Two Span Continuous Beam - Unequal Spans, Uniformly Distributed Load
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Span Continuous Beam - Unequal Spans, Uniformly Distributed Load formulas |
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\(\large{ R_1 = V_1 \;\;=\;\; \frac{M_1}{a} + \frac{w\;a}{2} }\) \(\large{ R_2 \;\;=\;\; w\;a + w\;b - R_1 - R_3 }\) \(\large{ R_3 = V_4 \;\;=\;\; \frac{M_1}{b} + \frac{w\;a}{2} }\) \(\large{ V_2 \;\;=\;\; w\;a - R_1 }\) \(\large{ V_3 \;\;=\;\; w\;b - R_3 }\) \(\large{ M_1 \;\;=\;\; \frac{w\;b^3 \;+\; w\;a^3}{8 \; \left( a\;+ \;b \right) } }\) \(\large{ M_1 \;\;=\;\; \frac{w\;b^3 \;+\; w\;a^3}{8 \; \left( a\;+ \;b \right) } }\) \(\large{ M_{x_2} \; \left( x_2 = \frac{R_3}{w} \right) \;=\; R_3 \;x_2 \; -\;\frac{w\;x_{2}{^2} }{2} }\) |
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| Symbol | English | Metric |
| \(\large{ \Delta }\) = deflection or deformation | \(\large{in}\) | \(\large{mm}\) |
| \(\large{ x }\) = horizontal distance from reaction to point on beam | \(\large{in}\) | \(\large{mm}\) |
| \(\large{ w }\) = load per unit length | \(\large{\frac{lbf}{in}}\) | \(\large{\frac{N}{m}}\) |
| \(\large{ M }\) = maximum bending moment | \(\large{lbf-in}\) | \(\large{N-mm}\) |
| \(\large{ V }\) = maximum shear force | \(\large{lbf}\) | \(\large{N}\) |
| \(\large{ R }\) = reaction load at bearing point | \(\large{lbf}\) | \(\large{N}\) |
| \(\large{ a, b }\) = span length under consideration | \(\large{in}\) | \(\large{mm}\) |
diagrams
- 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.
Tags: Beam Support Equations