Equilibrium definition and problem anshwer

Equilibrium definition and problem answer

This section will be limited to one- or two-dimensional systems, where all the forces and couples will be acting in on plane; such a system of forces is called a coplanar system. In two dimensions, equilibrium is acheved when the following laws are satisfied:

upward forces = downward forces.
forces to the left = forces to the right. 
clockwise couples = counter-clockwise couples.

 To demonstrate the use of these two-dimensional laws of equilibrium, the following problems will be considered.

Also read:- FLOW MEASURING DEVICES

Problem 1.2 : Determine the values of the reactions RA and RB, when a beam is simplysupported at its ends and subjected to a downward force of 5 kN.

Solution:

For this problem, it will be necessary to take moments. By taking moments, it is meant that the values of the moments must be considered about a suitable position. Suitable positions for takmg moments on this beam are A and B. This is because, if moments are taken about A, the unknown section RA will have no lever and hence, no moment about A, thereby simplifying the arithmetic. Similarly, by talung moments about B, the unknown RE will have no lever and hence, no moment about B, thereby simplifying the arithmetic. Taking moments about B.

clockwise moments = counter-clockwise moments

RAx(4+2) = 5x2

Or

RA = 10/6

RA = 1.667 kN

Resolving forces vertically upward forces = downward forces

RA+RB = 5

Or

RB = 5 - RA = 5 - 1.667

RA = 3.333kN Answer.

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