Why is the sin(60) term doubled in the truss equilibrium equation?

In summary, the conversation was about a problem involving the method of sections for solving statics equations. The equations provided were for determining the forces in different directions. However, there was confusion about the use of a double sine term in the vertical equation and whether the calculation was missing crucial information. Ultimately, it was suggested to only cut 3 members in the section for better accuracy.
  • #1
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truss.jpg


cannot understand something about this. here are the equations:

-T1-T3-T2cos(60)=0 x direction
2T2sin(60)-981N=0 y directionI don't understand why the sin(60) term is doubled in the y direction equation. Can anyone explain?
 
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  • #2
I guess you are using the "Method of Sections"?

However your diagram as you have drawn it is incomplete and it is impossible to complete the calculation as you need some geometrical information for the third (moment ) equation.

I agree that the vertical equilibrium, as shown, should not contain the factor of 2.
Is this a cantilever?
 
  • #3
Thanks for reply. I got the question from here:

http://en.wikibooks.org/wiki/Statics/Method_of_Sections

As I was reading through the double sine term seemed odd and wanted some clarification. As you can see on the website no moment calculations were done. Is that correct or is something in act missing? The diagram shown at the link looks fixed at the LHS.
 
  • #4
Well obviously you can't trust WikiXXX all the time!

If you think about it you have 2 equations and 3 unknowns, T1,T2 and T3.

If you take moments about the joint where T2 and T3 meet then you can solve for T1.

That is why it is normally recommended to only cut 3 members in the section.
 
  • #5


The reason for the doubled sin(60) term in the y direction equation is because of the geometry of the truss system. In this case, the truss is at an angle of 60 degrees with the horizontal. When we break down the forces in the y direction, we need to take into account the component of T2 that is acting in the vertical direction. This component is equal to T2sin(60), but since there are two sides of the truss that are experiencing this force, we need to double the value to account for both sides. This results in the equation 2T2sin(60) in the y direction. I hope this helps clarify the reasoning behind the equation.
 

FAQ: Why is the sin(60) term doubled in the truss equilibrium equation?

What is a truss and how does it relate to mechanics?

A truss is a structural element made up of connected bars or rods, typically arranged in triangular patterns. In mechanics, trusses are used to model the behavior of structures under external forces, such as tension and compression. They help us understand how forces are distributed and how a structure maintains equilibrium.

How do you determine the forces acting on a truss?

To determine the forces acting on a truss, we use the principles of equilibrium. This means that the sum of all forces in the horizontal and vertical directions must equal zero. We can also use the method of joints or the method of sections to solve for the unknown forces in a truss.

What is the difference between a stable and unstable truss?

A stable truss is one that can maintain its equilibrium under external forces without collapsing or moving. This means that all of its joints are properly connected and the forces acting on it are balanced. An unstable truss, on the other hand, is one that cannot maintain equilibrium and will collapse under the influence of external forces.

Can a truss experience both tension and compression forces?

Yes, a truss can experience both tension and compression forces. This is because the bars in a truss are designed to transfer forces from one point to another, and these forces can be either tensile (pulling) or compressive (pushing) depending on their direction and magnitude.

How do real-world factors such as material strength and weight affect the equilibrium of a truss?

Real-world factors such as material strength and weight can affect the equilibrium of a truss by altering the forces acting on it. For example, a heavier truss will experience greater forces under the same external load, which may require stronger materials to maintain equilibrium. Additionally, the strength and stiffness of the materials used can affect the overall stability and strength of the truss.

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