Thick walled pressurised cylinder

[Northyellow]

1. Investigate the stress generated during the operation, at 60 bar pressure, of a cylinder on the festo rig.

i) calculate the principal stresses on the cylinder surface
ii) Use strain gauges to measure the principal strains and hence confirm the above stress value.


2. relevant equations: lame equations, 1. σ(r) = A - B/r^2
2. σ(Ѳ) = A+ B/r^2



3. Attempt at an answer

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 do not understand, i am stupid :)

 

[Valkarie]

Principal stresses on the cylinder surface are σ(r) = 2105600 - 608.5/r^2 and σ(Ѳ) = 2105600 + 608.5/r^2.To measure the principal strains, strain gauges can be used. The strain gauges need to be attached to the cylinder surface and connected to a Wheatstone bridge circuit. The output voltage of the circuit can then be used to calculate the principal strains.