Two Span Continuous Beam - Equal Spans, Uniform Load on One Span

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 are

Two Span Continuous Beam - Equal Spans, Uniform Load on One Span formulas

$$R_1 \;=\; V_1 \;=\; 7\;w\;L\;/\;16$$

$$R_2 \;=\; V_2 + V_3 \;=\; 5\;w\;L\;/\;8$$

$$R_3 \;=\; V_3 \;=\; w\;L\;/\;16$$

$$V_2 \;=\; 9\;w\;L\;/\;16$$

$$M_{max} \; (at\; x = \frac{7\;L}{16} ) \;=\; 49\;w\;L^2\;/\;512$$

$$M_1 \; \left(at \;support\; R_2 \right) \;=\; w\;L^2\;/\;16$$

$$M_x \; \left( x < L \right) \;=\; (w\;x\;/\;16) \; ( 7\;L - 8\;x )$$

$$\Delta_{max} \; ( 0.472 \; L \; from\;R_1 ) \;=\; 0.0092 \; (w\;L^4\;/\; \lambda\; I )$$

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 $$lbf$$ $$N$$
$$\lambda$$   (Greek symbol lambda) = modulus of elasticity $$lbf\;/\;in^2$$ $$Pa$$
$$I$$ = second moment of area (moment of inertia) $$in^4$$ $$mm^4$$
$$R$$ = reaction load at bearing point $$lbf$$ $$N$$
$$L$$ = span length under consideration $$in$$ $$mm$$

Tags: Beam Support