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

Written by Jerry Ratzlaff on . Posted in Structural

### Two Member Frame - Fixed/Free Free End Bending Moment Formula

$$\large{ R_A = 0 }$$

$$\large{ H_A = 0 }$$

$$\large{ M_{max} = M_C }$$

$$\large{ \Delta_{Cx} = \frac{M_C\;h^2}{2\; \lambda \; I} }$$

$$\large{ \Delta_{Cy} = \frac{M_C\;L}{2\; \lambda \; I} \; \left( L + 2\;h \right) }$$

$$\large{ \theta_{C} = \frac{M_C}{ \lambda \; L} \; \left( L + h \right) }$$

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

$$\large{ A, B, C }$$ = 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