Question

A beam AB of length 5 m is subjected to a clockwise couple moment of 100 Nm at its center. The end A is hinged and B is supported by a roller. The magnitude of reaction at A and B are

Answer 1

Step-by-step explanation:

Let the reaction at B = R

Then Reaction at A = 2R

In vertical direction, the forces will be equal

Thus

W₁+ W₂ = 2R+R

W₁ + W₂

=

.(1)

Again Moment with respect to any point will be zero

Taking moment w.r.t. A

W₁ x 1 + W₂ x 3 =R x 5

W₁ + 3W₂ = 5R

W₁ + 3W₂ = 5(W₁+W2)

3W₁ + 9W₂ = 5W₁ + 5W₂

2W₁ = 4W₂

2 W₁ = ²

W₁ W₂ = 2:1

Therefore, the ratio of W₁ and W₂ is 2 : 1

Answer 2

The anwer of the given question

The magnitude of reaction at A and B are75 N, 75 N.