Three Member Frame - Pin/Pin Top Point Load

Written by Jerry Ratzlaff on . Posted in Structural

3fpbe 1Three Member Frame - Pin/Pin Top Point Load Formula

\(\large{ e  = \frac{h}{L}  }\)

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

\(\large{ R_A  =  P\; \frac{L\;-\;x}{L}  }\)

\(\large{ R_E  =  P\; \frac{x}{L}  }\)

\(\large{ H_A = H_E =  \frac{3\;P\;x}{2\;h\;L} \; \left( \frac{L\;-\;x}{2\; \beta\;e \;+\; 3} \right)   }\)

\(\large{ M_B = M_D =  \frac{3\;P\;x}{2\;L} \; \left( \frac{L\;-\;x}{2\; \beta\;e \;+\; 3} \right)   }\)

\(\large{ M_C =  \frac{P\;x \; \left( L\;-\;x \right) }{2\;L} \; \left( \frac{4\; \beta\;e \;+\; 3}{2\; \beta\;e \;+\; 3} \right)   }\)

Where:

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

\(\large{ x }\) =  horizontal distance from reaction point

\(\large{ H }\) =  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

\(\large{ P }\) = total concentrated load

 

Tags: Equations for Frame Support