# 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