DESIGNOFSTEELSTRUCTURES

D i f C i M bDesignofCompressionMember

Astructuralmembercarryingaxialoreccentricl ll bcompressiveloadiscalledcompressionmember.

Typesofcompressionmember:

TheverticalcompressionmemberinRCCbuildingisp gtermedascolumn,whereasforsteelstructureitiscalledstanchion.

Thecompressionmemberinrooftrussorbracingiscalledas strutasstrut.

Theprinciplecompressionmemberinacraneiscalledp p pboom.

Boom

Modeoffailureofcolumn:

Crushing Buckling Mixedof bothofboth

Crushingfailure: Thistypeoffailureoccurinshortcolumng ypSuchmemberhasacriticalloadcausematerialfailure. Bucklingfailure: ThistypeoffailureoccurinlongcolumnSuchmemberhasacriticalloadwhichcauseelasticinstabilityduetowhichthememberfail.Mixed mode of failure: The above two failure occur in theMixedmodeoffailure: Theabovetwofailureoccurintheextremecases.Forallintermediatevalueofslendernessratio the column fail due to combined effect. Most of theratiothecolumnfailduetocombinedeffect.Mostofthepracticalcolumnfailinthismode.

Effective length (l ) : It is the length between two adjacentEffectivelength(leff ): ItisthelengthbetweentwoadjacentPointofzeromoments.Thuslengthdependuponendcondition.

Where accurate frame analysis is not done the effective

From,IS800:1984,Clause5.2.2

Whereaccurateframeanalysisisnotdone,theeffectivelengthofacompressionmemberinagivenplanemaybeDeterminedbytheproceduregiveninAppendixC.ete ed by t e p ocedu e g e ppe d C.However,inmostcasestheeffectivelengthinthegivenplaneassessedonthebasisofTable5.2,wouldbeadequate.EffectivelengthasgiveninTable5.2mayalsobeadoptedwherecolumnsdirectlyformpartofframedstructures.

cK

+=

b

bc

K

KK1

+= bc KK2

K Flexural Rigidity of columnKc FlexuralRigidityofcolumn

Kb FlexuralRigidityofbeam.

Bucklingfailure:EulersTheory

Assumptions Made in Eulers Theory:

Th l i i iti ll t i ht (it i t k d) Thecolumnisinitiallystraight(itisnotcrooked)Theloadactingpassesthroughcenterline(axialcompression)compression)Theslendernessofcolumnishigh(Longcolumn)Thecrosssectionofcolumnissolid,withconstantsectionthroughoutheightofcolumnThecolumnmaterialishomogeneous,isotropic,andl ielasticTheboundaryconditionsareideallymet

PX Frommomentcurvaturerelation:

EIM

dxyd =2

2

2EIyPyM =

Y

CriticalLoad(Pc ) 2efflEI=

22 EEIPf cCriticalstress(c)

22,, AlAorf effc

ccc ===leffr

Ratiosslendernes eff=)(.

Columndesignformula

MerchantRankinformula111 + ny

ncc

n

fffff

+=

( ) nnynccycc

ff

fff 1+

= ( )y InWSMmethodofdesign

4.1=nS et od o des gAxialcompressionstrength(ac)=0.6f

For different grade of steel is given inFordifferentgradeofsteel,ac is given inTable 5.1

#AbuiltupcolumnconsistsoftwoISMC400@49.4Kg/mAndtwoplatesofsize500x10mm.thecleardistanceBetweenbacktobackofchannelsis200mm.oneplate

d h fl d h f l dIsconnectedtoeachflangeside.DeterminethesafeloadCarrycapacityofthesectioniftheeffectivelengthoftheColumn is 5 mColumnis5m.

Sol: Properties of ISMC 400: 400

100

Sol:

Thicknessofweb(tw)=8.6mmThickness of flange (t ) 15 3 mm

PropertiesofISMC400:

100Thicknessofflange(tf)=15.3mmCrosssectionareaofthesection(Ast)=6293mm2

MomentofinertiaalongXXaxis(Ixx)=150828x103 mm4

MomentofinertiaalongYYaxis(Iyy)=5048x103 mm4

Forbuiltupsection:

1 200

46

233

10989.721

20510500105001212101508282

mm

Ixx

=

++=

{ }46

3233

10576421

5001012122.12410293.621050482

I

I yy ++=min

4610576.421 Imm ==

Minimumradiusofgyration:

AIr

105002102936210576.421

3

6min

min +==

mmA

62.13610500210293.62

=+

Slenderness Ratio ( ) :SlendernessRatio( ):

59.365000 === leff 59.3662.136minr

From IS 800 : 1984, Table 5.1, Pg 39

MPaac 046.141=FromIS800:1984,Table 5.1,Pg 39

Safeloadforthesection(P)

( )KN

NAP ac6653185

046.14110500210293.62 3 +== KN665.3185=

Bendingstress: Ifcompressionflangeisrestrainedlaterallyagainstbucklingthenpermissiblecompressiveortensilebendingstressis(Clause6.2.1,Pg 55)

ybtbc f66.0/ = ybtbc f Forunrestrainedcompressionflange(Clause6.2.3)

ff

( ) nnyncbycb

bcff

ff166.0 +

=

fcb Elasticcriticalstressinbending(Clause6.2.4)

C( )1

221 C

CYKXKf bc =

510526 ftK 1=

Where,MPa

rl

Y

y

2105.26

=

Dor

tortw ,,

MPaDr

lYX

+=

2

2011

h

Dr y 20

1

1 )()(A

fKtCoefficien

==

C1 ,C2 respectivelythelesserandgreater

distancesfromthesectionneutrali t th t fib

2A

A1 Totalareaofbothflangesatthepointofleastbendingmoment.

axistotheextremefibers.

