Statics: Forces in a truss, method of joints

  • Thread starter yaro99
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Homework Statement


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

fmD0oXK.png


Homework Equations


ƩFx=0
ƩFy=0
ƩM=0

The Attempt at a Solution



I got the forces at C and D by using the equilibrium equations for the entire truss:
D = 30 kN ↑
Cx = 10 kN ←
Cy = 30 kN ↓

By anlaysis of the forces at joint C, I obtained:
FCD = 10 kN T
FBC = 30 kN T

My problem is joint with joint B. Here is my diagram of its forces:
DXUmvYU.png


ƩFx=0: 5 - (1/√5)*FBD = 0
FBD = 11.18 kN C

ƩFy=0: FAB - 30 + (2/√5)*11.18 = 0
FAB = 20 kN T


I got FAB correct, but FBD is supposed to be 30 kN T
 

Answers and Replies

  • #2
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Since FAB was correct, and your answer to FAB depended on your "incorrect" answer for FBD, I find it hard to believe that FAB was right and FBD was wrong.

Your reasoning looks sound and your understanding seems strong. At this point, I would start to be suspicious of whether the answer key you are using is correct. In my sophomore level Differential Equations class, it took us about a month to realize that the "solutions manual" kept giving incorrect solutions and that we were actually doing the problems correctly.
 
  • #3
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Since FAB was correct, and your answer to FAB depended on your "incorrect" answer for FBD, I find it hard to believe that FAB was right and FBD was wrong.

Your reasoning looks sound and your understanding seems strong. At this point, I would start to be suspicious of whether the answer key you are using is correct. In my sophomore level Differential Equations class, it took us about a month to realize that the "solutions manual" kept giving incorrect solutions and that we were actually doing the problems correctly.

I thought this was the case, but then I went ahead and found FAD using joint A, and took a look at joint D to see if I got the same answer for FBD.

Diagrams:
1WK23uh.png


Joint A:
5 = FAD/√5
FAD = 20.6 kN
This is correct according to the book.

Joint D:
This one is strange because the ratios don't add up
30/2 ≠ 10/1
At least one of the forces must be wrong, I can't figure it out.



EDIT: I realize I forgot to include FAD on joint D, going to try that now.

EDIT 2: It seems you're right. I solved joint D with all the forces and got my original answer. Must be a typo, my other answers were "correct" and I haven't had any other inconsistencies with other problems. In any case I'll keep this in mind.
 
Last edited:
  • #4
20
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Force AD Acting on Joint D?

You seem to have the force from the ground on D, the force from C on D and the force from B on D in your diagram. What about the force from A?
 

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