# Two Span Continuous Beam - Unequal Spans, Uniformly Distributed Load

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.

### Span Continuous Beam - Unequal Spans, Uniformly Distributed Load formulas

$$R_1 \;=\; V_1 \;=\; (M_1\;/\;a) + (w\;a\;/\;2)$$

$$R_2 \;=\; w\;a + w\;b - R_1 - R_3$$

$$R_3 \;=\; V_4 \;=\; (M_1\;/\;b) + (w\;a\;/\;2)$$

$$V_2 \;=\; w\;a - R_1$$

$$V_3 \;=\; w\;b - R_3$$

$$M_1 \;=\; (w\;b^3 + w\;a^3) \;/\;[\;8 \; ( a+b ) \;]$$

$$M_1 \;=\; (w\;b^3 + w\;a^3) \;/\; [\;8 \; ( a+ b) \;]$$

$$M_{x_2} \; ( x_2 = \frac{R_3}{w} ) \;=\; R_3 \;x_2 - (w\;x_2^2 \;/\; 2)$$

Symbol English Metric
$$\Delta$$ = deflection or deformation $$in$$ $$mm$$
$$x$$ = horizontal distance from reaction to point on beam $$in$$ $$mm$$
$$w$$ = load per unit length $$lbf\;/\;in$$ $$N\;/\;m$$
$$M$$ = 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 $$in$$ $$mm$$

Tags: Beam Support