1.2 properties of materials

7/23/2019 1.2 Properties of Materials

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MECHANICS OFDEFORMABLE

BODIES

(LECTURE)by Engr. Leo D. Hermano


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Strength of materials is the study ofmaterials

and structures in terms of their loadcarrying

ability.

It is also known as the mechanics ofmaterials

Applications includes the design ofcars,

air lanes shi s buildin s brid es

Strength of Materials(Mechanics of Deformable odies!


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In the study of strength ofmaterials we will

consider the internal e"ects offorces acting

on a body.

#he bodies will no longer beconsider to be

perfectly rigid as was assumed instatics.

$alculation of the deformations of

Strength of Materials(Mechanics of Deformable odies!


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Simple Stress

Simple stress is de%ned as theforce per unit area. & '

#ypical units of stress are Ma,

lbf)in*

andksi (thousand of pounds per s+uareinch!.

#he Ma is e+uivalent to M)m*

or)mm*

#he two basic types of stress

depending


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ormal Stress

ormal stress, &, is the type ofstress which

is caused by forces actingperpendicular to

the area resisting the forces.

ormal stress is also called asbearing stress.

#wo types of ormal Stress

#ensile stress are the normal forces

directed


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#ensile Stress $ompressiveStress


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Shear Stress

Shear stress, , is the type ofstress which is caused by forcesacting along or parallel to the arearesisting the forces.

Shear stress is also called astangential stress

Shear stress is denoted by '


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Simple Strain Strain refers to the elongation of the

material with respect to its originallength when sub/ected to a load.

0nits are mm)mm, inch)inch, or no unit

at all. Strain may be e1pressed as a

percentage of the original length

2 3

Strain45 '


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Ductile and rittle Materials

Metallic engineering materials are

commonly classi%ed as either ductileor brittle materials.

Ductile material is one having a

relatively large tensile strain up tothe point of rupture, i.e, structuralsteel and aluminum.

rittle material has a relatively smallstrain up to this same point, i.e. castiron 6 concrete.

An arbitrary strain of 7.78 in)in (or


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9ooke:s 2aw

;ormulated by ?@

which states that4 Bithin elastic limit, the stress isproportional

to strain.C

Mathematically4 & 5

& ' E5

'

E ' modulus of elasticity (Foung:s

Modulus!


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9ooke:s 2aw

Bhen material is sub/ected to a

shearing stress

' GHwhere4 G ' shear modulus

H


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Stress Strain Diagram

where4 A ' proportionality limit ' elastic limit

$ ' yield pointD ' ultimate strengthE ' rupture strength; ' actual rupture strength

Stress

StrainJ

KA

K BK C K D

K FK E


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Mechanical roperties of Materials

roportionality 2imit

#he ma1imum stress that may bedeveloped

during a simple tension test such

that the

stress is a linear function of strain.

MediumLcarbon structural steel,alloy steel,

hard steels and certain nonLferrousalloys are

materials with ro ortional limit.


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Elastic 2imit

Elastic limit is the ma1imum stressthat may

be developed during a simple

tension testsuch that there is no permanent orresidual

deformation when the load is entirelyremoved.

;or many materials the numerical

values of


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Elastic and lastic


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Field oint

Field point (&yp! refers to the

point where

there is an appreciable elongationoryielding

of the material even without anycorresponding

increase of load.

Some materials e1hibit two pointson the

stressLstrain curve at which there is an


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0ltimate Stress

0ltimate stress of the material is thehighest

point or ordinate in the stressLstrain

diagram.It is also called the ultimate strength.


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Modulus of


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Modulus of #oughness

#he work done on a unit volume ofmaterial,

such that as a simple tensile force is

graduallyincreased from ero to a value causingrupture.

#his may be calculated as theentire area

under the stressLstrain curve fromthe ori in


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ercentage


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ercentage Elongations

#he increase in length (of the gagelength!

after fracture divided by the initial

length,multiplied by =77 is the percentageelongation.

oth the percentage reduction inarea and

the percentage elongation areconsidered


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Borking Stress

All mentioned strength characteristicsmay be used to select a workingstress.

;re+uently such stress is determinedby dividing either the stress at yield orthe ultimate stress by a safety factor.

Selection of the safety factor is basedupon the designer:s /udgement ande1perience.

Jftentimes, speci%c safety factors are


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Stress Strain $urve showing typicalyield

ehavior for nonLferrous alloys4

1: True elastic limit

2: Proportionality limit3: Elastic limit

4: Offset yield strength


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Stress Strain $urve for StructuralSteel

=. 0ltimate Strength*. Field Strength

N.


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Stress Strain (2oad E1tension!$urve for

Di"erent Materials


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Shearing Stress for olts and


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Strain 9ardening

If a ductile material can be stressedconsiderably beyond the yield pointwithout failure, it is said to strain-

harden.#his is true for many structuralsteel.

onL2inear Stress Strain $urve

#he nonLlinear stressLstrain curve ofa brittle material characteriesseveral other strength measures that

cannot be introduced if the stressL


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Stress Strain $urve showing typicalyield

behavior for nonLferrous alloys4

1: True elastic limit

2: Proportionality limit3: Elastic limit

4: Offset yield strength


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Mechanical roperties of Materials in

onL2inear StressLStrain $urve

Field Strength

#he ordinate in the stressLstrain curvesuch that there is a permanent

deformation when load is removed. Inthe ;igure shown, it is taken to be7.77* or 7.77N8 in in)in or mm)mm.

#angent Modulus, Et

#he rate of change of stress withrespect to strain. #his is aninstantaneous modulus iven b 4 E


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#hermal Stress, 3#

#he stress on the material caused bythe internal forces due to change intemperature.

#he change in temperature can cause

a change in length, area and volume ofthe material.

#he temperature deformation (linear!

may be calculated using,

3# ' 2(P#!

2 3#


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$oefficient of 2inear E1pansion,

#he change of length per unit length of

a straight bar sub/ect to atemperature change of one degree.

#he value of this coeQcient is

independent of the unit of length butdoes depend upon the temperaturescale used.

#emperature changes in a structuregive rise to internal stresses, /ust as doapplied loads.

;or e1ample, from #able =L=, theL> R


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oisson:s


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Speci%c Strength

#he ratio of the ultimate (or tensile!

strength to speci%c weight (weight perunit volume!.

In 0S system, the unit is in inches

(lb)in* over lb)inN!. In SI system, theunit is in meter ()m* over )mN!

#his parameter is useful for

comparisons of material eQciencies.

Speci%c Modulus

#he ratio of the Foung:s modulus to

speci%c weight

1.2 properties of materials

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