_1 \;x \) \( V_x \; [ \; a < x < ( a + b) \;] \;=\; R_1 - w_1 \;a \) \( V_x \; [ \; x > ( a + b ) \;] \;=\; R_2 - [\; w_2 \;( 1 - x ) \;] \) \( M_{max} \; [\; at \; x = (R_1\;/\;w_1) \; when \; R_1 < w_1 \;a \;] \;=\; R_{1}{^2} \;/\; 2\;w_1 \) \( M_{max} \; [\; at \; x = L - (R_2\;/\;w_2) \; when \; R_2 < w_2 \;c \;] \;=\; R_{2}{^2} \;/\; 2\;w_2 \) \( M_x \; ( w < a ) \;=\; (R_1 \;x) - ( w_1 \;x^2\;/\; 2 ) \) \( M_x \; [\; a < x < ( a + b ) \;] \;=\; (R_1\; x) - [\;( w_1 \;a\;/\; 2 ) \; ( 2\;x - a )\;] \) \( M_x \; [\; x > ( a + b ) \;] \;=\; [\; R_2 \; ( L - x ) \;] - [\; w_2 \; ( L - x )^2 \;/\; 2 \;] \) |
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| Symbol | English | Metric |
| \( R \) = reaction load at bearing point | \(lbf\) | \(N\) |
| \( V \) = maximum shear force | \(lbf\) | \(N\) |
| \( M \) = maximum bending moment | \(lbf - in\) | \(N - mm\) |
| \( w_1, w_2 \) = load per unit length | \(lbf\;/\;in\) | \(N\;/\;m\) |
| \( L \) = span length of the bending member | \(in\) | \(mm\) |
| \( x \) = horizontal distance from reaction to point on beam | \(in\) | \(mm\) |
| \( a, b, c \) = width and seperation of UDL | \(in\) | \(mm\) |
Tags: Beam Support