2.1.1.a materialpropforces

7/24/2019 2.1.1.a MaterialPropForces

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Material Properties and Forces

2011 Project Lead The Way, Inc.Aerospace Engineering


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Centroid Principles

!ject"s center o# gra$ity or center o# %ass.

&raphically la!eled as


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Centroid Principles

ne can deter%ine a centroid location

!y 'tili(ing the cross)sectional $ie* o#a three)di%ensional o!ject.


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Centroid Location

+y%%etrical !jects

Centroid location is deter%ined !y an

o!ject"s line o# sy%%etry.

Centroid is located on

the line o# sy%%etry.

When an o!ject has %'ltiple lines o# sy%%etry,

its centroid is located at the intersection o# the

lines o# sy%%etry.


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o%ent o# Inertia Principles

o%ent o# Inertia -Iis a %athe%atical property o#

a cross section -%eas'red in inches/

that gi$esi%portant in#or%ation a!o't ho* that cross)sectional

area is distri!'ted a!o't a centroidal axis.

In general, a higher %o%ent o# inertia prod'ces a

greater resistance to de#or%ation.

+ti##ness o# an o!ject related to its shape.

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ea% aterial Length Width eight Area

A 3o'glas 4ir 5 #t 1 6 in. 7 6 in. 5 8 in.2

3o'glas 4ir 5 #t 7 6 in. 1 6 in. 5 8 in.2


T*o !ea%s o# e9'al cross)sectional area

3i##erence is the orientation o# the load


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Will !ea% A or !ea% ha$e a greater resistance to

!ending, res'lting in the least a%o'nt o# de#or%ation,

i# an identical load is applied to !oth !ea%s at the

sa%e location:

What disting'ishes !ea% A #ro% !ea% :



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Calc'lating o%ent o# Inertia;


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Calc'lating o%ent o# Inertia

Calc'late !ea% A %o%ent o# inertia

( ) ( ) 31.5 in. 5.5 in.=

12

( )( )3

1.5 in. 166.375 in.=12

4249.5625 in.

= 12

4= 21 in.


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Calc'lating o%ent o# Inertia

Calc'late !ea% %o%ent o# inertia

( ) ( )3

5.5 in. 1.5 in.=12

( )( )35.5 in. 3.375 in.= 12

418.5625 in.

=

12

4= 1.5 in.


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o%ent o# Inertia1>.7 ti%es

sti##er

ea%

A

ea%

4

AI = 21 in. 4BI = 1.5 in.


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+i%ple +hape $s. 4lange ea%sDoing more with less

I = 10.?@ in./

Area = 5.00 in.2

I = ?.05 in./

Area = 2.@7 in.2

Co%ple +hapesBse This Po*er


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o%ent o# Inertia ; Co%positesWhy are co%posite %aterials 'sed in

str'ct'ral design:

+tyro#oa%

-Wea

4i!erglass

+and*ich

-Wea+tyro#oa%

4i!erglass

-+trong

=


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od'l's o# Elasticity -EThe ratio o# theincre%ent o# so%e speci#ied #or% o# stress to theincre%ent o# so%e speci#ied #or% o# strain. Also

no*n as Do'ng"s od'l's.

In general, a higher

%od'l's o# elasticity

prod'ces a greater

resistance to

de#or%ation.

+tr'ct'ral e%!er Properties


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Tension +tress

Applied load di$ided !y cross)sectional area

The shape o# the cross section is not i%portant

Appropriate cross section is the s%allest areain the loaded part

A !ody !eing stretched


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Co%pression

Load di$ided !y area

nly #or parts that are $ery short co%pared

to cross sectional di%ensions or parts that

are laterally constrained

A !ody !eing s9'ee(ed


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od'l's o# Elasticity -E

The proportional constant -ratio o# stressand strain

A %eas're o# sti##ness ; The a!ility o# a

%aterial to resist stretching *hen loaded

Tensile Test ; +tress)+train C'r$e

stress = load

Area

strain = a%o'nt o# stretch

original length

or

or


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Plastic 3e#or%ation

Bnreco$era!le elongation !eyond

the elastic li%it

When the load is re%o$ed, only theelastic de#or%ation *ill !e reco$ered

Tensile Test ; +tress)+train C'r$e


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od'l's o# Elasticity Principles

