Thin And Thick Cylinders Strength Of Materials Pdf

thin and thick cylinders strength of materials pdf

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FL Multi-channel measuring amplifier. WP In contrast to thin-walled vessels, when designing thick-walled vessels allowance must be made for an uneven distribution of stresses through the thickness of the wall.

ANALYSIS OF A THIN AND THICK WALLED PRESSURE VESSEL FOR DIFFERENT MATERIALS

What is the difference in the analysis of think tubes compared to that for thin tubes? State the basic equations describing stress distribution in a thick tube. The difference in the analysis of stresses in thin and thick cylinder: i In thin cylinder, it is assumed that the tangential stress is uniformly distributed over the cylinder wall thickness. In thick cylinder, the tangential stress has highest magnitude at the inner surface of the cylinder and gradually decreases towards the outer surface. Basic equation for describing stress distribution in thick tube is Lame's equation. What is auto frettage? How does it help in increasing the pressure carrying capacity of a thick cylinder?

Shrinking a hoop over an inner cylinder-Self- hooping or Autofrettage. This allows the cylinder to operate at higher fluid pressure if l is the efficiency of a joint in the longitudinal direction, influencing the hoop stress, then the stress will be given as. Concept Problems: 1 A cylindrical boiler is 2. Find the stresses in the shell. If the shell is subjected to an internal pressure of 2. Previously asked problems 1 A thin walled spherical shell is subjected to an internal pressure. The self weight of the cylinder is negligible.

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Thin and Thick Cylinders

In Art. Also, in calculating the volumetric strain on the contents of a thin cylinder under pressure Examples 7 and 9, Chapter 13 , it is assumed that the radial stress is negligible in relation to the circumferential and longitudinal stresses. When the thickness of the cylinder is appreciable in relation to the diameter, however, these assumptions are no longer justified and the variation in radial and circumferential stresses across the thickness is obtained from Lame's Theory. The radial and circumferential stresses, and aCi have both been assumed to be compressive, which is considered positive. It is assumed that is constant across the thickness, i.

List out the modes of failure in thin cylindrical shell due to an internal pressure. What do you mean by principal plane? The planes which have no shear stress are known as principal planes. What are assumptions involved in the analysis of thin cylindrical shells? The material of the cylinder is homogeneous, isotropic and obeys Hook's law. What are principal planes and principal stress one end is fixed and other end is free?

In mechanics , a cylinder stress is a stress distribution with rotational symmetry; that is, which remains unchanged if the stressed object is rotated about some fixed axis. These three principal stresses- hoop, longitudinal, and radial can be calculated analytically using a mutually perpendicular tri-axial stress system. The classical example and namesake of hoop stress is the tension applied to the iron bands, or hoops, of a wooden barrel. In a straight, closed pipe , any force applied to the cylindrical pipe wall by a pressure differential will ultimately give rise to hoop stresses. Similarly, if this pipe has flat end caps, any force applied to them by static pressure will induce a perpendicular axial stress on the same pipe wall.


C H A P T E R 14 T H I C K C Y L I N D E R S Lame's Theory. In Art. , a formula is derived for the circum- ferential stress in a thin cylinder.


Thin and Thick Cylinders

Thus, equating the two strains in order that there shall be no distortion of the junction. This means thickness of cylindrical part should be more than the hemispherical part. Longitudinal tension is uniform across the thickness. Hoop tension vary form maximum at inner face to minimum at outer face hyperbolically. Radial compression varies from maximum at inner face to zero at outer face atm.

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Consider the following statements: [IES] In a thick walled cylindrical pressure vessel subjected to internal pressure, the Tangential and radial stresses are: 1. Minimum at outer side 2. Minimum at inner side 3.

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