Moment loads are divided into two categories such as bending moment and torsion moment. The stresses due to the moments can be illustrated as in the following figure 3.11; Figure 3.11 Stresses due to moments [3] As in the illustrated figure 3.11 the stress distribution is linear and highest at the outer surface of the pipe. The highest stresses due to the bending can be written as; by bz M y Z M z Z (Eq 3.41) [3] (Eq 3.42) [3] Where; Z (r 4 r 4 ) (Eq 3.43) [3] 4ro The resultant bending stress will be; 2 2 1 2 2 b by bz Z M y M z (Eq 3.44) [3] The bending stress due to the torsion moment Mx is uniformly distributed along the circumferential direction and maximum at the outer surface of the pipe. The …show more content…
• Modal analysis To find natural frequencies and mode shapes of the pipe, it is necessary to do a modal analysis. Various elastic piping components such as pipes, bends, tees, flanges and etc are part of a piping system and also the piping system is having uneven mass distribution because of size changes, different fittings and other various rigid components. Therefore once the system is displaced from static equilibrium, its components starts to oscillate at different mode shapes and starts to vibrate at associated frequencies. It is vital to find the natural frequency of the piping system in order to determine the dynamic load factors (DLF) and also to determine the pipe support span to avoid harmful vibrations. It is necessary to do the modal analysis before the other dynamic analysis since these are using the natural frequencies of the system obtained from the modal analysis. When a piping system is properly supported in according to the standards, the lowest natural frequency should not less than 4 or 5 Hz. • Harmonic
This is because the law only takes into account the length of the pipe, and the area that produces friction, but not the surface texture i.e. the roughness of the pipe, which affects the amount of friction produced over the area.
Where 훳 equals the angle of the arm with respect to the horizontal. There is also a torque acting in the counterclockwise direction. This force is caused by the mass of the arm. It can be reasonably assumed that the arm has a uniform density since the thickness is the same throughout and the arm is made of only one material, and so we can say that the center of mass must be located at the midpoint of the arm. Using this, we can model the torque caused by the mass of the arm by
Rigid body motion does not change the length of a vector joining the pair of points inside the body and has no concern with the strain analysis. When external forces are applied on an elastic body, the body undergoes deformation. Due to the elasticity of the body, there comes into play a force which resists the deformation. This force is called stress force. Clearly, the deformation of the body is accompanied by the stress force. In other words, stress and strain occur together in inelastic body. There are two types of elastic deformation: (i) Dilatation and (ii) Shear strain set up in the body in such a way that there is a change only in volume but no change in shape, is called dilatation. In the shear deformation, there is a change in the shape of the body without a change in its volume. Dilatations are further categorized into two kinds: compression, in which volume is reduced; and rarefaction, in which the volume is
Question: Discuss the importance of Relief Valves in the unit operations in detail, and give the design criteria/ parameters/ models available equations in the literature. Support your work by giving a typical example from the literature.
The structural torsional stiffness is calculated through finding the torque applied to the handle and dividing it by the angular deflection of the handle that is resulted from the torsional loading. It is expressed in term of Nm/degree of angular deflection. This calculation is shown below in figure 3.1
Swameer, P. K. and Jain, A. K., “Explicit equation for pipe flow problems”, Journal on Hydr.Divi., ASCE, 102 (5), 657-664, 1976.
where hfs, hff, hfc, and hfe represent the friction losses due to skin friction, fittings, contractions, and expansions, respectively. Since the diameters of pipes are constants in the system, we can assume that the contraction and expansion losses are negligible. As a result, the equation (2) turn out as below.
contains for stresses; there is a strong caesura in the middle of the lines and
This chart shows the relationship between the fanning friction factor and the Reynolds number over a wide range of flow rates, from which the roughness parameter (e/D) for the piping system can be estimated.
Had created the three dimensional model of steam turbine casing. As the model is complex, so they made some assumptions to simplify the model. Assumptions are as follows
The crankshaft is a structural component which converts the linear piston movement into rotary motion while the force connecting rod is transformed to torque. Crankshaft consists of two web and crankpin on which connecting rod is connected. A crankshaft is subjected to several forces that vary in magnitude and direction (multiaxial loading). Bending stress and shear stress due to twisting are also common stresses acting on crankshafts. The crankshaft main journals rotate in a set of supporting bearings (main bearings), causing the offset rod journals to rotate in a circular path (translation movement) around the main journal centers. The diameter of that path is the engine stroke when the piston moves up and down in its cylinder.
[9] O’Hara, G P, “Analysis of the Swage Autofrettage Process,” US Army ARDEC Technical Report ARCCB-TR-92016, Benét Laboratories, Watervliet Arsenal, NY 12189, USA, 1992. Even with the use of lubricants a considerable amount of axial force is applied by the mandrel to the tube, a need to constraint it raises. Constraint locations include either the mandrel entry or exit ends. The location determines whether the deformed length of tube is held is tension (the former case) or the un-deformed length is compressed (the latter). Just like the Open- and Closed-Ends cases of hydraulic autofrettage, these axial stresses effect the precision of the radial stress patterns developed. The tube modelled by O’Hara [9] was constrained at its mandrel entry end, around its OD. [9] O’Hara, G P, “Analysis of the Swage Autofrettage Process,” US Army ARDEC Technical Report ARCCB-TR-92016, Benét Laboratories, Watervliet Arsenal, NY 12189, USA,
The objective of this lab is to illustrated the procedures required to perform tensile tests. Using data obtained from the test will enable the student to determine various material characteristics that affect the design process. Some findings/interpretations are the stress vs strain curve will help us show how the metal reacted to the forces applied, and the point of failure is very important as it is the ultimate strength.
The channel section (both C and I) have higher bending stiffness as compared to solid square bar with equal cross section area. Considering the bending stiffness of solid square section as 1, the relative bending stiffness of other sections are: