design of pressure vessels
DESCRIPTION
check it out it will give you the method to determine the stresses on the vesselsTRANSCRIPT
Nitin Joshi B Tech Mechanical
CONTENTS Acknowledgement Introduction Stresses in Large Horizontal Cylindrical Pressure Vessels on Two Saddle
Supports Design of vertical pressure vessels for applied forces Design with Internal Pressure Pressure Vessel Design for Engineering Plastics Stresses in Thin Walled Vessels References
Nitin Joshi B Tech Mechanical
Introduction:-
My topic of term paper is to tell about the design of pressure vessels. In this firstly we will discuss about the pressure vessels & its types and then the designing of pressure vessels.
Pressure vessel is defined as the closed container used to store the gas and liquids at a pressure different from the ambient pressure. The different shapes of vessels are spherical, cylindrical vessel with hemispherical ends, cylindrical vessel with semi elliptical ends. We use vessels in both industry and private sector for storage of the hot water and compressed air. Figure given below show the steel pressure vessel. Pressure vessels are typically designed, fabricated, installed, inspected, and testedin accordance with the ASME Code Section VIII.
Stresses in Large Horizontal Cylindrical Pressure Vessels onTwo Saddle Supports:-For design purpose it is necessary to examine the each aspect related to vessels. The shell of the vessel made thick so that it can withstand the stresses applied on it. The basic purpose of this topic is to determine the stresses on various places so that we can make the vessel more efficient. When a cylindrical vessel acts as its own carrying beam across two symmetrically placed saddle supports, one-half of the total loads will be carried by each support. This would be true even if one support should settle more than the other. This would also be true if a differential in temperature or if the axial restraint of the supports should cause the vessel acting as a beam to bow up or down at the center. This fact alone gives the two-support system preference over a multiple-support system. The codes of the pressure vessels limit the contact angle of each saddle to a minimum of 120⁰ except for very small vessels. Sometimes a large contact angle can be used. Now the maximum longitudinal stress is to be calculating. The cylindrical shell acts as the beam over the two supports to resist the bending.Maximummoments occur at the mid-span and over the supports.Most vessels are of uniform thickness, the design formula involves only the maximum value of the longitudinal bending stress. The formula for this is given below. S1 = +- K1 Q L / π² L
Nitin Joshi B Tech Mechanical
Here K₁ is the constant for the given set of conditions. It varies with the ratio of A/L & H/L & R/L for different saddle angle. This maximum bending stress, S1, may be either tension or compression. The tension stress when combined with the axial stress due to internal pressure should not exceed the allowable tension stress of the material times the efficiency of the girth joints. The compression stress should not exceed one half of the compression yield point of the material or the value given which is based upon the accepted formula for buckling of short steel cylindrical columns. There will be tangential & load stresses which we should counter during the designing of the pressure vessels.
Design of vertical pressure vessels for applied forces:-
Forces are applied on the vessels when load is applied on them. The load applied can be of any type. These loads set the stresses on vessels. Vertical load cause the compressive stresses in the shell as well as bending stresses. The stresses are given by the following equations.
The horizontal loads on the vessel produce bending stresses in the shell. The bending moment at any section is equal to the resultant of the horizontal forces above the section multiplied by the distance between the line of action of the resultant and the section. The stress, set up in the outermost fiber of the shell by the action of horizontal loads, is equal to
The stresses due to external loads must be considered in combination with those due to pressure in determining the required shell thickness. For internal pressure, the stresses may be combined by simple addition. For external pressure, a more complicated procedure is required.
Designwith Internal Pressure:-
The axial stresses set up in the shell may be classified under three types: (a) The longitudinal stress produced by the internal pressure; (b) the uniform compressive stress produced by the sum of the weights assumed to act along the axis of the vessel; (c) the bending stress produced by the horizontal loads and by the resultant weight when eccentric to the axis of the vessel.The tension side of the shell has its highest stress when the vessel is under pressure. On the compression side, the highest stress occurs when the internal pressure is not acting. The stresses set up in the shell for these two conditions are
Nitin Joshi B Tech Mechanical
The factor W includes all the vertical loads and the factor M includes all the moments due to horizontal loads for the loading condition under consideration. Shell thickness should be taken into account.
Pressure Vessel Design for Engineering Plastics:-
Engineering plastics has been used for pressure vessels for a long time. The examples of this are ballcock valve, spray paint containers, lighter bodies. This method is growing rapidly with increase in quality of the plastics.
The first step in the design procedure is to determine a tentative wall thickness: Using the nominal hoop stress formula.
We can assume that the maximum stress will bewhere K is the stress concentration factor.
Stresses in Thin Walled Vessels:-
Nitin Joshi B Tech Mechanical
Stress in thin walled vessels is given by the equation
Whereσθ is the hoop stress, p is the gauge pressure, r is the inner radius and, t is the thickness. When the diameter of the vessel is 10 times more than the thickness then it is considered as thin walled vessel. This equation helps us to design the thin walled vessel for the stress. If the vessel is the form of long cylinder then stress is given by
An elastic calculation of strain in the hoop direction (q direction) can be converted to wc, the radially outward displacement of the center surface of the cylinder.
Except there are also thermal stress in the vessels given by
Where TR is a convenient reference temperature (e.g., 20°C); and where this integral provides eTas a function of T. The thermal stresses may be expressed in terms of the spatially average thermal strain (eT ) as follows:
Thus from the methods mention above to calculate the stresses in the pressure vessels helps us to design the pr. Vessels effectively for the various purposes. It is highly necessary to calculate the stresses for the designing purposes because vessels have to be work under the stresses for some time or for the whole life cycle.
Nitin Joshi B Tech Mechanical
References:-
I have taken the references from the following websites & links
1. www.google.co.in 2. www.wikipedia.com 3. Pressure vessel design using boundary element method with optimization by R.E.
Dippery, Jr. & D. SrivastavaKettering University, Michigan, USA4. Research paper by southwest research institute5. Structural design notes by J. E. Meyer.