Question

aaginal culindrical cylindrical thin walled rubber rubber e pressure vessel length :L+x plastic modUIUS R E radius: thickness : T poisson's Ratio : v =0.9. x: thermal expansion coefficient It is set to an initial internal pressure (p), then compressed by a neighboring moving plate that moves from 2 > LtX to 2 :1. This causes a toree F.. s from the outside we can cool the vessel, will F be reduced to zero? AYB ? a) EBD of cut vessel between in axial stress SS expression expression ulinder belore anal of given variables. y hoop stresses & hoop som load applied in

First figure is the original length, radius, thickness, etc according to given variables

Answer 1

Hi there!

I understand from the question that a cylindrical pressure vessel is fixed at an end and subjected to force F from other end so that the cylinder gets comprssed by x length.

as T. L3487. , x = X-BT/ (sau) a tot Ju Etx whered is the dia of pressure vessel d = 2R Axial stress due to force todas TaT4F Total (Net longitudinal ! stress te sted - ME Given that the plate is initially at a distance of Lane & gradually moved Ex = الله له . The strain caused in the pressure ressed due to for . - u Due to decrease in temp by st De = last f is Ex = 3 h = 4 x = 2 = ADT 0 from so LoT = + pd Longitudinal stress in the vessel leo tensile. (compressive in nature) eated 4€ Hoop stress (tensile in nature) – ира ate :07 pd. 15 -x) - 4F] 2 ( -M) - 48] CSScanned with SamScanner

but s MILID Ibu re (Hoop stress) = pd - Axial or de Clongitudinal) = pd o estress Tas When force E de applied on the pressure vessel, ule wa Je to 18 If the radial stress ao, Da 0-5. Axial strain in the Cylinder 643 epiculty Scanned with CamScanner

The last question C can be easily obtained by equating the strain caused by the external force F to the axial strain due to drop in temperature which is the compatibility equation.

Please let me know if you have any further doubts.

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