Application of theories of failure for thick walled pressure vessels. Having discussed the stresses in thick walled cylinders it is important to consider their failure criterion. The five failure theories will be considered in this regard and the variation of wall thickness to internal radius ratio t/ri or radius ratio ro/ri with p/σyp for

Stresses in thick cylinders For thick cylinders such as guns, pipes to hydraulic presses, high pressure hydraulic pipes the wall thickness is relatively large and the stress variation across the thickness is also significant. In this situation the approach made in the previous section is not suitable.

Stresses in thin cylinders If the wall thickness is less than about 7% of the inner diameter then the cylinder may be treated as a thin one. Thin walled cylinders are used as boiler shells, pressure tanks, pipes and in other low pressure processing equipments. In general three types of stresses are developed in pressure cylinders viz. circumferential or hoop stress, longitudinal stress in closed end cylinders and radial stresses.

Design of shaft for strength involves certain changes when it is acted upon by variable load. It is required to calculate the mean stress and stress amplitude for all the loads, namely, axial, bending and torsion. Thereafter, any of the design methods for variable load, that is, Soderberg, Goodman or Gerber criteria is utilized

Shaft is a common and important machine element. It is a rotating member, in general, has a circular cross-section and is used to transmit power. The shaft may be hollow or solid. The shaft is supported on bearings and it rotates a set of gears or pulleys for the purpose of power transmission. The shaft is generally acted upon by bending moment, torsion and axial force. Design of shaft primarily involves in determining stresses at critical point in the shaft that is arising due to aforementioned loading....

In order to have an idea of working principle of a leaf spring, let us think of the diving board in a swimming pool. The diving board is a cantilever with a load, the diver, at its free end. The diver initiates a to and fro swing of the board at the free end and utilizes the spring action of the board for jumping. The diving board basically is a leaf spring.

Design of helical spring for variable load In the earlier lecture, we have learned about design of helical springs for static loads. In many applications, as for example in railway carriages or in automobile suspension systems the helical springs used are constantly under variable load. Hence, it is understood that whenever there is a variable load on a spring the design procedure should include the effect of stress variation in the spring wire.

Mechanical springs have varied use in different types of machines. We shall briefly discuss here about some applications, followed by design aspects of springs in general.

Stresses in power screws Design of a power screw must be based on the stresses developed in the constituent parts. A power screw is subjected to an axial load and a turning moment. The following stresses would be developed due to the loading:

A power screw is a drive used in machinery to convert a rotary motion into a linear motion for power transmission. It produces uniform motion and the design of the power screw may be such that (a) Either the screw or the nut is held at rest and the other member rotates as it moves axially. A typical example of this is a screw clamp. (b) Either the screw or the nut rotates but does not move axially.

A typical rigid flange coupling is shown in Figure- . If essentially consists of two cast iron flanges which are keyed to the shafts to be joined. The flanges are brought together and are bolted in the annular space between the hub and the protecting flange. The protective flange is provided to guard the projecting bolt heads and nuts.

Couplings are used to connect two shafts for torque transmission in varied applications. It may be to connect two units such as a motor and a generator or it may be to form a long line shaft by connecting shafts of standard lengths say 6-8m by couplings. Coupling may be rigid or they

It is necessary to determine the stresses in screw fastening due to both static and dynamic loading in order to determine their dimensions. In order to design for static loading both initial tightening and external loadings need be known.

Bolts, screws and studs are the most common types of threaded fasteners. They are used in both permanent or removable joints. Bolts: They are basically threaded fasteners normally used with nuts. Screws: They engage either with a preformed or a self made internal threads. Studs: They are externally threaded headless fasteners. One end usually meets a tapped component and the other with a standard nut.

A cotter is a flat wedge-shaped piece of steel as shown in figure-4.2.1.1. This is used to connect rigidly two rods which transmit motion in the axial direction, without rotation. These joints may be subjected to tensile or compressive forces along the axes of the rods. Examples of cotter joint connections are: connection of piston rod to the crosshead of a steam engine, valve rod and its stem etc.

A machine or a structure is made of a large number of parts and they need be joined suitably for the machine to operate satisfactorily. Parts are joined by fasteners and they are conveniently classified as permanent or detachable fasteners. They are often sub- divided under the main headings as follows:

This is mainly applicable for short-lived devices where very large overloads may occur at low cycles. Typical examples include the elements of control systems in mechanical devices. A fatigue failure mostly begins at a local discontinuity and when the stress at the discontinuity exceeds elastic limit there is plastic strain. The cyclic plastic strain is responsible for crack propagation and fracture. Experiments have been carried out with reversed loading and

In developing a machine it is impossible to avoid changes in cross-section, holes, notches, shoulders etc. Some examples are shown in figure

Machine parts fail when the stresses induced by external forces exceed their strength. The external loads cause internal stresses in the elements and the component size depends on the stresses developed. Stresses developed in a link subjected to uniaxial loading is shown in figure-3.1.1.1. Loading may be due to: a) The energy transmitted by a machine element. b) Dead weight. c) Inertial forces. d) Thermal loading. e) Frictional forces.

No matter what stresses are imposed on an elastic body, provided the material does not rupture, displacement at any point can have only one value. Therefore the displacement at any point can be completely given by the three single valued components u, v and w along the three co-ordinate axes x, y and z respectively. The normal and shear strains may be derived in terms of these displacements.