Simple Beam - Uniformly Distributed Load
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Simple Beam - Uniformly Distributed Load formulas
| \(\large{ R = V_{max} = \frac{w \; L}{2} }\) | |
| \(\large{ V_x = w \; \left( \frac{L}{2} - x \right) }\) | |
| \(\large{ M_{max} }\) (at center) \(\large{ = \frac{w \; L^2}{8} }\) | |
| \(\large{ M_x = \frac{w \; x}{2} \; \left( L - x \right) }\) | |
| \(\large{ \Delta_{max} }\) (at center) \(\large{ = \frac{5 \;w \;L^4}{384\; \lambda \;I} }\) | |
| \(\large{ \Delta_x = \frac{w\; x}{24\; \lambda \;I} \; \left( L^3 - 2\;L\;x^2 + x^3 \right) }\) |
Where:
\(\large{ \Delta }\) = deflection or deformation
\(\large{ x }\) = horizontal distance from reaction to point on beam
\(\large{ w }\) = load per unit length
\(\large{ M }\) = maximum bending moment
\(\large{ V }\) = maximum shear force
\(\large{ \lambda }\) (Greek symbol lambda) = modulus of elasticity
\(\large{ I }\) = moment of inertia
\(\large{ R }\) = reaction load at bearing point
\(\large{ L }\) = span length of the bending member