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

$$R_1 \;=\; V_1 \;=\; R_3 \;=\; V_3 \;=\; 5\;P\;/\;16$$

$$R_2 \;=\; 2V_2 \;=\; 11\;P\;/\;8$$

$$V_2 \;=\; P - R_1 \;=\; 11\;P\;/\;16$$

$$V_{max} \;=\; V_2$$

$$M_1 \;=\; - \;(3\;P\;L\;/\;16)$$

$$M_2 \;=\; 5\;P\;L\;/\;32$$

$$M_x \; ( x < \frac{L}{2} ) \;=\; R_1\; x$$

Symbol English Metric
$$x$$ = horizontal distance from reaction to point on beam $$in$$ $$mm$$
$$M$$ = 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