L17 Composite Construction - Suranaree University of...

31
Lecture Lecture 17 17 Composite Construction Composite Construction Effective Flange Width Nonencased Composite Sections Shear Transfer Partially Composite Beams Timber and Steel Design Timber and Steel Design Mongkol JIRAVACHARADET S U R A N A R E E INSTITUTE OF ENGINEERING UNIVERSITY OF TECHNOLOGY SCHOOL OF CIVIL ENGINEERING

Transcript of L17 Composite Construction - Suranaree University of...

Page 1: L17 Composite Construction - Suranaree University of ...eng.sut.ac.th/ce/oldce/CourseOnline/430432/L17 Composite...Lecture 17 Composite Construction Effective Flange Width NonencasedComposite

Lecture Lecture 1717 Composite ConstructionComposite Construction

� Effective Flange Width

� Nonencased Composite Sections

� Shear Transfer

� Partially Composite Beams

Timber and Steel DesignTimber and Steel Design

Mongkol JIRAVACHARADET

S U R A N A R E E INSTITUTE OF ENGINEERING

UNIVERSITY OF TECHNOLOGY SCHOOL OF CIVIL ENGINEERING

Page 2: L17 Composite Construction - Suranaree University of ...eng.sut.ac.th/ce/oldce/CourseOnline/430432/L17 Composite...Lecture 17 Composite Construction Effective Flange Width NonencasedComposite

Shear connectors

Reinforced

concrete slab

Steel

stringer

Shear connectors

Reinforced

concrete slab

Steel

stringerPlaster

on lath

Shear transfer made by bond and friction

along top of W section and by the shearing

strength of the concrete along the dotted lines

Composite sectionsComprise a steel beam and a concrete slab,joined with shear connectors to achieve composite action between the two elements.

Page 3: L17 Composite Construction - Suranaree University of ...eng.sut.ac.th/ce/oldce/CourseOnline/430432/L17 Composite...Lecture 17 Composite Construction Effective Flange Width NonencasedComposite

Composite sections

Using formed steel deck

Ribs

Reinforced

concrete slab

Formed steel deck

Ribs

Reinforced

concrete slab

Formed steel deck

Page 4: L17 Composite Construction - Suranaree University of ...eng.sut.ac.th/ce/oldce/CourseOnline/430432/L17 Composite...Lecture 17 Composite Construction Effective Flange Width NonencasedComposite

Advantages of Composite Construction

- Increasing beam’s strength

- Less steel required

- Greater stiffness

- Smaller deflections

- Greater overload capacity

- Smaller floor depth

- Lower cost

Page 5: L17 Composite Construction - Suranaree University of ...eng.sut.ac.th/ce/oldce/CourseOnline/430432/L17 Composite...Lecture 17 Composite Construction Effective Flange Width NonencasedComposite

Design Issues

1. Flexural strength of section - Complete shear connection

Failure: Yielding of steel beam in tension

or Crushing of concrete slab in compression

2. Flexural strength of section - Partial shear connection

Failure occurs in shear connection

3. Longitudinal shear failure within the slab

Failure plane develops within the slab

4. Shear strength of section

Design for shear as a plain steel beam (ignore the concrete)

5. Deflection must be computed in 2 stages

5.1 Deflection of steel beam due to dead load of wet concrete

5.2 Deflection of composite section due to live load

Page 6: L17 Composite Construction - Suranaree University of ...eng.sut.ac.th/ce/oldce/CourseOnline/430432/L17 Composite...Lecture 17 Composite Construction Effective Flange Width NonencasedComposite

Effective Flange Widths, be

t = slab thickness

be = effective width of flange

1. 1/8 of beam span

2. 1/2 of beam distance

3. Beam centerline to edge of slab

be is the minimum of:

Page 7: L17 Composite Construction - Suranaree University of ...eng.sut.ac.th/ce/oldce/CourseOnline/430432/L17 Composite...Lecture 17 Composite Construction Effective Flange Width NonencasedComposite

