# Two Span Continuous Beam - Unequal Spans, Uniformly Distributed Load

on . Posted in Structural Engineering

## Span Continuous Beam - Unequal Spans, Uniformly Distributed Load formulas

$$\large{ R_1 = V_1 \;\;=\;\; \frac{M_1}{a} + \frac{w\;a}{2} }$$

$$\large{ R_2 \;\;=\;\; w\;a + w\;b - R_1 - R_3 }$$

$$\large{ R_3 = V_4 \;\;=\;\; \frac{M_1}{b} + \frac{w\;a}{2} }$$

$$\large{ V_2 \;\;=\;\; w\;a - R_1 }$$

$$\large{ V_3 \;\;=\;\; w\;b - R_3 }$$

$$\large{ M_1 \;\;=\;\; \frac{w\;b^3 \;+\; w\;a^3}{8 \; \left( a\;+ \;b \right) } }$$

$$\large{ M_1 \;\;=\;\; \frac{w\;b^3 \;+\; w\;a^3}{8 \; \left( a\;+ \;b \right) } }$$

$$\large{ M_{x_2} \; \left( x_2 = \frac{R_3}{w} \right) \;=\; R_3 \;x_2 \; -\;\frac{w\;x_{2}{^2} }{2} }$$

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 $$\large{lbf}$$ $$\large{N}$$
$$\large{ R }$$ = reaction load at bearing point $$\large{lbf}$$ $$\large{N}$$
$$\large{ a, b }$$ = 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. 