Three Member Frame - Fixed/Free Free End Bending Moment
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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