Two Member Frame - Fixed/Free Free End Bending Moment

Written by Jerry Ratzlaff on . Posted in Structural

2fff 3ATwo Member Frame - Fixed/Free Free End Bending Moment Formula

\(\large{ R_A  = 0  }\)

\(\large{ H_A = 0  }\)

\(\large{ M_{max}  = M_C  }\)

\(\large{ \Delta_{Cx}  = \frac{M_C\;h^2}{2\; \lambda \; I}  }\)

\(\large{ \Delta_{Cy}  = \frac{M_C\;L}{2\; \lambda \; I} \; \left( L + 2\;h \right)  }\)

\(\large{ \theta_{C}  = \frac{M_C}{ \lambda \; L} \; \left( L + h \right)  }\)

Where:

\(\large{ \Delta }\) = deflection or deformation

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

\(\large{ H }\) =  horizontal reaction load at bearing point

\(\large{ M }\) = maximum bending moment

\(\large{ \lambda }\)  (Greek symbol lambda) = modulus of elasticity

\(\large{ A, B, C }\) = points of intersection on frame

\(\large{ R }\) = reaction load at bearing point

\(\large{ I }\) = second moment of area (moment of inertia)

\(\large{ \theta }\)  (Greek symbol theta) = slope of member

\(\large{ L }\) = span length of the bending member

 

Tags: Equations for Frame Support