Nonencased Composite Sections

Modular ratio: n = Es/Ec

Es = 2.1 x 106 kg/cm2

′= 1.54,270c c cE w f

For wc = 1.45-2.48 ton/m3 (usually wc = 2.4 ton/m

3)

Before concrete hardens, bending stress in steel beam from dead

load of wet concrete and self-weight of beam must not exceed the

allowable bending stress of beam

Ds b

s

Mf F

S= ≤

where MD = Dead load moment and Ss = Section modulus of steel beam

Page 8: L17 Composite Construction - Suranaree University of ...eng.sut.ac.th/ce/oldce/CourseOnline/430432/L17 Composite...Lecture 17 Composite Construction Effective Flange Width NonencasedComposite

Flexural Strength of Composite Section

After concrete hardens

Transformed section (concrete to steel)

be

t

be / n

t

0.9D Ls y

s trbot

M Mf F

S S= + ≤Stress in steel:

0.45Lc c

trtop

Mf f

nS′= ≤Stress in concrete:

Page 9: L17 Composite Construction - Suranaree University of ...eng.sut.ac.th/ce/oldce/CourseOnline/430432/L17 Composite...Lecture 17 Composite Construction Effective Flange Width NonencasedComposite

��������� 16-1 ������������ ������������������������� ���������� AISC % ����&�����'�������& ����� ���()�������'���� *�+��'�������,���� ���&������-������ '.�� *��'�����* ��',

LL = 500 ��./�.2, ,�����6����,���� = 80 ��./�.2

,������),����'��� 10 9�. = 240 ��./�.2

f’c = 210 ��./9�.2, fc = 0.45 f’c = 94.5 ��./9�.2, n = 9, ��*<� A36

3 @ 2.5 m

= 7.5 m

8 m

10 cm concrete slab

W400x107 (A = 136.0 cm2,

d = 390 mm,bf = 300 mm,

Ix = 38,700 cm4, Sx = 1,980 cm

3)

Page 10: L17 Composite Construction - Suranaree University of ...eng.sut.ac.th/ce/oldce/CourseOnline/430432/L17 Composite...Lecture 17 Composite Construction Effective Flange Width NonencasedComposite

����� �����%����?:

������������������������������������ (75% ������*��D'. 28 ��)

�), = (2.5)(240) = 600 ��./����

�� = 107 ��./����

���,�����D�,��� = 707 ��./����

MD = 0.707(8)2/8 = 5.66 ��-����

������������������������������������

6����,���� = (2.5)(80) = 200 ��./����

LL = (2.5)(500) = 1250 ��./����

���,�����D�,��� = 1450 ��./����

ML = 1.45(8)2/8 = 11.6 ��-����

Page 11: L17 Composite Construction - Suranaree University of ...eng.sut.ac.th/ce/oldce/CourseOnline/430432/L17 Composite...Lecture 17 Composite Construction Effective Flange Width NonencasedComposite

��� ��!��"��#���$����"%�:

b = 2(1/8)(800) = 200 9�. (����� )

b = 2(1/2)(250) = 250 9�.

200/9 = 22.2 cm

W400x107 (A = 136.0 cm2,

Ix = 38,700 cm4, Sx = 1,980 cm

3)

10 cm

Neutral axis39 cmyb

��)# ���������!���*+,��"�����:

A = 136 + (10)(22.2) = 358 9�.2

yb = (136x19.5 + 10x22.2x44)/358

= 34.7 9�.

