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

Written by Jerry Ratzlaff on . Posted in Structural

### Three 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