Four Span Continuous Beam - Equal Spans, Uniformly Distributed Load
Four Span Continuous Beam - Equal Spans, Uniformly Distributed Load formulas |
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\(\large{ R_1 = V_1 = R_5 = V_5 \;\;=\;\; 0.393\;w\;L }\) \(\large{ R_2 = R_4 \;\;=\;\; 1.143\;w\;L }\) \(\large{ R_3 \;\;=\;\; 0.928\;w\;L }\) \(\large{ V_{2_1} = V_{4_2} \;\;=\;\; 0.607\;w\;L }\) \(\large{ V_{2_2} = V_{4_1} \;\;=\;\; 0.536\;w\;L }\) \(\large{ V_{3_1} = V_{3_2} \;\;=\;\; 0.464\;w\;L }\) \(\large{ M_1 \; \left(at\; 0.393\;L \; from \; R_1 \right) = M_7 \; \left(at\; 0.393\;L \; from \; R_5 \right) \;\;=\;\; 0.0772\;w\;L^2 }\) \(\large{ M_2 \; \left(at\; R_2 \right) \;\;=\;\; -\; 0.1071\;w\;L^2 }\) \(\large{ M_3 \; \left(at\; 0.536\;L \; from \; R_2 \right) = M_5 \; \left(at\; 0.536\;L \; from \; R_4 \right) \;\;=\;\; 0.0364\;w\;L^2 }\) \(\large{ M_4 \; \left(at\; R_3 \right) \;\;=\;\; -\; 0.0714\;w\;L^2 }\) \(\large{ \Delta_{max} \; \left(at\; 0.440\;L \; from \; R_1 \; and \; R_5 \right) \;\;=\;\; \frac{0.0065\;w\;L^4}{\lambda\; I} }\) |
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| Symbol | English | Metric |
| \(\large{ \Delta }\) = deflection or deformation | \(\large{in}\) | \(\large{mm}\) |
| \(\large{ w }\) = 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 | \(\large{lbf}\) | \(\large{N}\) |
| \(\large{ \lambda }\) (Greek symbol lambda) = modulus of elasticity | \(\large{\frac{lbf}{in^2}}\) | \(\large{Pa}\) |
| \(\large{ R }\) = reaction load at bearing point | \(\large{lbf}\) | \(\large{N}\) |
| \(\large{ I }\) = second moment of area (moment of inertia) | \(\large{in^4}\) | \(\large{mm^4}\) |
| \(\large{ L }\) = 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.
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Tags: Beam Support Equations