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Design of Bridge
g g
Main Girders
According to ECP
According to ECP
Assis. Prof. Dr. Ehab B. Matar
Design Phases of Main Girders
1. Structural analysis for the main system determining the max.
and min. straining actions at critical sections
2. Design of Web Plate
g
3. Design of Flange Plate
4. Design of Stiffeners (end bearing and intermediate)
5 Design of Connections between web plate and flange plate
5. Design of Connections between web plate and flange plate
6. Design of Splices
7. Check fatigue for all details
Bridges Main systems
1- Structural Analysis
 Structural analysis is carried out using either influence lines,
grillage analysis or finite elements depending on complexity of
grillage analysis or finite elements depending on complexity of
structures and its importance.
 Max. and Minimum shear, moments, reactions…. are determined
at critical sections
at critical sections.
Stress range
Stress range
Stress range
2- Design of Web Plate
 This includes the following tasks:
1. Determining Web height
2 Determining Web thickness
2. Determining Web thickness
3. Checking shear Buckling
2.1 Web height
 Overall depth, h:
 Lo/18 ≤ h ≤ Lo/12 (highway two lanes)
L /10 ≤ h ≤ L /7 ( il i l t k)
 Lo/10 ≤ h ≤ Lo/7 (railway single track)
 For double tracks railway or four lanes roadway, increase
the above limits by 60-85%
the above limits by 60 85%
 If the maximum moment is known; the web height can be
approximately calculated as
3
3 7
.
5
3
.
5
2
3
or
b
b F
M
F
Mk
d
h 


 d= plate girder depth (cm)
 M= maximum bending moment (t.cm)
k ratio of height to thickness of eb plate 100
b
b
 k= ratio of height to thickness of web plate  100
 Fb= allowable bending stress ≈ 0.58 Fy
2.2 Web Thickness
 web thickness, tw:
 tw ≥8mm
y
w F
t
d
In
830
case
any
* 
y
w F
t
d 190
used
are
stiffeners
sverse
when tran
* 
y
F
t
d 320
used
stiff.
e
transvers
and
d/5)
(at
al
longitudin
When
* 
y
w F
t
2 3 Shear Buckling
2.3 Shear Buckling
 No need to check shear buckling resistance if :
 No need to check shear buckling resistance if :
 for un-stiffened web
 for stiffened web
y
w
w F
t
d /
105
/ 
q
w
w
F
k
t
d /
45
/ 
y
w
w
F
1 0
f
)
/
34
5
(
4
shear
for
factor
buckling
K
2
q


where
/d
d
0
.
1
for
)
(4/
5.34
1.0
for
)
/
34
.
5
(
4
2
2












where /d
d1


where
d
d1
Shear Buckling Resistance
 If the above mentioned limits are exceeded the shear buckling
resistance should be checked as follows:
y
w
F
t
d
Calculate
*  
q
q
q
K
0.35F
q
then
8
.
0
For
*
57
Calculate
y
b





y
q
q
q
F
9
.
0
35
.
0
)
0.625
-
(1.5
q
then
2
.
1
0.8
For
* b
y

 


y
q
q F
35
.
0
*
9
.
0
q
then
2
.
1
For
* b

 

 It should be noted that longitudinal stiffener at mid depth would be
ff ti f ti bj t d t h th th t
more effective for sections subjected to pure shear than that
positioned at d/5 for pure bending.
 For continuous plate girder, the web panel over an interior
support will be subjected to simultaneous action of bending
support will be subjected to simultaneous action of bending
moment and shearing force. Therefore:
 If the actual shear stress qact ≤0.6qb then the allowable bending
stresses in the girder flanges will not be reduced and should
stresses in the girder flanges will not be reduced and should
not exceed 0.58Fy.
 If the actual shear stress qact >0.6qb then two alternatives may
be followed. The first is to reduce the allowable bending
g
stress for flange plates according to the following interaction
equation.
y
act
b F
q
F 












 36
.
0
8
.
0
 The second alternative is to design the girder flanges to
y
b
b
q








g g g
resist the whole acting bending moment without any
participation of web for resisting bending moment without
reducing the allowable bending stress.
Example
Design a continuous two spans welded plate girder as shown below for a
roadway bridge. The cross girders are arranged each 2.4m. The deck slab is 20cm
thick and the asphalt cover is 10cm. The steel used for the design of all elements is
St. 37. Moreover, design a field splice located at 16.8m from the end support. The
St. 37. Moreover, design a field splice located at 16.8m from the end support. The
bending moments and shearing forces at the critical locations are tabulated as
follows:
Sec. Md.l (t.m) Qd.l (t) Mll+I (t.m) Qll+I (t)
1 0 +38.2 0 +50.8
2 +171 0 +267 +4 43
2 +171 0 +267 +4.43
3 -305.3 -63.6 -296 -61.65
4 +96 -33.07 +96.69,-98.63 -34.92,+3.36
Solution
 Proportioning of plate girder
 cm
cm
F
Mk
d
b
190
186
4
.
1
*
2
100
*
100
*
)
3
.
305
296
(
*
3
2
3 3
3 



 where k is
assumed 100
 Design of web plate
 t
t
d 56
1
190
190
/ 


 cm
t
F
t
d w
y
w 56
.
1
122
/ 



 By using vertical stiffeners arranged @2.4m (distance between
cross girders), then,
 26
.
1
240
1



d

190
d
 85
.
7
)
26
.
1
/(
4
34
.
5
)
/
4
(
34
.
5 2
2




 
q
k
 37
.
81
4
.
2
85
.
7
45
45 


y
q
w F
k
t
d
190
 thcikness
large
a
is
which
34
.
2
37
.
81
190
cm
tw 


 Assume tw = 16mm and check shear buckling resistance.
 2
.
1
8
.
0
15
.
1
85
.
7
4
.
2
57
6
.
1
190
57





 q
q
y
w
q
k
F
t
d


q
 2
/
66
.
0
)
4
.
2
35
.
0
)(
15
.
1
625
.
0
5
.
1
(
)
35
.
0
)(
625
.
0
5
.
1
(
cm
t
q
x
x
F
q
b
y
q
b






 
 safe
/
41
.
0
6
.
1
190
25
.
125 2




 b
w
q
cm
t
x
A
Q
q

3- Design of Flange Plate
 This includes the following tasks:
1. Determining Flange cross section (using Flange Area
Method)
Method)
2. Determining Flange width and thickness
3. Checking Bending Stresses
3.1 Flange Area Method
MY
 Plate Girder



3
2
d
d
I
MY

c
tf
b










12
2
2
2
3
2
3
2
w
f
d
t
d
A
I
c
d










6
2
12
2
2
3
2
w
f
w
f
A
A
d
d
t
d
A
I
Welded Plate Girder








6
/ w
f
A
A
d
Y
I









w
f
b
A
A
d
M
F




 6
f
A
d
F
M
A w
b
f
6



A
d
F
M
A
d
F
M
A w
w
f
8
4
3
*
6
@4
arranged
bolts
assume
BUS
riveted
or
bolted
For






d
C
b
t
b
A
where
d
F
d
F
f
f
b
b
%
30
20
2
;
*
8
4
6




Section class Part Stress Profile
C tf C tf
D b
3.2 Local Buckling limits
Section class Part Stress Profile
Compact Flange Uniform Comp. Rolled Sec.
dw tw dw tw
Rolled section Welded section t
h
t
y
f F
t
C /
9
.
16
/ 
p
section
g p
B.U.S
Non-compact
section
Flange Uniform Comp. Rolled Sec.
y
f
y
f F
t
C /
3
.
15
/ 
y
f F
t
C /
23
/ 
section
B.U.S
y
f F
t
C /
21
/ 
Remember
 Whenever the width / thickness ratio of compression
flange exceeds the aforementioned limits, the flange should
be treated as a slender section and the effective flange
be treated as a slender section and the effective flange
area should be calculated to account for local buckling.
 The thickness of flange plates as well as web
 The thickness of flange plates as well as web
plates should be reduced by 1.0mm in design calculations
due to the effect of undercut in welding unless special
ti i th ldi t h i t k
precautions in the welding technique are taken.
Note that:
 When plates with
unequal thickness or
 Change of flange plate
width or thick.
q
width butt welded
together, the thicker or
g
wider plate should be
tapered with a slope
2−4mm
1
4
4
1
not exceeding one to
four as shown
2mm
R
=
6
0
c
m
R
3.3 Allowable Compressive Stresses
The allowable compressive
stresses in the compression
flange depend on whether the
flange is braced laterally or un-
flange is braced laterally or un-
braced. The lateral unsupported
length of the compression flange
Lu is calculated as follows:
For deck railway bridges with
For deck railway bridges with
open timber floor where there
exist upper wind bracing or not,
and with the existence of cross
girders that are rigidly connected
girders that are rigidly connected
to the main girder compression
flange, then, Lu = distance
between x-girders.
For deck railway bridges with
For deck railway bridges with
ballasted floor or for roadway
bridges where the compression
flange is supported by
continuous reinforced concrete
continuous reinforced concrete
or steel deck, where the frictional
or connection of the deck to the
flange is capable to resist a
lateral force of 2% of the flange
lateral force of 2% of the flange
force at maximum bending
moment, then, Lu = 0.
For continuous
deck roadway or
dec oad ay o
railway bridges
where the
compression flange
at interior supports
at interior supports
is located in the
bottom side of the
girder away from the
g y
deck slab, then,
Lu = the distance
between the centers
f i t ti f th
of intersection of the
lower wind bracing
with the
compression flange
compression flange
Lu = if there is no
lower wind bracing
or transverse bracing
g
then Lu is taken as
the distance from the
point of maximum
bending moment to
bending moment to
the point of contra-
flexure.
•Lateral unsupported length for through bridge (+M
a e a u suppo ed e g o oug b dge (
region)
 The lateral unsupported length of the
compression flange is taken as the full
4
*
5
.
2 a
EI
Lu y
 
compression flange is taken as the full
girder length if the compression flange is
unrestrained against lateral bending. If
the cross girders and the stiffeners
forming U-frames, then,
Wh
2
2
2
1
3
1
2
3 EI
B
d
EI
d



 Where
 E= The Young's modulus of steel (t/cm2)
 Iy= moment of inertia of the chord
member about the Y-Y axis (cm4) as
shown
d2
d1
I1
shown
 a = distance between the U- frames
(distance between x- girders)
  = the flexibility of the U- frame
d1 di t f th t id f th
I2
I1
 d1 = distance from the centroid of the
compression flange to the nearest face of
the cross girder of the U-frame.
 d2 = distance from the centroid of the
compression flange to the centroidal axis
B
compression flange to the centroidal axis
of the cross girder
 I1 = Moment of inertia of the vertical
member forming the arm of the U-frame
about the axis of bending.
 I2 = Moment of inertia of the cross girder
 B = distance between centers of
consecutive main girders connected by
U-frame.
Continue Example
7.5m
2.5m
1.25
1.0m 1.0m
1.25
2.5m
Continue Example Bridge Cross section
24m 24m
1 2 4 3
16.8
 Flange area Method
 For sec. 3, moment and shear acting together, therefore, checking
%
60
62
.
0
66
.
0
41
.
0



b
q
q
, then, a reduction in the allowable bending stress
should be carried out as follows
 Assuming the compression flange is braced laterally by the lower
wind bracing which has joints @240cm (distance between cross girders),
then Lu=240cm.
 Checking whether lateral torsional buckling controls the
allowable compression stresses or not as follows:
f x
b 60
20
20
24m 24m
should be carried out as follows

 
 
 
  2
/
38
.
1
4
.
2
66
.
0
/
41
.
0
36
.
0
8
.
0
/
36
.
0
8
.
0
cm
t
F
F
q
q
F
b
y
b
b





 Calculating the flange area at sec.3 as follows:
 2
66
.
178
6
6
.
1
190
190
38
1
2
3
.
601
6
cm
x
E
A
d
M
A w
f 




 u
y
f
L
cm
x
F
b


 6
.
774
4
.
2
60
20
20

u
b
y
f
b
y
f
L
cm
C
F
d
A
x
x
x
x
x
C
F
d
A


















86
.
580
.
.
1380
3
.
601
78
.
323
3
.
0
3
.
601
78
.
323
05
.
1
75
.
1
(
4
.
2
196
60
3
1380
.
.
1380 2
6
190
38
.
1
6 x
d
Fb
f
 Assuming bf=0.3d=0.3x190=57cm→60cm
 Then tf=178.66/60=2.98cm→3cm

y
f F
t
c 21
73
.
9
30
2
/
16
300




 Therefore Fbc =1.38t/cm2
& Ft=1.4 t/cm2
 /
38
.
1
543
,
43
2
3
.
601 2
cm
t
E
F 


 O.K safe in both tension and
compression.
 Checking fatigue stress by considering only 60% of the live loads
are acting i.e. 0.6x274.32=164.6tm.
2
6
164 E
 However, although the flange satisfied the limit of compact
section ( y
F
/
3
.
15 ) but the web is non-compact, therefore, the whole section
will be considered non-compact.
 Calculating the flange area at sec.2 as follows:
 2
114
6
.
1
190
2
438 x
E
A
M
A w
 Stress range = 2
/
378
.
0
543
,
43
2
6
.
164
cm
t
E

 For ADTT >2500 truck, No. of stress cycles =2E6 and for welded
plate girder Class B' is taken therefore the allowable fatigue stress range
Fsr=0.85t/cm2
. Therefore, the section is safe.
 Checking Actual stresses at section 2
     2
3
3
4
2
50
6
1
190 x
x 

 2
114
6
190
4
.
1
6
cm
x
d
F
A w
b
f 




 Assuming bf=50cm
 Then tf=114/50=2.28cm→2.4cm

y
f F
t
c 21
08
.
10
24
2
/
16
250





     
3
4
2
194
,
32
,
714
,
135
,
3
2
.
1
95
4
.
2
50
12
4
.
2
50
2
12
6
.
1
190
cm
Z
cm
I
x
x
x
x
x
I
gross
gross













 Assuming the compression flange is braced laterally by the
existence of R.C. deck directly rested over compression flange therefore,
Lu=0. Therefore, there is no need to check Fltb.
 Therefore Fb =1 4 t/cm2
& Ft=1 4 t/cm2
y
f
 Checking Actual stresses at section 3
     
3
4
2
3
3
543
,
43
,
213
,
267
,
4
5
.
1
95
3
60
12
3
60
2
12
6
.
1
190
cm
Z
cm
I
x
x
x
x
x
I
gross
gross













 Therefore Fbc 1.4 t/cm & Ft 1.4 t/cm
 /
36
.
1
194
,
32
2
438 2
cm
t
E
F 


 O.K safe in both tension and
compression.
 Checking fatigue stress by considering only 60% of the live loads
is acting. The live load is ranged at this section between +250.5 tm and -
73.971 tm. Then,
Example for through bridge
 A railway through plate girder
y g p g
bridge of 27 m simple span has
two main girders 9 m apart. The
bridge is for double track and has
bridge is for double track and has
an open timber floor. The cross
girders are arranged every 2.25 m.
The bridge is provided by stringer
 The bridge is provided by stringer
bracing, while braking force
bracing is not arranged. The
f
material of construction is steel 44;
the weight of the timber floor for
each track is 0.6 t/m’.
 Calculate Lu considering, for main
girder tw=20mm, dw=3000mm,
M =1060mt Q =160t while
Mmax=1060mt, Qmax=160t, while
for XG Pl#1000x20/2Pl#300*40mm
Solution
 For the main girder, tw=20mm,
dw=3000mm
 Af=M/(dFb)-Aw/6
Af M/(dFb) Aw/6
 Af=1060*100/(300*1.6)-
2*300/6=120.8cm2
 Bf=0.2*300=60cm
 tf>120.8/60>2.01cm
 c/t <21/sqrt(F )t =2 4cm
d2
d1
I1
 c/tf<21/sqrt(Fy)tf=2.4cm
 Z=(50x2x27.4+60x2.4x1.2)/(60x2.4+50
x2)=11.94cm
I2
B
 Iy=2.4x60^3/12+50X2^3/12=43233cm4
 I2=2X100^3/12+2x(30x4^3/12+30x4x5
2^2)=815947cm4
2 2)=815947cm
 d1= (302.4-100-11.94)=190.46cm
 d2= 190.46+100/2+4)=244.46cm
 B=930cm
 Upon calculating the
I1, the section is
composed of part of
composed of part of
the web plate (25
twxtw), vertical stiffener
assumed 250x20 mm
assumed 250x20 mm
(satisfying local
buckling) and the
b k t i t b
bracket is to be
defined according to
max. distance allowed
by train edges.
 Calculate the centriod
 X=(25x2x1+40x2x22+
 X=(25x2x1+40x2x22+
50x2x43+25x2x56.5)/(
2x(25+40+50+25)=31.
9
9cm
 I1=25x2x30.9^2+40^3x
2/12+40x2*9.91^2+50
EI
B
d
EI
d


2
3 2
2
2
1
3
1

x2x11^2+2x25^3/12+2
x25x24.6^2=111226c
m4 ok
m
a
cm
e
a
EI
L
cm
e
y
u 










25
.
2
379
2
6
.
2
*
225
*
43233
*
2100
*
5
.
2
5
.
2
2
6
.
2
815947
*
2100
*
2
930
*
2
^
46
.
244
111226
*
2100
*
3
3
^
46
.
190
4
4 

3- Design of Stiffeners
 This includes the following tasks:
D i f ti l tiff (Wh th d b i
1. Design of vertical stiffeners (Whether end bearing or
longitudinal stiffeners)
2. Design of horizontal stiffeners
g
Importance of stiffeners
 Reducing slenderness ratio of web plate
 Increase the shear capacity of web plate
p y p
Location of stiffeners
 Vertical stiffeners are located at location of X-
girders and at supports
 Horizontal stiffeners at a distance of d/5 from
compression flange and at d/2
A- Vertical Stiffeners
Compression Flange
x
Tension Flange
The outstanding length of vertical stiffeners
1- stiffeners in pairs x  dw/30 + 5 cm
2- single stiffeners x dw/30 + 10 cm
 Vertical intermediate stiffeners composed of single or
i f t i l ti hil E d b i tiff
pair of symmetrical sections while End bearing stiffeners
should be in pairs fastened on each side of the web
 End bearing stiffeners should be well ground or
machined to fit tightly against the top and bottom flange
angles and should never be crimped.
 Vertical stiffeners act as a compression members with
 Vertical stiffeners act as a compression members with
buckling length equal to 0.8dw
 For the sake of design of the vertical stiffeners it will be
considered as a column of cross section consisting of
considered as a column of cross section consisting of
the area of angles and a certain length of the web ( 25
tw for intermediate vertical stiffeners and 12 tw for end
bearing stiffeners)
bearing stiffeners).
6tw
6tw
25tw
End Bearing
Stiffener
Stiffener
Intermediate
• End Bearing Stiffeners
 Design Steps:
 1- Define the design force d.F (Max. Reaction at support)
 2- Choosing stiffeners in pairs x  dw/30 + 5 cm
 3- Required area of End bearing stiffeners
A d F/1 t/ 2 A + 12t 2
 Areq = d.F/1 t/cm2  Astiff + 12tw
2
 Astiff = (Areq - 12tw
2)
 4- Choose stiff. sections to avoid local buckling such that
f
t
x 21

 5- Calculate the slenderness ratio of the proposed column as follows
 calculate moment of inertia and cross sectional area Ix & A &
 Ix h
lb 8
0
y
stiff f
t

6- Calculate the permissible buckling stress Fpb
 7 Check that F = d F / A  F
A
Ix
i 
i
h
i
l w
b 8
.
0



 7- Check that Fact = d.F / A  Fpb
 8- Design the weld between the stiffeners and the web plate such that the weld
in upper and lower thirds can resist the whole design force
•Intermediate Vertical Stiffeners
 Design Steps:
 1- Define the design force d F = act
y
d Q
F
Q 






 1
35
.
0
65
.
0
 1 Define the design force d.F =

 2- Choosing single stiffeners x  dw/30 + 10 cm
 3- Required area of Intermediate vertical stiffeners
act
b
d Q
q
Q 



q
 Areq = d.F/1 t/cm2  Astiff + 25tw2
 Astiff = (Areq - 25tw2)
 4- Choose stiff. sections to avoid local buckling such that
f
t
x 21

