# Three Span Continuous Beam - Equal Spans, Uniform Load on Two Spans at Each End

on . Posted in Structural Engineering

### 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, Uniform Load on Two Spans at Each End formulas

$$R_1 \;=\; V_1 \;=\; R_4 \;=\; V_4 \;=\; 0.450\;w\;L$$

$$R_2 \;=\; V_2 \;=\; R_3 \;=\; V_3 \;=\; 0.550\;w\;L$$

$$M_1 \;=\; M_3 \; (at\; x = 0.450\;L \; from \; R_1 \; or \; R_2 ) \; \;=\; 0.1013\;w\;L^2$$

$$M_2 \; (at\;mid \;span ) \;=\; -\;(0.050\;w\;L)$$

$$\Delta_{max} \; ( at\; 0.479\;L \; from \; R_1 \; or \; R_4 ) \;=\; (0.0099\;w\;L^4) \;/\; (\lambda \;I)$$

Symbol English Metric
$$FB$$ = free body $$lbf$$ $$N$$
$$SF$$ = shear force $$lbf\;/\;in^2$$ $$Pa$$
$$BM$$ = bending moment $$lbf\;/\;sec$$ $$kg-m\;/\;s$$
$$UDL$$ = uniformly distributed load $$lbf$$ $$N$$
$$\Delta$$ = deflection or deformation $$in$$ $$mm$$
$$w$$ = load per unit length $$lbf\;/\;in$$ $$N\;/\;m$$
$$M$$ = maximum bending moment $$lbf-ft$$ $$N-m$$
$$V$$ = 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 $$in$$ $$mm$$

Tags: Beam Support