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

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 - Unequal Spans, Concentrated Load on Each Span Symmetrically Placed formulas

$$R_1 \;=\; V_1 \;=\; (M_2\;/\;a) + (P_1\;/\;2)$$

$$R_2 \;=\; P_1 + P_2 - R_1 - R_3$$

$$R_3 \;=\; V_4 \;=\; (M_2\;/\;b) + (P_2\;/\;2)$$

$$M_1 \;=\; R_1 \; (a\;/\;2)$$

$$M_2 \;=\; [\; -\; (3\;/\;16)\;] \; ( P_1\; a^2 \;+ \;P_2 \; b^2\;/\;a \;+\; b )$$

$$M_3 \;=\; R_3\; (b\;/\;2)$$

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

Tags: Beam Support