# Three Member Frame - Fixed/Free Free End Bending Moment

Written by Jerry Ratzlaff on . Posted in Structural

## Three Member Frame - Fixed/Free Free End Bending Moment formulas

 $$\large{ R_A = 0 }$$ $$\large{ H_A = 0 }$$ $$\large{ M_{max} = M_D }$$ $$\large{ \Delta_{Dx} = \frac{M_D\;h}{ \lambda \; I} \; \left( L+ 3\;h \right) }$$ $$\large{ \Delta_{Dy} = \frac{M_D\;L}{ 2\; \lambda \; I} \; \left( L+ 2\;h \right) }$$ $$\large{ \theta_{D} = \frac{M_D}{ \lambda \; I} \; \left( L+ 2\;h \right) }$$

### Where:

$$\large{ \theta }$$  (Greek symbol theta) = angle

$$\large{ \Delta }$$ = 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)

$$\large{ \theta }$$  (Greek symbol theta) = slope of member

$$\large{ L }$$ = span length of the bending member