timber and steel design lecture 18 built-up beams
TRANSCRIPT
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� 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
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Cover-plated Beams
d
tp
tp
2
22
reqd s
dI I A
= +
22 ( / 2)
/ 2reqd s
s
A dS S
d
S Ad
= +
= +
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��������� 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)
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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)
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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:
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��������� 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 ��.)
+��#$�*0��1�� 1.5 � 150 ��. (Aw = 225 ��.2)
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2
31 22 212
2 2
ffw
reqd
f f
thAt h
Sh h
t t
+ = +
+ +
�4�56�)�����*4�178��:
fv = 43,000/(1.5�150) = 191 ��./� .2
kv = 5.34 or = 0.676 < 0.8
Fv = 2,500/(2.89�0.676)=1,280 ��./� .2 > 191 ��./� .2
Since h/tw < 260 (AISC) and web shear stress < max. value
Stiffeners are not needed
/�41+8�/*0��-./:
Sreqd = 215 x 105 / 1,650 = 13,030 � .3
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( )2
3 146 21 2(1.5) 1462 21213,030
146 1462 2
2 2
fA + = +
+ +
� �&' tf = 2 � .
Af = UD����)��%,�����)(�� = 53.7 � .2 (#$� 2××××28 ��.)
1+8�/#$�*0��1�� 1.5××××146 ��. *+,*0��-./ 2××××28 ��.
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PLATE GIRDERS
Riveted or bolted
WT
WT
PL
Welded Welded box girder
PL girder (may be for
full depth of story)
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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
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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
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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:
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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
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Tension Field Action
Pratt Truss
Weak tension field
in end panels
Tension field
action
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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≤
+
−+=
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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)
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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
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��������� 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
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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 � .
+��#$�*0��1�� 1 � 142 ��. (Aw = 142 ��.2)
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( )2230.3(100)108.1 cm
(1.5)(142)f
b
MA
F h≈ = = ×USE 3 40 cm
��/*))-./<��1)8;�����:
������������� � = (2�3�40+1�142)(7,850)/1002
= 299.87 � 300 ��./- &� OK
�4�56�)/�4%/��1��,17=�,� ���&������� 6-1 �������)����������&���"���� ��(��&"���� ������������+��������������
( )0.46 0.46
4.05 4.050.414
142/ck
h t= = =-D������ h/t > 70 �����
795 79510.23
/ 2,500 /0.414yf c
b
t F k= = =��������(�&��B "�� ������
406.67 10.23
2 2(3)
f
f
b
t= = < OK��&���"�)���(�&�����#!(
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<>?6�)���@���������*+,�4�56�)�����*4�:
142 cm
1 cm
3 cm
148 cm
3 cm
40 cm
142 6,360 6,360Since 142 164 , 1.0
1 1,500PG
w b
hR
t F
= = < = = =
Flange and web are made of A36: Re = 1.0
I = (1/12)(1.0)(142)3+(2)(3x40)(72.5)2
= 1,500,107 � .4
S = 1,500,107/74 = 20,272 � .3
fb �������!"���� = (230.3x105)/20,272
= 1,136 ��./� .2
b b PG e bF F R R F′ = =
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����� Fb ������&����������"�-�� �(�)(���D� 0.6Fy = 1,500 ��./� .2
(-D������-��B "�� �������"� Fb ���&(��B "-�' 0.6Fy)
37,173 1050047.39 53.56
10.55 2,500
b
T
CL
r
× ×= = < =
����* Iy �� rT )��%,��� + 1/6 �6"-��
16,000
143.7
Iy = (1/12)(3)(40)3 = 16,000 � .4
Af + 1/6 web = (3)(40) + (1/6)(1)(142) = 143.7 � .2
rT = = 10.55 � .
#!(�"� Cb = 1.0 -D������ - &+ ���������������!"����(230.3 &�-- &�)���-�'�)��
*. ������B " ����������� ��"� ����"� - &+(222.5 &�-- &�)���%����������
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*0��164��/��+��*)/����;�����//4,��1-A�5>�:
3 cm
0.6 cm
k=3.6 cm
32,000
( 5 ) 1.0(0 5 3.6)
1,778 ksc 0.66 1,650 ksc
w
y
R
t N k
F
=+ + ×
= > =
Check web yielding for interior loads
Bearing stiffeners are required
�"�����-HD����%�����
fv = 50.75(1,000)/(142x1) = 357 ��./� .2
a/h = 500/142 = 3.52
h/tw = 142 > 3,179 / 2,500 63.58=
/�4��/*))*0��164��/��+��4,�����$���:
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���������&���"� 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 � . (#$� 2.5 1��4)
*0��164��/��+��*0��*4/����5�/-+��<�� 2.5 1��4
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a/h = 250/142 = 1.76
&��������� &(������6"-��' ������� ��"��!"��-U'� -&' #!"�����
V = 50.75 – 2.5(2.5) = 44.5 &�
fv = (44.5)(1,000)/(142) = 313.4 ��./� .2
� � ����6"-��' �������6"���[��������������-%V��� = 5 Z 2.5 = 2.5 - &�
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( )2 2
4.00 4.005.34 5.34 6.63
1.76/vk
a h= + = + =
( )2 2
3,165,000 3,165,000(6.63)0.416
(2,500)(142)/
vv
y w
kC
F h t= = =
2,500(0.416) 360 ksc 313.4 ksc
2.89 2.89
y
v v
FF C= = = > OK
No need for additional intermediated stiffeners
�����U'���*� Fv ���������&���"� a/h > 1.0
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��/*))*0��164��/��+��: #!(�6"-��' ������-�����
22
2
1 0.416 1.761.76 (142)(1.0) 9.53 cm
2 1 1.76stA
−= − =
+
#$�*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
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���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 � .
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*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 ��.
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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