Itr = 38,700+136(34.7-19.5)2+(1/12)(22.2)(10)3+10(22.2)(44-34.7)2

= 91,172 9�.4

Str bot = 91,172/34.7 = 2,627 9�.3

Str top = 91,172/(49-34.7) = 6,376 9�.3

Page 12: L17 Composite Construction - Suranaree University of ...eng.sut.ac.th/ce/oldce/CourseOnline/430432/L17 Composite...Lecture 17 Composite Construction Effective Flange Width NonencasedComposite

5.66(1,000)(100)286 ksc < [0.66 1,650 ksc]

1,980

Ds y

s

Mf F

S= = = = OK

���-#�����������+��*�.������!���*:

������'� �<����

�*������'� �<����

11.6(1,000)(100)286

2,627

728 ksc < [0.9 2,250 ksc]

D Ls

s trbot

y

M Mf

S S

F

= + = +

= = OK

11.6(1,000)(100)

9 6,376

20.2 ksc < [0.45 94.5 ksc]

Lc

trtop

c

Mf

nS

f

= =×

′= = OK

Page 13: L17 Composite Construction - Suranaree University of ...eng.sut.ac.th/ce/oldce/CourseOnline/430432/L17 Composite...Lecture 17 Composite Construction Effective Flange Width NonencasedComposite

Shear Connectors

Weld Stud connectors

Weld Channel connectors

Weld Spiral connectors

Page 14: L17 Composite Construction - Suranaree University of ...eng.sut.ac.th/ce/oldce/CourseOnline/430432/L17 Composite...Lecture 17 Composite Construction Effective Flange Width NonencasedComposite

Horizontal Shear Transfer

C

T

C

T

Page 15: L17 Composite Construction - Suranaree University of ...eng.sut.ac.th/ce/oldce/CourseOnline/430432/L17 Composite...Lecture 17 Composite Construction Effective Flange Width NonencasedComposite

Allowable Horizantal Shear Load

For one connector (q), ton

CONNECTOR210 245 280

f’c , ksc

≥12 x 50 mm hooked or hooked end 2.27 2.45 2.63

16 x 62.5 mm hooked or hooked end 3.57 3.84 4.11

19 x 75 mm hooked or hooked end 5.13 5.58 5.94

22 x 87.5 mm hooked or hooked end 6.96 7.5 8.04

Channel C75 x 6.92 0.78w 0.85w 0.91w

Channel C100 x 9.36 0.83w 0.91w 0.96w

Channel C125 x 13.4 0.90w 0.96w 1.02w

w = length of channel, cm

Page 16: L17 Composite Construction - Suranaree University of ...eng.sut.ac.th/ce/oldce/CourseOnline/430432/L17 Composite...Lecture 17 Composite Construction Effective Flange Width NonencasedComposite

Design of Shear Connectors

Neutral axis in slab

Neutral axis in beam

Total horizantal force

below plane between beam

and slab = As Fy

0.85f’c

Fy

Total horizantal force

above plane between beam

and slab = 0.85 Ac f’c

0.85f’c

Fy

Fy

2

ys

h

FAV =

2

85.0 cc

h

AfV

′=

N1 = Number of connectors = Vh/q

q = Strength of one connector, ton

Page 17: L17 Composite Construction - Suranaree University of ...eng.sut.ac.th/ce/oldce/CourseOnline/430432/L17 Composite...Lecture 17 Composite Construction Effective Flange Width NonencasedComposite

��������� 16-2 ����� ������� ��� &6��% ������*<� A36 *��������

AISC ������������� +��'�������,���� ��+�I���()��&� *���-������ '.��

������������� �������,��������D&���D'. *�,��������D&��� ��������* ��',:

LL = 500 ��./�.2, ,������� � = 50 ��./�.2

,�����6����, = 75 ��./�.2, ,���������'� = 2,400 ��./�.3

f’c = 210 ��./9�.2, fc = 94.5 ��./9�.2, n = 9

A

A

9 m

3 @ 3 m

= 9 m

10 cm concrete slab

2 cm plasterd ceiling

on metal lath

Section A-A

Page 18: L17 Composite Construction - Suranaree University of ...eng.sut.ac.th/ce/oldce/CourseOnline/430432/L17 Composite...Lecture 17 Composite Construction Effective Flange Width NonencasedComposite

����� �����%����? *� ���()�:

��������������)����#�!��

�), = (0.10)(2,400)(3.0) = 720 ��./����

���&��,�������(W400x66) = 66 ��./����

,�����D�,��� = 786 ��./����

MD = (0.786)(9)2/8 = 7.96 ��-����

������������������������������

�� � = 3(50) = 150 ��./����

6����, = 3(75) = 225 ��./����

LL = 3(500) = 1500 ��./����

,�����D�,��� = 1875 ��./����

ML = (1.875)(9)2/8 = 18.98 ��-����

Page 19: L17 Composite Construction - Suranaree University of ...eng.sut.ac.th/ce/oldce/CourseOnline/430432/L17 Composite...Lecture 17 Composite Construction Effective Flange Width NonencasedComposite

%����?���D'.�& Mmax = MD + ML=7.96+18.98 = 26.94 ��-����

���+�0��1,!��!���* W400x66 (As = 84.12 ; .2, d = 400 .,

tw = 8 ., tf = 13 ., Is = 23,700 ; .4, Ss = 1,190 ; .3)

���()����D'.�& Vmax =(9/2)(0.786+1.875) = 11.97 ��

��� ��!��"��#���$����F0��:

b = (1/4)(900) = 225 9�. (����� )

b = 300 9�.

G *H��#��!���*��!�����:

Str ������� Mmax= (26.94)(100)/(0.66 x 2.5) = 1,633 9�.3

���&�����'����K ��,� ��������������L���� ����

Ss ������� MD = (7.96)(100)/(0.66 x 2.5) = 482 9�.3

Page 20: L17 Composite Construction - Suranaree University of ...eng.sut.ac.th/ce/oldce/CourseOnline/430432/L17 Composite...Lecture 17 Composite Construction Effective Flange Width NonencasedComposite

��)# ���������!���*��#*�$# :

A = 84.12 + (10)(225/9) = 334 9�.2

yb = (84.12x20 + 10x25x45)/334 = 38.7 9�.

Itr = 23,700+84.12(38.7-20)2+(1/12)(25)(10)3

+ 10(25)(45-38.7)2 = 65,122 9�.4

Str bot = 65,122/38.7 = 1,683 9�.3

Str top = 65,122/(50-34.7) = 5,763 9�.3

W400x66

225/9 = 25 cm

10 cm

yb = 38.7 cm

Page 21: L17 Composite Construction - Suranaree University of ...eng.sut.ac.th/ce/oldce/CourseOnline/430432/L17 Composite...Lecture 17 Composite Construction Effective Flange Width NonencasedComposite

�����������������

fs2 = fs1 + ML/Strbot = 669 + 18.98(1,000)(100)/1,683

= 1,797 ��./9�.2 < 0.9Fy = 2,250 ��./9�.2 OK

fc = ML/Strtop = 18.98(1,000)(100)/(9x5,763)

= 36.6 ��./9�.2 < fc = 94.5 ��./9�.2 OK

�����������������

fs1 = MD/Ss = 7.96(1,000)(100)/1,190

= 669 ��./9�.2 < 0.66Fy = 1,650 ��./9�.2 OK

���-#�����������+��*�.������!���*:

Page 22: L17 Composite Construction - Suranaree University of ...eng.sut.ac.th/ce/oldce/CourseOnline/430432/L17 Composite...Lecture 17 Composite Construction Effective Flange Width NonencasedComposite

���6�N��?�*���*����*'�����D'.�& = 2.5 tf = 2.5(1.3)

= 3.25 9�. > 1.9 9�. OK

4

6

5 7.86 900

384 (2.1 10 )(23,700)DL

×∆ =

×

4

6

5 18.75 900

384 (2.1 10 )(65,122)LL

×∆ =

×

�����)�����������:

������'� �<����

= 1.35 9�. < [900/360 = 2.5 9�.] OK

�*������'� �<����

= 1.17 9�. < [900/360 = 2.5 9�.] OK

�&����?�K ��� ���()���������O��������� &6����<�D'.:

���1,!#���+���� 19 . ��� 7.5 ; .

