bülent akbaş- advanced steel structures

DYB 654: ADVANCED STEEL STRUCTURES - IIAssoc Prof Bülent AKBAŞAssoc.Prof.Bülent AKBAŞ

Department of Earthquake andSt t l E i iStructural EngineeringCrown Hall at IIT Campus

Chicago . IllinoisLudwig Mies van der Rohe

Composite Beamsd Sh St dand Shear Studs

Composite Beams and Shear Studs

•Composite Beams

•Nominal Bending Strength of Fully Composite Beams

•Nominal Bending Strength of Fully Composite Beams

•Elastic Behavior and Moment of Inertia of Composite Beams for Deflection•Elastic Behavior and Moment of Inertia of Composite Beams for Deflection

Calculation

Composite Beams

Nominal Bending (Flexural) Strength of Fully Composite Beams

Nominal Bending (Flexural) Strength of Fully Composite Beamsb

Yconhr

tc=Ycon‐hr

Concrete below the top of theConcrete below the top of thedeck is neglected

deck ribs perpendicular (beam)

b

hrYcon

tc=Ycon‐hr/2

average thickness can be used

deck ribs parallel (girder)

Figure . Effective slab depth


t Y h

b '85.0 cfbafC c'85.0= (compression)

tc=Ycon‐hrhr

a

e

fc

Y2 In this case the concretecompression flange thickness “a” is less than the slab thickness

( p )

dPNA

(plastic neutral axis)sy AfT = (tension)

FyY2=Ycon‐a/2

PNA in concrete slab

TeCeM n ==


tc=Ycon‐hr

b '85.0 cf

a ccc AfC '85.0= (compression)

d

hr

PNA (plastic neutral axis)

Y2yffl FYbC 1= (compression)Y1

d (plastic neutral axis)

yfsystyb FYbAfAfT 1−== (tension)

Fy

PNA within beam flangeY2=Ycon‐a/2

abAc =

PNA within beam flange

yf

ccsy

FbAfAF

Y2

85.0 '

1

−=

)]2

()2

(2)(85.0[( 11

121' YdFAYYFbYYAfM ysyfccbnb −+++=φφ

900φ 90.0=bφ


tc=Ycon‐hr

b '85.0 cf

a ccc AfC '85.0= (compression)

d

hr

PNA

Y2flC (compression)

Y1wC (compression)

d PNA (plastic neutral axis) bT (tension)

Fy

PNA within beam webY2=Ycon‐a/2

PNA within beam web

fyw

yffccsy tFt

FtbAfAfY +

−−=

2285.0 '

1

)]2

()2

)((2)2

(2)(85.0[( 11

1121' YdFA

tYtYFt

tYFtbYYAfM ys

ffyw

fyffccbnb −+

−−+−++=φφ

900φ 90.0=bφ


(MPa)

21 MPa 70 MPa21 MPa 70 MPa

21 MPa 42 MPa

525 MPa


kN

kN

tension area

Example

2250 mm 28 MPa

82.5 mm

37.5 mm

120 mm

250MP16 26 4 960 2 399250MPa16x26 4,960 mm2 399 mm

23.2 mm

+Ycon‐a/2=308mmcon /

382 kNm

Nominal Bending (Flexural) Strength of Partially Composite Beams

Elastic Behavior and Moment of Inertia of CompositeBeams for Deflection Calculation

(mm)

200 000 MPa200,000 MPa

)(043.0 '5.1 MPafwE ccc =

(kg/m3)for 1.44 t/m3< wc < 2.5t/m3

(Mpa)

)(4700 ' MPafE cc = For wc > 2.5t/m3

(Mpa)