 5- Calculate the slenderness ratio of the proposed column as follows
 calculate moment of inertia and cross sectional area Ix & A &

y
stiff f
t
I h
l 8
0


6- Calculate the permissible buckling stress Fpb
A
Ix
i 
i
h
i
l w
b 8
.
0



p
 7- Check that Fact = d.F / A  Fpb
 8- Design the weld between the stiffeners and the web plate such that the
weld in upper and lower thirds can resist the whole design force
•Horizontal Stiffeners
 The Egyptian code of practice requires that the
hori ontal stiffeners satisfies the follo ing
horizontal stiffeners satisfies the following
stiffness:
F hl Stiff At d/5 t f i ti >4d(t )3
 For hl. Stiff. At d/5, moment of inertia >4d(tw)3
 For hl. Stiff. At d/2, moment of inertia>d(tw)3
 Local buckling should be checked to satisfy the
relation of x 21

y
stiff f
t

4-Curtailment of Flange Plates
 Why curtailment is needed?
 Bending moment varies along bridge span, therefore it may be
i t h th l t i d ti t t i
economic to change the plate girder section to get maximum
utilization of steel strength.
Ho co ld e specif the c rtailment location?
 How could we specify the curtailment location?
 based on developed formulas by Johnson et al [1] to find the
minimum volume of steel that will yield minimum steel weight
y g
1. For Parabolic variation of bending moment
for simple or continuous girder
6
.
1
w
b
f
A
F
d
M
A 

f2
A
f1
A
6
.
max
2
w
b
f
A
F
d
M
A 

L
x
 
2
.
.
3
2
2
3
1
2
L
A
x
Lx
x
L
L
M
x
A
x
L
A
Vol f
f



 




 M Mmax
6
.
2
.
. 2
max L
A
L
x
Lx
x
L
L
F
d
M
Vol w
b








 

4
0
.)
( 2
2






 L
x
L
Lx
x
vol
5
A
and
3
3
3
0
f1







x
Lx
x
x
9
Af2

2. For Parabolic variation of bending
g
moment for cantilever girder
3
2
2
max






 

 wL
A
x
x
L
L
M
vol
3
0
)
(
6
.
2
2
2









b
L
x
L
x
vol
L
F
d
vol
1
3
3
0
)
(
1






f
A
x
L
x
x
3
1
2
1

f
f
A
5- Connection between Flange
and web plates
 Connection is either by using bolts or welds
m
1.5mm
Procedure
 ECP recommends continuous fillet weld between flange
and web plates in case of dynamic loading
 The size of welding is given by
s
f
QY
q 2

 Where
 Q = maximum shearing force at support
s
f
I
Q
q weld 2
.


g pp
 Y = first moment of area of flange plate about centroidal axis of the
section
I M t f i ti f l t i d
 I = Moment of inertia of plate girder
 s = size of welding
 f ld = allowable stresses in fillet weld = 0 2Fu
 fweld allowable stresses in fillet weld 0.2Fu
 Fu = ultimate strength of the base metal.
Minimum sizes of weld
tmax S mm
tmax
mm
S mm
10 4
10-20 5
20 30
20-30 6
30-50 8
50-100 10
Fatigue strength of the fillet weld under the effect of shear flow due to
live load plus impact should be checked, the connection is detailed as
class D (Group 3 Fasteners)
Example
 Given: Qt=125 25t& Ql l=57 15t I=4 267 213cm4 &
 Given: Qt 125.25t& Ql.l 57.15t , I 4,267,213cm4 &
M.G.2Pl#600X30/1900X16mm, St. 37
 Design of the connection between the flange plate and the web plate.
 Maximum shear flow is at sec 3 where Q=125 25t
 Maximum shear flow is at sec. 3 where Q 125.25t.
 Y=first moment of area of flange plate about N.A.
 3
370
,
17
)
95
5
.
1
(
3
60 cm
x
x
Y 


x
Y
Q 370
17
25
125
 cm
t
x
I
Y
Q
q /
51
.
0
213
,
267
,
4
370
,
17
25
.
125
.



 Assuming direct contact between the web plate and the flange
cm
x
F
Sx
q 1
2
.
0
2

therefore,
mm
cm
x
x
S
cm
x
F
Sx
q u
6
35
.
0
6
.
3
2
.
0
2
51
.
0
1
2
.
0
2




based on the maximum thickness of
flange plate = 30mm.
flange plate 30mm.
 Checking the fatigue resistance where 60% of live load is only
considered i.e. 0.6x57.15=34.29t.
 The shear flow due to this live load cm
t
x
q /
14
0
370
,
17
29
.
34
 The shear flow due to this live load cm
t
q I
ll /
14
.
0
213
,
267
,
4


 The allowable stress range based on No. of stress cycles of 2E6
and Detail D Group 3, is 0.71t/cm2
.
p

safe
O.k
1
.
0
14
.
0
71
.
0
2
2
cm
S
Sx
q
SxF I
ll
sr





 
6- Splices
 why a plate girder may be spliced?
y p g y p
 Un-sufficient plates lengths (Web plates ≈ 6m long,
Flange plates ≈12-18m).
Th d i d i li d j i id
 The designer may desire to use spliced joints to aid
in cambering.
 Change the girder cross section to fit the actual
 Change the girder cross section to fit the actual
bending moment.
 Transportation of full length plate girders plays an
p g p g p y
important role in locating spliced joints. Highway
road system conditions, maximum limit of legal
loads over existed bridges and maximum crane
loads over existed bridges and maximum crane
capacities limits the maximum length and weight of
plate girders to be transmitted in one time.
Shop Splicing
 Generally, flange and web plates are spliced using single or
double V-joints.
 J and U joints require the least amount of weld of metal but
 J and U joints require the least amount of weld of metal but
require the plates to be prepared by planning or milling which is
impractical in most structural fabricating shops.
This limits the preparation to flame beveling giving a V joint
 This limits the preparation to flame beveling giving a V-joint.
Single V-joint may be acceptable if the plate thickness is up to
25mm.
 For thicker plates double V-joints are preferred since they require
less weld metal.
 It should be remembered that a single V-joint will produce more
g j p
angular distortion which is increased rapidly as the flange
thickness increases.
Design forces
 Splices in webs of plate girders must be
designed to resist the moments and shearing
designed to resist the moments and shearing
forces at that section. The principle stresses
in welds are determined from:
in welds are determined from:
 The greatest bending moment at the splice
d th di h i f
and the corresponding shearing force.
 The greatest shearing force at the splice and
the corresponding bending moment.
q
f
Fig. (17) Staggering compression and tension flanges butt weld
The stresses in butt welds:
F th b
weld
Good
for
35
.
0

