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Cover-plated Beams Built-up W Sections Plate Girder Stiffeners 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 Lecture Lecture 1 1 8 8 Built Built - - up Beams up Beams

Timber and Steel Design Lecture 18 Built-up Beams

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Page 1: Timber and Steel Design Lecture 18 Built-up Beams

� Cover-plated Beams

� Built-up W Sections

� Plate Girder

� Stiffeners

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

Lecture Lecture 1188 BuiltBuilt--up Beamsup Beams

Page 2: Timber and Steel Design Lecture 18 Built-up Beams
Page 3: Timber and Steel Design Lecture 18 Built-up Beams

Cover-plated Beams

d

tp

tp

2

22

reqd s

dI I A

= +

22 ( / 2)

/ 2reqd s

s

A dS S

d

S Ad

= +

= +

Page 4: Timber and Steel Design Lecture 18 Built-up Beams

��������� 17.1 ������������ ���� ������������ 60 � . ��������������������� !"�������#�$% � �&'�"��� �����������(�)(����"��� �$�*+�������%,������������ ��"������������� #�(-�"���� 1,400 ��./� .2 #!(�(�&�� W600�137

�� �6"-��7���( 12 t/m

7 m

����� � �&'�"������ = 180 ��./- &�

M = (12.18)(7)2/8 = 74.6 &�-- &�

Sreqd = (74.6�105)/1,400 = 5,329 � .3

������� W600�137 (I = 103,000 ��.4 S = 3,530 ��.3)

Page 5: Timber and Steel Design Lecture 18 Built-up Beams

58.2 cm 59.0 cm59.8 cm <

max. 60 cm

����*�"� S �����(��'�:

S = (103,000 + 2(36)(29.5)2)/29.9

= 5,540 � .3 > 5,329 � .2 OK

#$�������� W600 � 137 %��� PL8 � 450 ��. )�*��+,-./

� �&'�"�#!(�6"-��7��� 8 .

Sreqd = Ss + A d

5,329 = 3,530 + A (59.0)

A = 30.5 � .2

+��#$�*0��1�+2/ PL 8 � 450 ��. )�*��+,-./ (A = 36 ��.2)

Page 6: Timber and Steel Design Lecture 18 Built-up Beams

Built-up wide-flange sections

h

Af = area of flange

tw

tf

Built-up W sections: / 6,360 /w bh t F≤

/ 6,360 /w bh t F>Plate girder:

Page 7: Timber and Steel Design Lecture 18 Built-up Beams

��������� 17.2 ���������� W %� ������ 1.50 - &���B " ����#!(�6"-��' ���������)����������!"����-����� 20 - &� �������������6"� ���-� � 4 &�/- &� �����������)��&��-�� � �&'�"� �����������(�)(��� �$�*+�������%,���������� #!(-��7� A36 ���-!D�� ���EF�-�& �� ���-!D�� E70

d/t = 150/1.5 = 100 < 107 OK

5,355 5,355107

2,500y

d

t F≤ = =

����� - &+�� ���-HD� �������� ��� �&'�� ������� = 300 ��./- &�

M = (4.3)(20)2/8 = 215 &�-- &�

V = (10)(4.3) = 43 &�

)��)���6"-�����&(������������ Compact section (&������� 6-1)

Min tw = 150/107 = 1.4 � . (#$� 1.5 ��.)

+��#$�*0��1�� 1.5 � 150 ��. (Aw = 225 ��.2)

Page 8: Timber and Steel Design Lecture 18 Built-up Beams

2

31 22 212

2 2

ffw

reqd

f f

thAt h

Sh h

t t

+ = +

+ +

�4�56�)�����*4�178��:

fv = 43,000/(1.5�150) = 191 ��./� .2

kv = 5.34 or = 0.676 < 0.8

Fv = 2,500/(2.89�0.676)=1,280 ��./� .2 > 191 ��./� .2

Since h/tw < 260 (AISC) and web shear stress < max. value

Stiffeners are not needed

/�41+8�/*0��-./:

Sreqd = 215 x 105 / 1,650 = 13,030 � .3

Page 9: Timber and Steel Design Lecture 18 Built-up Beams

( )2

3 146 21 2(1.5) 1462 21213,030

146 1462 2

2 2

fA + = +

+ +

� �&' tf = 2 � .

Af = UD����)��%,�����)(�� = 53.7 � .2 (#$� 2××××28 ��.)

