# Four Span Continuous Beam - Equal Spans, Uniform Load on Two Spans

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.

### Four Span Continuous Beam - Equal Spans, Uniform Load on Two Spans formula

$$R_1 \;=\; V_1 \;=\; 0.446\;w\;L$$

$$R_2 \;=\; 0.572\;w\;L$$

$$R_3 \;=\; 0.464\;w\;L$$

$$R_4 \;=\; 0.572\;w\;L$$

$$R_5 \;=\; - \;0.054\;w\;L$$

$$V_{2_1} \;=\; 0.0554\;w\;L$$

$$V_{2_2} \;=\; V_{3_1} \;=\; 0.018\;w\;L$$

$$V_{3_2} \;=\; 0.482\;w\;L$$

$$V_{4_1} \;=\; 0.518\;w\;L$$

$$V_{4_2} \;=\; V_5 \;=\; 0.054\;w\;L$$

$$M_1 \; \left( 0.446\;L \; from \; R_1 \right) \;=\; 0.0996\;w\;L^2$$

$$M_2 \; \left(at\; R_2 \right) \;=\; -\; (0.0536\;w\;L^2 )$$

$$M_3 \; \left(at\; R_3 \right) \;=\; - \; (0.0357\;w\;L^2 )$$

$$M_4 \; \left( 0.518\;L \; from \; R_4 \right) \;=\; 0.805\;w\;L^2$$

$$M_5 \; \left(at\; R_4 \right) \; \;=\; -\; (0.0536\;w\;L^2)$$

$$\Delta_{max} \; \left(at\; 0.477\;L \; from \; R_1 \right) \;=\; (0.0097\;w\;L^4) \;/\; (\lambda\; I)$$

Symbol English Metric
$$\Delta$$ = deflection or deformation $$in$$ $$mm$$
$$w$$ = 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 $$lbf\;/\;in^2$$ $$Pa$$
$$R$$ = reaction load at bearing point $$lbf$$ $$N$$
$$I$$ = second moment of area (moment of inertia) $$in^4$$ $$mm^4$$
$$L$$ = span length under consideration $$in$$ $$mm$$

Tags: Beam Support