# Three Member Frame - Fixed/Free Side Top Point Load

Written by Jerry Ratzlaff on . Posted in Structural

### Three Member Frame - Fixed/Free Side Top Point Load Formula

$$\large{ R_A = 0 }$$

$$\large{ H_A = P }$$

$$\large{ M_{max} \left(at \;point\; A\right) = P\;h }$$

$$\large{ \Delta_{Cx} = \frac{P\;h^3}{3\; \lambda \; I} }$$

$$\large{ \Delta_{Cy} = \frac{P\;L\;h^2}{2\; \lambda \; I} }$$

$$\large{ \Delta_{Dx} = \frac{P\;h^3}{2\; \lambda \; I} }$$

$$\large{ \Delta_{Dy} = \frac{P\;L\;h^2}{2\; \lambda \; I} }$$

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