Two Member Frame - Fixed/Pin Side Point Load

Written by Jerry Ratzlaff on . Posted in Structural

2ffp 2Two Member Frame - Fixed/Pin Side Point Load Formula

\(\large{ e  = \frac{h}{L}  }\)

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

\(\large{ R_A = R_D =  \frac{3\;P\;y \; \left( h\;-\;y^2 \right) }{h\;L^2} \; \left( \frac{ \beta }{ 3\;\beta\;e \;+\; 4} \right) }\)

\(\large{ H_A  =  \frac{P\;y}{h}  \; \left[ 1+ \; \frac{h\;-\;y}{h^2} \; \left( \frac{  3\;x\;\beta\;e \;+\; 2\; \left( h\;+\;y \right) }{ 3\;\beta\;e \;+\; 4} \right) \right] }\)

\(\large{ H_D  =  P - H_A }\)

\(\large{ M_A =  \frac{P\;x \; \left( h\;-\;y \right) }{h^2} \; \left( \frac{  3\;x\;\beta\;e \;+\; 2\; \left( h\;+\;y \right) }{ 3\;\beta\;e \;+\; 4} \right) }\)

\(\large{ M_B =  H_A \; \left( h\;-\;y \right) - M_A  }\)

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

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

\(\large{ A, B, C, D }\) = 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 to reaction point

 

Tags: Equations for Frame Support