How Is the Right Triangle Used in Truss Force Calculations?

[mohamadali]

Hi, I have a, I believe simple, problem. I am studying for a Statics final and while doing problems with a Truss I came to a problem that I did not know how to solve. It is already solved for me, but I do not get how. The truss has a force coming out from the side but instead of an angle there is a right triangle. I do not understand how to use the triangle. I will upload a picture of the problem and the answer. If anyone can help me understand how the triangle is being used to compute the problem I would greatly appreciate it! Thanks in advance!

For example I do not understand where or why they get (4/5)Tcd or 130(12/13)

Direct Link:: http://i.imgur.com/ee9zP.jpg

 

[mohamadali]

oh nvm i think i got it, 3, 4 , 5 triangle!

 

[radou]

Shouldn't you be familiar with basic trigonometry in order to deal with statics? What are the relations in a right triangle?

 

[TaxOnFear]

I think you need to do some revision before your final. Look up the ratios of sine, cosine and tan.

 

[asteriatic]

Hello,

I would be happy to help you understand how the triangle is being used in this truss problem. First, let's review some basic principles of truss analysis. A truss is a structure made up of interconnected members that are subjected to external loads. These members are connected at joints, and the forces acting on each member are transmitted to the joints. The goal of truss analysis is to determine the internal forces (tension or compression) in each member of the truss.

In this problem, we have a truss with a force acting on the side. The right triangle that you see is a representation of this force and its components. The force acting on the side can be broken down into two components: a horizontal component (Tch) and a vertical component (Tcv). The angle of the triangle (12 degrees) is the angle between the force and the horizontal component. This angle is important because it allows us to use trigonometric functions to solve for the forces in the truss members.

Now let's look at the solution. The first step is to draw a free body diagram of the entire truss. This will help us visualize the forces acting on the truss and determine the equations needed to solve for the unknown forces. In this case, we have 5 unknown forces (Tab, Tbc, Tcd, Tce, and Tde) and 3 equations (sum of forces in the x-direction, sum of forces in the y-direction, and sum of moments about a point).

Next, we need to choose a point to take moments about. In this problem, the point chosen is the joint between members bc and cd. This is because there are only two unknown forces acting at this joint (Tbc and Tcd) and taking moments about this point will eliminate the unknown forces from the moment equation.

Now, let's focus on the sum of forces in the x-direction. We know that the horizontal component of the force acting on the side (Tch) is equal to the sum of the horizontal forces in the truss (Tbc and Tcd). Using trigonometric functions, we can write the following equation:

Tch = Tbc cos(12) + Tcd cos(12)

We also know that the sum of forces in the x-direction is equal to 0 (since the truss is in equilibrium). So we can write the following equation:

0 = Tbc cos(12)