Find out the reactions at hinge, Mechanical Engineering

Find out the reactions at hinge:

A board ABCD is held in position as shown in Figure by a cable BE and a hinge at A. If the weight of the board is 5 kN, find out the reactions at hinge A and the tension T in the cable.

1463_Find out the reactions at hinge.png

Solution

Assume the components of the reaction at A be HA and VA as illustrated in Figure. The board is at rest under the action of four forces HA, VA, T and W.

Taking moments of all of forces about A, we obtain

∑ M A = 0

                               ∴ - (T sin 30o) × 1.6 + W × 0.8 = 0

                                 ∴ - 0.8T + 5 × 0.8 = 0

                                  ∴ T = 4 /0.8 = 5 kN

And, ∑ Fx = 0

∴ H A  - T cos 30o  = 0

∴ H A  = T cos 30o

 (On putting T = 5 kN) ∴ H A  = 5 × 0.866 = 4.33 kN

Also, ∑ Fy  = 0

                     ∴ VA  + T sin 30o  - W = 0

                      ∴ V A  = W - T sin 30o

                                  = 5 - 5 × 0.5

                                  = 2.5 kN

Now

549_Find out the reactions at hinge1.png

                               = 5 kN

θ = tan -1  ( VA / H A)

= tan -1  (2.50 /4.33)

= 30o

Reaction RA has a magnitude of 5 kN and is inclined at 30o to the horizontal.

[Note : You can attempt the same problem considering the board to be subjected to 3 forces only viz., RA, T and W. As three of the forces keep the body at rest, these should be concurrent. Find the point of concurrence and get the values of unknowns RA and T, using

                  ∑ Fx  = 0   and             ∑ F= 0

knowing the direction of RA, you might also use Lami's theorem either.]

Posted Date: 1/28/2013 5:09:40 AM | Location : United States







Related Discussions:- Find out the reactions at hinge, Assignment Help, Ask Question on Find out the reactions at hinge, Get Answer, Expert's Help, Find out the reactions at hinge Discussions

Write discussion on Find out the reactions at hinge
Your posts are moderated
Related Questions
Determine the centroidal moment of inertia: Determine the centroidal moment of inertia of a thin flat disc shown in Figure which is having a mass m kg. By using the parallel a


At a point in a beam, the bending stress is 50 MPa shear stress and tensile is 20 MPa. Calculate :- (i) The principal stress and maximum shear stress. (ii) The tensile stress

proportional controller for lube oil temperature of engine working diagram

A Boot Strap Cooling system of 10 TR capacity is used in an aeroplane. The ambient air pressure and temperature are 0.85 and 20 0 C bar respectively. The pressure of air increases

Pola r Modulus(Z p ):   It is the ratio of polar moment of the inertia to outer radius. Z p = J / R Polar Modulus of solid body ( Z p ) =[  ?/32. D 4 ]/ D


Control of the guide vanes shall be by means of an external linkage connected to the internal control ring Steam Generator piping. Inlet guide vanes shall be furnished with the

Proof of parallelogram law of forces

Answer any five questions. a) Describe calibration and state its types. b) Which are the kinds of test signals? c) What is the basic working principle of piezo-electric tr