 y
F
A
Q
q
 For the web
weld
Excellent
for
0.385Fy

y
w
A
 For the flange
weld
Good
for
0.4F
0.7x0.58F
i.e.
7
.
0 y
y 


 pt
F
I
My
f
 For the flange
weld
Excellent
for
0.58Fy

I
Field Splicing
 Arrangement: Generally each girder of a bridge is
assembled of two or three parts at the bridge
location cite
location cite.
 Methods: The girder assembly is carried out either
by welding or by bolting.
 Design forces: The ECP [2] cl. 7.5 recommends
that, splices should be designed on the maximum
bending resistance of the girder section and the
bending resistance of the girder section and the
actual shearing force at the splice location.
 Execution: Generally welded field splices requires
y p q
testing either by ultrasonic, X-ray or any other
testing technique which increases the cost.
Welded field splices
the German window splices as shown in Fig. (18) Which is assembled as
follows:
(2)
(4)
(2)
(3)
(1)
(3)
(1)
(2)
(3)
(1)
(3)
(1)
German Window
Fig. (18) The German window for field splice
 A short portion of web is omitted and the adjacent parts of the web are
shop welded to the flanges (see ends of weld 1).
 The flanges welded first where they are not restrained by the web.
Moreover, the roots of these welds are fully accessible.
Th i d i th i i i f th b i th i t d It i
 The window i.e. the missing piece of the web is then inserted. It is
slightly curved so that no shrinkage stresses will arise when the piece is
welded to the remainder of the web.
 The remainder welds between the web and the flanges are deposited
 The remainder welds between the web and the flanges are deposited
last.
Bolted field splice
Bolted field splice
Q Q Q
Q
Q Q
S2
S2
Q
Q
S2 S2
Detail of Field Splice in bolted Main Girder
Flange Pl. Spl. : Direct Method
m m
m
m
m
m
in welded plate girder
Detail of Field Splice
g p
Flange < Spl. : Two Cuts in welded plate girder
Q
Q tsp2
S2 S2
m m m m m
m
Flange Pl Spl : Direct Method
Detail of Field Splice in bolted Main Girder
m m m m m
m
Flange Pl. Spl. : Direct Method
Flange < Spl. : Two Cuts
Remember
Ignorance with Code
leads to
leads to
Thank you
Thank you

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Design of Main Girder [Compatibility Mode].pdf

