How do I calculate the forces in a Truss?

In summary: However, if you have the equations for both compression and tension forces, you can use the laws of mechanics to work out the answer.
  • #1
tandennis0703
8
3

Homework Statement


Truss_question.png


Homework Equations


Untitled.png


The Attempt at a Solution


I have spent the last 2 hours trying to figure out which part of the truss is compression or tension. Hopefully the second screenshot I took is correct. I tried figuring out the first few parts, just want to make sure that at least I am on the right track.

scan_help.png
 
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  • #2
tandennis0703 said:
trying to figure out which part of the truss is compression or tension.
Although it is usually easy to figure out in simple cases, it can be quite tricky. Fortunately, you rarely need to. Just make a stab at it in each case and write the equations accordingly. If the answer comes out negative then you guessed wrong, but so what? You still have the answer.

In fact, in the annotated diagram you put under "relevant equations" you seem to have guessed most wrongly.
And that is not what the "relevant equations" section is for. It's for standard equations that can be applied to a whole class of questions.

In the image of your working, how do you get Cx+Dx=0?
(Please do not post images of your algebra. Take the trouble to type it in. That makes it easier to read and easier to comment on. Images should be for diagrams and textbook extracts.)
 
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  • #3
Scan_20160819.png


Sorry for the mistakes. I never took statics in my course. I redid everything and used the method of summing the resultant forces in both the x and y direction. I am still a bit confused as to how to figure out whether or not it is a compression/ tension force. Hopefully my calculations are correct.
 
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  • #4
tandennis0703 said:
Scan_20160819.png


Sorry for the mistakes. I never took statics in my course. I redid everything and used the method of summing the resultant forces in both the x and y direction. I am still a bit confused as to how to figure out whether or not it is a compression/ tension force. Hopefully my calculations are correct.
I did ask you to type in your algebra. I am having trouble reading some of the image, and if I want to comment on an equation I have no easy way to refer to it.
Check the signs in your equations for point B.
 
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  • #5
haruspex said:
I did ask you to type in your algebra. I am having trouble reading some of the image, and if I want to comment on an equation I have no easy way to refer to it.
Check the signs in your equations for point B.

Joint A:

+^ΣFy=0 ; -2P+(2/3.61)FAB=0
FAB=3.61P

>+ ΣFx=0; -FAE+(3/3.61)(3.61)P=0
FAE=3P

Joint E:


+^ΣFy=0; FEB-P=0
FEB=P

>+ ΣFx=0; 3P - FED=0
FED=3P

Joint B:

+^ΣFy=0; (2/3.61)FBD-P-(2/3.61)(3.61)(P)=0
(2/3.61)FBD=3P
FBD=5.415P

>+ΣFx=0; FBC -(5.415)(3/3.61)(P)-(3.61)(P)(3/3.61)=0
FBC=7.5P

Hence:

stress BC= 7.5P/340 = 250

P=11333N
 
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  • #6
tandennis0703 said:
Joint B:

+^ΣFy=0; (2/3.61)FBD-P-(2/3.61)(3.61)(P)=0
According to what you calculated at joint A, is AB under compression or
tandennis0703 said:
Joint A:

+^ΣFy=0 ; -2P+(2/3.61)FAB=0
FAB=3.61P

>+ ΣFx=0; -FAE+(3/3.61)(3.61)P=0
FAE=3P

Joint E:


+^ΣFy=0; FEB-P=0
FEB=P

>+ ΣFx=0; 3P - FED=0
FED=3P

Joint B:

+^ΣFy=0; (2/3.61)FBD-P-(2/3.61)(3.61)(P)=0
(2/3.61)FBD=3P
FBD=5.415P

>+ΣFx=0; FBC -(5.415)(3/3.61)(P)-(3.61)(P)(3/3.61)=0
FBC=7.5P

Hence:

stress BC= 7.5P/340 = 250

P=11333N
Now I can read it, it all looks right.
 
  • #7
haruspex said:
According to what you calculated at joint A, is AB under compression or

Now I can read it, it all looks right.

Thanks for the reply. However I am still a bit confused as to how I know whether or not a bar is undergoing compression or tension. Do I need my calculations in order to figure that out?
 
  • #8
tandennis0703 said:
Thanks for the reply. However I am still a bit confused as to how I know whether or not a bar is undergoing compression or tension. Do I need my calculations in order to figure that out?
In general, yes. As I posted, it is not always possible to figure it out by simple inspection.
 

1. How do I determine the external forces acting on a truss?

To calculate the forces in a truss, you first need to identify all the external forces acting on the truss. This can include applied loads, reactions at supports, and self-weight of the truss. Once you have all the external forces, you can move on to solving for the internal forces in the truss members.

2. What is the method for calculating the forces in a truss?

The most common method for calculating the forces in a truss is the method of joints. This involves analyzing each joint in the truss and applying the equations of equilibrium to solve for the forces in each member connected to that joint. Another method is the method of sections, which involves cutting the truss into sections and analyzing the forces in each section.

3. Can I use a computer program or software to calculate the forces in a truss?

Yes, there are many computer programs and software available that can calculate the forces in a truss. These programs use numerical methods to solve for the forces and can handle complex truss structures. However, it is still important to have an understanding of the principles and methods used in truss analysis to interpret the results from these programs.

4. How do I account for the weight of the truss itself when calculating forces?

The weight of the truss itself is considered an external force and should be included in the analysis. This can be done by breaking the truss down into smaller sections and considering the weight of each section as an applied load. Alternatively, you can also consider the weight of the entire truss as a distributed load and apply it to the joints in proportion to the length of each member.

5. Are there any assumptions made when calculating the forces in a truss?

Yes, there are a few assumptions made when calculating the forces in a truss. These include assuming the truss is in equilibrium, that all the members are connected by ideal pins or hinges, and that the members are only subjected to axial forces. Additionally, truss analysis assumes that the joints are rigid, meaning they do not deform under the applied loads.

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