Page 23: L17 Composite Construction - Suranaree University of ...eng.sut.ac.th/ce/oldce/CourseOnline/430432/L17 Composite...Lecture 17 Composite Construction Effective Flange Width NonencasedComposite

1,!#���+���� 19 . ��� 7.5 ; . 41 ��� �������+��L��� 20 ���1������*!�� �����.����������,��������!���* W400x66

0.85 0.85(0.21)(225 10)201 ton

2 2

c ch

f AV

′ ×= = =

84.12 2.5105 ton

2 2

s y

h

A FV

×= = =

���+M0�� ���#�*1�������:

Control

��������D'. 16-1 �� q = 5.13 ��/�& ��

�����& ��D'.������� = N = Vh /q = 105/5.13

= 20.47 ���� �*� ������& %����?������D'.�&

20 studs 20 studs

Page 24: L17 Composite Construction - Suranaree University of ...eng.sut.ac.th/ce/oldce/CourseOnline/430432/L17 Composite...Lecture 17 Composite Construction Effective Flange Width NonencasedComposite

Partially Composite Beams

When allowable moment more then the requirement no need for shear

connectors of full composite action.

So we reduce the number of shear connectors to save the money.

( )heff s tr s

h

VI I I I

V

′= + −

Effective Moment of Inertia:

2

reqd s

h h

tr s

S SV V

S S

− ′ =

0.25h hV qN V′ = ≥

Reduced Shear Force:

Live load deflection:

partially composite fully composite trLL LL

eff

I

I

∆ = × ∆

Page 25: L17 Composite Construction - Suranaree University of ...eng.sut.ac.th/ce/oldce/CourseOnline/430432/L17 Composite...Lecture 17 Composite Construction Effective Flange Width NonencasedComposite

��������� 16-3 ��� ���& ���������� 16-2 �������'���*����'�����������%����?���D'.�& D'.�����D�� *���������� �������,��������D&������ ���

����� Seff = Str D'.������� = 1,633 9�.3 ����������D'. 16-2

2 21633 1190

105 84.8 ton1683 1190

reqd s

h h

tr s

S SV V

S S

− − ′ = = = − −

0.25 Vh = 0.25(105) = 26.3 �� < 84.8 �� OK

�����& ��D'.������� = N = Vh/q = 84.8/5.13 = 16.53 ���

� �*� ������& %����?������D'.�&

1,!#���+���� 19 . ��� 7.5 ; . -����� 34 ���

Page 26: L17 Composite Construction - Suranaree University of ...eng.sut.ac.th/ce/oldce/CourseOnline/430432/L17 Composite...Lecture 17 Composite Construction Effective Flange Width NonencasedComposite

�����)�����������:

V’h = (5.13)(17) = 87.21 ��

4

( )

87.2123700 (65122 23700)

105

61,450 cm

heff s tr s

h

VI I I I

V

′= + −

= + −

=

∆LL = (65,122/61,450)(1.17)

= 1.24 ; . < [900/360 = 2.5 9�.] OK

Page 27: L17 Composite Construction - Suranaree University of ...eng.sut.ac.th/ce/oldce/CourseOnline/430432/L17 Composite...Lecture 17 Composite Construction Effective Flange Width NonencasedComposite

Composite Beams with Formed Steel Deck

1. Rib height max. = 7.5 cm

2. Avg. width of concrete rib min. = 5 cm

3. Shear connector dia. max. = 19 mm

4. Concrete slab above steel deck min. = 5 cm

5. ribs perpendicular to beam neglect lower concrete rib

slab

rib

Stud dia. not greater then 19 mm4 cm or more

5 cm or more

7.5 cm or more

Reduced factor for q

0.851.0 1.0sr

r rr

Hw

h hN

− ≤

Parallel ribs:

Perpendicular ribs:

