Download General shear stress

Machines Design
1- What are the various steps involved in design synthesis? Explain in detail.
In general, the noun synthesis (from the ancient Greek σύνθεσις, σύν "with" and θέσις "placing")
refers to a combination of two or more entities that together form something new; alternately, it
refers to the creating of something by artificial means. The corresponding verb, to synthesize (or
synthesise), means to make or form a synthesis.
Chemistry and biochemistry

Chemical synthesis, the execution of chemical reactions to form a more complex
molecule from chemical precursors

Organic synthesis, the chemical synthesis of organic compounds

Total synthesis, the complete organic synthesis of complex organic
compounds, usually without the aid of biological processes

Convergent synthesis or linear synthesis, a strategy to improve the
efficiency of multi-step chemical syntheses

Dehydration synthesis, a chemical synthesis resulting in the loss of a water
molecule

Paal–Knorr synthesis, a chemical reaction named after Carl Paal and Ludwig
Knorr

Biosynthesis, the creation of an organic compound in a living organism, usually aided by
enzymes

Photosynthesis, a biochemical reaction using a carbon molecule to produce an
organic molecule, using sunlight as a catalyst

Chemosynthesis, the synthesis of biological compounds into organic waste,
using methane or an oxidized molecule as a catalyst

Amino acid synthesis, the synthesis of an amino acid from its constituents*

Peptide synthesis, the biochemical synthesis of peptides using amino
acids

Protein biosynthesis, the multi-step biochemical synthesis of
proteins (long peptides)

DNA synthesis (disambiguation), several biochemical processes for making DNA

DNA replication, DNA biosynthesis in vivo


Synthesis (cell cycle)
RNA synthesis, the synthesis of RNA from nucleic acids, using another nucleic
acid chain as a template

ATP synthesis, the biochemical synthesis of ATP
[edit]Electronics

Logic synthesis The process of converting a higher-level form of a design into a lowerlevel implementation

High-level synthesis, an automated design process that interprets an algorithmic
description of a desired behavior and creates hardware that implements that behavior
[edit]Speech

and sound creation
Sound synthesis, various methods of sound generation in audio electronics

wave field synthesis, a spatial audio rendering technique, characterized by
creation of virtual acoustic environments

Subtractive synthesis, a method of creating a sound by removing harmonics,
characterised by the application of an audio filter to an audio signal

Frequency modulation synthesis, a form of audio synthesis where the timbre of a
simple waveform is changed by frequency modulating it with a modulating frequency that
is also in the audio range

