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Question
In figure, a uniform bar of length l m is supported at its ends and loaded by a weight W kgf at its middle. In equilibrium, find the reactions R1 and R2 at the ends.
`["Hint:" "In equilibrium" "R"_1 + "R"_2 = "W" "and" "R"_1 xx l/2 = "R"_2 xx l/2]`
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Solution
As D is the mid-point of AB `(l)`
∴ AD = DB = `l/2`
The usual responses R1 and R2, which act upward, balance the bar's weight W, which acts downward toward the center of the earth.
∴In equilibrium, R1 + R2 = W
Total upward reaction = (R1 × AD) + (R2 × DB)
= `(R_1 xx l/2) + (R_2 xx l/2)`
∵ `R_1 xx l/2 + R_2 xx l/2 = R` ...(suppose)
Total upward reaction = downward wt. of bar.
∴ R + R = W
2R = W
R = `"W"/2`
∴ R1 = `"W"/2 " kgf"` and R2 = `"W"/2 " kgf"`
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