  • 1. Design of Bridge g g Main Girders According to ECP According to ECP Assis. Prof. Dr. Ehab B. Matar
  • 2. Design Phases of Main Girders 1. Structural analysis for the main system determining the max. and min. straining actions at critical sections 2. Design of Web Plate g 3. Design of Flange Plate 4. Design of Stiffeners (end bearing and intermediate) 5 Design of Connections between web plate and flange plate 5. Design of Connections between web plate and flange plate 6. Design of Splices 7. Check fatigue for all details
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  • 12. 1- Structural Analysis  Structural analysis is carried out using either influence lines, grillage analysis or finite elements depending on complexity of grillage analysis or finite elements depending on complexity of structures and its importance.  Max. and Minimum shear, moments, reactions…. are determined at critical sections at critical sections. Stress range Stress range Stress range
  • 13. 2- Design of Web Plate  This includes the following tasks: 1. Determining Web height 2 Determining Web thickness 2. Determining Web thickness 3. Checking shear Buckling
  • 14. 2.1 Web height  Overall depth, h:  Lo/18 ≤ h ≤ Lo/12 (highway two lanes) L /10 ≤ h ≤ L /7 ( il i l t k)  Lo/10 ≤ h ≤ Lo/7 (railway single track)  For double tracks railway or four lanes roadway, increase the above limits by 60-85% the above limits by 60 85%  If the maximum moment is known; the web height can be approximately calculated as 3 3 7 . 5 3 . 5 2 3 or b b F M F Mk d h     d= plate girder depth (cm)  M= maximum bending moment (t.cm) k ratio of height to thickness of eb plate 100 b b  k= ratio of height to thickness of web plate  100  Fb= allowable bending stress ≈ 0.58 Fy
  • 15. 2.2 Web Thickness  web thickness, tw:  tw ≥8mm y w F t d In 830 case any *  y w F t d 190 used are stiffeners sverse when tran *  y F t d 320 used stiff. e transvers and d/5) (at al longitudin When *  y w F t
  • 16. 2 3 Shear Buckling 2.3 Shear Buckling
  • 17.
  • 18.  No need to check shear buckling resistance if :  No need to check shear buckling resistance if :  for un-stiffened web  for stiffened web y w w F t d / 105 /  q w w F k t d / 45 /  y w w F 1 0 f ) / 34 5 ( 4 shear for factor buckling K 2 q   where /d d 0 . 1 for ) (4/ 5.34 1.0 for ) / 34 . 5 ( 4 2 2             where /d d1   where d d1
  • 19. Shear Buckling Resistance  If the above mentioned limits are exceeded the shear buckling resistance should be checked as follows: y w F t d Calculate *   q q q K 0.35F q then 8 . 0 For * 57 Calculate y b      y q q q F 9 . 0 35 . 0 ) 0.625 - (1.5 q then 2 . 1 0.8 For * b y      y q q F 35 . 0 * 9 . 0 q then 2 . 1 For * b    
  • 20.  It should be noted that longitudinal stiffener at mid depth would be ff ti f ti bj t d t h th th t more effective for sections subjected to pure shear than that positioned at d/5 for pure bending.  For continuous plate girder, the web panel over an interior support will be subjected to simultaneous action of bending support will be subjected to simultaneous action of bending moment and shearing force. Therefore:  If the actual shear stress qact ≤0.6qb then the allowable bending stresses in the girder flanges will not be reduced and should stresses in the girder flanges will not be reduced and should not exceed 0.58Fy.  If the actual shear stress qact >0.6qb then two alternatives may be followed. The first is to reduce the allowable bending g stress for flange plates according to the following interaction equation. y act b F q F               36 . 0 8 . 0  The second alternative is to design the girder flanges to y b b q         g g g resist the whole acting bending moment without any participation of web for resisting bending moment without reducing the allowable bending stress.
  • 21. Example Design a continuous two spans welded plate girder as shown below for a roadway bridge. The cross girders are arranged each 2.4m. The deck slab is 20cm thick and the asphalt cover is 10cm. The steel used for the design of all elements is St. 37. Moreover, design a field splice located at 16.8m from the end support. The St. 37. Moreover, design a field splice located at 16.8m from the end support. The bending moments and shearing forces at the critical locations are tabulated as follows: Sec. Md.l (t.m) Qd.l (t) Mll+I (t.m) Qll+I (t) 1 0 +38.2 0 +50.8 2 +171 0 +267 +4 43 2 +171 0 +267 +4.43 3 -305.3 -63.6 -296 -61.65 4 +96 -33.07 +96.69,-98.63 -34.92,+3.36 Solution  Proportioning of plate girder  cm cm F Mk d b 190 186 4 . 1 * 2 100 * 100 * ) 3 . 305 296 ( * 3 2 3 3 3      where k is assumed 100  Design of web plate  t t d 56 1 190 190 /     cm t F t d w y w 56 . 1 122 /      By using vertical stiffeners arranged @2.4m (distance between cross girders), then,  26 . 1 240 1    d  190 d  85 . 7 ) 26 . 1 /( 4 34 . 5 ) / 4 ( 34 . 5 2 2       q k  37 . 81 4 . 2 85 . 7 45 45    y q w F k t d 190  thcikness large a is which 34 . 2 37 . 81 190 cm tw     Assume tw = 16mm and check shear buckling resistance.  2 . 1 8 . 0 15 . 1 85 . 7 4 . 2 57 6 . 1 190 57       q q y w q k F t d   q  2 / 66 . 0 ) 4 . 2 35 . 0 )( 15 . 1 625 . 0 5 . 1 ( ) 35 . 0 )( 625 . 0 5 . 1 ( cm t q x x F q b y q b          safe / 41 . 0 6 . 1 190 25 . 125 2      b w q cm t x A Q q 
  • 22. 3- Design of Flange Plate  This includes the following tasks: 1. Determining Flange cross section (using Flange Area Method) Method) 2. Determining Flange width and thickness 3. Checking Bending Stresses
  • 23. 3.1 Flange Area Method MY  Plate Girder    3 2 d d I MY  c tf b           12 2 2 2 3 2 3 2 w f d t d A I c d           6 2 12 2 2 3 2 w f w f A A d d t d A I Welded Plate Girder         6 / w f A A d Y I          w f b A A d M F      6 f
  • 24. A d F M A w b f 6    A d F M A d F M A w w f 8 4 3 * 6 @4 arranged bolts assume BUS riveted or bolted For       d C b t b A where d F d F f f b b % 30 20 2 ; * 8 4 6     Section class Part Stress Profile C tf C tf D b 3.2 Local Buckling limits Section class Part Stress Profile Compact Flange Uniform Comp. Rolled Sec. dw tw dw tw Rolled section Welded section t h t y f F t C / 9 . 16 /  p section g p B.U.S Non-compact section Flange Uniform Comp. Rolled Sec. y f y f F t C / 3 . 15 /  y f F t C / 23 /  section B.U.S y f F t C / 21 / 
  • 25. Remember  Whenever the width / thickness ratio of compression flange exceeds the aforementioned limits, the flange should be treated as a slender section and the effective flange be treated as a slender section and the effective flange area should be calculated to account for local buckling.  The thickness of flange plates as well as web  The thickness of flange plates as well as web plates should be reduced by 1.0mm in design calculations due to the effect of undercut in welding unless special ti i th ldi t h i t k precautions in the welding technique are taken.
  • 26. Note that:  When plates with unequal thickness or  Change of flange plate width or thick. q width butt welded together, the thicker or g wider plate should be tapered with a slope 2−4mm 1 4 4 1 not exceeding one to four as shown 2mm R = 6 0 c m R
  • 27. 3.3 Allowable Compressive Stresses The allowable compressive stresses in the compression flange depend on whether the flange is braced laterally or un- flange is braced laterally or un- braced. The lateral unsupported length of the compression flange Lu is calculated as follows: For deck railway bridges with For deck railway bridges with open timber floor where there exist upper wind bracing or not, and with the existence of cross girders that are rigidly connected girders that are rigidly connected to the main girder compression flange, then, Lu = distance between x-girders. For deck railway bridges with For deck railway bridges with ballasted floor or for roadway bridges where the compression flange is supported by continuous reinforced concrete continuous reinforced concrete or steel deck, where the frictional or connection of the deck to the flange is capable to resist a lateral force of 2% of the flange lateral force of 2% of the flange force at maximum bending moment, then, Lu = 0.
  • 28. For continuous deck roadway or dec oad ay o railway bridges where the compression flange at interior supports at interior supports is located in the bottom side of the girder away from the g y deck slab, then, Lu = the distance between the centers f i t ti f th of intersection of the lower wind bracing with the compression flange compression flange Lu = if there is no lower wind bracing or transverse bracing g then Lu is taken as the distance from the point of maximum bending moment to bending moment to the point of contra- flexure.
