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

on . Posted in Structural Engineering

cb3s 7A

Article Links

 

 

 

 

 

 

 

 

 

 

 

 

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

\(\large{ R_1 = V_1   \;\;=\;\;  \frac{M_2}{a}  +  \frac{P_1}{2}   }\) 

\(\large{ R_2   \;\;=\;\;  P_1 + P_2 - R_1 - R_3   }\) 

\(\large{ R_3 = V_4   \;\;=\;\;  \frac{M_2}{b}  +  \frac{P_2}{2}   }\) 

\(\large{ M_1   \;\;=\;\;  R_1 \;\frac{a}{2}   }\)

\(\large{ M_2   \;\;=\;\; -\; \frac{3}{16}  \;  \left(  \frac{P_1\; a^2 \;+ \;P_2 \; b^2}{a \;+\; b}  \right)  }\)

\(\large{ M_3   \;\;=\;\;  R_3\; \frac{b}{2}   }\)

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

 

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.

 

Piping Designer Logo 1

Tags: Beam Support Equations