Elastic Behavior and Moment of Inertia of Composite Beams for Deflection Calculation


mm2

mm2


AISC 360‐05 , Commentary I3.1

Shear Connectors

Shear Connectors

2mm2

mm2

Bülent

Rectangle

Shear Connectors

Shear Connectors

kN

kN

Shear Connectors

Top flange

Shear Connectors

Bülent

Rectangle

Bülent

Rectangle

Shear Connectors

345MPa

=450MPa) 28MPa

12cm 7.5cm

4.80kN/m2 1.0kN/m2

Shear Connectors

3.65m=10.95m

12.80m12cm

7.5cm

Shear Connectors

12cm

3.2m

3 60kN/m2

7.5cm3.60kN/m

0.40kN/m2

0.50kN/m2

=4.50kN/m2

4.80kN/m2

3.65m

=4.50x3.65=16.43kN/m

=4.80x3.65=17.52kN/m

=(3 60+0 40)x3 65=14 60kN/m=(3.60+0.40)x3.65=14.60kN/m

=(1.00)x3.65=3.65kN/m

Shear Connectors

=1.2x16.43+1.6x17.52

=47 75kN/m

=16.43+17.52

=33 95kN/m=47.75kN/m

47.75*12.802=977.92 kNm

=33.95kN/m

33.95*12.802=695.30 kNm

47.75*12.80=305.6 kN 33.95*12.80=217.28 kN

Shear Connectors

28MPa =345MPa =450MPa)

mm

Shear Connectors

{12.80/4, (3.65/2+3.65/2)}=3.20m

345 x 8709.66

0.85 x 28 x 3200= 39.45mm = 120mm

Shear Connectors

458.72195

39.45404.64mm

345 x 8709.66 x 404.64 = 1216 kNm

0.9 x 1216

1094.4 kNm > 977.92 kNm

1216/1.67

728.1 kNm > 695.30 kNm1094.4 kNm > 977.92 kNm 728.1 kNm > 695.30 kNm

Shear Connectors

MPafwE mkgccc 753,2628)2400(043.0043.0 5.1/'5.1 3

===

46.7== s

EEn

MPaEs 000,200=cE

3.2m mmnb mmeff 43046.7/3200/ ==mmy 10541)2/1207572.458)(430*120(2/72.458*66.8709

=+++

=

75mm

120mm

effmmyb 10.541)430*120(66.8709

=+

=

])2/7245810541(668709109642[ 28xI −+=

mm62.52

mmyb 10.541=mmd 72.458=

]62.5243012012

120430[

])2/72.45810.541(66.870910964.2[

23

xxx

xItr

++

+

4910348.1 mmxItr =

4910011.175.0 mmxIt = 10011.175.0 mmxItr

Shear Connectors

mmLmmx

xxIE

Lw mmNL 56.35

360800,12

36029.30

)100111)(000200(384800,1252.175

)750(3845

9

4/4

==<===Δ O.K.xIE tr 360360)10011.1)(000,200(384)75.0(384

Shear Connectors

=1.2x14.60+1.6x3.65

=23.36kN/m

23 36*12 802=478 41 kNm

=14.60+3.65

=18.25kN/m

18 25*12 802=373 76 kNm23.36 12.80 =478.41 kNm

0 9(F Z )=0 9(345x1 486 307mm3)

18.25*12.802=373.76 kNm

(F Z )/1 67=(345x1 486 307mm3)/1 670.9(FyZx)=0.9(345x1,486,307mm )=461.5kNm<478.41kNm

(FyZx)/1.67=(345x1,486,307mm3)/1.67=307.1kNm<373.76kNm

Shear Connectors

mm

Shear Connectors

345 x 10,451,59

0.85 x 28 x 3200= 47.35mm < t = 120mm

460195‐

47.35401.33mm

345 x 10,451. x 401.33 =1,447.2 kNm

Shear Connectors

0.9 x 1,447.2 1,447.2/1.67

1,302.5 kNm > 977.92 kNm 866.6 kNm > 695.30 kNm

Shear Connectors

0.85x28x3200x47.35=3,606kN

10,451.59 (345)==3,606kN

1,302.5

977.921.33 (33% over‐strength)

Shear Connectors

977.92kNm

977.92kNm

Shear Connectors

kN

kNkN

partially composite beam

Shear Connectors

Shear Connectors

977.92kNmtry to make

kNFA ys 606,3)345)(10452( ==

Also assume 55% composite action

for a W18x55 beamys ,))((

kNQn 983,1)606,3(55.0 ==∑

mmbf

Qa

Nn 04.26

)2003)(28(850000,983,1

850' ' === ∑

bf effc )200,3)(28(85.085.0

mmaYY con 20.181204.26195

2'

2 =−=−= con 222

Shear Connectors

00163012)04.263200)(28(85.0)452,10(34585.0 '

