Three Member Frame - Pin/Pin Side Point Load

Written by Jerry Ratzlaff on . Posted in Structural

3fpbe 3Three Member Frame - Pin/Pin Side Point Load Formula

\(\large{ e  = \frac{h}{L}  }\)

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

\(\large{ R_A  = R_E = \frac{ P \; \left(h\;-\;y\right) }{L}  }\)

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

\(\large{ H_E =  \frac{P\; \left( h\;-\;y \right) }{2\;h}  \; \left( 1+\; \frac{ y\; \beta \; \left( 2\;h\;-\;y\right) }{h\;\left( 2\;h\; \beta\;+\; 3\;L\right) } \right) }\)

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

\(\large{ M_C =  \frac{P\; \left( h\;-\;y \right) }{2}  \; \left( 1-\; \frac{ y\; \beta \; \left( 2\;h\;-\;y\right) }{h\;\left( 2\;h\; \beta\;+\; 3\;L\right) } \right) }\)

\(\large{ M_D =  \frac{P\; \left( h\;-\;y \right) }{2}  \; \left( 1+\; \frac{ y\; \beta \; \left( 2\;h\;-\;y\right) }{h\;\left( 2\;h\; \beta\;+\; 3\;L\right) } \right) }\)

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

\(\large{ y }\) = vertical distance from reaction point

 

Tags: Equations for Frame Support