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

on . Posted in Structural Engineering

### diagram Symbols

• 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.

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

$$R_1 \;=\; V_1 \;=\; (P\;b\;/\;4\;L^3) \; [\; 4\;L^2 - a \; ( L + a ) \;]$$

$$R_2 \;=\; (P\;a\;/\;2\;L^3) \; [\; 2\;L^2 + b \; ( L + a ) \;]$$

$$R_3 \;=\; V_3 \;=\; [\; -\; (P\;a\;b\;/\;4\;L^3 )\;] \; ( L + a )$$

$$V_2 \;=\; (P\;a\;/\;4\;L^3) \; [\; 4\;L^2 + b \; ( L + a ) \;]$$

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

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

Symbol English Metric
$$a, b$$ = horizontal distance to point load $$in$$ $$mm$$
$$M$$ = maximum bending moment $$lbf-in$$ $$N-mm$$
$$V$$ = maximum shear force $$lbf$$ $$N$$
$$R$$ = reaction load at bearing point $$lbf$$ $$N$$
$$L$$ = span length under consideration $$in$$ $$mm$$
$$P$$ = total consideration load $$lbf$$ $$N$$

Tags: Beam Support