Simple Beam - Two Equal Point Loads Unequally Spaced

Written by Jerry Ratzlaff on 23 April 2018. Posted in Structural

(Eq. 1) \(\large{ R_1 = V_1 }\) max. when \(\large{ \left( a < b \right) = \frac {P} {L} \left( L - a + b \right) }\)

(Eq. 2) \(\large{ R_2 = V_2 }\) max. when \(\large{ \left( a < b \right) = \frac {P} {L} \left( L - b + a \right) }\)

(Eq. 3) \(\large{ V_x \; }\) when \(\large{ \left( x > a \right) \; }\) and \(\large{ < \left( L - b \right) = \frac {P} {L} \left( b - a \right) }\)

(Eq. 4) \(\large{ M_1 }\) max. when \(\large{ \left( a > b \right) = R_1 a }\)

(Eq. 5) \(\large{ M_2 }\) max. when \(\large{ \left( a < b \right) = R_2 b }\)

(Eq. 6) \(\large{ M_x }\) max. when \(\large{ \left( x < a \right) = R_1 x }\)

(Eq. 7) \(\large{ M_x \; }\) when \(\large{ \left( x > a \right) \; }\) and \(\large{ < \left( L - b \right) = R_1 x - P \left( x - a \right) }\)

Where:

\(\large{ I }\) = moment of inertia

\(\large{ L }\) = span length of the bending member

\(\large{ a, b }\) = length to point load

\(\large{ M }\) = maximum bending moment

\(\large{ P }\) = total concentrated load

\(\large{ R }\) = reaction load at bearing point

\(\large{ V }\) = maximum shear force

\(\large{ x }\) = horizontal distance from reaction to point on beam

\(\large{ \lambda }\) (Greek symbol lambda) = modulus of elasticity