Statics Equilibrium problem

  • Thread starter JasonR2
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  • #1
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Question:

Three forces of magnitude 45 kN, 24 kN and 12 kN are applied to the truss connection as shown. Knowing that the connection is in equilibrium, determine the magnitude of the forces C and T.

fI9E29j.jpg




Equations:

Fx = 0
Fy = 0

My attempt:

Fx=0:

-24kN + Tcos40 + Csin20 = 0

Fy = 0:

45kN + Tsin40 - Ccos20 = 0

By substitution:

Divide first equation by sin20:

2.24T + C = 70.17 kN ---> C = 70.17kN - 2.24T (Plug that C into equation 2.)

Tsin40 - (70.17kN - 2.24T)(cos20) = -45kN

2.75T = 20.94

T = 7.62kN (Plug that back into equation 1 to find C)

C = 53.10 kN

However the answer is supposed to be C = 44.89kN and T = 4.35kN

What am I doing wrong?
 

Answers and Replies

  • #2
robphy
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How do you get your Fx equation?
 
  • #3
For a start sign convention:
∧ +ve & >+ve

v=0
-24 + CCos70 = TCos40 +12​
h=0
-CSin70 = TSin40 +45

from here you should be able to get answer​
 
  • #4
34
1
I think you missed the 12 kN in your Fx equation. I didn't go through the math though.
 

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