# Three Member Frame - Fixed/Free Top Uniformly Distributed Load

Written by Jerry Ratzlaff on . Posted in Structural

### Three Member Frame - Fixed/Free Top Uniformly Distributed Load Formula

$$\large{ R_A = w\;L }$$

$$\large{ H_A = 0 }$$

$$\large{ M_{max} \left(at \;points\; A\; and \;B\right) = \frac{w\;L^2}{2} }$$

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

$$\large{ \Delta_{Dy} = \frac{w\;L^3}{ 8\; \lambda \; I} \; \left( L+ 4\;h \right) }$$

Where:

$$\large{ \Delta }$$ = deflection or deformation

$$\large{ h }$$ = height of frame

$$\large{ H }$$ =  horizontal reaction load at bearing point

$$\large{ w }$$ = load per unit length

$$\large{ M }$$ = 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