Speech synthesis, the artificial production of human speech
2- A round steel bar having Sy= 800 MPa is subjected to loads producing calculated
stresses of and
In continuum mechanics, stress is a measure of the internal forces acting within a deformable
body. Quantitatively, it is a measure of the average force per unit area of a surface within the
body on which internal forces act. These internal forces arise as a reaction to external forces
applied on the body. Because the loaded deformable body is assumed to behave as a continuum,
these internal forces are distributed continuously within the volume of the material body, and
result in deformation of the body's shape. Beyond certain limits of material strength, this can lead
to a permanent shape change or structural failure.
The stresses considered in continuum mechanics are only those produced during the application
of external forces and the consequent deformation of the body, sc. relative changes in
deformation are considered rather than absolute values. A body is considered stress-free if the
only forces present are those inter-atomic forces (ionic, metallic, and van der Waals forces)
required to hold the body together and to keep its shape in the absence of all external influences,
including gravitational attraction.[2][3] Stresses generated during manufacture of the body to a
specific configuration are also excluded.
The dimension of stress is that of pressure, and therefore the SI unit for stress is
the pascal (symbol Pa), which is equivalent to one newton (force) per square meter (unit area),
that is N/m2. In Imperial units, stress is measured in pound-force per square inch, which is
abbreviated as psi
Stress" measures the average force per unit area of a surface within a deformable body on which
internal forces act, specifically the intensity of the internal forces acting between particles of a
deformable body across imaginary internal surfaces.[4] These internal forces are produced
between the particles in the body as a reaction to external forces. External forces are
either surface forces or body forces. Because the loaded deformable body is assumed to behave
as a continuum, these internal forces are distributed continuously within the volume of the
material body, i.e. the stress distribution in the body is expressed as a piecewise continuous
function of space and time.
[edit]Normal
stress
For the simple case of an axially loaded body, e.g., a bar subjected to tension or compression by
a force passing through its center (Figures 1.2 and 1.3) the stress
(sigma), or intensity of
internal forces, can be obtained by dividing the total normal force
by the bar's cross-sectional
area . In the case of a prismatic bar axially loaded, the stress
is represented by
a scalar called engineering stress or nominal stress that represents an average stress (
)
over the area, meaning that the stress in the cross-section is uniformly distributed. Thus, we have
.
The normal force can be a tensile force if acting outward from the plane, or compressive
force if acting inward to the plane.
Normal stress can be caused by several loading methods, the most common being axial
tension and compression, bending, and hoop stress. For the case of axial tension or
compression (Figure 1.3), the normal stress is observed in two planes
and
of the axially loaded prismatic bar. The stress on plane
, which is closer
to the point of application of the load , varies more across the cross-section than that of
plane
. However, if the cross-sectional area of the bar is very small, i.e. the bar is
slender, the variation of stress across the area is small and the normal stress can be
approximated by
. On the other hand, the variation of shear stress across the section of
a prismatic bar cannot be assumed to be uniform.
3- Sketch Mohr’s circle showing the relative locations of maximum normal stress and Max.
Shear stress.
Normal Stress
Stress analysis is the determination of the internal distribution of stresses in a structure. It is
needed in engineering for the study and design of structures such as tunnels, dams, mechanical
parts, and structural frames, under prescribed or expected loads. To determine the distribution of
stress in a structure, the engineer needs to solve a boundary-value problem by specifying the
boundary conditions. These are displacements and forces on the boundary of the structure.
Constitutive equations, such as Hooke’s law for linear elastic materials, describe the stressstrain relationship in these calculations.
When a structure is expected to deform elastically (and resume its original shape), a boundaryvalue problem based on the theory of elasticity is applied, with infinitesimal strains, under design
loads.
When the applied loads permanently deform the structure, the theory of plasticity applies.
Stress analysis is simplified when the physical dimensions and the distribution of loads allow the
structure to be treated as one- or two-dimensional. For a two-dimensional analysis a plane
stress or aplane strain condition can be assumed. Alternatively, stresses can be experimentally
determined.
Computer-based approximations for boundary-value problems can be obtained through numerical
methods such as the finite element method, the finite difference method, and the boundary
element method. Analytical or closed-form solutions can be obtained for simple geometries,
constitutive relations, and boundary conditions.
A shear stress, denoted (Greek: tau), is defined as the component of stress coplanar with a
material cross section. Shear stress arises from theforce vector component parallel to the cross
section. Normal stress, on the other hand, arises from the force vector
component perpendicular orantiparallel to the material cross section on which it acts.
General shear stress
The formula to calculate average shear stress is[citation needed]:
where
τ = the shear stress;
F = the force applied;
A = the cross-sectional area of material with area parallel to the applied force vector.
[edit]Other
[edit]Pure
forms of shear stress
shear
Pure shear stress is related to pure shear strain, denoted γ, by the following
equation:[1]
where G is the shear modulus of the material, given by
Here E is Young's modulus and ν is Poisson's ratio.
[edit]Beam
shear
Beam shear is defined as the internal shear stress of a beam caused by the
shear force applied to the beam.
where
V = total shear force at the location in question;
Q = statical moment of area;
t = thickness in the material perpendicular to the shear;
I = Moment of Inertia of the entire cross sectional area.
This formula is also known as the Jourawski formula.[2]
[edit]Semi-monocoque
shear
Shear stresses within a semi-monocoque structure may
be calculated by idealizing the cross-section of the
structure into a set of stringers (carrying only axial loads)
and webs (carrying only shear flows). Dividing the shear
flow by the thickness of a given portion of the semimonocoque structure yields the shear stress. Thus, the
maximum shear stress will occur either in the web of
maximum shear flow or minimum thickness.
Also constructions in soil can fail due to shear; e.g., the
weight of an earth-filled dam or dike may cause the
subsoil to collapse, like a small landslide.
[edit]Impact
shear
The maximum shear stress created in a solid round bar
subject to impact is given as the equation:
where
U = change in kinetic energy;
G = shear modulus;
V = volume of rod;
and
= mass moment of inertia;
= angular speed.
Shear stress in fluids
Viscosity, Couette flow, Hagen-Poiseuille equation, Depth-slope product, and Simple shearAny
real fluids (liquids and gases included) moving along solid boundary will incur a shear stress on
