# Four Span Continuous Beam - Equal Spans, Uniformly Distributed Load

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, Uniformly Distributed Load formulas

$$R_1 \;=\; V_1 \;=\; R_5 \;=\; V_5 \;=\; 0.393\;w\;L$$

$$R_2 = R_4 \;=\; 1.143\;w\;L$$

$$R_3 \;=\; 0.928\;w\;L$$

$$V_{2_1} \;=\; V_{4_2} \;=\; 0.607\;w\;L$$

$$V_{2_2} \;=\; V_{4_1} \;=\; 0.536\;w\;L$$

$$V_{3_1} \;=\; V_{3_2} \;=\; 0.464\;w\;L$$

$$M_1 \; (at\; 0.393\;L \; from \; R_1 ) = M_7 \; \left(at\; 0.393\;L \; from \; R_5 \right) \;=\; 0.0772\;w\;L^2$$

$$M_2 \; (at\; R_2 ) \;=\; -\; (0.1071\;w\;L^2)$$

$$M_3 \; (at\; 0.536\;L \; from \; R_2 ) = M_5 \; \left(at\; 0.536\;L \; from \; R_4 \right) \;=\; 0.0364\;w\;L^2$$

$$M_4 \; (at\; R_3 ) \;=\; -\; (0.0714\;w\;L^2)$$

$$\Delta_{max} \; (at\; 0.440\;L \; from \; R_1 \; and \; R_5 ) \;=\; (0.0065\;w\;L^4) \;/\; (\lambda\; I)$$

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