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7.3 StressDavid Che

Geneva College

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How to describe thestrength of a

particular type ofmaterial?

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Class demoPush and pull on the arm

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Assumptions & denitionhe material is continuous

!o voids

he material is cohesive

!o crac"s# brea"s# or separations

AFstress

A =

0lim

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!ormal stress$ntensity of force%orce per unit areaActing normal to the

unit area

Pull tensilePush

compressive

A

FzA

z

= 0lim

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earstress

$ntensity of force# orforce per unit area#

acting tangent to area

A

FxA

zx

= lim0

A

FyAzy

=0

lim

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stress

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A

FyA

zy

=0

lim

A

Fz

Az

=0

lim

A

FxA

zx

= lim0

'ubscript

notation

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General state ofstress

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(nits for stress'$ units)

!*m+,# or pascal -. Pa / . !*m+,0

"Pa# 1Pa# GPa# are used more often. !*mm+,/ .1!*m+,/.1pa

(' Customary or %oot2Pound2'econd -%P'0

system)pounds per s3uare inch -psi0"si 2 "ilo2pounds -"ip0 per s3uare inch

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. verageNormal Stress in

an Axially LoadedBar

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he section denes

the cross2sectionalarea of the bar

'ince all such cross

sections are thesame# the bar isreferred to as beingprismatic

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nshe bar remains straight both

before and after the load isapplied

he cross section remains 4at

or plane during the deformationhe hori5ontal and vertical grid

lines inscribed on the bar willdeform uniformly when the bar

is sub6ected to the load

Here we will not considerregions of the bar near its ends#

where application of the

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Assumptions -continued0Homogeneous material)

'ame physical and mechanical propertiesthroughout its volume

$sotropic material)

'ame physical and mechanical properties in alldirections

1any engineering materials t this bill'teel contains thousands of randomly oriented

crystals in each cubic millimeter of its volumeCold2rolled steel and wood are both anisotropic

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AdAdFP

===

A

P=

bartheofareasectional-crossA

mequilibriuofequationstheandsectionsofmethod

theusingdeterminedisParea.sectional-crosstheofcentroid

hethrough tappliediswhichforce,normalresultantinternalP

areasectional-crosson thepointanyatstressnormalaverage

=

=

=

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83uilibrium) 0= ZF

0)()( = AA

=(nia7ial stress) two normal stresscomponents on the element mustbe e3ual in magnitude but opposi

$n direction

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a7imum average normal stress

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87ample 9:;

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87ample 9:;

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'olution)

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Condoor 8ngineering 'tatics Page ,egency al"way

Courtesy Dr: @ee @owery# r:# P:8:

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Condoor 8ngineering 'tatics Page B

he Collapse of the =ansas CityHyatt >egency al"way

he wal"way that collapsed connected thesecond and the fourth 4oors across a multi2storied atrium:

A ma6or design change was introducedduring construction:

n uly .9# .

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Condoor 8ngineering 'tatics Page B.

Collapse of =ansas City Hyatt>egency al"way

riginal design 1odied design

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Homewor"Problems %929F 92,F 92B9

Due) %riday# .*B.*,.