Chapter 11 Diaphragms and Cross Frames
Bridge Engineering
1
Introduction –Functions of diaphragms and cross frames
Used to resist lateral wind loads by transferring them from the superstructure up into the deck Large stiffness of the deck in horizontal plane will carry the loads to the supports At the supports, the diaphragms or cross frames transfer the loads down from the deck to bearings Bridge Engineering
2
Introduction –Functions of diaphragms and cross frames
They also improve vertical loads distribution to longitudinal members If closely spaced and placed at supports, they transfer live loads more uniformly They create lateral stability during construction.
Bridge Engineering
3
Different types of bracings and diaphragms
Cross frames
X type K type
Non-composite diaphragms Composite diaphragms Top chord bracing Steel box girder Distortional bracing Tie, etc. Bridge Engineering
4
Different types of bracings and diaphragms
Bracings to reduce distortion and rotation
Ties Distortional bracing Torsion box Top chord bracing End diaphragms Bridge Engineering
5
Different types of bracings and diaphragms
Bridge Engineering
6
Different types of bracings and diaphragms
Bridge Engineering
7
Design considerations
Intermediate ones
End ones
Carry proportional to tributary area Carry all accumulated loads to the bearings
Do not use too many Code practice, more or less arbitrary
Bridge Engineering
8
Beam-and-Slab Bridges
Improve load distribution charactersitics Characterizing parameters of such bridges are: α=
( Dxy + D yx + D1 + D2 ) 2( Dx D y ) 0.5
b ⎛⎜ Dx ⎞⎟ θ= ⎜ ⎟ L ⎝ Dy ⎠
0.25
Minimum 2 diaphragms or bracings per span near to one third of the span, or Bridge Engineering
9
Beam-and-Slab Bridges
Minimum 3, placed at quarter and mid span points Reduced form of α is valid for characterizing load distributions in beam and slab bridges α=
( Dxy + D yx ) 2( Dx D y ) 0.5
D y =(total flexural rigidity of deck plus diaphragm)/span In calculating α ignore the torsional rigidity of the diaphragms Bridge Engineering
10
Beam-and-Slab Bridges
Recommended design procedure
Use (α , θ ) method for slab-on-girder bridges, if there min. 2 diaphragms per span, or 3 spans per span Calculate α as follows:
( D +D ) α= 2(D D )0.5 xy
x
yx
y
D y =(total flexural rigidity of deck plus diaphragm)/span Bridge Engineering
11
Beam-and-Slab Bridges
If plate type diaphragms, obtain effective flexural rigidity by considering diaphragm bending about its neutral axis If cross-bracings, calculate effective moment of inertia as follows Ad s 3 h 2 I effective = 6 L3d Ad is the cross-sectional are of diagonal members
Bridge Engineering
12
is the length of diagonal Ld = s + h members s is the spacing of the longitudinal girders h is the depth of the cross bracing 2
2
Relate diaphragm size to optimum value of θ No need for heavy diaphragms to achieve optimum transverse load distribution.
Ad
h
s
Bridge Engineering
13
Example
Bridge Engineering
14
Example
Bridge Engineering
15
Example
Bridge Engineering
16
Example
Bridge Engineering
17
Example
Bridge Engineering
18
Example
Bridge Engineering
19
Example
Bridge Engineering
20
Example
Bridge Engineering
21
Example
Bridge Engineering
22
Example
Bridge Engineering
23
Example
Bridge Engineering
24
Example
Bridge Engineering
25
Example
Bridge Engineering
26
Example
Bridge Engineering
27
Example
Bridge Engineering
28
Example
Bridge Engineering
29
Example
Bridge Engineering
30
Example
Bridge Engineering
31
Example
Bridge Engineering
32
Example
Bridge Engineering
33
Example
Bridge Engineering
34
Example
Bridge Engineering
35
Example
Bridge Engineering
36
Example
Bridge Engineering
37
Example
Bridge Engineering
38
Example
Bridge Engineering
39
Example
Bridge Engineering
40
Example
Bridge Engineering
41
Example
Bridge Engineering
42
Example
Bridge Engineering
43
Example
Bridge Engineering
44
Steel Box Girder Bridge
Bracings and diaphragms are to resist wind and construction loads and maintain stability Stresses due to bending and torsion as a result of eccentric live loads are:
Bending stress Mixed torsion stress Bending distortion stress Torsional distortion stress Bridge Engineering
45
Steel Box Girder Bridge
Bracing systems
Ties Distortional bracings Torsion Box Top chord bracings End Diaphragms
Bridge Engineering
46
Steel Box Girder Bridge P
Pc
Pc
Pt
Pt
ex
Loading C om ponents Pc
Pc
Longitudinal bending
Pt
Bending distorsion
Pt
M ixed torsion
Torsional distorsion
Bridge Engineering
47
Bridge Engineering
48
Bridge Engineering
49
Bridge Engineering
50
Bridge Engineering
51
Bridge Engineering
52
Bridge Engineering
53
Bridge Engineering
54
Steel Box Girder Bridge Recommendations for design 1) Distortion during construction
Place ties at top flanges every 1/8 length of the span (overcome distortion from concentric construction loads) Place transverse web stiffeners that increase transverse web stiffness at least 50 times (overcome distortion due to construction twist loads) Bridge Engineering
55
Steel Box Girder Bridge
Horizontal bracing shall be placed below the level of top flanges Inter-connecting bracings shall be mounted between boxes. These bracing systems shall be placed at the same sections as the interior distortional bracings
Bridge Engineering
56
Steel Box Girder Bridge 2) Overall Stability during construction
If
M0 < 0.15 , where M 0 is the mid-span M cr
bending moment and M cr is the cracking moment
Use linear analysis with St. Venant and warping stiffness to compute girder rotations
For higher loads,
Calculate real rotations and warping stiffness considering non-linear effects Bridge Engineering
57
CHBDC requirements
1) General requirements
5.4.6. (p 170) A 5.1 d (p 202)
2) Concrete
8.18.5 Diaphragms (p 367) 8.20.8 Concrete girder (p 371) 8.22.3 Segmental construction (p 372)
Bridge Engineering
58
CHBDC requirements
3) Steel
10.10.9 (p 462) lateral bracing, cross –frames and diaphragms 10.10.9.1 and 10.10.9.2, 10.10.9.3 Load distribution & stability
10.10.9 Composite beams and girders (p 462) load distribution and stability 10.12.6 Composite box girders (p 473)
10.13.5 Horizontally curved girders (p 474) 10.14.3 Trusses (p 480) 10.16.5 Orthotropic Decks (p 482) Bridge Engineering
59
Specific requirements
Bridge Engineering
60
CHBDC Specifications
End floor beams and end diaphragms under expansion joints that are exposed to surface runoff should be easily maintainable Floor beams and diaphragms at piers and abutments to be designed to allow jacking of the superstructure, unless longitudinal members can be jacked directly.
