- See Article - Beam Design Formulas
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.
Overhanging Beam - Uniformly Distributed Load Overhang Both Supports formulas |
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\( R_1 \;=\; \dfrac{ w\cdot L \cdot ( L - 2 \cdot c ) }{ 2 \cdot b } \) \( R_2 \;=\; \dfrac{ w\cdot L \cdot ( L - 2 \cdot a ) }{ 2 \cdot b } \) \( V_1 \;=\; w\cdot a \) \( V_2 \;=\; R_1 - V_1 \) \( V_3 \;=\; R_2 - V_4 \) \( V_4 \;=\; w\cdot c \) \( V_{x_1} \;=\; V_1 - (\; w \cdot ( a - x_1 ) \;) \) \( V_x \; ( x < b ) \;=\; R_1 - (\; w \cdot ( a + x ) \;) \) \( M_1 \;=\; - \; \dfrac{ w\cdot a^2 }{ 2 } \) \( M_2 \;=\; - \; \dfrac{ w \cdot c^2 }{ 2 } \) \( M_3 \;\;=\;\; R_1 \cdot \left( \dfrac{ R_1 }{ 2\cdot w } - a \right) \) \( M_x \;=\; R_1 \cdot x \cdot -\; \dfrac{ w \cdot ( a + x )^2 }{ 2 } \) |
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| Symbol | English | Metric |
| \( x \) = horizontal distance from reaction to point on beam | \(in\) | \(mm\) |
| \( w \) = load per unit length | \(lbf\;/\;in\) | \(N\;/\;m\) |
| \( M \) = maximum bending moment | \(lbf-in\) | \(N-mm\) |
| \( V \) = maximum shear force | \(lbf\) | \(N\) |
| \( \lambda \) (Greek symbol lambda) = modulus of elasticity | \(lbf\;/\;in^2\) | \(Pa\) |
| \( R \) = reaction load at bearing point | \(lbf\) | \(N\) |
| \( I \) = second moment of area (moment of inertia) | \(in^4\) | \(mm^4\) |
| \( L \) = span length of the bending member | \(in\) | \(mm\) |
| \( a, b, c \) = span length under consideration | \(in\) | \(mm\) |
