Practice Question: Maximum Shear for Two Equal Concentrated Loads

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Solution

It is clear from given diagram that:

\(R_A\) = Reaction at left support “A” due to two point loads
\(R_B\) = Reaction at right support “B” due to two point loads
\(a\) = Distance to point loads from supports
\(l\) = Total length of beam

Taking the sum of the moments about “B”:

\[∑M_B=0\]

\[R_A  (l)-P(l-a)-P(a)=0\]\[R_A  (l)=P(l-a)+P(a)\]
\[R_A  (l)=P(l)-Pa+Pa\]

\[R_A=P\]Sum of vertical forces:\[∑F_y=0\]\[R_A+R_B-P-P=0\]\[P+R_B-P-P=0\]
\[R_B=P\]

Given that no reaction is greater than force "P," the maximum shear cannot be less than or greater than "P."
 

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