The truss above is designed in such a way that all compression and tension members have an area of 400 mm^2 and 150 mm^2 respectively. If the force P= 59 kN and all the member lengths are equal, determine the stress (MPa) of member CE

Elements Of Electromagnetics
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Author:Sadiku, Matthew N. O.
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Good day. I recently asked this question and I was wondering how to get the “b=0.866a” the one in red box. Thank u so much, having a hard time understanding it, also kinda urgent ty! The truss above is designed in such a way that all compression and tension members have an area of 400 mm^2 and 150 mm^2 respectively. If the force P= 59 kN and all the member lengths are equal, determine the stress (MPa) of member CE
Step1
a)
According to the question data
A loading structure ABCDEFG is given
compressive member area=400mm²
Tensile member area=150mm²
We need to find
Stress in the member CE
Step2
b)
Considering free body diagram as below
M
1b
FE
C
SO
B
59KN
a
Assume all the length of the member is equal to a
b = a²
2
b=0.8669
= 0.866a
2
Taking moment about Point D
✩ ΣMp=0⇒ [59x (a +0.5a)] + FCE (0.866a)
100 103001
Transcribed Image Text:Step1 a) According to the question data A loading structure ABCDEFG is given compressive member area=400mm² Tensile member area=150mm² We need to find Stress in the member CE Step2 b) Considering free body diagram as below M 1b FE C SO B 59KN a Assume all the length of the member is equal to a b = a² 2 b=0.8669 = 0.866a 2 Taking moment about Point D ✩ ΣMp=0⇒ [59x (a +0.5a)] + FCE (0.866a) 100 103001
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