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
What are types of raft foundation? Define according to rigid mat deign. One of the common types of raft foundation is the flat concrete slab 0.75 to 2.00 m thick with a two way

GENERAL TOOLS: General tools include spanners, screw drivers, files, pliers, vices, punches, mallets, chisels, grinders, drilling machine, oil and grease guns, etc.



SURFACE MODELING: The process of modeling is built much easier for a mathematical description of an object or at least on a part of the object might be applied. Surfaces might

(a) Explain briefly the functions of the spiral casing guide vanes, and draft tube of a reaction water. (b) A Kaplan turbine developing 3250 KW under a head of 6m has a draft tu

Internal combustion engine - Thermodynamics: Internal combustion engine is popularly known as I.C. engine, is heat engine that converts the heat energy released by the combust

The tapered, two-cell beam is subjected to a pure torque of 50,000 in-lb counter clockwise. The length of the beam (normal to the figure) is 100 in. The flange areas are 1 sq in an

Illustrate following key terms with suitable example :- (a) Co-planar parallel force. (b) Co-planar non concurrent force. (c) Non co-planar concurrent force.

Evolution of Specific volume of wet saturated steam -thermodynamics : Specific volume of wet saturated steam (V we t ) It is volume occupied by unit mass of wet satu