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?