Determine the reactions at the supports, Mechanical Engineering

Assignment Help:

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

Solution

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)


Related Discussions:- Determine the reactions at the supports

Difference between, Difference between path function and point function

Difference between path function and point function

Robotic and manufacturing automation, Consider the robotic manipulator of F...

Consider the robotic manipulator of Fig. 1, with a Revolute and a Prismatic Joint. Figure 1, shows the side view of the manipulator while figure 2. shows the top view of the manipu

Illustrate the euler-poincare formula, The Euler-Poincare Formula  The ...

The Euler-Poincare Formula  The Euler-Poincaré formula describes the relationship of the number of vertices, the number of edges and the number of faces of a manifold. It has b

Calculate the moment of inertia , Calculate the centroid (use point A as th...

Calculate the centroid (use point A as the reference) and the moment of inertia of the shape shown in Figure. The dimensions are given in centimeters.  Calculate the moment

Mechanical equipment specifications, The specifications for use on a projec...

The specifications for use on a project will be as defined in the Project Execution plan. The Specification requirements will be clarified in the Engineering Estimate or at the Pr

Material Science, What is tetra & octahedral voids & how are they formed ?

What is tetra & octahedral voids & how are they formed ?

Cooling period of furnace pipe, We shutdown our furnace and always encounte...

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

Show the procedure of compute flange stresses, Q. Show the Procedure of Com...

Q. Show the Procedure of Compute flange stresses? Compute flange stresses and the actual bolt stress using: - COLT values for gasket seating stress, ‘y' and the gasket facto

Stresses., temparature stresses in composite bars

temparature stresses in composite bars

Manufacturing , Differentiate between hot working and cold working process

Differentiate between hot working and cold working process

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