Determine the reactions at the supports, Mechanical Engineering

Determine the reactions at the supports:

A smooth sphere weighing 200 N is resting as shown in Figure. Determine the reactions at the supports.

1662_Determine the reactions at the supports.gif


Let us first ascertain the directions of reactions. As the wall is vertical and smooth, the reaction at A shall be horizontal, i.e. normal to the wall. Similarly, the reaction at B shall be normal to the line inclined at 60o to the horizontal. Both these reactions shall pass through O, the centre of sphere, because these are normal drawn to the tangents of the sphere at A and B. The weight of the sphere may be supposed concentrated at O. Therefore; there concurrent forces keep the sphere at rest. Let us apply conditions of equilibrium:

∑ Fx = 0

∴ RA - RB cos θ = 0

θ = 30o by the geometry of the figure

And, ∑ Fy = 0

 ∴ RA  = 0.866 RB

RB  sin 30o  - W = 0

∴ RB  (0.5) = 200

∴ RB  = 200 /0.5 = 400 N

∴ RA  = 0.866 × 400 = 346.4 N

The same problem may be solved using Lami's theorem which states, "If three of the forces (coplanar) acting on a body keep it at rest then each force is proportional to the sin of the angle between the other two forces"

            RA/ sin (90o + θ) =       RB /sin 90o  =   W/ sin (180o  - θ)

Posted Date: 1/28/2013 5:07:03 AM | Location : United States

Related Discussions:- Determine the reactions at the supports, Assignment Help, Ask Question on Determine the reactions at the supports, Get Answer, Expert's Help, Determine the reactions at the supports Discussions

Write discussion on Determine the reactions at the supports
Your posts are moderated
Related Questions
Metallurgy of Electron Beam Welding EBW is capable of joining a variety of materials in a broader thickness range than any other fusion welding process. This is being in

SHIELDING GAS The primary function of the shielding gas is to exclude the atmospheric air from the arc zone. However, the shielding gas has significant influence on the arc cha

Relation between intensity bending moment and shear force: What is the relation between load intensity bending moment and shear force Consider the beam subjected to any t

Chisel: Chisels are used in the combination of hammer to remove metals. A set of chisels is shown in Figure. Figure: Chisel

Explain Cutting Speed - Cutting Parameters It is relative speed (V 1 ) between wheel and the Work piece. It is expressed in m/sec.   V=Cutting speed=V 1   =

We shutdown our furnace and always encountered crack on our piping at the weld joints. I investigated that upon shutdown the furnace cracking, our maintenance immediately remove th

Describe Inversion and Mechanism. Illustrate in detail all inversions of 4-Bar chain Mechanism. (a) Explain all the types of constrained motion with examples. (b) Explain in

discus the method to finding the width of impeller blades in a rotary air compressor

calculate the head required

(a) Briefly explain the following performance parameters of I.C. engine : (i) Indicated men effective pressure (Pim) (ii) Brake power (BP) (iii) Indicated power (IP) (