# Three Member Frame - Pin/Roller Outer Side Uniformly Distributed Load

Written by Jerry Ratzlaff on . Posted in Structural Engineering

## Three Member Frame - Pin/Roller Outer Side Uniformly Distributed Load formulas

 $$\large{ R_A = R_D = \frac{w\;h^2}{2\;L} }$$ $$\large{ H_A = w\;h }$$ $$\large{ M_C = \frac{w\;h^2}{2} }$$ $$\large{ M_{max} \;(at \; B) = w\;h^2 }$$ $$\large{ \Delta_{Dx} = \frac{w\;h^3}{24 \; \lambda \; I} \; \left( 18\;L + 11\;h \right) }$$

### Where:

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

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

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

$$\large{ M }$$ = maximum bending moment

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

$$\large{ \lambda }$$  (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