Engineering Mechanics DistributedForces

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Distributed ForcesDistributed Forces

Than Lin, Ph.D.

Instructor, Undergraduate Program

Asian Institute of Technology

Engineering Mechanics 3(3-0), AIT-UG (Sept2011)


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Presentation Outline

Introduction

Center of Mass

Centroids (Line, Area, Volume)

Composite Bodies and Figures

Theorem of PappusSpecial Topics

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-Beams-Internal Effects

Flexible CablesFluid Statics



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Introduction

When forces are applied over a region whose dimensions are not

neg g e compare w t ot er pert nent mens ons, we must

account for the actual manner in which the force is distributed by.

For this purpose, we need to know the intensity of the force at any

location and we will use the integration to find their total effects.

Area Distribution

Line Distribution

Volume Distribution



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Centers of Mass & Centroids



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Center of Mass

CG: point where the resultant gravitational force W acts

Location of the CG and CM are found by the principle of moment

sum of the moments = moment of the sum



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Centroids of lines, areas, volumes



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Composite Bodies and Figures;



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Approximation Method



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Irregular Volume



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Locate the center of mass of the bracket and shaft combination. The vertical face is

made from sheet metal which has a mass of 25 kg/m . The material of the horizontal

base has a mass of 40 kg/m2, and the steel shaft has a density of 7.83 Mg/m3.



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Theorem of Pappus



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Theorem of Pappus

Several practical objects have their surface or volume created

by revolving the planar curve or the planar area about thenonintersecting line in its plane.

revolved object.

This is done by dividing the object into infinitesimal circular-arc

strips along the axis of revolution. Then the total area or volume

may be determined from integrating the infinitesimal area or

volume of these strips.



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Theorem of Pappus

= dLyA 2

LA 2=

dAyV = 2

AyV 2=

Engineering Mechanics 3(3-0), AIT-UG (Sept2011)AyV=

LyA =


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S i l T i


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Special Topics- -

Various Types of Beam Loading and Support

Beam - structural member designed to supportoa s app e at var ous po nts a ong ts engt .

Beam can be subjected to concentrated loads or

distributed loads or combination of both.


S i l T i


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Special Topics- -

Type of Beams

eams are c ass e accor ng to way n w c t ey are supporte .

Reactions at beam supports are determinate if they involve only three


unknowns. Otherwise, they are statically indeterminate.


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Distributed Loads



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Beam design is two-step process:

moments produced by applied loads2) select cross-section best suited to resist

shearing forces and bending moments



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Wish to determine bending moment and

shearing force at any point in a beam

subjected to concentratedand distributed

loads.

Determine reactions at supports by treating

w o e eam as ree- o y.

u eam a an raw ree- o y

diagrams for AC and CB. By definition,

positive sense for internal force-couple

.

From equilibrium considerations, determine


an .


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Shear and Bendin Moment Dia rams

Variation of shear and bending moment along beam may

Determine reactions at supports.

Cut beam at C and consider member AC,

==

Cut beam at E and consider

member EB,

( ) 22 xLPMPV +==

For a beam subjected to concentrated loads, shear is

constant between loadin oints and moment varies


linearly.


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Engineering Mechanics DistributedForces

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