Timber and Steel Design Lecture 18 Built-up Beams

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Transcript of 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

Cover-plated Beams

d

tp

tp

2

22

reqd s

dI I A

= +

22 ( / 2)

/ 2reqd s

s

A dS S

d

S Ad

= +

= +

��������� 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)

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)

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:

��������� 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)

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

( )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 ��.

PLATE GIRDERS

Riveted or bolted

WT

WT

PL

Welded Welded box girder

PL girder (may be for

full depth of story)

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

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

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:

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

Tension Field Action

Pratt Truss

Weak tension field

in end panels

Tension field

action

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≤

+

−+=

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)

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

��������� 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

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)

( )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��&���"�)���(�&�����#!(

<>?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′ = =

����� 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 &�-- &�)���%����������

*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,�����$���:

���������&���"� 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

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 - &�

( )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

��/*))*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

���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 � .

*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 ��.

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