section propoerties civl3111

8/12/2019 Section Propoerties CIVL3111

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AS4100 Standard Grades and

Sections

Asst. Prof. Hang Thu Vu

[email protected]


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Lecture outline Industry uses AS4100 for general urose steel structure analysis

and design. !ithin "IV#$111% we will refer to this standard as the&ain design code. 'eneral &aterial roerties to use for design to AS4100

(iscuss availa)le standard grades and sections for design toAS4100

'rades* overview of availa)ility. +ield stress and tensile strength Sections* overview of availa)ility. ,ffects of shaes on section

caacity against loading actions Study the &eanings% usages and how to co&ute section

ara&eters I% -% S

ending of steel &e&)ers in elastic and lastic ranges Second &o&ent of area I ,lastic section &odulus - Plastic section &odulus S


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Basic parameter values and adjustment

for elevated temperatures


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Standard Grades


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Designation of Grades

Table 2.1 in AS4100. This ta)le gives values of yieldstress and ulti&ate tensile strength for steelroducts that co&ly with the re/uire&ents of AS%AS-S &anufacturing standards

Standard grade usually starts with the nu&)er of thestandard then characters and digits to stand for thegrade. ,2a&le* AS-S $35.1 $60#0

ote* AS-S 1654 uses a different syste& ofgrade designation. 7efer to AS-S 1654 Section

1.4


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Hot-rolled and cold-form grades Hot8rolled roducts 9lates and sections: are in

grades ;00% ;60% $00% $60% 400% 460% 600.These &ay )e o)tained with notch ductile/ualities 9with suffi2 #0 or #16: andor weather8resistant /ualities 9with refi2 !7:. !eatheringsteels are in 'rade $60 only

Hot8rolled welded sections are roduced fro&AS-S $3< lates= oularly in 'rades $00%400% !7$60

"old8for&ed hollow sections are with refi2es ".They are roduced in 'rades ";60% "$60% and"460. They &ay co&e with notch ductile #0/uality


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Hot-rolled and cold-form grades

(ata for design to AS4100 for

the &ost co&&only used

sections and lates in 'rades;60% $00% $60


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alues of !ield stress f!


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#$istence of residual stress

Tis of flanges and &iddle of we) cool and harden% &ore

/uic?ly than the rest of the cross8section.

The harder arts are in a state of co&ression. The>unctions% )eing held )y the harder arts and una)le to

contract as far as they would otherwise% are laced in

tension.


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Standard sections and plates

Steel roducts are rovided in standard siesand shaes. or &aterial availa)ility and cost

asect% it is reco&&ended to use standard

sections in your design. elow are funda&ental

sections


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Standard sections and plates


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#ffects of s"apes on mem%er strengt"

It is o)served that steel is roduced in various sections.

These include BlateB% Brounds% )ars and rodsB% BanglesB%BchannelsB and BI8sectionsB.

The I8sections are roduced as B)ea&B sections with I yy

&uch less than I22and Bcolu&nB sections with Iyyof closer

value to I22. Cost of these sections are roduced )y rolling red hot

steel. Cost sections have arallel flanges 9the BuniversalB)ea& and colu&n sections% and the channels:. So&eBtaer flangeB Is and channels are also roduced.

It is ossi)le to &a?e very large sections 9e.g. for )ridge)ea&s: )y welding late into the for& of an I or )o2.#engths are availa)le fro& a &ini&u& of 3 &etres to a&a2i&u& of $0 &etres. 7efer to Ta)le ;% DneSteel BHot7olled and Structural ProductsB% 6thed.


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#ffects of s"apes on mem%er strengt"

However% if )uc?ling occurs% the )uc?ling loadthat the &e&)er can withstand deends onsecond &o&ent of area I22and Iyy.

As the colu&n )uc?le a)out the a2is which is ofwea?er I% it is i&ortant to have I22and Iyyofsi&ilar &agnitude 9Eniversal colu&ns: whenthere is no lateral )racing for wea? a2is

&

&

'(kL

EIP

cr

=


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#ffects of s"apes on mem%er strengt" Bending* stress in a )ea& deends on the second

&o&ent of areaI

The )ending &o&ent which a )ea& can carry )efore itsflange starts to yield is CF-fy% where - is the elastic&odulus.

If the &o&ent is increased further% yielding sreadsthroughout the cross section. Total collase occurs at a&o&ent CFSfywhere S is the lastic section &odulus9study later:.