ea% aterial Length Width eight Area I

A 3o'glas 4ir 5 #t 1 6 in. 7 6 in. 5 8 in.2 20.5 in./

A+ plastic 5 #t 1 6 in. 7 6 in. 5 8 in.2 20.5 in./


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What disting'ishes !ea% A #ro% !ea% :Will !ea% A or !ea% ha$e a greater resistance to

!ending, res'lting in the least a%o'nt o# de#or%ation,

i# an identical load is applied to !oth !ea%s at the

sa%e location:

d l # El ti it P i i l


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Why did !ea% ha$e greater de#or%ation than

!ea% A:


3i##erence in %aterial %od'l's o# elasticity

The a!ility o# a %aterial to de#or% and ret'rn to

its original shape

Applied #orce or load

Length o# span !et*een s'pports

od'l's o# elasticity

o%ent o# inertia

Characteristics o# o!jects that i%pact de#lection

-AF


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Calc'lating ea% 3e#lection

ea% aterial Length

-L

o%ento# Inertia

-I

od'l's o#Elasticity

-E

4orce-4

A 3o'glas 4ir 5 #t 20.5 in./ 1,500,000

psi

270 l!#

A+ Plastic 5 #t 20.5 in./ /1G,000psi

270 l!#

a= 4 L>

/5 E I


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ea% aterial Length I E Load

A 3o'glas 4ir 5 #t 20.5 in./ 1,500,000

psi

270 l!#

Calc'late !ea% de#lection #or !ea% A

a= 4 L>

/5 E I

a= 270 l!#-G? in.>

/5 -1,500,000 psi -20.5 in./

Max= 0.123 in.


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ea% aterial Length I E Load

A+ Plastic 5 #t 20.5 in./ /1G,000

psi

270 l!#

a= 4 L>

/5 E I

Calc'late !ea% de#lection #or !ea%

a= 270 l!#-G? in.>

/5 -/1G,000 psi -20.5 in./

Max= 0.53 in.

+


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3o'glas 4ir $s. A+ Plastic

/.2/

Ti%es

less

de#lection

Max A= 0.123 in. Max B= 0.53 in.


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+tatics

The st'dy o# #orces and their e##ects

on a syste% in a state o# restor'ni#or% %otion

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E ili! i


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E9'ili!ri'%

Translational e9'ili!ri'%HThe state in *hich there are no 'n!alanced

#orces acting on a !ody

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alanced Bn!alanced

+tatic e9'ili!ri'%H

A condition *here there are no net eternal#orces acting 'pon a particle or rigid !odyand the !ody re%ains at rest or contin'esat a constant $elocity

x

y

F =0

F =0

E ili! i


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E9'ili!ri'%


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Tr'ss Analysis

Pri%ary tr'ss loads ; loads calc'lated *ith

ideal ass'%ptionsBsed in *elded steel)t'!e #'selages, piston)

engine %otor %o'nts, ri!s, and landing gear

T A l i E i E l


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Tr'ss Analysis ; Engine o'nt Ea%ple

Line o# #orce is #ro% the center o# gra$ity o#

the engine,200l!#

+


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+'%%ary

Centroid is o!ject"s center o# gra$ity or

center o# %ass o%ent o# Inertia -I is a %athe%atical

property o# a cross section

+igni#icant

in#l'ence

+


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+'%%ary

Co%posite shapes 'sed in

str'ct'ral design to createlight*eight, strong %aterial

od'l's o# Elasticity -E

The ratio o# the incre%ent o#so%e speci#ied #or% o# stress

to the incre%ent o# so%e

speci#ied #or% o# strain 3e#lection calc'lated 'sing

%od'l's o# elasticity a= 4 L>

/5 E I

+


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+'%%ary

E9'ili!ri'% Translational

2.1.1.a materialpropforces

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