Overhanging Beam - Uniformly Distributed Load Over Supported Span
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Overhanging Beam - Uniformly Distributed Load Over Supported Span formulas
| \(\large{ R = V = \frac{w\; L }{2} }\) | |
| \(\large{ V_x = w \; \left( \frac{L}{2} - x \right) }\) | |
| \(\large{ M_{max} \; }\) (at center) \(\large{ = \frac{w\; L^2 }{8} }\) | |
| \(\large{ M_x = \frac{w\; x }{2} \; \left( L - x \right) }\) | |
| \(\large{ \Delta_{max} \; }\) (at center) \(\large{ = \frac{5\;w\; L^4 }{348\; \lambda \; I} }\) | |
| \(\large{ \Delta_x = \frac{w\; x }{24\; \lambda\; I} \; \left( L^3 - 2\;L\;x^2 + x^3 \right) }\) | |
| \(\large{ \Delta_{x_1} = \frac{ -\; w \; L^3 \;x_1 }{24\; \lambda\; I} }\) |
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