# Three Member Frame - Pin/Roller Side and Bottom Point Load

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## Three Member Frame - Pin/Roller Side and Bottom Point Load formulas

\(\large{ R_A = R_D = 0 }\) | |

\(\large{ H_A = P }\) | |

\(\large{ M_{max} \;(at \; B \;and\; C) = P\;h }\) | |

\(\large{ \Delta_{Dx} = \frac{P\;h^2}{3 \; \lambda \; I} \; \left(3\;L+2\;h\right) }\) |

### 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

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

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

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

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

\(\large{ P }\) = total concentrated load