Overhanging Beam - Point Load on Beam End
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Overhanging Beam - Point Load on Beam End formulas
| \(\large{ R_1 = V_1 = \frac{P\;a}{L} }\) | |
| \(\large{ R_2 = V_1 + V_2 = \frac{ P }{L} \; \left( L + a \right) }\) | |
| \(\large{ V_2 = P }\) | |
| \(\large{ M_{max} \; }\) at \(\large{ \left( R_2 \right) = P\;a }\) | |
| \(\large{ M_x \; }\) (between supports) \(\large{ = \frac{P\;a\;x}{L} }\) | |
| \(\large{ M_{x_1} \; }\) (for overhang) \(\large{ = P \left( a - x_1 \right) }\) | |
| \(\large{ \Delta_x \; }\) (between supports) \(\large{ = \frac{ -\;P\;a\;x }{6\; \lambda \;I\;L} \; \left( L^2 - x^2 \right) }\) | |
| \(\large{ \Delta_{x_1} \; }\) (overhang) \(\large{ = \frac{ P\;x_1 }{6\; \lambda\; I } \; \left( 2\;a\;L + 3\;a\;x_1 - x_{1}{^2} \right) }\) | |
| \(\large{ \Delta_{max} \; }\) for overhang at \(\large{ \left(x_1 = a \right) = \frac{ P\;a^2 }{3\; \lambda \;I } \; \left( L + a \right) }\) | |
| \(\large{ \Delta_{max} \; }\) between supports at \(\large{ \left( x = \frac{L}{\sqrt{3}} \right) = \frac{ -\;P\;a\;L^2 }{9\; \sqrt{3} \; \lambda\; I } = 0.06415 \; \frac{ P\;a\;L^2 }{ \lambda\; I } }\) |
Where:
\(\large{ I }\) = moment of inertia
\(\large{ L }\) = span length of the bending member
\(\large{ M }\) = maximum bending moment
\(\large{ P }\) = total concentrated load
\(\large{ R }\) = 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