Three Member Frame - Fixed/Fixed Center Point Load

Written by Jerry Ratzlaff on . Posted in Structural

3fbe 2Three Member Frame - Fixed/Fixed Center Point Load Formula

\(\large{ e  = \frac{h}{L}  }\)

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

\(\large{ R_A = R_E  =  \frac{ P }{ 2 }   }\)

\(\large{ H_A = H_E =  \frac{3\;P\;L}{8\;h\; \left( \beta\;e\;+\;2 \right) }    }\)

\(\large{ M_A = M_E =  \frac{P\;L}{8\; \left( \beta\;e\;+\;2 \right) }    }\)

\(\large{ M_B = M_D =  \frac{P\;L}{4\; \left( \beta\;e\;+\;2 \right) }    }\)

\(\large{ M_C =  \frac{P\;L}{4}  \;  \left(  \frac{ \beta\;e\;+\;1 }{ \beta\;e\;+\;2 }  \right)  }\)

Where:

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

\(\large{ H }\) =  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