1.Equilibrium of Deformable Body

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Mechanics of Solids (VDB1063)

Equilibrium of Deformable Body

Lecturer: Dr. Montasir O. Ahmed

Universiti Teknologi PETRONASCivil Engineering Department


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LECTURE OUTLINES

Introduction

Equilibrium of Deformed Body


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Mechanics of materialsis a branch of mechanics that studies the internal effects of stress

and strainin a solid body that is subjected to an external loading.

Stressis associated with the strength of the material from which the body is made, while

strainis a measure of the deformation of the body.

INTRODUCTION


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Surface Forces: Caused by the direct contactof one body with

the surface of other. The resultant force FR acts through the

centroid Cor geometric centre of this area.

A body force: is developed when one body exerts a

force on another body without direct physical contact

between the bodies such as the earths gravitation

whereas the force is called weightand acts through the

bodyscentre of the gravity.



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Support reactionsare forces that develop at the supports or point of contact between bodies.

If the supportprevents translationin a given direction, then aforce must be developedon the

member in that direction. Likewise, if rotation is prevented, a couple moment must be

exerted on the member.



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Equation of Equilibrium

In general, equilibrium of body requires:

1. Balance of forces to prevent the body from translating. = 0

2. Balance of moments to prevent the body from rotating. = 0

If anx,y,zcoordinate system is established with the origin at point O, then the equation

of equilibrium become:

= 0, = 0, = 0, = 0 , = 0, = 0

If the forces lie in the x-y plane (coplanar forces), then the conditions for equilibrium of

the body can be specified as:

= 0, = 0, = 0

The best way to account for all these forces is to draw the bodysfree-body diagram.



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Internal Resultant Loadings

The criteria for determination of the internal loadingsis:

1. Pass an imaginary sectionthrough the region where the internal loadings

are to be determined (Fig. a).

2. Draw thefree body diagram of one of the parts as shown in Fig. b.

3. Use the equations of equilibrium to relate the external forces in the free

body diagram to the distributionsresultant internal forces and moments,

and



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Four different types of internal resultant loadings can

then be defined as follows:

1. Normal Force, N: This force acts perpendicular to the

area. It is developed whenever the external loads tend to

push or pull on the two segments of the body.

2. Shear Force, V: This force lies in the plane of the area

and it is developed when the external loads tend to

cause the two segments of the body to slide over one an

other.

3. Torsional Moment or Torque, T: This effect is developedwhen the external loads tend to twist one segment of the

body with respect to the other about an axis

perpendicular to the area.

4. Bending Moment, M: It cause by the external loads that

tend to bend the body about an axis lying within the

plane of the area



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Important Points in the Lecture

External forces can be applied as distributed, concentratedsurface loading and body

forces.

Linear distributed loadings produce resultant force having magnitudeequal to the area

under the load and having a locationthat passes through the centroidof this area.

A support produces aforceif itprevents translation, and it produces a couple moment

on the member if itprevents rotation.


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= 0 and = 0 must be satisfied in order topreventa body from translatingand

from rotating.

When applying the equations of equilibrium, itsimportant to first draw thefree body

diagram.

Method of sections is used to determine the resultant normal force, shear force,

torsional moment, and bending moment.

Important Points in this Lecture


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Stress

Normal Stress

Shear Stress

Design of Simple Connections

allowable stresses

Strain

Normal strain

Shear strain

Next Class


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Thank You

1.Equilibrium of Deformable Body

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