# Two Span Continuous Beam - Equal Spans, Concentrated Load at Any Point

on . Posted in Structural Engineering

## Two Span Continuous Beam - Equal Spans, Two Equal Concentrated Loads Symmetrically Placed  formulas

$$\large{ R_1 = V_1 \;\;=\;\; \frac{P\;b}{4\;L^3} \; \left[ 4\;L^2 - a \; \left( L + a \right) \right] }$$

$$\large{ R_2 \;\;=\;\; \frac{P\;a}{2\;L^3} \left[ 2\;L^2 + b \; \left( L + a \right) \right] }$$

$$\large{ R_3 = V_3 \;\;=\;\; -\; \frac{P\;a\;b}{4\;L^3} \; \left( L + a \right) }$$

$$\large{ V_2 \;\;=\;\; \frac{P\;a}{4\;L^3} \; \left[ 4\;L^2 + b \; \left( L + a \right) \right] }$$

$$\large{ M_1 \; \left(at\; support\; R_2 \right) \;\;=\;\; \frac{P\;a\;b}{4\;L^2} \; \left( L + a \right) }$$

$$\large{ M_{max} \;\;=\;\; \frac{P\;a\;b}{4\;L^3} \; \left[ 4\;L^2 - a \; \left( L + a \right) \right] }$$

Symbol English Metric
$$\large{ a, b }$$ = horizontal distance to point load $$\large{in}$$ $$\large{mm}$$
$$\large{ M }$$ = 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 $$\large{lbf}$$ $$\large{N}$$
$$\large{ L }$$ = 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. 