Statics: Forces in a truss, method of joints

[yaro99]

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.

Homework Equations

ƩF_x=0
ƩF_y=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 ↑
C_x = 10 kN ←
C_y = 30 kN ↓

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

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

ƩF_x=0: 5 - (1/√5)*F_BD = 0
F_BD = 11.18 kN C

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


I got F_AB correct, but F_BD is supposed to be 30 kN T

 

[sonnyfab]

Since F_AB was correct, and your answer to F_AB depended on your "incorrect" answer for F_BD, I find it hard to believe that F_AB was right and F_BD 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.

 

[yaro99]

Since F_AB was correct, and your answer to F_AB depended on your "incorrect" answer for F_BD, I find it hard to believe that F_AB was right and F_BD 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 F_AD using joint A, and took a look at joint D to see if I got the same answer for F_BD.

Diagrams:

Joint A:
5 = F_AD/√5
F_AD = 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 F_AD 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.

 

[sonnyfab]

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?

 

[Nickie]

.

As a scientist, it is important to note that the method of joints is a widely used technique in structural engineering to analyze the forces in truss structures. By applying the principles of equilibrium, we can determine the forces in each member of the truss and whether they are in tension or compression. In this particular problem, the forces at joint C and D were found to be in tension, while the force at joint B was found to be in compression. It is also important to note that due to the symmetry of the truss, the forces at joint B and D should be equal, which can help in verifying the accuracy of our calculations. In this case, there may have been an error in the calculation for FBD, which resulted in a discrepancy from the expected value of 30 kN T. As a scientist, it is important to always double check our calculations and results to ensure accuracy and reliability.