A2 Totalareaofbothflangesatthepointofmaximumbendingmoment.

cfyyIfKtCoefficien 2 )()( =

fyy

cfyy

I ,,=

Iyy,cf Momentofinertiaofthecompressionflangealone.I Moment of inertia of the both flanges abo t its o nIyy,f Momentofinertiaofthebothflangesaboutitsownaxisparalleltotheyyaxisofthegirder,.

Bendingcompressionstrength=bcFor different grade of steel, bc is given inFordifferentgradeofsteel,bc is given inTable 6.1A to F

CombinedAxialCompressionandBending:FromIS800:1984,Clause 7.1.1,Pg 90

Memberssubjectedtoaxialcompressionandbendingj p gshallbeproportionedtosatisfythefollowingrequirements:

CC 0.1

1601 ,

,

,

,,

+

+bcy

calac

calbcymy

bcxcalac

calbcxmx

ac

calac C

f

C

6.06.0 bcyccybcxccx ff

850CSwayframeorNonswaywithendsarerestrained

i t t ti

014.04.06.0

85.0Cm

==

=

againstrotation.

Nonswayandnotsubjecttotransverseloading

max

min

0.1

MM=

=

Nonswaywithendsareunrestrainedagainstrotation

thenIf calac ,15.0, ,

#DesignasteelcolumnfortheloadingasshowninfigureasIS 800 1984 t l i F 250perIS800:1984,steelisFe250. 80KN

BSol:

5KN/m6m

Effectivelengthfortheproppedcantilevercolumn(leff )

mll ff 8480 == mlleff 8.48.0 ==

( ) ( ) KNKNselfWt 8880801.080. =+=+=TotalAxialLoadA

( ) ( )MaximumbendingmomentisatsupportAis:

mKNwlM A === 5.22865

8

22

Lets assume = 80 MPaLetsassume,ac/bc = 80 MPa

Thus,,Requiredsectionalareaandsectionalmodulesofthecolumnis:

21100100088.LAA

36

2

281250105.22

110080

mmMZ

mmA

A

acreq

===

28125080

mmZbc

Areq ===

TrywithISMB300@44.2Kg/my @ g/

Checkforaxialcompression:MPacalac 64.155626

1088 3, ==

Slenderness ratio ( ) OKleff 1800116910008.4 == OKMPaf calbtybt ,16566.0 , >==

Checkforbendingcompression:

MPaZM A

calbc 22.39106.573105.22

3

6

, ===

Z xx 106.573

412tFor,ISMB300@44.2Kg/m

5241

26533.15.74.12

FromIS8001984,Table 6.1B,Pg 58

D/ 20 25 24.193Leff/ry

160 101 93 94.2912

170 98 89 90.4526

OKMP832690 > OKMPa calbcbc ,8326.90 , >= CombinedAxialCompressionandBendingcheck:

MPaMPa accalac 6.36,64.15, == MPaMPa bccalbc 83.90,22.39, ==

For,ISMB300@44.2Kg/m

d f l

mmr 7.123=RadiusofGyrationalongXXaxis:

80.387123

10008.4 === effxx lmmrxx 7.123 7.123xxxx rMPaEf xxcc 19.1311

1022

52

2

2

=== f xxcc 8.38 22, C calbcxmxcalac

Frominteractionformula

f bcxxxcccalac

calbcxmx

ac

calac

6.01

,

,

,,

+

839064.151

22.3985.06.36

64.15,

+=

OK,0.1801.0

83.9019.13116.0

1

#Designasteelcompoundcolumnfortheloadingasshownin figure as per IS 800 :1984 steel is Fe250infigureasperIS800:1984,steelisFe250.

1000KN

Sol

8mEffectivelengthforthecolumn(leff )

mll ff 162 == mlleff 162 ==Assumeslendernessratio( )=100,ac = 80 MPa

rl eff=

mml

rso effreq 160100100016, ===

RequiredRadiusofGyration

23

1250080

101000 mmPAac

req === RequiredSectionalArea

Letstrywith2XISHB350@67.4Kg/m

285912,3.149 mmAmmrxx ==250

2 S44

44

1042451

107.19159

mmImmIxx

=104.2451 mmI yy =

yyxx II =For yy{ }S8591104.24512107.191592 244 +=mmmmS 14046.139 =

slendernessratio()

OKrl

xx

eff ,1806.1073.149

1016 3

FromIS800:1984,Table 5.1,Pg 39

MPaac 75=

OKMPaAP

accalac ,2.5817182101000 3

,

IS800:1984,Clause5.7.5,Pg 51

{ }00 70,40

Lets0

CC 50