Method of joints, force in each member

In summary, the conversation revolves around solving a truss problem using the method of joints. The solution involves calculating the forces in each member and determining whether they are in compression or tension. The conversation also discusses using moments to solve the problem and the importance of using a sign convention to determine the direction of the forces. The conversation also includes a request for a free body diagram to better understand the solution.
  • #1
togo
106
0

Homework Statement


Using method of joints, determine the force in each member of the truss. State whether each member is in compression or tension.
6zlziq.jpg


Homework Equations


joint method, I'm not sure how to describe it.

The Attempt at a Solution


2w6rkax.jpg


The answer is of course
Fab = 261.8 lb T
Fbc = 78.9 lb C
Fac = 39.4 lb T
 
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  • #2
did you guys actually remove his post? It's very difficult to get anyone to help you here, why would you ever do that. Its the only resource I know of.
 
  • #3
Do realize how hard it is to figure out what you did by looking at that image?

It looks like there is some work relating to other problems.

I'll try to take a closer look soon.
 
  • #4
alright so I checked out the example again and can't quite see what's wrong with my method (force triangles). Isn't it possible to break down that angled force into horizontal and vertical component, two separate forces, then use a force triangle for each force and add up the resultants somehow?
 
  • #5
SammyS said:
Do realize how hard it is to figure out what you did by looking at that image?

It looks like there is some work relating to other problems.

I'll try to take a closer look soon.

I'm not asking you to decipher what I did. I pretty much just posted it out of desperation.

and yes there is calculus on the top of the page
 
  • #6
2w5jf5k.jpg


This is the example question I base my method off. To find Fab & Fad:

200lb/4 = Fab/3 = Fad/5

(although the previously erased solution is making sense to me, I'm not sure if a question asks you to solve method of joints, that you are allowed to use moments?

http://img291.imagevenue.com/img.php?image=875779209_1_122_404lo.jpg

http://img158.imagevenue.com/img.php?image=875790153_2_122_257lo.jpg

http://img255.imagevenue.com/img.php?image=875803217_3_122_240lo.jpg

http://img240.imagevenue.com/img.php?image=875815914_4_122_538lo.jpg)
 
Last edited:
  • #7
I'm the guy who gave the other solution.

It had later occurred to me about using moments. I realize that it would have been easier to do a force triangle at joint B. Unfortunately, I can't quite follow your photographed page
I think that it's still method of joints so long as you use joint method to find each member. I just used moments to find one of the reactions first.

If you have the time to post a better picture of how you tried to solve it then I'm sure that someone will 'lawfully' tell you what you did wrong (or I will try to).
 
  • #8
again thanks for your help, the question is not typical of the kind coming out of this chapter.. (ch6 of mechanics for engineers, statics, 5th ed) as the forces in the other questions are all perpendicular. So I'm moving on to them.
 
  • #9
togo said:

Homework Statement


Using method of joints, determine the force in each member of the truss. State whether each member is in compression or tension.
6zlziq.jpg



The Attempt at a Solution


http://i41.tinypic.com/2w6rkax.jpg

The answer is of course
Fab = 261.8 lb T
Fbc = 78.9 lb C
Fac = 39.4 lb T
I get that Fcv=68.297 lb (up).

However, that is based on moments, which I believe is what you did. That's not the method of joints.

By the method of joints, joint B is in equilibrium (as are all the joints), so
ƩFx=0 → (FAC)cos(50°) - (FBC)cos(60°)+240=0

ƩFy=0 → (FAC)sin(50°) + (FBC)sin(60°)+100=0

(I chose the signs to assume each beam was under compression.)​
 
  • #10
one more question though, is there a way to know which members are in tension or compression?
 
  • #11
togo said:
one more question though, is there a way to know which members are in tension or compression?
Yes, of course.

Use a sign convention. In my suggestion, I assumed compression was positive.

BTW: You should be able to check your solution by comparing what you got using moments.
 
  • #12
SammyS said:
I get that Fcv=68.297 lb (up).

However, that is based on moments, which I believe is what you did. That's not the method of joints.

By the method of joints, joint B is in equilibrium (as are all the joints), so
ƩFx=0 → (FAC)cos(50°) - (FBC)cos(60°)+240=0

ƩFy=0 → (FAC)sin(50°) + (FBC)sin(60°)+100=0

(I chose the signs to assume each beam was under compression.)​

You know I'm not quite seeing this, would it be possible for you to do a free body diagram? thanks

(shouldn't Fac in your equation actually be Fba?)
 
Last edited:

1. What is the method of joints?

The method of joints is a technique used in structural analysis to determine the forces acting on each member of a truss. It involves breaking the truss into smaller sections and analyzing the equilibrium of forces at each joint.

2. How does the method of joints work?

The method of joints works by assuming that all joints in a truss are in equilibrium and that the forces acting on each joint are concurrent. By applying the principles of equilibrium, the force in each member can be calculated using simple trigonometry and the summation of forces in the x and y directions.

3. What are the assumptions made in the method of joints?

The main assumptions made in the method of joints are that all joints are in equilibrium, all forces acting on each joint are concurrent, and the members of the truss are connected with frictionless pins. These assumptions allow for a simplified analysis of the forces in each member.

4. Can the method of joints be used for any type of truss?

Yes, the method of joints can be used for any type of truss, including simple, compound, and complex trusses. It is a versatile technique that can be applied to analyze the forces in any type of truss structure.

5. What are some limitations of the method of joints?

One limitation of the method of joints is that it can only be used for statically determinate trusses, meaning trusses with a fixed number of reactions and unknowns. It also assumes that all joints are pinned, which may not always be the case in real-world structures.

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