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

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

$$\large{ R_1 = V_1 = R_5 = V_5 \;\;=\;\; 0.393\;w\;L }$$

$$\large{ R_2 = R_4 \;\;=\;\; 1.143\;w\;L }$$

$$\large{ R_3 \;\;=\;\; 0.928\;w\;L }$$

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

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

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

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

$$\large{ M_2 \; \left(at\; R_2 \right) \;\;=\;\; -\; 0.1071\;w\;L^2 }$$

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

$$\large{ M_4 \; \left(at\; R_3 \right) \;\;=\;\; -\; 0.0714\;w\;L^2 }$$

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

Symbol English Metric
$$\large{ \Delta }$$ = deflection or deformation $$\large{in}$$ $$\large{mm}$$
$$\large{ w }$$ = load per unit length $$\large{\frac{lbf}{in}}$$ $$\large{\frac{N}{m}}$$
$$\large{ M }$$ = maximum bending moment $$\large{lbf-in}$$ $$\large{N-mm}$$
$$\large{ V }$$ = maximum shear force $$\large{lbf}$$ $$\large{N}$$
$$\large{ \lambda }$$   (Greek symbol lambda) = modulus of elasticity $$\large{\frac{lbf}{in^2}}$$ $$\large{Pa}$$
$$\large{ R }$$ = reaction load at bearing point $$\large{lbf}$$ $$\large{N}$$
$$\large{ I }$$ = second moment of area (moment of inertia) $$\large{in^4}$$ $$\large{mm^4}$$
$$\large{ L }$$ = span length under consideration $$\large{in}$$ $$\large{mm}$$

## diagrams

• 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. 