LECTURE 1 : STATICS - Resultant of concurrent force

We'll start with the basics.

First of all, What is Statics in Civil Engineering?

It is the study of effects of forces on a rigid body at rest.

Above, we can see the formula for the magnitude of resultant which we'll refer to as R

What is Rx and Ry?

Rx is the summation of forces along the X-component and Ry is the summation of forces along Y-component.

An example of forces would be presented later on. Here's​ a tip. What would really help you out with the computation of Rx and Ry is by mastering that basic trigonometric functions of a right triangle. We could remember this by uttering​ SOH-CAH-TOA. An image is provided below for further understanding of the identities.                           

The next picture would show a presentation of slanting force and on how to compute for Rx and Ry given the Resultant force and angle.

Why is it important to master this topic? The computations of forces like this will be one of the primary foundations on further study of civil engineering. Now, back to the example.

With the Resultant and angle given, We could first consider angle teta. Rx would then be equal to Fcos(teta). We could obtain this equation by picturing a right triangle.

We could see that the side with the given values are the hypotenuse (R) and the angle teta. By recalling SOH-CAH-TOA, and looking the figure. We can use the function 'CAH' to solve for Rx. And the function SOH to solve for Ry. 

So: 

Rx= Fcos(teta)

Ry = Fsin(alpha)

Note: if there would be two or more forces you are then required to do the summation of forces along x and along y and by doing so you can compute for the resultant by using the first given formula.

Note: Do not forget the proper sign convention, (it will not be discussed since I think we all knows that) I hope I helped. Feel free to comment if you have any question. 

(Please watch my YouTube video tutorial for the application problems)

HW : GIVEN THAT R = 120 N , ALPHA = 60 compute Rx and Ry (ignore angle teta) 

I'll be waiting for your answers in the comment section.

- Frustrated teacher, C.E. at heart