background theory

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Background Theory

1 Introduction

ngineers design endless variety of objects to serve the basic needs of society. Factors to be

nsidered in design included functionality, strength, appearance, economics and environmental

otection. The background theory related to the loading frame elements design will be presented

this chapter.

2 Design Against Static Load

2.1 Modes of failure

he load is designed as static load if it is gradually applied to a mechanical component and does

t change its magnitude or direction with respect to time. The engineering materials can be

assified into two group's ductile and brittle materials. A ductile material has a relatively large

nsile strain before fracture occurs; on the other hand, a brittle material has a relatively small

nsile strain prior to fracture. A tensile strain of about 5% is considered to be the dividing line

tween brittle and ductile material [4].

mechanical component may fail this is may be unable to perform its function satisfactorily, as a

sult of any one of the following three modes of failure.

Failure by elastic deflection.

Failure by general yielding.

Failure by fracture.

application like transmission shaft supporting gears, the maximum force acting on the shaft,

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thout affecting its performance, is limited by the permissible elastic deflecting. Lateral or

rsional rigidity is considered as the criterion of design in such cases. Sometimes, the elastic

flection result in unstable conditions, such as buckling of columns or vibration. The design of

e mechanical component, in all these cases, is based on the permissible lateral or torsional

flecting. The stresses induced in the component are not significant and the properties of the

aterial, such as yield strength or ultimate tensile strength, are not of primary importance. The

odulus of elasticity and rigidity are the important properties and the dimensions of the

mponent are determined by the load deflection equation.

mechanical component made of ductile material loses its engineering usefulness due to a large

mount of plastic deformation after the yield point stress is reached. A considerable portion of the

mponent is subjected to plastic deformation called general yielding. There is a basic difference

tween general yielding and localised yielding. The localised yielding in the region of stress

ncentration is restricted to a very small portion of the component and is not considered

gnificant. The yield strength of a material is an important property when a component is

signed against failure due to general yielding.

Components made of brittle materials cease to function satisfactorily because of the

dden fracture without any plastic deformation. The failure in this case is sudden and total. The

timate tensile strength of the material in an important property for determining the dimensions

these components.

In the light of the above the design of components on both strength and rigidity basis is

pected.

2.2 Safety factor

he loads that a structure is capable of supporting must be greater than the load it will be

bjected to when in service if the structure failure is to be avoided. The strength is the ability of



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structure to resist loads; the actual strength of a structure must exceed the required strength. The

ctor of safety is the ratio of the actual strength to the required strength.

(2.1)

he factor of safety must be of course greater than 1.0 if failure is to be avoided. Factors of

fety from slightly above 1.0 to a much as 10 are used. Since both strength and failure have

any different meanings, the incorporation of factors of safety in design is not a simple matter.

rength may be measured by the load carrying capacity of a structure, or it may be measured

y the stress in the material. Failure may mean the fracture and complete collapse of a structure

it may mean that the deformation have become so large that the structure can no longer

rform its intended functions. The latter type of failure may take place at loads much smaller

an those that cause collapse. The determination of a factor of safety must also take into

count such matters as the following: probability of accidental overloading of the structure by

ads that exceed the design loads; types of loads (static or dynamic); whether the loads are

plied once or are repeated; how accurately the loads are known; possibilities for fatigue

ilure; inaccuracies in construction; variability in the quality of workmanship; variations in

operties of materials; deterioration due to corrosion or other environmental effects; accuracy

the methods of analysis; whether failure is gradual (ample warning) or sudden (no warning);

nsequences of failure (minor damage or major catastrophe); and other such consideration. If

e factor of safety is too low, the likelihood of failure will be high and the structure will be

acceptable; if the factor is too large, the structure will be wasteful of material and perhapssuitable for its function (for instance, it may be too heavy).

There are many international codes and regulations which proscribe the factor of safety

here danger to human life is involved. The provisions of codes and specification are intended

provide reasonable level of safety without unreason able costs.



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2.3 Allowable stresses and allowable loads

Factors of safety are defined and implemented in various ways. As mentioned in the

eceding section while designing a component it is necessary to ensure sufficient reserve

ength in case of an accident. It is ensured by taking a suitable factor of safety (n). The factor

safety may be defined as

(2.2)

(2.3)

The allowable stress (or working stress) value is used in design to determine the

mension of the component. It is considered as a stress which the designer excepts will not be

ceeded under normal operations.

or ductile materials the allowable stresses in normal and shear are obtained by the following

uation:

(2.4)

r

(2.5)

or brittle material, the relationships are:

(2.6)

(2.7)

The allowable load (the permissible load or the safe load) can be obtained knowing the

owable stress and the geometry of the component.

2.4 Elements design



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ar subjected to normal load

he stress is given by

(2.8)

he strain is given by

(2.9)

he elongation (contraction) is given by:

(2.10)

esign criteria

(2.11)

(2.12)omponents subject to direct shear stress

he average shear stress is given by

(2.13)

hear strain is given by

(2.14)

he design criteria

he permissible shear stress is given by

(2.15)

here

is the yield strength in shear equals

50% and 57.7% of the yield strength in tension, according to the principle shear stress theory

d the distortion energy theory of failure respectively[5].

ar subjected to torsion moment



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(2.16)

(2.17)

(2.18)

(2.19)

esign criteria

(2.20)

(2.21)

here is the angle of twist

2.5 Members subjected to buckling load.

oad carrying structures may fail in variety of ways depending upon the type of structure the

nditions of support the kind of loads and the materials used. For instance, an axle in a vehicle

ay fracture suddenly from repeated cycles of loading, or a beam may deflect excessively, so

at the structure is unable to perform its intended function. These kinds of failures are prevented

y designing structures so that the maximum stresses and maximum displacement remain within

lerable limits. Thus, strength and stiffness are important factors in design.