  • 29. •Lateral unsupported length for through bridge (+M a e a u suppo ed e g o oug b dge ( region)  The lateral unsupported length of the compression flange is taken as the full 4 * 5 . 2 a EI Lu y   compression flange is taken as the full girder length if the compression flange is unrestrained against lateral bending. If the cross girders and the stiffeners forming U-frames, then, Wh 2 2 2 1 3 1 2 3 EI B d EI d     Where  E= The Young's modulus of steel (t/cm2)  Iy= moment of inertia of the chord member about the Y-Y axis (cm4) as shown d2 d1 I1 shown  a = distance between the U- frames (distance between x- girders)   = the flexibility of the U- frame d1 di t f th t id f th I2 I1  d1 = distance from the centroid of the compression flange to the nearest face of the cross girder of the U-frame.  d2 = distance from the centroid of the compression flange to the centroidal axis B compression flange to the centroidal axis of the cross girder  I1 = Moment of inertia of the vertical member forming the arm of the U-frame about the axis of bending.  I2 = Moment of inertia of the cross girder  B = distance between centers of consecutive main girders connected by U-frame.
  • 30. Continue Example 7.5m 2.5m 1.25 1.0m 1.0m 1.25 2.5m Continue Example Bridge Cross section 24m 24m 1 2 4 3 16.8  Flange area Method  For sec. 3, moment and shear acting together, therefore, checking % 60 62 . 0 66 . 0 41 . 0    b q q , then, a reduction in the allowable bending stress should be carried out as follows  Assuming the compression flange is braced laterally by the lower wind bracing which has joints @240cm (distance between cross girders), then Lu=240cm.  Checking whether lateral torsional buckling controls the allowable compression stresses or not as follows: f x b 60 20 20 24m 24m should be carried out as follows          2 / 38 . 1 4 . 2 66 . 0 / 41 . 0 36 . 0 8 . 0 / 36 . 0 8 . 0 cm t F F q q F b y b b       Calculating the flange area at sec.3 as follows:  2 66 . 178 6 6 . 1 190 190 38 1 2 3 . 601 6 cm x E A d M A w f       u y f L cm x F b    6 . 774 4 . 2 60 20 20  u b y f b y f L cm C F d A x x x x x C F d A                   86 . 580 . . 1380 3 . 601 78 . 323 3 . 0 3 . 601 78 . 323 05 . 1 75 . 1 ( 4 . 2 196 60 3 1380 . . 1380 2 6 190 38 . 1 6 x d Fb f  Assuming bf=0.3d=0.3x190=57cm→60cm  Then tf=178.66/60=2.98cm→3cm  y f F t c 21 73 . 9 30 2 / 16 300      Therefore Fbc =1.38t/cm2 & Ft=1.4 t/cm2  / 38 . 1 543 , 43 2 3 . 601 2 cm t E F     O.K safe in both tension and compression.  Checking fatigue stress by considering only 60% of the live loads are acting i.e. 0.6x274.32=164.6tm. 2 6 164 E  However, although the flange satisfied the limit of compact section ( y F / 3 . 15 ) but the web is non-compact, therefore, the whole section will be considered non-compact.  Calculating the flange area at sec.2 as follows:  2 114 6 . 1 190 2 438 x E A M A w  Stress range = 2 / 378 . 0 543 , 43 2 6 . 164 cm t E   For ADTT >2500 truck, No. of stress cycles =2E6 and for welded plate girder Class B' is taken therefore the allowable fatigue stress range Fsr=0.85t/cm2 . Therefore, the section is safe.  Checking Actual stresses at section 2      2 3 3 4 2 50 6 1 190 x x    2 114 6 190 4 . 1 6 cm x d F A w b f       Assuming bf=50cm  Then tf=114/50=2.28cm→2.4cm  y f F t c 21 08 . 10 24 2 / 16 250            3 4 2 194 , 32 , 714 , 135 , 3 2 . 1 95 4 . 2 50 12 4 . 2 50 2 12 6 . 1 190 cm Z cm I x x x x x I gross gross               Assuming the compression flange is braced laterally by the existence of R.C. deck directly rested over compression flange therefore, Lu=0. Therefore, there is no need to check Fltb.  Therefore Fb =1 4 t/cm2 & Ft=1 4 t/cm2 y f  Checking Actual stresses at section 3       3 4 2 3 3 543 , 43 , 213 , 267 , 4 5 . 1 95 3 60 12 3 60 2 12 6 . 1 190 cm Z cm I x x x x x I gross gross               Therefore Fbc 1.4 t/cm & Ft 1.4 t/cm  / 36 . 1 194 , 32 2 438 2 cm t E F     O.K safe in both tension and compression.  Checking fatigue stress by considering only 60% of the live loads is acting. The live load is ranged at this section between +250.5 tm and - 73.971 tm. Then,
  • 31. Example for through bridge  A railway through plate girder y g p g bridge of 27 m simple span has two main girders 9 m apart. The bridge is for double track and has bridge is for double track and has an open timber floor. The cross girders are arranged every 2.25 m. The bridge is provided by stringer  The bridge is provided by stringer bracing, while braking force bracing is not arranged. The f material of construction is steel 44; the weight of the timber floor for each track is 0.6 t/m’.  Calculate Lu considering, for main girder tw=20mm, dw=3000mm, M =1060mt Q =160t while Mmax=1060mt, Qmax=160t, while for XG Pl#1000x20/2Pl#300*40mm
  • 32. Solution  For the main girder, tw=20mm, dw=3000mm  Af=M/(dFb)-Aw/6 Af M/(dFb) Aw/6  Af=1060*100/(300*1.6)- 2*300/6=120.8cm2  Bf=0.2*300=60cm  tf>120.8/60>2.01cm  c/t <21/sqrt(F )t =2 4cm d2 d1 I1  c/tf<21/sqrt(Fy)tf=2.4cm  Z=(50x2x27.4+60x2.4x1.2)/(60x2.4+50 x2)=11.94cm I2 B  Iy=2.4x60^3/12+50X2^3/12=43233cm4  I2=2X100^3/12+2x(30x4^3/12+30x4x5 2^2)=815947cm4 2 2)=815947cm  d1= (302.4-100-11.94)=190.46cm  d2= 190.46+100/2+4)=244.46cm  B=930cm
  • 33.  Upon calculating the I1, the section is composed of part of composed of part of the web plate (25 twxtw), vertical stiffener assumed 250x20 mm assumed 250x20 mm (satisfying local buckling) and the b k t i t b bracket is to be defined according to max. distance allowed by train edges.  Calculate the centriod  X=(25x2x1+40x2x22+  X=(25x2x1+40x2x22+ 50x2x43+25x2x56.5)/( 2x(25+40+50+25)=31. 9 9cm  I1=25x2x30.9^2+40^3x 2/12+40x2*9.91^2+50 EI B d EI d   2 3 2 2 2 1 3 1  x2x11^2+2x25^3/12+2 x25x24.6^2=111226c m4 ok m a cm e a EI L cm e y u            25 . 2 379 2 6 . 2 * 225 * 43233 * 2100 * 5 . 2 5 . 2 2 6 . 2 815947 * 2100 * 2 930 * 2 ^ 46 . 244 111226 * 2100 * 3 3 ^ 46 . 190 4 4  
  • 34. 3- Design of Stiffeners  This includes the following tasks: D i f ti l tiff (Wh th d b i 1. Design of vertical stiffeners (Whether end bearing or longitudinal stiffeners) 2. Design of horizontal stiffeners g
  • 35. Importance of stiffeners  Reducing slenderness ratio of web plate  Increase the shear capacity of web plate p y p Location of stiffeners  Vertical stiffeners are located at location of X- girders and at supports  Horizontal stiffeners at a distance of d/5 from compression flange and at d/2
  • 36. A- Vertical Stiffeners Compression Flange x Tension Flange The outstanding length of vertical stiffeners 1- stiffeners in pairs x  dw/30 + 5 cm 2- single stiffeners x dw/30 + 10 cm
  • 37.  Vertical intermediate stiffeners composed of single or i f t i l ti hil E d b i tiff pair of symmetrical sections while End bearing stiffeners should be in pairs fastened on each side of the web  End bearing stiffeners should be well ground or machined to fit tightly against the top and bottom flange angles and should never be crimped.  Vertical stiffeners act as a compression members with  Vertical stiffeners act as a compression members with buckling length equal to 0.8dw  For the sake of design of the vertical stiffeners it will be considered as a column of cross section consisting of considered as a column of cross section consisting of the area of angles and a certain length of the web ( 25 tw for intermediate vertical stiffeners and 12 tw for end bearing stiffeners) bearing stiffeners). 6tw 6tw 25tw End Bearing Stiffener Stiffener Intermediate
  • 38. • End Bearing Stiffeners  Design Steps:  1- Define the design force d.F (Max. Reaction at support)  2- Choosing stiffeners in pairs x  dw/30 + 5 cm  3- Required area of End bearing stiffeners A d F/1 t/ 2 A + 12t 2  Areq = d.F/1 t/cm2  Astiff + 12tw 2  Astiff = (Areq - 12tw 2)  4- Choose stiff. sections to avoid local buckling such that f t x 21   5- Calculate the slenderness ratio of the proposed column as follows  calculate moment of inertia and cross sectional area Ix & A &  Ix h lb 8 0 y stiff f t  6- Calculate the permissible buckling stress Fpb  7 Check that F = d F / A  F A Ix i  i h i l w b 8 . 0     7- Check that Fact = d.F / A  Fpb  8- Design the weld between the stiffeners and the web plate such that the weld in upper and lower thirds can resist the whole design force
