Stress Nd Strain

7/25/2019 Stress Nd Strain

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curve


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When some external forces are applied to abody . than the body oers internal resistanceto these force. the magnitude of the internalresistance force is numerically equal to theapplied force.


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stress=appliedload /area


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Tensile stressCompressive stress

Shear stress


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Tensile strain

Compressive strain

Shear strain


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tan=dl/l


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Methods of analysisMethods of analysis

(Load-stress load-deflection relations)

Method of mechanics ofmaterial

Method of continuum

mechanics & Elasticity

Energy methods

Equations of

equilibriumContinuity

condition

/ = E

Equilibrium equationfor elemental volume

Differential

compatibility equation

Generalized Hookeslaw

Also called scalar

method

!lane crosssection ofmember remainplane afterdeformation


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Stress-Strain RelationsStress-Strain Relations

Stress components must be relatedto the strain components.


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Material PropertiesMaterial Properties

! "odulus of#lasticity

! $oisson%s &atio! Shear "odulus

! $ercent#longation

'ield Strength

! (ltimate tensile

Strength! 'ield $oint

! "odulus of&esilience


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Engineering Stress and StrainEngineering Stress and Strain

0

P

LL L

e

=

= =


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!rue Stress and Strain!rue Stress and Strain

( )t

t

t

t

tt

t

L

t t

L

P

L L

dLd

L

Ld ln ln "

L

e

e

=

= +

=

+ = = = +


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Structural steel

ll dim# in mm

$$


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-20

-2

16

34

52

70

S

tre

ss

(k

s

i)

0 0.05 0.1 0.15 0.2 0.25 0.3Strain (in/in)

E%perimental Stress-Strain plot for "0" steel

Structural steel


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0 0.002 0.004 0.0060.008

Strain

0

125

250

375

500

Stress(!"

a)

#ra$ Cast %ron

Characteristic stress-

strain curve for brittle

materialCast Iron

0 0.06 0.12 0.180.24Strain

0

125

250

375

500

Stress(!"a)

2024-T351 &lu'inu' &llo$

Characteristic stress-strain curve for ductile

material

Aluminum


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Stress-strain curve for compression

Cast Iron

Copper


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Poissons ratio

Poisson's ratio can e determined indirectly from

stress-strain cure y *no+ing the change in the

cross-sectional area of the specimen at a point

along the elastic region of the stress-strain cure#

lateral strain

= -

axial strain


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"he !oisson ratio for most metals falls between#$% to #&%

'ubber has a !oisson ratio close to #% and istherefore almost incompressible(

Cork has a !oisson ratio close to zero )"his

makes cork function well as a bottle stopper* sincean a+ially,loaded cork will not swell laterally toresist bottle insertion-

"he !oisson.s ratio is bounded by two theoretical

limits/ it must be 0reater than ,1* and less than orequal to #%*

)2t is rare to encounter en0ineerin0 materials withne0ative !oisson ratios-

Some interesting points about Poissons ratio


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Failure and limits on design: (isotropicmaterial)

Stress based criteriaMaterial

TypeFailure Theories

Ductile 3a+imum shear stress criterion* von 3ises criterion

4rittle 3a+imum normal stress criterion* 3ohr.s theory

on-Stress based criteria

5tiffness* vibrational characteristics*fati0ue resistance* creep resistance

etc

,oulom-Mohr criteria

6or isotropic materials* only twoindependent elasticconstants areneeded for describin0 the stress,

strain relationship*

ie* Hooke.s 7aw ! = "


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or .uctile materialor .uctile material

or /rittle materialor /rittle material


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Common failure modes of a structural member:

"# ailure y e%cessie deflection"# ailure y e%cessie deflection

# ailure y general yielding# ailure y general yielding

1# ailure y fracture1# ailure y fracture

2# ailure y instaility (uc*ling)2# ailure y instaility (uc*ling)

"lastic deflection

#eflection by creep

Sudden $brittle% fracture

Fracture of crac&ed member

Progressive fracture' Fatigue

Stress Nd Strain

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