Two Span Continuous Beam - Equal Spans, Concentrated Load at Any Point
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Two Span Continuous Beam - Equal Spans, Two Equal Concentrated Loads Symmetrically Placed formulas |
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\(\large{ R_1 = V_1 \;\;=\;\; \frac{P\;b}{4\;L^3} \; \left[ 4\;L^2 - a \; \left( L + a \right) \right] }\) \(\large{ R_2 \;\;=\;\; \frac{P\;a}{2\;L^3} \left[ 2\;L^2 + b \; \left( L + a \right) \right] }\) \(\large{ R_3 = V_3 \;\;=\;\; -\; \frac{P\;a\;b}{4\;L^3} \; \left( L + a \right) }\) \(\large{ V_2 \;\;=\;\; \frac{P\;a}{4\;L^3} \; \left[ 4\;L^2 + b \; \left( L + a \right) \right] }\) \(\large{ M_1 \; \left(at\; support\; R_2 \right) \;\;=\;\; \frac{P\;a\;b}{4\;L^2} \; \left( L + a \right) }\) \(\large{ M_{max} \;\;=\;\; \frac{P\;a\;b}{4\;L^3} \; \left[ 4\;L^2 - a \; \left( L + a \right) \right] }\) |
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Symbol | English | Metric |
\(\large{ a, b }\) = horizontal distance to point load | \(\large{in}\) | \(\large{mm}\) |
\(\large{ M }\) = 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 | \(\large{lbf}\) | \(\large{N}\) |
\(\large{ L }\) = 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