I

My=

ma$y

IZ=


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)ompare section properties for sections

of same amount of material Area A F 13000 &&;

Sread &aterial further away fro& neutral a2is to

&a?e rectangle% I shae 9310 E 1;6:% truss


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Bending of steel mem%er in elastic and

plastic ranges


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*evision+ Structural anal!sis


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*evision+ Structural anal!sis

!e want to calculate the &a2i&u& values ofactions 9&o&ent% shear force% a2ial force ..:for &e&)er design

ree )ody diagra&

Vertical reaction Ay% e/uivalent load P. At thecut of distance fro& left end* shear force V%)ending &o&ent C


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*evision+ Structural anal!sis The reaction at A is The e/uivalent oint load at a distance 2; fro& A is Ta?e &o&ent a)out the cut%

orce e/uili)riu& for y direction%

Ca2i&u& shear force haens at end Ca2i&u& )ending &o&ent haens at &iddle

wLAy&

1=

wxP=

&&

1

0&&

1

&wxwLxM

xwxwLxM

=

=+

wxwLV

wxwLV

=

=+

&

1

0&

1

wLV&

1

ma$=

,

&

ma$

wLM =


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Bending of a %eam mem%er

ending stress J22of the cross8section of a )ea& varies along the)ea& height

The )ea& is under &a2i&u& stress when CFC&a2and yFy&a2Fd;

The e2tre&e fi)re of the cross8section starts to yield when J22F fy.Hence% the &o&ent caacity that a cross8section can ta?e is

Z

M

I

My==

ZfM yy=


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!hen the whole cross section yields the &o&ent

caacity increases to Cs. or design urose 9lower )ound of lasticity:% strain

hardening is ignored. The &aterial is ter&ed as ure

lasticity 9see )elow figure:.

It is assu&ed that the &a2i&u& stress that anywhere in

the cross section can reach is fy9see )elow figure:


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- is ter&ed elastic section &odulus

S is ter&ed lastic section &odulus


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Second moment of area


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ormulae Second Co&ent of Area* also ?nown with other na&es

Second Co&ent Df Inertia% Area Co&ent of Inertia The &athe&atical e/uations to calculate the Second

Co&ent of Area *

y is the distance fro& the neutral a2is 22 to aninfinitesi&al area dA

2 is the distance fro& the neutral a2is yy to aninfinitesi&al area dA

=

=

A

yy

A

xx

dAxI

dAyI

&

&


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#$ample 1+ *ectangular section

( )

1&

,,..

.

..&

&

.&

&

&&

bdI

ddbybbdyydAyI

xx

d

d

d

dA

xx

=

+====


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#$ample &+ Hollo/ sections

7ectangular hollow sections

I sections

1&1&

.

&&

.

11 dbdb

Ixx =

1&&

1&

.. chbdIxx =


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#$ample .+ )ircular sections and

)ircular "ollo/ sections

4

4rIxx

=

( )4

&

4

14 rrIxx =


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eutral a$is (A' of non-s!mmetric

sections !hen the section is non8sy&&etric% we need to find the

location ycof the neutral a2is with resect to a datu&

which is usually chosen at the )ase of the section

The sign shows the contri)utions fro& all nele&ents of the cross section.

=

==n

i

i

n

i

ii

c

A

hAy

1

1


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2arallel a$is t"eorem The second &o&ent of area for the whole section

with resect to the located neutral a2is is calculatedfro& the Parallel A2is Theore&

I* the second &o&ent of area

Ii* the second &o&ent of area of ele&ent ith

Ai* area of ele&ent ith

di* distance )etween the neutral a2is of ele&ent ith

and the neutral a2is of the whole section

=

+=n

i

iii dAII1

&


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#$ample+ )alculate 3$$for section

d1F 610 8 $36.6 F 144.6 &&

d;F $36.6 8 ;60 F 116.6 &&

I22F ;002;0$1; K ;002;029144.6:;

K 102600$1; K 10260029116.6:;

Hence

I22F ;64%6;;%;60 &&4

=

+=n

i

iii dAII1

&


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#lastic section modulus


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ormulae

Elasticsection modulus- of a )ea& is the ratio of

a cross sectionLs second &o&ent of area I to the

distance of the extreme compressive fibrefro& the

neutral a2is

The elastic section &odulus &ar?s the yield oint ofthe &aterial when the &ost outer fi)re starts to yield

due to )ending &o&ent CyF-fy

ma$y

IZ=


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2lastic section modulus


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Define location of t"e 2A

The lastic neutral a2is PA% which is also referred to as

the e/ual area a2is% is the a2is that slits the cross

section into two e/ual areas. These areas refer to the

e/ual a&ount of fi)res yielded under co&ression and

tension resectively. or sy&&etric section% the lastic and elastic neutral

a2is coincide. They are the a2is through the centroid of

the section.

or non8sy&&etric section% location y the PA withresect to a datu& which is usually chosen at the )ase

of the section is defined


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)alculate S

S is co&uted as the su& of &o&ent of ele&ent

areas a)out the PA

S* the lastic section &odulus

Ai* area of ele&ent ith

ei* distance )etween the neutral a2is of ele&ent ith

and the lastic neutral a2is of the whole section.

==n

iiieAS 1


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#$ample+ section

yF$00

S F 9;00 2 40 2 1;0: K 9100 2 40 2 60: K 9$002 40 2 160:

Hence% S F ;530 2 10$&&$


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e$t lecture

Investigate the loads acting on the structure

in ter&s of Per&anent load 9dead load:

I&osed load 9live load: #oad factors to co&ly with li&it state design and

&e&)er design to AS4100

7eadAS-S 110.1*;00;

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