1+8�/#$�*0��1�� 1.5××××146 ��. *+,*0��-./ 2××××28 ��.

Page 10: Timber and Steel Design Lecture 18 Built-up Beams

PLATE GIRDERS

Riveted or bolted

WT

WT

PL

Welded Welded box girder

PL girder (may be for

full depth of story)

Page 11: Timber and Steel Design Lecture 18 Built-up Beams
Page 12: Timber and Steel Design Lecture 18 Built-up Beams

Plate Girder Design

Intermediate

stiffeners do not

have to run all the

way to the tension

flange

Stiffeners

Allowable Bending Stresses < 0.66Fy

Allowable Shear Stresses < 0.40Fy

Intermediate Stiffeners

Page 13: Timber and Steel Design Lecture 18 Built-up Beams

Proportions of Plate Girders

Web Size:Vertical component in

compression flange

Web

Vertical component in

tension flange

1. No transverse stiffeners or stiffeners spacing > 1.5 h

( )160,1

000,984

+≤

yfyfw FFt

h

2. Use transverse stiffeners with spacing 1.5h≤

yfw Ft

h 670,16≤

Depth: about 1/6 - 1/15 of span

Page 14: Timber and Steel Design Lecture 18 Built-up Beams

Flange:

h

Af

Af

tw

23

212 2

wf

t h hI A

= +

( )23

3

2 / 2/12

/ 2 / 2

6

fw

wf

A ht hS

h h

t hA h

= +

= +

Equating required section modulus to S :

2

6

wf

b

t hMA h

F= +

6

wf

b

t hMA

F h= −

0.60f

y

MA

F h≈

Assume Fb = 0.60Fy:

Page 15: Timber and Steel Design Lecture 18 Built-up Beams

Allowable Bending Stress

′ ≤b b PG eF F R R

No reduction in Fb due to unbraced length because of large size of PL girder

6,360where 1 0.005 1.0w

PG

f w b

A hR

A t F

= − − ≤

Girder

xb

x

Mf

S=

Increase in compression

flange stress due to lateral

buckling of web

Dotted line shows a linear

stress variation while solid

curved line shows actual variation

( )212 3

1.0

12 2

w

f

e

w

f

A

AR

A

A

α α

+ − = ≤

+

where α = 0.6 Fyw /Fb � 1.0

Page 16: Timber and Steel Design Lecture 18 Built-up Beams

Tension Field Action

Pratt Truss

Weak tension field

in end panels

Tension field

action

Page 17: Timber and Steel Design Lecture 18 Built-up Beams

Intermediate Stiffeners

when h/tw > 260 ( ) yv

y

v FCF

F 40.089.2

≤=

where( )

and 0.8 than less is when /

000,165,32 v

wy

v

v CthF

kC =

0.8 than more is when /

585,1v

y

v

w

CF

k

th=

( )and 1.0 than less is when

/

34.500.4

2 h

a

hakv +=

( )1.0 than more is when

/

00.434.5

2 h

a

ha+=

If include tension field action, allowable shear stress may be increased to:

( )y

v

v

y

v Fha

CC

FF 40.0

/115.1

1

89.2 2≤

+

−+=

Page 18: Timber and Steel Design Lecture 18 Built-up Beams

Panel aspect ratio: 0.3/

260/

2

wthha

Moment of inertia:4

50

≥h

I st

Total area: ( )( )

w

v

st YDhtha

ha

h

aCA

+−

−=

2

2

/1

/

2

1

- D�� Y = ��&���"� Fyw &"� Fy )���6"-��' ������

D = 1.0 ��������6"-��' ������-%V�$"

= 1.8 ��������6"-��' ������-�����-%V#!(-��7�H��

= 2.4 ��������6"-��' ������-�����-%V#!(�6"-��7�

3

34012.0

= yw

vs

Fhf

Shear transfer between stiffener and web (due to tension field action)

Page 19: Timber and Steel Design Lecture 18 Built-up Beams

Bearing Stiffeners

Width outside of fillets

Chamfer

Filler PLs

Stiffener LStiffener

PLs

Corners are cut to avoid

flange-to-web weld.

