# Thin And Thick Cylinders Strength Of Materials Pdf

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- Thin and Thick Cylinders
- Strength of Materials || THICK CYLINDERS
- Strength of Materials || THICK CYLINDERS
- Thin and Thick Cylinders

*List out the modes of failure in thin cylindrical shell due to an internal pressure.*

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## Thin and Thick Cylinders

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Published on May 11, Shivendra Nandan Galgotias University. SlideShare Explore Search You. Submit Search. Home Explore. Successfully reported this slideshow. We use your LinkedIn profile and activity data to personalize ads and to show you more relevant ads. You can change your ad preferences anytime. Thin and thick cylinders. Upcoming SlideShare. Like this presentation? Why not share! Embed Size px. Start on. Show related SlideShares at end.

WordPress Shortcode. Published in: Engineering. Full Name Comment goes here. Are you sure you want to Yes No. Titus Titus. Show More. No Downloads. Views Total views. Actions Shares. No notes for slide. Thin and thick cylinders 1. Eg: Pipes, Boilers, storage tanks etc. These cylinders are subjected to fluid pressures. When a cylinder is subjected to a internal pressure, at any point on the cylinder wall, three types of stresses are induced on three mutually perpendicular planes.

This is also tensile in nature and tends to increase the length. Radial pressure pr — It is compressive in nature. Its magnitude is equal to fluid pressure on the inside wall and zero on the outer wall if it is open to atmosphere. Thus, there will be increase in diameter. Magnitude of radial pressure is very small compared to other two stresses in case of thin cylinders and hence neglected. Longitudinal axisLongitudinal stress Circumferential stress t The stress acting along the circumference of the cylinder is called circumferential stresses whereas the stress acting along the length of the cylinder i.

The bursting will take place if the force due to internal fluid pressure acting vertically upwards and downwards is more than the resisting force due to circumferential stress set up in the material. The horizontal components cancel out when integrated over semi-circular portion as there will be another equal and opposite horizontal component on the other side of the vertical axis.

The strains due to these stresses i. It is subjected to internal pressure of 1. If the thickness of the sheet is 12mm, find the circumferential stress, longitudinal stress, changes in diameter, length and volume.

A copper tube having 45mm internal diameter and 1. The tube is subjected to internal pressure of 3 MPa and at the same time pulled in axial direction with a force of 3 kN. Compute: i the change in length between the plugs ii the change in internal diameter of the tube. It is required to withstand a pressure of m of water.

Thickness from Hoop Stress consideration: Hoop stress is critical than long. Thickness from Shear Stress consideration: 3.

It is initially filled with water at atmospheric pressure. Determine the pressure at which an additional water of 0. Hence whenever larger size cylinders like boilers are required, a number of plates are to be connected. This is achieved by using riveting in circumferential and longitudinal directions as shown in figure. Due to the holes for rivets, the net area of cross section decreases and hence the stresses increase.

If the efficiencies of these joints are known, the stresses can be calculated as follows. Longitudinal stress is given by, Circumferential rivets Longitudinal rivets A cylindrical tank of mm internal diameter, 12mm thickness and 1. Also calculate the change in volume.

The wall thickness is such that the safe maximum tensile stress in the boiler material is 35 MPa. Find the thickness of the metal if the working stress in the pipe metal is 30 MPa. It is subjected to an internal fluid pressure of 1. Calculate the hoop and longitudinal stresses induced in the pipe material. If a factor of safety 4 was used in the design, what is the ultimate tensile stress in the pipe material?

Compute hoop and longitudinal stresses. How much is the percentage change in the volume of the cylinder? Also calculate the error of calculation in the quantity of oil in the tank if the volumetric strain of the tank is neglected. Magnitude of radial stress pr is large and hence it cannot be neglected.

The circumferential stress is also not uniform across the cylinder wall. The radial stress is compressive in nature and circumferential and longitudinal stresses are tensile in nature. The stresses are within proportionality limit. Plane sections of the cylinder normal to its axis remain plane and normal even under pressure. Consider the longitudinal section XX of the ring as shown in the fig. Let it be equal to 2a. NOTE: 1. Variations of Hoop stress and Radial stress are parabolic across the cylinder wall.

At the inner edge, the stresses are maximum. Determine the maximum hoop stress developed and draw the variation of hoop stress and radial stress across the thickness. Show at least four points for each case. Determine the maximum hoop stress developed in the cross section. What is the percentage error if the maximum hoop stress is calculated by the equations for thin cylinder? The internal diameter of the cylinder is mm and the length is 1. The longitudinal stress is Find, i Max shear stress at the inner edge.

PROBLEM 5: Find the max internal pressure that can be allowed into a thick pipe of outer diameter of mm and inner diameter of mm so that tensile tress in the metal does not exceed 16 MPa if, i there is no external luid pressure, ii there is a fluid pressure of 4. Case ii — When there is an external fluid pressure of 4.

Calculate the maximum and minimum intensities of circumferential stresses induced. Ans: Sketch also the radial pressure and hoop stress distributions across the thickness. Determine the thickness of the cylinder if the maximum shear stress in the cylinder is not to exceed 65 MPa.

What will be the increase in the volume of the cylinder? The internal diameter of the cylinder is mm and the external diameter is mm. You just clipped your first slide! Clipping is a handy way to collect important slides you want to go back to later.

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## Strength of Materials || 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. Equations It is assumed in Lam's Theory that the longitudinal stress, is uniform across a cross-section and its value is obtained by considering the equilibrium of the forces exerted on the end of the cylinder.

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.

## Strength of Materials || THICK CYLINDERS

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.

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.

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.

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### Thin and Thick Cylinders

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.

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. Maximum at inner side and both reduce to zero at outer wall 4. Consider the following statements at given point in the case of thick cylinder subjected to fluid pressure: [IES] 1. Radial stress is compressive 2. Hoop stress is tensile 3.

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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Problem The mild steel block has cross-section of 50x50mm carries an axial load of 35KN which is compressive in nature. Find the normal, tangential stresses across the plane through the point of 30 to the axis of the block. Also find the maximum shear stress in the block. A member subjected to a pull of two pieces wooden frame of cross section 35x15 mm connected by bolts joints. Angle of cross section is A 5mm thick aluminium plate has a width of mm and a length of mm subjected to pull of N,N respectively in axial transverse directions.

Thus, equating the two strains in order that there shall be no distortion of the junction.

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. The stress state in a thick-walled vessel under internal pressure is triaxial. The direct stresses and strains occur: radial, circumferential, hoop and axial.

*Это кошмар наяву. Я понимаю, ты расстроена из-за Дэвида.*