Three Member Frame - Fixed/Free Free End Bending Moment

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Three Member Frame - Fixed/Free Free End Bending Moment formulas

\(\large{ R_A  = 0  }\)
\(\large{ H_A = 0  }\)
\(\large{ M_{max}  = M_D  }\)
\(\large{ \Delta_{Dx}  = \frac{M_D\;h}{ \lambda \; I} \; \left( L+ 3\;h \right) }\)
\(\large{ \Delta_{Dy}  = \frac{M_D\;L}{ 2\; \lambda \; I} \; \left( L+ 2\;h \right)  }\)
\(\large{ \theta_{D}  = \frac{M_D}{ \lambda \; I} \; \left( L+ 2\;h \right)  }\)

Where:

\(\large{ \theta }\)  (Greek symbol theta) = angle

\(\large{ \Delta }\) = 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

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