Three Span Continuous Beam - Equal Spans, Uniformly Distributed Load
- See Article Link - 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.
Three Span Continuous Beam - Equal Spans, Uniformly Distributed Load formulas |
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\(\large{ R_1 = V_1 = R_4 = V_4 \;\;=\;\; 0.400\;w\;L }\) \(\large{ R_2 = R_3 \;\;=\;\; 1.100\;w\;L }\) \(\large{ V_{2_1} = V_{3_2} \;\;=\;\; 0.500\;w\;L }\) \(\large{ V_{2_2} = V_{3_1} \;\;=\;\; 0.600\;w\;L }\) \(\large{ M_1 = M_5 \; \left(at\; 0.400\;L \; from \; R_1 \;or\; R_4 \right) \;\;=\;\; 0.080\;w\;L^2 }\) \(\large{ M_2 = M_4 \; \left(at\; R_2 \;or\; R_3 \right) \;\;=\;\; 0.100\;w\;L^2 }\) \(\large{ M_3 \; \left(at \;mid \;center \;span \right) \;\;=\;\; 0.025\;w\;L^2 }\) \(\large{ \Delta_{max} \; \left(at\; 0.446\;L \; from \; R_1 \;or\; R_4 \right) \;\;=\;\; \frac{0.0069\;w\;L^4}{\lambda\; I} }\) |
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3 S C B - E S, Unif Dist Load - Solve for R1\(\large{ R_1 = 0.400 \; w \; L }\)
3 S C B - E S, Unif Dist Load - Solve for R2\(\large{ R_2 = 1.100\;w\;L }\)
3 S C B - E S, Unif Dist Load - Solve for V21\(\large{ V_{2_1} = 0.500\;w\;L }\)
3 S C B - E S, Unif Dist Load - Solve for V22\(\large{ V_{2_2} = 0.600\;w\;L }\)
3 S C B - E S, Unif Dist Load - Solve for M1\(\large{ M_1 = 0.080\;w\;L^2 }\)
3 S C B - E S, Unif Dist Load - Solve for M2\(\large{ M_2 = 0.100\;w\;L^2 }\)
3 S C B - E S, Unif Dist Load - Solve for M3\(\large{ M_3 = 0.025\;w\;L^2 }\)
3 S C B - E S, Unif Dist Load - Solve for Δmax\(\large{ \Delta_{max} = \frac{0.0069\;w\;L^4}{\lambda\; I} }\)
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Symbol | English | Metric |
\(\large{ R }\) = reaction load at bearing point | \(\large{lbf}\) | \(\large{N}\) |
\(\large{ V }\) = maximum shear force | \(\large{lbf}\) | \(\large{N}\) |
\(\large{ M }\) = maximum bending moment | \(\large{lbf-ft}\) | \(\large{N-m}\) |
\(\large{ \Delta }\) = deflection or deformation | \(\large{in}\) | \(\large{mm}\) |
\(\large{ w }\) = load per unit length | \(\large{\frac{lbf}{in}}\) | \(\large{\frac{N}{m}}\) |
\(\large{ L }\) = span length under consideration | \(\large{in}\) | \(\large{mm}\) |
\(\large{ \lambda }\) (Greek symbol lambda) = modulus of elasticity | \(\large{\frac{lbf}{in^2}}\) | \(\large{Pa}\) |
\(\large{ I }\) = second moment of area (moment of inertia) | \(\large{in^4}\) | \(\large{mm^4}\) |
Tags: Beam Support Equations