Two Span Continuous Beam - Unequal Spans, Concentrated Load on Each Span Symmetrically Placed
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Two Span Continuous Beam - Unequal Spans, Concentrated Load on Each Span Symmetrically Placed formulas |
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\(\large{ R_1 = V_1 \;\;=\;\; \frac{M_2}{a} + \frac{P_1}{2} }\) \(\large{ R_2 \;\;=\;\; P_1 + P_2 - R_1 - R_3 }\) \(\large{ R_3 = V_4 \;\;=\;\; \frac{M_2}{b} + \frac{P_2}{2} }\) \(\large{ M_1 \;\;=\;\; R_1 \;\frac{a}{2} }\) \(\large{ M_2 \;\;=\;\; -\; \frac{3}{16} \; \left( \frac{P_1\; a^2 \;+ \;P_2 \; b^2}{a \;+\; b} \right) }\) \(\large{ M_3 \;\;=\;\; R_3\; \frac{b}{2} }\) |
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| Symbol | English | Metric |
| \(\large{ M }\) = 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 | \(\large{in}\) | \(\large{mm}\) |
| \(\large{ P }\) = total consideration load | \(\large{lbf}\) | \(\large{N}\) |
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