MOM Chapter1

8/13/2019 MOM Chapter1

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LECTURE 1

INTRODUCTION AND REVIEW

Preamble

Engineering science is usually subdivided into number of topics such as

1. Solid Mechanics

2. Fluid Mechanics

3. Heat Transfer

. !roperties of materials and soon "lthough there are close lin#s bet$een them in terms of the physical principlesinvolved and methods of analysis employed.

The solid mechanics as a sub%ect may be defined as a branch of applied mechanics that deals $ith behaviours of

solid bodies sub%ected to various types of loadings. This is usually subdivided into further t$o streams i.e Mechanicsof rigid bodies or simply Mechanics and Mechanics of deformable solids.

The mechanics of deformable solids $hich is branch of applied mechanics is #no$n by several names i.e. strength ofmaterials& mechanics of materials etc.

Mechanics of rigi boies!

The mechanics of rigid bodies is primarily concerned $ith the static and dynamic behaviour under e'ternal forces ofengineering components and systems $hich are treated as infinitely strong and undeformable !rimarily $e deal here$ith the forces and motions associated $ith particles and rigid bodies.

Mechanics of eformable solis !

Mechanics of solis!

The mechanics of deformable solids is more concerned $ith the internal forces and associated changes in thegeometry of the components involved. (f particular importance are the properties of the materials used& the strengthof $hich $ill determine $hether the components fail by brea#ing in service& and the stiffness of $hich $ill determine$hether the amount of deformation they suffer is acceptable. Therefore& the sub%ect of mechanics of materials orstrength of materials is central to the $hole activity of engineering design. )sually the ob%ectives in analysis here $illbe the determination of the stresses& strains& and deflections produced by loads. Theoretical analyses ande'perimental results have an e*ual roles in this field.

Anal"sis of s#ress an s#rain !

Conce$# of s#ress ! +et us introduce the concept of stress as $e #no$ that the main problem of engineering

mechanics of material is the investigation of the internal resistance of the body& i.e. the nature of forces set up $ithina body to balance the effect of the e'ternally applied forces.

The e'ternally applied forces are termed as loads. These e'ternally applied forces may be due to any one of thereason.

,i- due to service conditions

,ii- due to environment in $hich the component $or#s


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,iii- through contact $ith other members

,iv- due to fluid pressures

,v- due to gravity or inertia forces.

"s $e #no$ that in mechanics of deformable solids& e'ternally applied forces acts on a body and body suffers adeformation. From e*uilibrium point of vie$& this action should be opposed or reacted by internal forces $hich are setup $ithin the particles of material due to cohesion.

These internal forces give rise to a concept of stress. Therefore& let us define a stress Therefore& let us define a termstress

%#ress!

+et us consider a rectangular bar of some cross sectional area and sub%ected to some load or force ,in /e$tons -

+et us imagine that the same rectangular bar is assumed to be cut into t$o halves at section 00. The each portion ofthis rectangular bar is in e*uilibrium under the action of load ! and the internal forces acting at the section 00 hasbeen sho$n

/o$ stress is defined as the force intensity or force per unit area. Here $e use a symbol to represent the stress.

here " is the area of the 0 section


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Here $e are using an assumption that the total force or total load carried by the rectangular bar is uniformlydistributed over its cross section.

ut the stress distributions may be for from uniform& $ith local regions of high stress #no$n as stress concentrations.

f the force carried by a component is not uniformly distributed over its cross sectional area& "& $e must consider a

small area& 4"5 $hich carries a small load !& of the total force 4!5& Then definition of stress is

"s a particular stress generally holds true only at a point& therefore it is defined mathematically as

Uni#s !

The basic units of stress in S. units i.e. ,nternational system- are / 6 m2,or !a-

M!a 7 189!a

:!a 7 18;!a

Some times / 6 mm2units are also used& because this is an e*uivalent to M!a. hile )S customary unit is pound pers*uare inch psi.

T&PE% O' %TRE%%E% !

only t$o basic stresses e'ists = ,1- normal stress and ,2- shear shear stress. (ther stresses either are similar to thesebasic stresses or are a combination of these e.g. bending stress is a combination tensile& compressive and shearstresses. Torsional stress& as encountered in t$isting of a shaft is a shearing stress.

+et us define the normal stresses and shear stresses in the follo$ing sections.

Normal s#resses !e have defined stress as force per unit area. f the stresses are normal to the areas concerned&

then these are termed as normal stresses. The normal stresses are generally denoted by a :ree# letter , -


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This is also #no$n as unia'ial state of stress& because the stresses acts only in one direction ho$ever& such a staterarely e'ists& therefore $e have bia'ial and tria'ial state of stresses $here either the t$o mutually perpendicularnormal stresses acts or three mutually perpendicular normal stresses acts as sho$n in the figures belo$ =

Tensile or com$ressi(e s#resses !

The normal stresses can be either tensile or compressive $hether the stresses acts out of the area or into the area

)earing %#ress ! hen one ob%ect presses against another& it is referred to a bearing stress , They are in fact thecompressive stresses -.


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%hear s#resses !

+et us consider no$ the situation& $here the cross sectional area of a bloc# of material is sub%ect to a distribution offorces $hich are parallel& rather than normal& to the area concerned. Such forces are associated $ith a shearing of

the material& and are referred to as shear forces. The resulting force interistes are #no$n as shear stresses.

The resulting force intensities are #no$n as shear stresses& the mean shear stress being e*ual to

here ! is the total force and " the area over $hich it acts.

"s $e #no$ that the particular stress generally holds good only at a point therefore $e can define shear stress at apoint as

The gree# symbol , tau - , suggesting tangential - is used to denote shear stress.

Ho$ever& it must be borne in mind that the stress , resultant stress - at any point in a body is basically resolved into

t$o components and one acts perpendicular and other parallel to the area concerned& as it is clearly defined in

the follo$ing figure.


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The single shear ta#es place on the single plane and the shear area is the cross > sectional of the rivett& $hereas thedouble shear ta#es place in the case of utt %oints of rivetts and the shear area is the t$ice of the 0 > sectional area ofthe rivett.

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MOM Chapter1