Simple Beam - Load Increasing Uniformly to Center
Simple Beam - Load Increasing Uniformly to Center Formula
(Eq. 1) \(\large{ R = V_{max} = \frac {W } {2} }\)
(Eq. 2) \(\large{ V_x \; }\) when \(\large{ \left( x < \frac {L}{2} \right) = \frac {W} {2L^2} \left( L^2 - 4x^2 \right) }\)
(Eq. 3) \(\large{ M_{max} }\) (at center) \(\large{ = \frac {W L} {6} }\)
(Eq. 4) \(\large{ M_x \; }\) when \(\large{ \left( x < \frac {L}{2} \right) = Wx \left( \frac {1}{2} - \frac {2x^2}{3L^2} \right) }\)
(Eq. 5) \(\large{ \Delta_{max} }\) (at center) \(\large{ = \frac {W L^3} {60 \lambda I } }\)
(Eq. 6) \(\large{ \Delta_x = \frac {W x} {480 \lambda I L^2} \left( 5L^2 - 4x^2 \right)^2 }\)
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
\(\large{ V }\) = maximum shear force
\(\large{ w }\) = highest load per unit length of UIL
\(\large{ W }\) = total load or wL/2
\(\large{ x }\) = horizontal distance from reaction to point on beam
\(\large{ \lambda }\) (Greek symbol lambda) = modulus of elasticity
\(\large{ \Delta }\) = deflection or deformation