0.6 1.0 1.0sr

r r

Hw

h h

− ≤

Page 28: L17 Composite Construction - Suranaree University of ...eng.sut.ac.th/ce/oldce/CourseOnline/430432/L17 Composite...Lecture 17 Composite Construction Effective Flange Width NonencasedComposite

��������� 16-4 D��9,���������D'. 16-2 % ���� ����*<� 6�K,���(����,�(���������*<�) �������������D���� 5 9�. *��),����'��� 5 9�. ���&�� wr �D���� 6 9�. �� � �����

Stud 19mm x 9cm

t = 5 cm

hr = 5 cm9 cm

6 cm 9 cm6 cm

15 cm rib spacing

����� ��������������)����#�!��

,������), *�������������D'. 16-2 = 786 ��./����

���&��,����� ����*<� = 30(3) = 90 ��./����

���,�����D�,��� = 876 ��./����

MD = (0.876)(9)2/8 = 8.87 ��-����

Page 29: L17 Composite Construction - Suranaree University of ...eng.sut.ac.th/ce/oldce/CourseOnline/430432/L17 Composite...Lecture 17 Composite Construction Effective Flange Width NonencasedComposite

������������������������������

ML = 18.89 ��-���� ����������D'. 16-2

%����?���D'.�& Mmax= MD + ML= 8.87+18.98 = 27.76 ��-����

���()����D'.�& Vmax = (9/2)(0.876+1.875) = 12.38 ��

��������������DP�6*����), b = 225 9�. ���)�������� 16-2

G *H��#��!���*��!�����:

Str ������� Mmax= (27.76)(100)/(0.66�2.5) = 1,682 9�.3

Ss ������� MD = (8.87)(100)/(0.66� 2.5) = 538 9�.3

���+�0��1,!��!���* W400x94.3 (As = 120.1 ; .2, d = 386 .,

tw = 9 ., tf = 14 ., Is = 33,700 ; .4, Ss = 1,740 ; .3)

Page 30: L17 Composite Construction - Suranaree University of ...eng.sut.ac.th/ce/oldce/CourseOnline/430432/L17 Composite...Lecture 17 Composite Construction Effective Flange Width NonencasedComposite

��)# ���������!���*��#*�$# :

A = 120.1 + (5)(225/9) = 245.1 9�.2

yb = (120.1x19.3+5x25x41.1)/245.1 = 30.4 9�.

Itr = 33,700+120.1(30.4-19.3)2+(1/12)(25)(5)3

+ 5(25)(41.1-30.4)2 = 63,069 9�.4

Str bot = 63,069/30.4 = 2,075 9�.3

Str top = 63,069/(43.6-30.4) = 4,778 9�.3

���������� �� *���� �����������+ �

�&����?�K ���()�����*����*'�� 19 ��. ��� 9 9�.

���6�N��?�*���*����*'�����D'.�& = 2.5 tf = 2.5(1.3)

= 3.25 9�. > 1.9 9�. OK

Page 31: L17 Composite Construction - Suranaree University of ...eng.sut.ac.th/ce/oldce/CourseOnline/430432/L17 Composite...Lecture 17 Composite Construction Effective Flange Width NonencasedComposite

21682 1740

105 3.15 ton < 0.25(105) 26.3 ton2075 1740

hV−

′ = = = −

���()����D'.�& � �� Vh = 105 �� ����������D'. 16-2

��������D'. 16-1 �� q = 5.13 ��/�& ��

�����������* ���*���*����*'�� Nr = 1, Hs = 9 9�. *���� hr = 5 9�. wr = 6 9�.

0.85 6 91

5 51

������* �� = = 0.816

q D'.* �� *�� = 0.816(5.13) = 4.19 ��

Nreqd = 105/4.19 = 25.1 (1,! 50 #���+����)

1,!#���+���� 25 ����������*!���.���������

��� ���*����*'����������O��������� &6�������:

N = 26.3/4.24 = 6.2 1,!#���+���� 6 ����������*!���.���������