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

on . Posted in Structural Engineering

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

$$\large{ R_1 = V_1 \;\;=\;\; \frac{7\;w\;L}{16} }$$

$$\large{ R_2 = V_2 + V_3 \;\;=\;\; \frac{5\;w\;L}{8} }$$

$$\large{ R_3 = V_3 \;\;=\;\; \frac{w\;L}{16} }$$

$$\large{ V_2 \;\;=\;\; \frac{9\;w\;L}{16} }$$

$$\large{ M_{max} \; \left(at\; x = \frac{7\;L}{16} \right) \;\;=\;\; \frac{49\;w\;L^2}{512} }$$

$$\large{ M_1 \; \left(at \;support\; R_2 \right) \;\;=\;\; \frac{w\;L^2}{16} }$$

$$\large{ M_x \; \left( x < L \right) \;\;=\;\; \frac{w\;x}{16} \; \left( 7\;L - 8\;x \right) }$$

$$\large{ \Delta_{max} \; \left( 0.472 \; L \; from\;R_1 \right) \;\;=\;\; 0.0092 \; \frac{w\;L^4}{ \lambda\; I} }$$

Symbol English Metric
$$\large{ \Delta }$$ = deflection or deformation $$\large{in}$$ $$\large{mm}$$
$$\large{ x }$$ = horizontal distance from reaction to point on beam $$\large{in}$$ $$\large{mm}$$
$$\large{ w }$$ = 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 $$\large{\frac{lbf}{in^2}}$$ $$\large{Pa}$$
$$\large{ I }$$ = second moment of area (moment of inertia) $$\large{in^4}$$ $$\large{mm^4}$$
$$\large{ R }$$ = reaction load at bearing point $$\large{lbf}$$ $$\large{N}$$
$$\large{ L }$$ = 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.