Bridge Engineering
61
CHBDC- Beams, Girders and Composite Beams
Spacing of intermediate diaphragms or cross-frames:
Lateral torsional buckling resistance of girders Need for transfer of lateral wind load Need for torsional resistance due to torsion load Design for lateral load + 1% of compression flange force, if girder not solely for lateral loads If considered in analysis, design for their share of load Bridge Engineering
62
CHBDC- Beams, Girders and Composite Beams
The bracing should be stable under the compression force that it receives from the compression flange Steel or concrete slab, if attached sufficiently to compression flange will suffice Place perpendicular to main girder, when supports are skewed more than 20 0 and design to the force they attract Unless otherwise justified by analysis, girder spans in excess of 50 m shall be provided with lateral bracing at or close to bottom flanges
Bridge Engineering
63
CHBDC- Beams, Girders and Composite Beams
Use cross-frames and diaphragms at piers or abutments of beam or girder bridges Use cross-frames as deep as practical Where practical, diaphragms shall support the end of the deck slab.
Bridge Engineering
64
CHBDC- Composite Box Girders
Internal diaphragms, cross-frames or other means, at supports to resist transverse rotation, displacements and distortion and transfer vertical, transverse and torsional loads to the bearings Consider the effect of access holes and provide adequate reinforcement Intermediate cross-frames and diaphragms to be used during fabrication, transportation and construction. Bridge Engineering
65
CHBDC- Composite Box Girders
Vertical stiffeners used as connecting plates for diaphragms or cross-frames shall be connected to both flanges Single box girder, place diaphragms and crossframes every 8 m unless shown cross-sectional distortion is not critical For multiple open box girders, the bracing of top flanges of the boxes should be provided adequately Put lateral bracing at top flange of single, through box section girders. Bridge Engineering
66
CHBDC- Composite Box Girders
Design the bracings for shear flow before concrete is cured. Also consider bending forces. The structural section assumed to resist the portion of factored horizontal wind or seismic loading in the plane of bottom flange shall consist of the bottom flange acting as the web and 12 times the thickness of the webs acting as the flanges.
Bridge Engineering
67
Horizontally curved girders
Unless otherwise approved, the girders shall be connected at each support by diaphragms to resist twisting of the girders Place diaphragms or cross-frames on I girders between supports to resist twisting. Extend them across the whole width of the bridge. Place diaphragms or cross-frames between box girders to resist torsion. Place them inside box girders in line with those in between girders. Treat them as main elements. They shall be as deep as the girders and shall carry all the load they attract.
Bridge Engineering
68
Horizontally curved girders
In addition, place extra diaphragms or crossframes to resist the distortional effects of eccentric loads on the cross-section. Lateral bracing for construction, wind and service load shall be placed on top flange of I girders or box girders.
Bridge Engineering
69
Trusses
Through-truss, deck-truss shall have top and bottom lateral bracing systems. If shallower than the chord, the bracing needs approval Connect the bracings to top and bottom chords effectively For through trusses, have portal bracing rigidly connected to the end post and top chord flanges.
Bridge Engineering
70
Trusses
For through trusses, portal bracings should take the full reaction of the top chords, and end posts should be designed accordingly. For through trusses, sway bracings shall be installed at necessary points. For deck trusses, install sway bracing at the plane of end posts. For deck trusses, install sway bracing at intermediate panel points, unless analysis shows unnecessary. Bridge Engineering
71
Trusses
For deck trusses, the sway bracing shall have the full depth of the truss below the floor. For deck trusses, the end sway bracing shall carry the entire upper lateral forces to the supports through the end posts. Bracings between straight compression members or flanges shall carry the shear force due to lateral loads plus 1% of the compression forces in the supported members. Bridge Engineering
72
Trusses
Factored compressive resistance of the column shall be at least equal to the maximum force in any panel of the top chord resulting from loads at the ULS. Vertical truss members, floor beams, and connections between them shall not carry less than (ULS) 8 kN/m lateral force applied at the top chord panel points.
Bridge Engineering
73
Orthotropic Decks
Place diaphragms or cross-frames at each support, sufficient to transmit lateral forces to the bearings and to resist transverse rotation, displacement and distortion. Place diaphragms or cross-frames at intermediate locations consistent with the analysis of the girders. Bridge Engineering
74
