# Two Span Continuous Beam - Unequal Spans, Concentrated Load on Each Span Symmetrically Placed

on . Posted in Structural Engineering

## Two Span Continuous Beam - Unequal Spans, Concentrated Load on Each Span Symmetrically Placed formulas

$$\large{ R_1 = V_1 \;\;=\;\; \frac{M_2}{a} + \frac{P_1}{2} }$$

$$\large{ R_2 \;\;=\;\; P_1 + P_2 - R_1 - R_3 }$$

$$\large{ R_3 = V_4 \;\;=\;\; \frac{M_2}{b} + \frac{P_2}{2} }$$

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

$$\large{ M_2 \;\;=\;\; -\; \frac{3}{16} \; \left( \frac{P_1\; a^2 \;+ \;P_2 \; b^2}{a \;+\; b} \right) }$$

$$\large{ M_3 \;\;=\;\; R_3\; \frac{b}{2} }$$

Symbol English Metric
$$\large{ M }$$ = 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 $$\large{in}$$ $$\large{mm}$$
$$\large{ P }$$ = total consideration load $$\large{lbf}$$ $$\large{N}$$

## 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. 