Difficult to analyze because support load with web

Portion of web to support load: 12tw at girder ends

25tw at interior concentrated loads

Effective length of bearing stiffener columns: KL = 0.75 h

Page 20: Timber and Steel Design Lecture 18 Built-up Beams

��������� 17.3 ��������%� ���!"��-����� 15 - &� ����������6" 2.2 &�/- &� �� ������

32 &� ���� � 1/3 !"���� �����������(�)(���������%,����������������������%W'�'�'���� ���

�������� ���-%V��� #!(-��7� A36 �� UX&'��� �� ������

����� � �&'�������� = 300 ��./- &�, -)���6Y$ '���-HD��� - &+���������

32 ton 32 ton

2.5 ton/m

5 m 5 m 5 m50.75t 50.75t

50.75t

50.75t

38.25t

6.25t

38.25t

6.25t

222.5t-m 222.5t-m230.3t-m

Page 21: Timber and Steel Design Lecture 18 Built-up Beams

6,360 6,360164

1,500w b

h

t F= = =

( )984,000 984,000

3252,500(2,500 1,160)1,160w yf yf

h

t F F≤ = =

++

142w

h

t=

��/*))*0��1��1)8;�����: � �&'��� ���)���� = (1/10)(1500) = 150 � .

� �&'��� ���)��-�� = 150 Z 8 = 142 � .

��&���"� h/tw ��������)��-�����B "&(�����"������������� #�(�D�

tw = 142/164 = 0.866 � .

[(�B " ��6"-��' ���������)�����D�[(� ��&"�"�� ����"� 1.5 -�"�� � � ��"��%,���

tw = 142/325 = 0.437 � .

��� ��(��������-UD��%\������������"� tw = 0.8 � .

+��#$�*0��1�� 1 � 142 ��. (Aw = 142 ��.2)

Page 22: Timber and Steel Design Lecture 18 Built-up Beams

( )2230.3(100)108.1 cm

(1.5)(142)f

b

MA

F h≈ = = ×USE 3 40 cm

��/*))-./<��1)8;�����:

������������� � = (2�3�40+1�142)(7,850)/1002

= 299.87 � 300 ��./- &� OK

�4�56�)/�4%/��1��,17=�,� ���&������� 6-1 �������)����������&���"���� ��(��&"���� ������������+��������������

( )0.46 0.46

4.05 4.050.414

142/ck

h t= = =-D������ h/t > 70 �����

795 79510.23

/ 2,500 /0.414yf c

b

t F k= = =��������(�&��B "�� ������

406.67 10.23

2 2(3)

f

f

b

t= = < OK��&���"�)���(�&�����#!(

Page 23: Timber and Steel Design Lecture 18 Built-up Beams

<>?6�)���@���������*+,�4�56�)�����*4�:

142 cm

1 cm

3 cm

148 cm

3 cm

40 cm

142 6,360 6,360Since 142 164 , 1.0

1 1,500PG

w b

hR

t F

= = < = = =

Flange and web are made of A36: Re = 1.0

I = (1/12)(1.0)(142)3+(2)(3x40)(72.5)2

= 1,500,107 � .4

S = 1,500,107/74 = 20,272 � .3

fb �������!"���� = (230.3x105)/20,272

= 1,136 ��./� .2

b b PG e bF F R R F′ = =

Page 24: Timber and Steel Design Lecture 18 Built-up Beams

����� Fb ������&����������"�-�� �(�)(���D� 0.6Fy = 1,500 ��./� .2

(-D������-��B "�� �������"� Fb ���&(��B "-�' 0.6Fy)

37,173 1050047.39 53.56

10.55 2,500

b

T

CL

r

× ×= = < =

����* Iy �� rT )��%,��� + 1/6 �6"-��

16,000

143.7

Iy = (1/12)(3)(40)3 = 16,000 � .4

Af + 1/6 web = (3)(40) + (1/6)(1)(142) = 143.7 � .2

rT = = 10.55 � .

#!(�"� Cb = 1.0 -D������ - &+ ���������������!"����(230.3 &�-- &�)���-�'�)��

*. ������B " ����������� ��"� ����"� - &+(222.5 &�-- &�)���%����������

Page 25: Timber and Steel Design Lecture 18 Built-up Beams

*0��164��/��+��*)/����;�����//4,��1-A�5>�:

3 cm

0.6 cm

k=3.6 cm

32,000

( 5 ) 1.0(0 5 3.6)

1,778 ksc 0.66 1,650 ksc

w

y

R

t N k

F

=+ + ×

= > =

Check web yielding for interior loads

Bearing stiffeners are required

�"�����-HD����%�����

fv = 50.75(1,000)/(142x1) = 357 ��./� .2

a/h = 500/142 = 3.52

h/tw = 142 > 3,179 / 2,500 63.58=

/�4��/*))*0��164��/��+��4,�����$���:

