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

Article Links

Beam Design Formulas Frame Design Formulas Plate Design Formulas Geometric Properties of Structural Shapes Welding Stress and Strain Connections Welding Symbols

 

 

 

 

 

 

 

 

 

 

 

 

Two Span Continuous Beam - Equal Spans, Uniform Load on One Span formulas
\(\large{ R_1 = V_1   \;\;=\;\; \frac{7\;w\;L}{16}    }\)  \(\large{ R_2 = V_2 + V_3   \;\;=\;\; \frac{5\;w\;L}{8}    }\)  \(\large{ R_3 = V_3   \;\;=\;\; \frac{w\;L}{16}    }\)  \(\large{ V_2   \;\;=\;\; \frac{9\;w\;L}{16}    }\) \(\large{ M_{max} \; \left(at\; x = \frac{7\;L}{16} \right)    \;\;=\;\; \frac{49\;w\;L^2}{512}    }\) \(\large{ M_1 \; \left(at \;support\; R_2 \right)  \;\;=\;\; \frac{w\;L^2}{16}    }\) \(\large{ M_x \;  \left( x < L \right)  \;\;=\;\; \frac{w\;x}{16} \; \left( 7\;L - 8\;x \right)  }\) \(\large{ \Delta_{max} \; \left( 0.472 \; L \; from\;R_1 \right)  \;\;=\;\; 0.0092 \; \frac{w\;L^4}{ \lambda\; I}    }\)
Symbol	English	Metric
\(\large{ \Delta }\) = deflection or deformation	\(\large{in}\)	\(\large{mm}\)
\(\large{ x }\) = horizontal distance from reaction to point on beam	\(\large{in}\)	\(\large{mm}\)
\(\large{ w }\) = load per unit length	\(\large{\frac{lbf}{in}}\)	\(\large{\frac{N}{m}}\)
\(\large{ M }\) = maximum bending moment	\(\large{lbf-in}\)	\(\large{N-mm}\)
\(\large{ V }\) = maximum shear force	\(\large{lbf}\)	\(\large{N}\)
\(\large{ \lambda  }\)   (Greek symbol lambda) = modulus of elasticity	\(\large{\frac{lbf}{in^2}}\)	\(\large{Pa}\)
\(\large{ I }\) = second moment of area (moment of inertia)	\(\large{in^4}\)	\(\large{mm^4}\)
\(\large{ R }\) = reaction load at bearing point	\(\large{lbf}\)	\(\large{N}\)
\(\large{ L }\) = span length under consideration	\(\large{in}\)	\(\large{mm}\)

 

diagrams

• 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.