Simple Beam - Two Equal Point Loads Unequally Spaced

Simple Beam - Two Equal Point Loads Unequally Spaced Formula

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

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

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

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

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

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

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

Where:

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

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

\(\large{ M }\) = 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

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