Statics question - Method of joints

Click For Summary

Discussion Overview

The discussion revolves around solving a statics problem involving a truss structure, specifically focusing on finding the force in member BC and the reactions at supports E and G. Participants explore various methods, including the method of joints and the method of sections, while addressing the complexities introduced by the geometry of the truss and the forces acting on it.

Discussion Character

  • Technical explanation
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One participant seeks clarification on how to find the x displacement of point G from E to calculate the moment at point E about G.
  • Another participant suggests that the force in member FG is axial and proposes writing expressions for Gx and Gy in terms of G, followed by equilibrium equations to solve for unknowns.
  • Some participants propose using the method of sections to find the force in member BC without needing to know the reaction forces at points E and G.
  • There is a discussion about the definition of axial force, with one participant expressing confusion about its implications for finding supports without using moments.
  • A participant shares their calculations for forces at joints A and B, noting a discrepancy in their results for F_BC and seeking help to identify potential mistakes.
  • Another participant emphasizes the importance of ratios of lengths in statically determinate frames, suggesting that the actual lengths are not critical for force distribution.

Areas of Agreement / Disagreement

Participants express differing views on the necessity of using moments to find support reactions, with some asserting it is essential while others suggest alternative methods. There is no consensus on the correct approach to resolving the calculations for forces in the truss members.

Contextual Notes

Participants mention the need for careful algebraic manipulation and the importance of understanding the geometry of the truss, indicating that some assumptions or simplifications may be necessary for clarity.

Patdon10
Messages
85
Reaction score
0
The problem is attached. I have to solve for the force in the member BC. The thing I need help with is solving for the two attachments. I already broke it down into the forces and directions, but what do I do with the lower attachment? How do I find the x displacement of point G from E if I'm trying to find the moment at point E about G. I understand the ratio is supposed to help me, but how? This problem would be much simpler if truss FG wasn't there, and the support was at point F.
 

Attachments

  • statics.jpg
    statics.jpg
    18.3 KB · Views: 564
Physics news on Phys.org
Patdon10: You know the force in member FG is axial, because it is a truss member. You have three equations, and three unknowns (Ex, Ey, and G). Write an expression for Gx in terms of G. Write an expression for Gy in terms of G. Then write equilibrium equations, and solve for the three unknowns.
 
It is interesting to note that if your only objective is to find the force in member BC, then using method of sections, using a vertical section cut through points D and C, you could find the force in member BC, without knowing the reaction forces at points E and G.

Alternately, without doing any of the above, you could apply method of joints at point A, then apply method of joints at point B, and solve for the force in member BC, without knowing the reaction forces at points E and G.
 
nvn said:
Patdon10: You know the force in member FG is axial, because it is a truss member. You have three equations, and three unknowns (Ex, Ey, and G). Write an expression for Gx in terms of G. Write an expression for Gy in terms of G. Then write equilibrium equations, and solve for the three unknowns.

To be honest. I'm not sure I understand what an 'axial force' is. A web search didn't really help me too much either. Are you saying I can find both supports without using a moment?

So in other words, it needs to be...
G_x = G*cos(53.13)
G_y = G*sin(53.13)

Summation_F_x = -E_x + G*cos(53.13) = 0
Summation_F_y = (G*sin(53.13) - 900 - 1200 - E_y) = 0

I have 3 unknowns, and only 2 equations. What am I missing?
 
An Axial Force is one whose direction coincides with the length of the member in which it occurs.
 
F_BD = 1000 lbs (C). using the method of joints in the way you described I found it to be 562.5 lbs. Maybe you'd be able to spot my mistake? it's a lot of work, but I can try...

Joint A
-----------
F_x = F_AB*cos(36.87) - F_AC = 0
F_y = -900 + F_AB*sin(36.87) = 0
F_AB = 1500 lb (T)
F_AC = 1200 lb (C)

Joint B (There is lots of solving for angles in here)
----------
F_x = -1500*cos(36.87) + F_BD*cos(36.87) + F_BC*cos(36.87) = 0
F_y = -1200 - F_BC*sin(36.87) + F_BD*sin(36.87) - 1500*sin(36.87)

I had 2 equations and 2 unknowns. Used F_x to solve for F_BD = 1500 - F_BC
Plugged F_BD into the F_y to solve for F_BC. F_BC = -562.5 so it'd be 562.5 (C).
 
Patdon10 said:
Are you saying I can find both supports without using a moment?
No.

Regarding post 6, you did excellent work. It appears you made some algebra mistake (not shown). Try again, and watch your algebra.
 
I can't find the mistake. I looked everything over and it looks correct. I'll worry about that later.

Can you give me a nudge in the right direction for solving for those supports? What am I missing?
 
Write a summation of moment equation.
 
  • #10
nvn said:
Write a summation of moment equation.

Sure.

I have:
summation of M_E = 1200(14) + 900(18) - (G_y)(x_displacement) + Gx (y displacement) = 0

I simply don't know how to find those displacements.
 
  • #11
No, it should not be displacement. Change those to x and y distance from point E.
 
  • #12
yeah. that's what i meant. How would I go about finding those distances though?
 
  • #13
Patdon10: Go ahead and assume the length of member FG is 1.
 
  • #14
That would make the problem fairly easy, but can you do that? I literally posted all the information I was given in the problem.
 
  • #15
In statically determinate frames like this one, the lengths themselves are unimportant. It's the ratios of lengths that determine the force distribution. (That is why it doesn't matter if the units are feet or metres or anything else you want, the forces are the same).
 
  • #16
pongo38 said:
In statically determinate frames like this one, the lengths themselves are unimportant. It's the ratios of lengths that determine the force distribution. (That is why it doesn't matter if the units are feet or metres or anything else you want, the forces are the same).

I guess that makes sense. So as long as the ratio corresponds to the length of that member, everything will check out.
 

Similar threads

Engineering Two approaches in statics not adding up
  • · Replies 5 ·
Replies
5
Views
2K
Calculating Support Reaction Forces using Method of Joints
  • · Replies 3 ·
Replies
3
Views
2K
Identifying Pin Joints & Rollers - Structural Analysis Homework Help
  • · Replies 20 ·
Replies
20
Views
5K
Engineering 2nd Degree Inderteminacy for Structure Using Force Method
  • · Replies 3 ·
Replies
3
Views
3K
Engineering Struggling with a Structural Analysis Problem?
  • · Replies 1 ·
Replies
1
Views
3K
Truss Analysis : Method of Joints only (Picture provided)
  • · Replies 1 ·
Replies
1
Views
2K
Method of joints & forces between joints
  • · Replies 1 ·
Replies
1
Views
2K
Engineering Instantaneous Center of Rotation (Polplan in german) and STATICS
  • · Replies 1 ·
Replies
1
Views
2K
Understanding Method of Joints for Solving Statics Problems
  • · Replies 2 ·
Replies
2
Views
4K
Engineering Question about Truss Analysis (Statics)
  • · Replies 1 ·
Replies
1
Views
2K