Three Member Frame - Pin/Pin Top Uniformly Distributed Load

Written by Jerry Ratzlaff on . Posted in Structural

3fpbe 4Three Member Frame - Pin/Pin Top Uniformly Distributed Load Formula

\(\large{ e  = \frac{h}{L}  }\)

\(\large{ \beta = \frac{I_h}{I_v}  }\)

\(\large{ R_A  = R_E = \frac{ w\;L }{2}  }\)

\(\large{ H_A  = H_E = \frac{ w\;L }{4\;e\; \left( 2\;\beta\;e \;+\; 3 \right)  }  }\)

\(\large{ M_B  = M_D = \frac{ w\;L^2 }{4\; \left( 2\;\beta\;e \;+\; 3 \right)  }  }\)

\(\large{ M_C  =   \frac{w\;L^2}{8}   \;   \left(  \frac{ 2\;\beta\;e \;+\; 1 }{ 2\;\beta\;e \;+\; 3 } \right)  }\)

Where:

\(\large{ h }\) = height of frame

\(\large{ H }\) =  horizontal reaction load at bearing point

\(\large{ M }\) = maximum bending moment

\(\large{ A, B, C, D, E }\) = points of intersection on frame

\(\large{ R }\) = reaction load at bearing point

\(\large{ I }\) = second moment of area (moment of inertia)

\(\large{ I_h }\) = horizontal second moment of area (moment of inertia)

\(\large{ I_v }\) = vertical second moment of area (moment of inertia)

\(\large{ L }\) = span length of the bending member

 

Tags: Equations for Frame Support