Find out the reactions at hinge, Mechanical Engineering

Assignment Help:

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.]


Related Discussions:- Find out the reactions at hinge

Relationship between two specific heat, Relationship between two specific h...

Relationship between two specific heat ? Sol:   dQ = dU + dW; for a perfect gas dQ at constant pressure dU at Constant volume; = mC v dT = mC v (T 2  - T 1 ) dW at

Essence of second law - thermodynamics, Essence of Second Law: Sol: ...

Essence of Second Law: Sol: First law deals with conservation and conversion of energy. But it fails to state the conditions under which the energy conversion are possible.

Determine the process of modelling, Determine the process of modelling ...

Determine the process of modelling The process of modelling is much easier, if mathematical description of an object, or at least of part of an object may be applied. In the fi

Reactions at grouted end of cantilever beam, Reactions at grouted end of ca...

Reactions at grouted end of cantilever beam: Q: Find reactions at grouted end of cantilever beam shown in figure given below     Draw free body diagram of the beam

Determine the deflection of the spring, Determine the deflection of the spr...

Determine the deflection of the spring: A close coiled helical spring deflects 25 mm under a certain axial load. Determine the deflection of the second spring under the simila

Engine oil replacement procedure, Engine oil replacement Motorcycle i...

Engine oil replacement Motorcycle is thoroughly drained by kicking the vehicle several times. Inspect the drain bolt washer and replace if necessary. Tighten the drai

Handling suspect material, Q. Handling Suspect Material? • Material or ...

Q. Handling Suspect Material? • Material or items at a Supplier's facility or those received or stored in the warehouse or other construction site location that require PMI-tes

Rcc pipe culverts, RCC Pipe Culverts: Reinforced cement concrete pipe...

RCC Pipe Culverts: Reinforced cement concrete pipe culverts are ideal for dealing with small discharges. The advantages are : (a) They are very economical, since a circula

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd