Three Member Frame - Pin/Roller Central Bending Moment

Three Member Frame - Pin/Roller Central Bending Moment Formula

\(\large{ R_A = R_B  = \frac{M_C}{L}  }\)

\(\large{ H_A = 0  }\)

\(\large{ M_{max} \;(at \; C)  =  \frac{M_C}{2}   }\)

\(\large{ \theta \;(at \; C) =  \frac{M_C\;L}{12 \; \lambda \; I}  }\)

Where:

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

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

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

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

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

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

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

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