  • 39. •Intermediate Vertical Stiffeners  Design Steps:  1- Define the design force d F = act y d Q F Q         1 35 . 0 65 . 0  1 Define the design force d.F =   2- Choosing single stiffeners x  dw/30 + 10 cm  3- Required area of Intermediate vertical stiffeners act b d Q q Q     q  Areq = d.F/1 t/cm2  Astiff + 25tw2  Astiff = (Areq - 25tw2)  4- Choose stiff. sections to avoid local buckling such that f t x 21   5- Calculate the slenderness ratio of the proposed column as follows  calculate moment of inertia and cross sectional area Ix & A &  y stiff f t I h l 8 0   6- Calculate the permissible buckling stress Fpb A Ix i  i h i l w b 8 . 0    p  7- Check that Fact = d.F / A  Fpb  8- Design the weld between the stiffeners and the web plate such that the weld in upper and lower thirds can resist the whole design force
  • 40. •Horizontal Stiffeners  The Egyptian code of practice requires that the hori ontal stiffeners satisfies the follo ing horizontal stiffeners satisfies the following stiffness: F hl Stiff At d/5 t f i ti >4d(t )3  For hl. Stiff. At d/5, moment of inertia >4d(tw)3  For hl. Stiff. At d/2, moment of inertia>d(tw)3  Local buckling should be checked to satisfy the relation of x 21  y stiff f t 
  • 41. 4-Curtailment of Flange Plates  Why curtailment is needed?  Bending moment varies along bridge span, therefore it may be i t h th l t i d ti t t i economic to change the plate girder section to get maximum utilization of steel strength. Ho co ld e specif the c rtailment location?  How could we specify the curtailment location?  based on developed formulas by Johnson et al [1] to find the minimum volume of steel that will yield minimum steel weight y g
  • 42. 1. For Parabolic variation of bending moment for simple or continuous girder 6 . 1 w b f A F d M A   f2 A f1 A 6 . max 2 w b f A F d M A   L x   2 . . 3 2 2 3 1 2 L A x Lx x L L M x A x L A Vol f f           M Mmax 6 . 2 . . 2 max L A L x Lx x L L F d M Vol w b            4 0 .) ( 2 2        L x L Lx x vol 5 A and 3 3 3 0 f1        x Lx x x 9 Af2 
  • 43. 2. For Parabolic variation of bending g moment for cantilever girder 3 2 2 max           wL A x x L L M vol 3 0 ) ( 6 . 2 2 2          b L x L x vol L F d vol 1 3 3 0 ) ( 1       f A x L x x 3 1 2 1  f f A
  • 44. 5- Connection between Flange and web plates  Connection is either by using bolts or welds m 1.5mm
  • 45. Procedure  ECP recommends continuous fillet weld between flange and web plates in case of dynamic loading  The size of welding is given by s f QY q 2   Where  Q = maximum shearing force at support s f I Q q weld 2 .   g pp  Y = first moment of area of flange plate about centroidal axis of the section I M t f i ti f l t i d  I = Moment of inertia of plate girder  s = size of welding  f ld = allowable stresses in fillet weld = 0 2Fu  fweld allowable stresses in fillet weld 0.2Fu  Fu = ultimate strength of the base metal.
  • 46. Minimum sizes of weld tmax S mm tmax mm S mm 10 4 10-20 5 20 30 20-30 6 30-50 8 50-100 10 Fatigue strength of the fillet weld under the effect of shear flow due to live load plus impact should be checked, the connection is detailed as class D (Group 3 Fasteners)
  • 47. Example  Given: Qt=125 25t& Ql l=57 15t I=4 267 213cm4 &  Given: Qt 125.25t& Ql.l 57.15t , I 4,267,213cm4 & M.G.2Pl#600X30/1900X16mm, St. 37  Design of the connection between the flange plate and the web plate.  Maximum shear flow is at sec 3 where Q=125 25t  Maximum shear flow is at sec. 3 where Q 125.25t.  Y=first moment of area of flange plate about N.A.  3 370 , 17 ) 95 5 . 1 ( 3 60 cm x x Y    x Y Q 370 17 25 125  cm t x I Y Q q / 51 . 0 213 , 267 , 4 370 , 17 25 . 125 .     Assuming direct contact between the web plate and the flange cm x F Sx q 1 2 . 0 2  therefore, mm cm x x S cm x F Sx q u 6 35 . 0 6 . 3 2 . 0 2 51 . 0 1 2 . 0 2     based on the maximum thickness of flange plate = 30mm. flange plate 30mm.  Checking the fatigue resistance where 60% of live load is only considered i.e. 0.6x57.15=34.29t.  The shear flow due to this live load cm t x q / 14 0 370 , 17 29 . 34  The shear flow due to this live load cm t q I ll / 14 . 0 213 , 267 , 4    The allowable stress range based on No. of stress cycles of 2E6 and Detail D Group 3, is 0.71t/cm2 . p  safe O.k 1 . 0 14 . 0 71 . 0 2 2 cm S Sx q SxF I ll sr       
  • 48. 6- Splices  why a plate girder may be spliced? y p g y p  Un-sufficient plates lengths (Web plates ≈ 6m long, Flange plates ≈12-18m). Th d i d i li d j i id  The designer may desire to use spliced joints to aid in cambering.  Change the girder cross section to fit the actual  Change the girder cross section to fit the actual bending moment.  Transportation of full length plate girders plays an p g p g p y important role in locating spliced joints. Highway road system conditions, maximum limit of legal loads over existed bridges and maximum crane loads over existed bridges and maximum crane capacities limits the maximum length and weight of plate girders to be transmitted in one time.
  • 49. Shop Splicing  Generally, flange and web plates are spliced using single or double V-joints.  J and U joints require the least amount of weld of metal but  J and U joints require the least amount of weld of metal but require the plates to be prepared by planning or milling which is impractical in most structural fabricating shops. This limits the preparation to flame beveling giving a V joint  This limits the preparation to flame beveling giving a V-joint. Single V-joint may be acceptable if the plate thickness is up to 25mm.  For thicker plates double V-joints are preferred since they require less weld metal.  It should be remembered that a single V-joint will produce more g j p angular distortion which is increased rapidly as the flange thickness increases.
  • 50. Design forces  Splices in webs of plate girders must be designed to resist the moments and shearing designed to resist the moments and shearing forces at that section. The principle stresses in welds are determined from: in welds are determined from:  The greatest bending moment at the splice d th di h i f and the corresponding shearing force.  The greatest shearing force at the splice and the corresponding bending moment.
  • 51. q f Fig. (17) Staggering compression and tension flanges butt weld The stresses in butt welds: F th b weld Good for 35 . 0   y F A Q q  For the web weld Excellent for 0.385Fy  y w A  For the flange weld Good for 0.4F 0.7x0.58F i.e. 7 . 0 y y     pt F I My f  For the flange weld Excellent for 0.58Fy  I
  • 52. Field Splicing  Arrangement: Generally each girder of a bridge is assembled of two or three parts at the bridge location cite location cite.  Methods: The girder assembly is carried out either by welding or by bolting.  Design forces: The ECP [2] cl. 7.5 recommends that, splices should be designed on the maximum bending resistance of the girder section and the bending resistance of the girder section and the actual shearing force at the splice location.  Execution: Generally welded field splices requires y p q testing either by ultrasonic, X-ray or any other testing technique which increases the cost.
  • 53. Welded field splices the German window splices as shown in Fig. (18) Which is assembled as follows: (2) (4) (2) (3) (1) (3) (1) (2) (3) (1) (3) (1) German Window Fig. (18) The German window for field splice  A short portion of web is omitted and the adjacent parts of the web are shop welded to the flanges (see ends of weld 1).  The flanges welded first where they are not restrained by the web. Moreover, the roots of these welds are fully accessible. Th i d i th i i i f th b i th i t d It i  The window i.e. the missing piece of the web is then inserted. It is slightly curved so that no shrinkage stresses will arise when the piece is welded to the remainder of the web.  The remainder welds between the web and the flanges are deposited  The remainder welds between the web and the flanges are deposited last.
  • 54. Bolted field splice Bolted field splice Q Q Q Q Q Q S2 S2 Q Q S2 S2 Detail of Field Splice in bolted Main Girder Flange Pl. Spl. : Direct Method m m m m m m in welded plate girder Detail of Field Splice g p Flange < Spl. : Two Cuts in welded plate girder
  • 55.
  • 56. Q Q tsp2 S2 S2 m m m m m m Flange Pl Spl : Direct Method Detail of Field Splice in bolted Main Girder m m m m m m Flange Pl. Spl. : Direct Method Flange < Spl. : Two Cuts