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ironlight
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"A hydraulic cylinder has an inner diameter 25mm, an outer diameter 34mm and an internal pressure of 60bar. Calculate the principal stresses on the cylinder surface."
2) Listed in the revision notes are several different equations for this question. I've tried each one from thick cylinders to cylinders with internal pressure only, and each one gives me a completely different answer. Listed in the exam papers are Lamé's Equations
1. σ(r) = A - B/r^2
2. σ(Ѳ) = A+ B/r^2
but I'm not sure if this will give the right answer either.
I've also tried Thick Cylinders with Internal Pressure Only:
maximum σc= (r1^2+ r2^2)/(r2^2- r1^2 ) " x" P
maximum σl= (Pr1^2)/(r2^2- r1^2 )
3. I've tried this way first:
r1 = 25/2 = 12.5mm = 0.0125m
r2 = 34/2 = 17mm = 0.017m
maximum σc= (r1^2+ r2^2)/(r2^2- r1^2 ) " x" P
maximum σc= (12.5〖 "x10^-3" 〗^2+17〖 "x10^-3" 〗^2)/(17〖 "x10^-3" 〗^2- 12.5〖 "x10^-3" 〗^2 ) " x" P
maximum σc= (12.5〖 "x10^-3" 〗^2+17〖 "x10^-3" 〗^2)/(17〖 "x10^-3" 〗^2- 12.5〖 "x10^-3" 〗^2 ) " x" 60
maximum σc= (0.156"x10^-3" +0.289"x10^-3" )/(0.289"x10^-3" - 0.156"x10^-3" ) " x" 60
maximum σc= (0.445"x" 10^-3)/(0.133"x" 10^-3) " x" 60
maximum σc= 3.346 "x" 60
maximum σc= 200.76 N/m2
The same figures are used to find the stress of l, σl.
maximum σl= (Pr1^2)/(r2^2- r1^2 ) " "
maximum σl= (60 "x" 12.5〖 "x10^-3" 〗^2)/(17〖 "x10^-3" 〗^2- 12.5〖 "x10^-3" 〗^2 ) " "
maximum σl= (60 "x" 0.156"x10^-3" )/(17〖 "x10^-3" 〗^2- 12.5〖 "x10^-3" 〗^2 )
maximum σl= (9.36"x" 〖10〗^(-3))/(17〖 "x10^-3" 〗^2- 12.5〖 "x10^-3" 〗^2 )
maximum σl= (9.36"x" 〖10〗^(-3))/(0.289"x10^-3" - 0.156"x10^-3" )
maximum σl= (9.36"x" 〖10〗^(-3))/(0.133"x" 〖10〗^(-3) )
maximum σl=22.02"x" 〖10〗^(-6) N/m2
This seems a little odd, so I tried Lamés equations to compare:
Inside radius 12.5mm
Outside radius 17mm
6x10^6 = a - b/r^2
0 = a +b/r^2
6x10^6 = a - b/0.0125^2
a = 6x10^6 + b/0.0125^2
0 = a + b/r^2
0 = 6x10^6 + b/0.0125^2 + b/0.017^2
-6x10^6 = b (1/0.0125^2 + 1/0.017^2)
-6x10^6 = b(9860.2)
b = -608.5
6x10^6 = a - (-)608.5/0.0125^2
6x10^6 - 608.5/0.0125^2 = a
a = 2105600
I also have no idea what a and b should be on here; I just guessed!
Any help appreciated!
2) Listed in the revision notes are several different equations for this question. I've tried each one from thick cylinders to cylinders with internal pressure only, and each one gives me a completely different answer. Listed in the exam papers are Lamé's Equations
1. σ(r) = A - B/r^2
2. σ(Ѳ) = A+ B/r^2
but I'm not sure if this will give the right answer either.
I've also tried Thick Cylinders with Internal Pressure Only:
maximum σc= (r1^2+ r2^2)/(r2^2- r1^2 ) " x" P
maximum σl= (Pr1^2)/(r2^2- r1^2 )
3. I've tried this way first:
r1 = 25/2 = 12.5mm = 0.0125m
r2 = 34/2 = 17mm = 0.017m
maximum σc= (r1^2+ r2^2)/(r2^2- r1^2 ) " x" P
maximum σc= (12.5〖 "x10^-3" 〗^2+17〖 "x10^-3" 〗^2)/(17〖 "x10^-3" 〗^2- 12.5〖 "x10^-3" 〗^2 ) " x" P
maximum σc= (12.5〖 "x10^-3" 〗^2+17〖 "x10^-3" 〗^2)/(17〖 "x10^-3" 〗^2- 12.5〖 "x10^-3" 〗^2 ) " x" 60
maximum σc= (0.156"x10^-3" +0.289"x10^-3" )/(0.289"x10^-3" - 0.156"x10^-3" ) " x" 60
maximum σc= (0.445"x" 10^-3)/(0.133"x" 10^-3) " x" 60
maximum σc= 3.346 "x" 60
maximum σc= 200.76 N/m2
The same figures are used to find the stress of l, σl.
maximum σl= (Pr1^2)/(r2^2- r1^2 ) " "
maximum σl= (60 "x" 12.5〖 "x10^-3" 〗^2)/(17〖 "x10^-3" 〗^2- 12.5〖 "x10^-3" 〗^2 ) " "
maximum σl= (60 "x" 0.156"x10^-3" )/(17〖 "x10^-3" 〗^2- 12.5〖 "x10^-3" 〗^2 )
maximum σl= (9.36"x" 〖10〗^(-3))/(17〖 "x10^-3" 〗^2- 12.5〖 "x10^-3" 〗^2 )
maximum σl= (9.36"x" 〖10〗^(-3))/(0.289"x10^-3" - 0.156"x10^-3" )
maximum σl= (9.36"x" 〖10〗^(-3))/(0.133"x" 〖10〗^(-3) )
maximum σl=22.02"x" 〖10〗^(-6) N/m2
This seems a little odd, so I tried Lamés equations to compare:
Inside radius 12.5mm
Outside radius 17mm
6x10^6 = a - b/r^2
0 = a +b/r^2
6x10^6 = a - b/0.0125^2
a = 6x10^6 + b/0.0125^2
0 = a + b/r^2
0 = 6x10^6 + b/0.0125^2 + b/0.017^2
-6x10^6 = b (1/0.0125^2 + 1/0.017^2)
-6x10^6 = b(9860.2)
b = -608.5
6x10^6 = a - (-)608.5/0.0125^2
6x10^6 - 608.5/0.0125^2 = a
a = 2105600
I also have no idea what a and b should be on here; I just guessed!
Any help appreciated!