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]`

Answer 1

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"`