Page 26: Timber and Steel Design Lecture 18 Built-up Beams

���������&���"� a/h > 1.0

( )2 2

4.00 4.005.34 5.34 5.66

3.52/vk

a h= + = + =

( )2 2

3,165,000 3,165,000(5.66)0.355

(2,500)(142)/

vv

y w

kC

F h t= = =

2,500(0.355)

2.89 2.89

307 ksc 357 ksc

y

v v

FF C= =

= < NG

USE intermediate stiffeners

��&����"��6"-��' ������&�����#!(&���� �.3 �� Fv = 357 ksc, h/tw = 142,

a/h = 1.81 a = 1.81(142) = 257 � . (#$� 2.5 1��4)

*0��164��/��+��*0��*4/����5�/-+��<�� 2.5 1��4

Page 27: Timber and Steel Design Lecture 18 Built-up Beams

a/h = 250/142 = 1.76

&��������� &(������6"-��' ������� ��"��!"��-U'� -&' #!"�����

V = 50.75 – 2.5(2.5) = 44.5 &�

fv = (44.5)(1,000)/(142) = 313.4 ��./� .2

� � ����6"-��' �������6"���[��������������-%V��� = 5 Z 2.5 = 2.5 - &�

Page 28: Timber and Steel Design Lecture 18 Built-up Beams

( )2 2

4.00 4.005.34 5.34 6.63

1.76/vk

a h= + = + =

( )2 2

3,165,000 3,165,000(6.63)0.416

(2,500)(142)/

vv

y w

kC

F h t= = =

2,500(0.416) 360 ksc 313.4 ksc

2.89 2.89

y

v v

FF C= = = > OK

No need for additional intermediated stiffeners

�����U'���*� Fv ���������&���"� a/h > 1.0

Page 29: Timber and Steel Design Lecture 18 Built-up Beams

��/*))*0��164��/��+��: #!(�6"-��' ������-�����

22

2

1 0.416 1.761.76 (142)(1.0) 9.53 cm

2 1 1.76stA

−= − =

+

#$�*0��164��/��+��1���� 0.8 x 12 ��. (Ast

= 9.6 ��.2)

����������-HD��� �������"� &���������������������������

fv = (38.25)(1,000)/(142) = 269 ��./� .2

Fb = (0.825 – 0.375(269/360))(2,500)

= 1,362 ��./� .2 > 269 ��./� .2 OK

Page 30: Timber and Steel Design Lecture 18 Built-up Beams

���4�6���<���/�������<������

12 79515 15.9

0.8yF

= < =

4 4

4142Min 65.05 cm

50 50st

hI

= = =

Actual Ist using depth from web to outside of stiffener

Moment of inertia:

#$�*0��164��/��+��4,�����$��� 0.8××××12××××136 ��.

Ist = (1/3)(0.8)(12.5)3 = 521 � .4 > 65.05 � .4 OK

��� ���(�������� = 142 – 0.6 – 6(1) = 135.4 � .

Page 31: Timber and Steel Design Lecture 18 Built-up Beams

*0��164��/��+��*)/��: ����������%W'�'�'�����%���

fa = ���%W'�'�'�� / Aeff = 50.75(1,000)/48

= 1,057 ��./� .2 < 1,457 ��./� .2 OK

88.748

979,2=

<����?�����*4����#�*0��164��/��+��

I = (1/12)(1.2)(31)3 = 2,979 � .4

Aeff = (2)(15)(1.2) + (12)(1) = 48 � .2

r = � .

KL = (0.75)(142) = 106.5 � .

KL/r = 106.5/7.88 = 13.52

Fa = 1,457 ��./� .2 ���&������� ).1

Web

12 mm

Aeff shown shaded15 cm

1 cm

15 cm

31 cm

12tw = 12 cm

+��#$� 2 PL 1.2 ×××× 15 ��. ���#�4B-

#$�*0��164��/��+��*)/�� 2 PL 1.2 x 15 x 140 ��.

Page 32: Timber and Steel Design Lecture 18 Built-up Beams

2.5 m 2.5 m 2.5 m 2.5 m 2.5 m 2.5 m

5.0 m 5.0 m 5.0 m

PL 0.8 x 12 cm2 PL 1.2 x 15 cm 2 PL 1.2 x 15 cm

FINAL DESIGN