Two Member Frame - Fixed/Pin Top Point Load

Written by Jerry Ratzlaff on . Posted in Structural

2ffp 1ATwo Member Frame - Fixed/Pin Top Point Load Formula

\(\large{ e  = \frac{h}{L}  }\)

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

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

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

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

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

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

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

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

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