Another type of failure is buckling. We will consider specifically the buckling of

lumns, which are long slender structural members loaded axially in compression (Figure. 2.1).a compression member is relatively slender, it may deflect laterally and fail by bending rather

an failing by direct compression of material. You can demonstrate this behavior by

mpressing a plastic ruler or other slender object. When lateral bending occurs, we say that the

lumn has buckled. Under an increasing axial load, the lateral deflection will increase too, and



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Le = effective length = KLFigure 2.2: Critical loads, effective lengths, and effective-length factors for idealcolumns.[5]

K = effective length factor (Figure 2.2)

L = actual length of the column

ritical Stress

(2.23)

2.6 Power screwspower screw is a mechanical devise meant for converting rotary motion into translation motion

d for transmitting power. The main application pf power screws are as follows:

to load a specimen, e.g. universal testing machine; to raise the load, e.g. screws-jack; to obtain accurate motion in machining operations, e.g. lead-screws of lath; to clamp a work piece, e.g. vice;

orms of threads

There are four type of thread used for power screws square, acme, I.S.O. metric

apezoidal, and buttress, as shown in figure 2.3. The guidelines for the selection of a proper

read profile for the power screws are as follows: The efficiency of square threads is more than that of other types of threads. Square threads are difficult to manufacture. Square threads have limited application due to

difficulties in their manufacture. The strength of a screw depends upon the thread thickness at the core diameter. As seen in

figure 2.3(a), (b) and (c), acme and trapezoidal threads are stronger than square threads due to

more thread thickness. The wear of the thread surface becomes a serious problem in applications.



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Buttress threads can transmit power and motion only in one direction, while square, acme

and trapezoidal threads can transmit force and motion in both directions.

Square threads are used for screw-jacks, presses and clamping devise. Acme and trapezoidal

threads are used for the lead-screw and other power transmission devise in machine tools.

Buttress threads are used in vices, where force is applied only in one direction.

Figure 2.3: Threads for power screw

resses in screw

he body of a screw is subjected to an axial force W and torsional moment (M t) as shown in

gure 2.4. The direct compressive stress is given by

(2.24)



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Figure 2.4: Stresses in screw

or long and slender screws, buckling is considered instead of compression. The torsional shear

ress is given by

(2.25)

he principle (max) shear stress given by,

(2.26)

he threads of the screw which are engaged with the nut are subjected to transverse shear

esses. The screw will tend to shear off the threads at the core diameter under the section of load

. the shear area of one thread is dc t. the transverse shear stress in the screw is given by

(2.27)heretransverse shear stress at the root of the screw (N/mm 2)

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= thread thickness at the core diameter (mm)= number of threads in engagement

he transverse shear stresses in the nut are determined in a similar way. Under the action of load

, the thread on the nut will tend to shear off at the nominal diameter. The shear area of one

read is d t. Therefore,

(2.28)here= transverse shear stress at the root of the nut (N/mm 2)

= thread thickness at the root of the nut (N/mm)

he bearing pressure between the contacting surface of the screw and the nut is an importantnsideration in design. The bearing area between the screw and the nut for one thread is [ /4

]. Therefore,

(2.29)

(2.30)here

b = unit bearing pressure (N/mm 2)

he permissible bearing pressure depends upon the materials of the screw and the nut, and the

bbing velocity. The permissible values of unit bearing pressure are given in Table 2.1 [4].

Table 2.1 Unit bearing pressure for power screws

3 Thermodynamics background

The main thermodynamics principle used in this project to design the conditioning

amber is the energy balance. Energy balance states that the net change in the total energy of



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e system during a process is equal to the difference between the total energy entering and the

tal energy leaving the system. In mathematical form, this can describe as follows:

(2.31)

The system used in this project is an open system operating under steady flow conditions,

the equation of the energy balance will be:

2.32)

the studied furnace, we need to calculate the heat transferred from the hot water to the

ecimen. In this case, changes in potential and kinetic energy are negligible and there is no work

teraction between system and its surrounding. Therefore, the final form of the energy equation

at gives the rate of heat transferred to the specimen becomes:

(2.33)

y applying the first law of thermodynamics to the hot water entering, we can calculate the rate

heat transfer to the specimen as follows:

(2.34)

4 Heat transfer modes

Heat is defined as the form of energy that can be transferred from one system to another

cause of temperature difference. The science that deals with the determination of the rates of

ch energy transfers is the heat transfer. The transfer of energy as heat is always from the higher

mperature medium to the lower temperature one.



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eat can transfer in three different modes:

1- Conduction

2- Convection

3- Radiation

In our project, heat transferred from hot water to the specimen takes place by convection a

ief description of these modes is given below.

4.1 Convection heat transfer:

Convection is the mode of energy transfer between a solid surface and the adjacent liquid

gas that is in motion. The faster the fluid motion, the greater the convection heat transfers.

y the following equation, we can calculate the heat transfer to the system:

(2.35)

om the following Table 2.2 we can find the convective heat transfer coefficient:

Table 2.2: Heat transfer convective [5].

background theory

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