Three Member Frame - Pin/Roller Side and Top Point Load

Written by Jerry Ratzlaff on . Posted in Structural

3fpr 2AThree Member Frame - Pin/Roller Side and Top Point Load Formula

\(\large{ R_A = R_D  =  \frac{ P\;h }{ L }   }\)

\(\large{ H_A =  P   }\)

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

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

\(\large{ \Delta_{Cy}  = 0  }\)

\(\large{ \Delta_{Dx}  =  \frac{P\;h^2}{6 \; \lambda \; I} \; \left(3\;L+2\;h\right)  }\)

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

 

Tags: Equations for Frame Support