Calculating Forces in Truss Members using Method of Section

In summary, the conversation revolved around finding the reaction forces at points A and B, calculating the forces in all members using the method of Resolution at the Joints, and determining which member would fail first and why. The equations used were ƩFx = 0, ƩFy = 0, and ƩM = 0. The forces in all members were correctly calculated and it was determined that members AC and BE have no force, member AF is under 4000N of compression, member BK is under 6000N of compression, member FC is under 5000N of compression, and member FG is under 3000N of compression. The minus sign indicates compression, while a positive
  • #1
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Homework Statement



a) Find the reactions provided by the foundations at A and B.
b) Use the method of Resolution at the Joints to calculate the forces in all the members.
c) Which member will fail first and why ?

Homework Equations



ƩFx = 0
ƩFy = 0
ƩM = 0

The Attempt at a Solution



I am really just concerned with whether I have got the following correct. If I have, then I have grasped the concept if not then if someone could point me in the right direction and advise me on where to go next of what I am doing wrong I would be very grateful.

Horizontal Reaction Forces in the X direction at point A = 0
Vertical Reaction Forces in the Y direction at A = 4000N Upwards
Reaction Forces about the moment A at point B = 6000 Newtons Upwards

Forces in Member AC = 0N (0 + AC + AF = 0)
Forces in Member AF = 4000N in Compression (4000 + AC + AF = 0)
Forces in Member BK = 6000N in Compression (6000 + FBK.Sin(90) + FBE = 0)
Forces in Member BE = 0N (-FBE + FBK = 0)

Thanks
 

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  • #2
This is all good, you got them all correct:smile::approve::cool:
 
  • #3
Thanks very much! One last thing. I am now finding the forces in Members FC and FG. Am I right in saying:

Forces in direction:
-(-4000) - FC x sin(53.1) = 0 and then I just rearrange for FC = 5000 Newtons

and now I know FC I can do the following:

Force in direction:
0 + (FC x cos(53.1)) + FG = 0 and again rearrange for FG = -3002 Newtons
 
  • #4
Mattmiles said:
Thanks very much! One last thing. I am now finding the forces in Members FC and FG. Am I right in saying:

Forces in direction:
-(-4000) - FC x sin(53.1) = 0 and then I just rearrange for FC = 5000 Newtons
yes , compression or tension?
and now I know FC I can do the following:

Force in direction:
0 + (FC x cos(53.1)) + FG = 0 and again rearrange for FG = -3002 Newtons
You have a round off error, these are 3-4-5 right triangles, FG = -3000 N. What does the minus sign mean?
 
  • #5
Sorry a negative number means it is compression and a positive number means it is in tension.
 
  • #6
Mattmiles said:
Sorry a negative number means it is compression and a positive number means it is in tension.
OK, you are again correct.
 

What is the Method of Section for calculating forces in truss members?

The Method of Section is a technique used in structural analysis to determine the internal forces in specific members of a truss. It involves isolating a section of the truss and analyzing it as a free body, using equations of equilibrium to calculate the unknown forces.

Why is the Method of Section useful in structural analysis?

The Method of Section is useful because it allows for the determination of specific forces in truss members without having to analyze the entire truss. This can save time and effort in the design process and is especially helpful for complex truss structures.

What are the key steps in using the Method of Section?

The key steps in using the Method of Section are: 1) choosing a section of the truss to isolate, 2) drawing a free body diagram of the isolated section, 3) applying equations of equilibrium to solve for the unknown forces, and 4) checking the solution for consistency and accuracy.

How do I know if a truss is stable or if it will fail?

A truss is considered stable if all of its joints are in equilibrium, meaning that the sum of the forces acting on each joint must equal zero. If the truss is properly designed and has sufficient support, it should be able to withstand the applied loads without failure. However, it is important to perform a structural analysis, such as using the Method of Section, to ensure the truss is capable of supporting the intended loads.

Can the Method of Section be used for any type of truss?

Yes, the Method of Section can be used for any type of truss, including simple, compound, and complex truss structures. The key is to properly isolate a section of the truss that can be analyzed as a free body. However, in some cases, other methods of structural analysis may be more suitable for certain types of trusses.

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