Two Span Continuous Beam - Equal Spans, Uniform Load on One Span

on 26 May 2018. Posted in Structural Engineering

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 are

Two Span Continuous Beam - Equal Spans, Uniform Load on One Span formulas
\( R_1 \;=\; V_1 \;=\; 7\;w\;L\;/\;16 \) \( R_2 \;=\; V_2 + V_3 \;=\; 5\;w\;L\;/\;8 \) \( R_3 \;=\; V_3 \;=\; w\;L\;/\;16 \) \( V_2 \;=\; 9\;w\;L\;/\;16 \) \( M_{max} \; (at\; x = \frac{7\;L}{16} ) \;=\; 49\;w\;L^2\;/\;512 \) \( M_1 \; \left(at \;support\; R_2 \right) \;=\; w\;L^2\;/\;16 \) \( M_x \; \left( x < L \right) \;=\; (w\;x\;/\;16) \; ( 7\;L - 8\;x ) \) \( \Delta_{max} \; ( 0.472 \; L \; from\;R_1 ) \;=\; 0.0092 \; (w\;L^4\;/\; \lambda\; I ) \)
Symbol	English	Metric
\( \Delta \) = deflection or deformation	\(in\)	\(mm\)
\( x \) = horizontal distance from reaction to point on beam	\(in\)	\(mm\)
\( w \) = load per unit length	\(lbf\;/\;in\)	\(N\;/\;m\)
\( M \) = maximum bending moment	\(lbf-in\)	\(N-mm\)
\( V \) = maximum shear force	\(lbf\)	\(N\)
\( \lambda \) (Greek symbol lambda) = modulus of elasticity	\(lbf\;/\;in^2\)	\(Pa\)
\( I \) = second moment of area (moment of inertia)	\(in^4\)	\(mm^4\)
\( R \) = reaction load at bearing point	\(lbf\)	\(N\)
\( L \) = span length under consideration	\(in\)	\(mm\)

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