Overhanging Beam - Uniformly Distributed Load Overhanging Both Supports
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Overhanging Beam - Uniformly Distributed Load Overhang Both Supports formulas
\(\large{ R_1 = \frac{w\; L \; \left( L\; -\; 2\;c \right) }{2\;b} }\) | |
\(\large{ R_2 = \frac{w\; L \; \left( L \;-\; 2\;a \right) }{2\;b} }\) | |
\(\large{ V_1 = w\;a }\) | |
\(\large{ V_2 = R_1 - V_1 }\) | |
\(\large{ V_3 = R_2 - V_4 }\) | |
\(\large{ V_4 = w\;c }\) | |
\(\large{ V_{x_1} = V_1 - w \; \left( a - x_1 \right) }\) | |
\(\large{ V_x \;\left( x < b \right) = R_1 - w \; \left( a + x \right) }\) | |
\(\large{ M_1 = \frac{w\; a^2}{2} }\) | |
\(\large{ M_2 = \frac{w \;c^2}{2} }\) | |
\(\large{ M_3 = R_1 \; \left( \frac{R_1}{2\;w} - a \right) }\) | |
\(\large{ M_x = R_1 \; x \; \frac{ w \; \left( a \;+\; x \right)^2}{2} }\) |
Where:
\(\large{ I }\) = moment of inertia
\(\large{ L }\) = span length of the bending member
\(\large{ M }\) = maximum bending moment
\(\large{ R }\) = reaction load at bearing point
\(\large{ V }\) = shear force
\(\large{ w }\) = load per unit length
\(\large{ W }\) = total load from a uniform distribution
\(\large{ x }\) = horizontal distance from reaction to point on beam
\(\large{ \lambda }\) (Greek symbol lambda) = modulus of elasticity
\(\large{ \Delta }\) = deflection or deformation