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Module # 6
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  NPTEL  –  Chemical Engineering  –  Chemical Engineering Design - II   Joint initiative of IITs and IISc  –  Funded by MHRD Page 1  of 29   Module # 6 DESIGN OF TALL VESSELS: INTRODUCTION, AXIAL STRESS DUE TO DEAD LOADS, AXIAL STRESSES DUE TO PRESSURS, LONGITUDINAL BENDING STRESSES DUE TO DYNAMIC LOADS, DESIGN CONSIDERATIONS OF DISTILLATION (TALL) AND ABSORPTION COLUMN (TOWER)   1.   INTRODUCTION 2.   STRESSES IN THE SHELL (TALL VERTICAL VESSEL) 3.   AXIAL AND CIRCUMFERENTIAL PRESSURE STRESSES 3.1 Tensile stresses resulting from internal pressure 4. COMPRESSIVE STRESS CAUSED BY DEAD LOADS 5. THE AXIAL STRESSES (TENSILE AND COMPRESSIVE) DUE TO WIND LOADS ON SELF SUPPORTING TALL VERTICLE VESSEL 6. THE STRESS RESULTING FROM SEISMIC LOADS 7. STRESS DUE TO ECCENTRICITY OF LOADS (TENSILE OR COMPRESSIVE) 8. ESTIMATION OF HEIGHT OF THE TALL VESSEL (X) 9. COLUMN INTERNALS 9.1 Design and construction features of plate and trays 9.1.1 Loading conditions of trays and plates 9.1.2 Deflection and stresses  NPTEL  –  Chemical Engineering  –  Chemical Engineering Design - II   Joint initiative of IITs and IISc  –  Funded by MHRD Page 2  of 29   Lecture 1: INTRODUCTION, AXIAL STRESS DUE TO DEAD LOADS 4.   INTRODUCTION Self supporting tall equipments are widely used in chemical process industries. Tall vessels may or may not be designed to be self supporting. Distillation column, fractionating columns, absorption tower, multistage reactor, stacks, chimneys etc. comes under the category of tall vertical vessels. In earlier times high structure (i.e. tall vessels) were supported or stabilized by the use of guy wires. Design of self supporting vertical vessels is a relatively recent concept in equipment design and it has been widely accepted in the chemical industries because it is uneconomical to allocate valuable space for the wires of guyed towers. In these units ratio of height to diameter is considerably large due to that these units are often erected in the open space, rendering them to wind action. Many of the units are provided with insulation, number of attachments, piping system etc. For example distillation and absorption towers are associated with a set of auxiliary equipments i.e. reboiler, condenser, feed preheater, cooler and also consists of a series of internal accessories such as plates or trays or variety of packings. Often the vertical vessels/columns are operated under severe conditions, and type of the material these columns handles during operation may be toxic, inflammable or hazardous in other ways. Structural failure is a serious concern with this type of columns. As a result the, the  prediction of membrane stresses due to internal or external pressure will not be sufficient to design such vessels. Therefore, special considerations are necessary to take into account and predict the stresses induced due to dead weight, action of wind and seismic forces. 5.   STRESSES IN THE SHELL (TALL VERTICAL VESSEL) Primarily the stresses in the wall of a tall vessel are: a) circumferential stress, radial stress and axial stress due to internal pressure or vacuum in the vessel, b) compressive stress caused by dead load such as self weight of the vessel including insulation, attached equipments and weight of the contents.  Dead load   is the weight of a structure itself, including the weight of fixtures or equipment  permanently attached to it;  Live load   is moving or movable external load on a structure. This includes the weight of furnishing of building, of the people, of equipment etc. but doesn‟t include wind load.  If the vessels are located in open, it is important to note that wind load also act over the vessel. Under wind load, the column acts as cantilever beam as shown (Figure 6.1). Therefore while designing the vessel stresses induced due to different parameters have to be considered such as i) compressive and tensile stress  NPTEL  –  Chemical Engineering  –  Chemical Engineering Design - II   Joint initiative of IITs and IISc  –  Funded by MHRD Page 3  of 29   induced due to bending moment caused by wind load acting on the vessel and its attachments; ii) stress induced due to eccentric and irregular load distributions from  piping, platforms etc. iii) stress induced due to torque about longitudinal axis resulting from offset piping and wind loads and iv) stress resulting from seismic forces. Apart from that, always there are some residual stresses resulting due to methods of fabrication used like cold forming, bending, cutting, welding etc. Figure 6.1: Bending moment diagram under wind load 3. AXIAL AND CIRCUMFERENTIAL PRESSURE STRESSES  3.1 Tensile stresses resulting from internal pressure The simple equation may be derived to determine the axial and circumferential stresses due to internal pressure in the shell of a closed vessel. Figure (6.2a) shows a diagram representing a thin walled cylindrical vessel in which a unit form stress,  f  , may be assumed to occur in the wall as a result of internal pressure. Where, l = length, inches d = inside diameter, inches t = thickness of shell, inches and p = internal pressure, pounds/square inch gage    NPTEL  –  Chemical Engineering  –  Chemical Engineering Design - II   Joint initiative of IITs and IISc  –  Funded by MHRD Page 4  of 29    Longitudinal stress: In case of longitudinal stress, if the analysis limits to pressure stresses only, the longitudinal force,  P  , resulting from an internal pressure,  p , acting on a thin cylinder of thickness t  , length l  , and diameter d   is: P = force tending to rupture vessel longitudinally = (p   d 2 )/4 And a = area of metal resisting longitudinal rupture = t   d Therefore  f = stress = P/a = 2 /4 = = induced stress, pounds per square inch4  p d pd t d t       or 4  p d t  f      (6.1)   Figure 6.2a: Longitudinal forces acting on thin cylinder (internal pressure)  NPTEL  –  Chemical Engineering  –  Chemical Engineering Design - II   Joint initiative of IITs and IISc  –  Funded by MHRD Page 5  of 29   Circumferential stresses:  Fig (6.2b) shows the circumferential force acting on the thin cylinder under internal pressure. The following analysis may be developed, if one considers the circumferential stresses are induced by the internal pressure only. P = force tending to rupture vessel circumferentially =  p × d × l   a = area of metal resisting force = 2 × t × l     f   = stress = 22  P pdl pd a tl t      or 2  pd t  f      (6.2)   Figure 6.2b: Circumferential forces acting on thin cylinder (internal pressure) Equation 6.1 and 6.2 indicates that for a specific allowable stress, fixed diameter and given pressure, the thickness required to restrain the pressure for the condition of eq. (6.2) is double than that of the equation (6.1). Therefore, the thickness as determined by equation (6.2) is controlling and is the commonly used thin walled equation referred to in the various codes for vessels. The above equation makes no allowances for corrosion and does not recognize the fact that welded seams or joints may cause weakness. Experience has shown that an allowance may be made for such weakness by introducing a joint efficiency factor “j” in  the equations and this factor is always less than unity and is specified for a given type of welded construction in the various codes. The thickness of metal, c, allowed for any anticipated corrosion is then added to the calculated required
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