KOtxAfAFY ccsy <

−−

Assume that Y1 is within the top flange of the beam:

..00.1630.12345)26.191(2

))((),(21 KOmmtmm

FbY f

yf

y =<===

4603012 )]30.122

460)(345)(452,10()230.12)(30.12)(345)(26.191(2)20.18130.12)(04.263200)(28(85.0[( −+++= xM n

kNmM n 179,1=

900=φ 671=Ω

kNmkNm 92.977061,1 > kNmkNm 30.695706 >

90.0=bφ 67.1=Ωb

Shear Connectors

MPafwE mkgccc 753,2628)2400(043.0043.0 5.1/'5.1 3

===

467sE

MPaEs 000,200=

46.7==c

s

En

mmxxyb 5.533)2/12075460)(430120(2/460452,10=

+++=

120mm

3.2m mmnb mmeff 43046.7/3200/ ==x

yb )430120(452,10 +

mm5.61

mmyb 5.533=]5.61430120

12120430[

])2/4605.533(452,1010704.3[

23

28

xxx

xItr

++

−+= 75mm

ybmmd 460=

4910590.1 mmxItr =

4910193.175.0 mmxItr =

Bülent

Rectangle

Shear Connectors

mmLmmx

xxIE

Lw mmNL 56.35

360800,12

36067.25

)101931)(000200(384800,1252.175

)750(3845

9

4/4

==<===Δ O.K.xIE tr 360360)10193.1)(000,200(384)75.0(384

Shear Connectors

W 18x55

=1.2x14.60+1.6x3.65

=23.36kN/m

23 36*12 802=478 41 kNm

=14.60+3.65

=18.25kN/m

18 25*12 802=373 76 kNm23.36 12.80 =478.41 kNm

0 9(F Z )=0 9(345x1 835 351mm3)

18.25*12.802=373.76 kNm

(F Z )/1 67=(345x1 835 351mm3)/1 67

W 18x550.9(FyZx)=0.9(345x1,835,351mm )=570kNm<478.41kNm

(FyZx)/1.67=(345x1,835,351mm3)/1.67=379kNm<373.76kNm

mmLmmx

xxIE

Lw mmN

x

L 56.35360

800,12360

22.17)10704.3)(000,200(384

800,1265.35)(384

58

4/4

==<===Δ O.K.

Shear Connectors

28MPa concretemm19

kNQn 5.76= (See the next slide)

kNQ 983,1=∑ kNQn 983,1∑

9.255.76

983,1= (use 26)

52226 =xmm150 )150( apartmm

m303 )300( tmm

upper flute

m30.3 )300( apartmm

mmx 114196 =mmx 9601208 =

lower flute

Note: usual rib (deck flute) spacing is about 150mm

Shear Connectors

22

5.2834

)19( mmAsc ==π

MPafwE mkgccc 753,2628)2400(043.0043.0 5.1/'5.1 3

===

kNkNQn 5.76)450)(5.283)(6.0)(0.1(7.122)753,26(28)5.283(5.0 =≤==

Shear Connectors

CL

mmmm 600,12150@84 =

ribspacingmm150

)(3300 everyflutemm150@20

)(4650 uteeverytwoflmm )(4650 uteeverytwoflmmmm150@16 150@16

mm800.12

mm150@20mm150@16 mm150@16

Shear Connectors

kN944)460)(91.9)(345(6.0 =kN850)944(9.0 = kN6.305

kN56567.1/944 = kN28.217

MPaFy 345=

mmfiftytwo 19

Shear Connectors

N C it D i f th BNon‐Composite Design of the Beam:

=1.2x16.43+1.6x17.52

=47 75kN/m

=16.43+17.52

=33 95kN/m=47.75kN/m

47.75*12.802=977.92 kNm

=33.95kN/m

33.95*12.802=695.30 kNm

6

47.75*12.80=305.6 kN 33.95*12.80=217.28 kN

336

, 10150,3)345(9.0

1092.977 mmxxZ reqx == 336

, 10366,3)67.1/345(

1030.695 mmxxZ reqx ==

3310450,39718

mmxZxWuse

x =

References

• h d d l l• Shen, J., Advanced Steel Structures, Class Notes, IIT, 2009.

bülent akbaş- advanced steel structures

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