Two Member Frame - Fixed/Fixed Top Point Load

Written by Jerry Ratzlaff on . Posted in Structural

2ffbe 1Two Member Frame - Fixed/Fixed Top Point Load Formula

\(\large{ e  = \frac{h}{L}  }\)

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

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

\(\large{ R_D  =  P - R_A  }\)

\(\large{ H_A = H_D =  \frac{3\;P\;x^2}{2\;h\;L^2} \; \left( \frac{L\;-\;x}{ \beta\;e \;+\; 1} \right) }\)

\(\large{ M_A =  \frac{P\;x^2}{2\;L^2} \; \left( \frac{L\;-\;x}{ \beta\;e \;+\; 1} \right)   }\)

\(\large{ M_B =  \frac{P\;x^2}{L^2} \; \left( \frac{L\;-\;x}{ \beta\;e \;+\; 1} \right)   }\)

\(\large{ M_C =  R_B\;x - M_B  }\)

\(\large{ M_D =  \frac{P\;x \;\left( L \;-\; 1 \right)  }{ 2\;L^2 }  \; \left(   \frac{ \beta\;e\;\left( 2\;L \;-\; x \right) \;+\;2\;\left( L \;-\; x \right)   }{\beta \;e\;+\;1}  \right)  }\)

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