Find out the reactions at point, Mechanical Engineering

Find out the reactions at point:

A beam AB is hinged at A and is supported at C. It is loaded as revealed in Figure. Find out the reactions at A and C.

2314_Find out the reactions at point.png

Solution

Let the reaction components at A be HA and VA as illustrated in Figure. The reaction at C shall be acting vertically upwards. As the beam is at rest under the action of the forces, the conditions of equilibrium may be applied.

Taking moments of all of forces about A, we obtain

∑ M A  = 0

18 × 3 × (3/2) + (40 sin 60o ) × 5 - Rc × 7 + 24 × 9 = 0

∴ 81 + 173.2 - 7 Rc + 216 = 0

∴ Rc = (81 + 173.2 + 216) /7

= 67.171 kN

 [Note : Moments because of HA, VA and 40 cos 60o regarding A are zero as they pass through point A. Clockwise moments are taken as +ve.]

Now, ∑ Fx  = 0

∴ H A - 40 cos 60o  = 0

∴ H A = 40 × 0.5 = 20 kN

and, ∑ Fy  = 0

∴ VA  - (18 × 3) - 40 sin 60o  + Rc  - 24 = 0

∴ VA  = 54 + 34.64 - 67.171 + 24

= 45.469 kN

1555_Find out the reactions at hinge2.png

 = 49.673 kN

tan θ= VA / H A = 45.469/20  = 2.2734

∴ θ = 66.257o  = 66o 15′ 25′′

The reaction at A contain a magnitude of 49.673 kN and is inclined at 66o 15′ 25′′ with respect to horizontal whereas reaction at C is working vertically upwards and has a magnitude of 67.171 kN.

Posted Date: 1/28/2013 5:11:05 AM | Location : United States







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