that boundary. The no-slip condition[3] dictates that the speed of the fluid at the boundary (relative
to the boundary) is zero, but at some height from the boundary the flow speed must equal that of
the fluid. The region between these two points is aptly named the boundary layer. For
all Newtonian fluidsin laminar flow the shear stress is proportional to the strain rate in the fluid
where the viscosity is the constant of proportionality. However for Non Newtonian fluids, this is no
longer the case as for these fluids the viscosity is not constant. The shear stress is imparted onto
the boundary as a result of this loss of velocity. The shear stress, for a Newtonian fluid, at a
surface element parallel to a flat plate, at the point y, is given by:
4- Determine the safety factor with respect to initial yielding according to the Max. shear
stress theory and according to Max. distortion energy theory.
In finance, the term yield describes the amount in cash that returns to the owners of a security.
Normally it does not include the price variations, at the difference of the total return. Yield applies
to various stated rates of return on stocks (common and preferred, and convertible), fixed income
instruments (bonds, notes, bills, strips, zero coupon), and some other investment type insurance
products (e.g. annuities).
The term is used in different situations to mean different things. It can be calculated as a ratio or
as an internal rate of return (IRR). It may be used to state the owner's total return, or just a
portion of income, or exceed the income.
Because of these differences, the yields from different uses should never be compared as if they
were equal. This page is mainly a series of links to other pages with increased details.
The nominal yield or coupon yield is the yearly total of coupons (or interest) paid divided by the
Principal (Face) Value of the bond.
The current yield is those same payments divided by the bond's spot market price.
The yield to maturity is the IRR on the bond's cash flows: the purchase price, the coupons
received and the principal at maturity.
The yield to call is the IRR on the bond's cash flows, assuming it is called at the first opportunity,
instead of being held till maturity.
The yield of a bond is inversely related to its price today: if the price of a bond falls, its yield goes
up. Conversely, if interest rates decline (the market yield declines), then the price of the bond
should rise (all else being equal).
There is also TIPS (Treasury Inflation Protected Securities), also known as Inflation Linked fixed
income. TIPS are sold by the US Treasury and have a "real yield". The bond or note's face value
is adjusted upwards with the CPI-U, and a real yield is applied to the adjusted principal to let the
investor always outperform the inflation rate and protect purchasing power. However, many
economists believe that the CPI under-represents actual inflation. In the event of deflation over
the life of this type of fixed income, TIPS still mature at the price at which they were sold (initial
face). Losing money on TIPS if bought at the initial auction and held to maturity is not possible
even if deflation was long lasting.
[edit]Preferred
shares
Like bonds, preferred shares compensate owners with scheduled payments which resemble
interest. However, preferred "interest" is actually in the form of a dividend. This is a significant
accounting difference as preferred dividends, unlike debt interest, are charged after taxes and
below net income, therefore reducing net income and ultimately earnings per share. Preferred
shares may also contain conversion privileges which allow for their exchange into common stock.
The dividend yield is the total yearly payments divided by the principal value of the preferred
share.
The current yield is those same payments divided by the preferred share's market price.
If the preferred share has a maturity (not always) there can also be a yield to maturity and yield
to call calculated, the same way as for bonds.
5- Design a cast iron protective type flange coupling to connect two shafts in order to
transmit 12 KW at 500 rpm. The following permissible stresses may be used.
Shear stress for shaft, bolt and key material: 40 MPa Crushing stress for bolt and key: 80
MPa Shear stress for cast iron : 80 MPa.
A coupling is a device used to connect two shafts together at their ends for the purpose of
transmitting power. Couplings do not normally allow disconnection of shafts during operation,
however there are torque limiting couplings which can slip or disconnect when some torque limit
is exceeded.
The primary purpose of couplings is to join two pieces of rotating equipment while permitting
some degree of misalignment or end movement or both. By careful selection, installation and
maintenance of couplings, substantial savings can be made in reduced maintenance costs and
downtime.
Rigid
A rigid coupling is a unit of hardware used to join two shafts within a motor or mechanical system.
It may be used to connect two separate systems, such as a motor and a generator, or to repair a
connection within a single system. A rigid coupling may also be added between shafts to reduce
shock and wear at the point where the shafts meet.
When joining shafts within a machine, mechanics can choose between flexible and rigid
couplings. While flexible units offer some movement and give between the shafts, rigid couplings
are the most effective choice for precise alignment and secure hold. By precisely aligning the two
shafts and holding them firmly in place, rigid couplings help to maximize performance and
increase the expected life of the machine. These rigid couplings are available in two basic
designs to fit the needs of different applications. Sleeve-style couplings are the most affordable
and easiest to use. They consist of a single tube of material with an inner diameter that's equal in
size to the shafts. The sleeve slips over the shafts so they meet in the middle of the coupling. A
series of set screws can be tightened so they touch the top of each shaft and hold them in place
without passing all the way through the coupling.
Clamped or compression rigid couplings come in two parts and fit together around the shafts to
form a sleeve. They offer more flexibility than sleeved models, and can be used on shafts that are
fixed in place. They generally are large enough so that screws can pass all the way through the
coupling and into the second half to ensure a secure hold.Flanged rigid couplings are designed
for heavy loads or industrial equipment. They consist of short sleeves surrounded by a
perpendicular flange. One coupling is placed on each shaft so the two flanges line up face to
face. A series of screws or bolts can then be installed in the flanges to hold them together.
Because of their size and durability, flanged units can be used to bring shafts into alignment
before they are joined together. Rigid couplings are used when precise shaft alignment is
required; shaft misalignment will affect the coupling's performance as well as its life. Examples:

Sleeve or muff coupling

Clamp or split-muff or compression coupling
[edit]Flexible
Flexible couplings are used to transmit torque from one shaft to another when the two shafts are
slightly misaligned. Flexible couplings can accommodate varying degrees of misalignment up to
3°. In addition to allowing for misalignment, flexible couplings can also be used for vibration
damping or noise reduction. Flexible couplings are designed to transmit torque while permitting
some radial, axial, and angular misalignment. Flexible couplings can accommodate angular
misalignment up to a few degrees and some parallel misalignment.