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8/13/2019 Up-Down Stand Design
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S.NO. Page
No
1 Introduction
2 Estimation of Seismic Coefficent
3 Summary of Bearing Reactions
4 Design of End Diapghragm for Longitudinal
Seismic Forces
5 Design of Shear Key For Longitudinal
Seismic Forces
6 Design of Shear Key For Transverse
Seismic Forces
Appendix -A Analysisis of Precast Girder
Appendix -B Grillage Analysisis of Deck
For SIDL
Appendix -C Grillage Analysisis of Deck
For Live Load
Design of Diaphragms and Seismic Restrainer for bridge at ch. 55.460
Contents
ITEM
(Span Arrangement 27.59 m c/c Bearing)
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1.0 Introduction
This note presents the detailed design of diaphrams and Seismc restrainer for
bridge at ch 55.460 on proposed Rajkot-Jamnagar-Vadinar in Gujrat. The
bridge is 3 lane with a deck width of 12.0m and carriageway width of 8.75 m
with safe kerb and footpath.The supersrtuctrue comprises of Precast Post
Tensioned Beams with cast in situ deck slab on Elastomeric Bearings. The
Elastomeric bearings are primarily designed to cater for reactions and rotations
due to vertical loads and translations due to temeprature, shrinkage, creep and
elastic shortening.The seismic and braking forces are to be transferred through
concrete shear keyi.e. an upsatnad from pier cap. Under lonfgitudinal seismic
condition, the upstand transfers the loangitunal forces by abuting against End
Diapghragms of superstructure.
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2.0 Estimation of Seismic coefficient
Horizontal Seismic Coefficient ( cl 222.5 of IRC:6-2000)
h =
For Zone IV, Z = 0.24 ( Table 5 of IRC:6-2000)
Sa/g = 2.5 ( Fig 12 5 of IRC:6-2000)
R = 2.5
I = 1.5 (For Important Bridge)
Substituting for above values , we get
h = 0.18
Vertical Seismic Coeffic ient ( cl 222.3 of IRC:6-2000)
v = 0 5 h= 0.09
Considering the bridge location and the Seismic Zoning map of India as per Fig
11 of IRC:6-2200, the bridge is likely to fall in the boundary of zone
demarcation line between Zone III and Zane IV and therefore the higher zone
i.e. Zone IV has been considered for design and detailing.
(Z/2). ( Sa/g)
(R/I)
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3.0 Estimation of Bearing reactions
The summary of Bearings reactions are presnted in the subsequent sheets
The Dead Laod reactios i.e. weight of Precast girder and , deck slab are
obtained by analysis of Precast Girder ( Appendix A) and whereas those due to
SIDL and live laod are obtained by Grillage Analysis (Refer appendix B and
Appendix C)
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3.1 Synopsis of Bearing Reaction due to Dead Load & SIDL
27 m c/c EJ
26 m
3.00 m
1.5 m
C/L of Bridge
1.5 m
3.00 m
Fig. 6.1 Bearing Node Numbering
(Not to Scale)
Load Load Support Node Force-Y Total Total Support Node
Case List No. (t) V (t) MT (tm) No.
A 102 31.43 4.500 141.44 A 102
302 31.43 1.500 47.15 302
Distance
from C/L of
Bridge (m)
Associ ated
MT (tm)
cast
102
302
A
502
702
112
312
B
512
712
502 31.43 -1.500 -47.15 502
702 31.43 -4.500 -141.44 125.72 0.00 702
B 112 31.43 4.500 141.44 B 112
312 31.43 1.500 47.15 312
512 31.43 -1.500 -47.15 512
712 31.43 -4.500 -141.44 125.72 0.00 712
A 102 24.10 4.500 108.45 A 102
302 24.10 1.500 36.15 302
502 24.10 -1.500 -36.15 502
702 24.10 -4.500 -108.45 96.40 0.00 702
B 112 24.10 4.500 108.45 B 112312 24.10 1.500 36.15 312
512 24.10 -1.500 -36.15 512
712 24.10 -4.500 -108.45 96.40 0.00 712
A 102 55.53 4.500 249.89 A 102
302 55.53 1.500 83.30 302
502 55.53 -1.500 -83.30 502
702 55.53 -4.500 -249.89 222.12 0.00 702
B 112 55.53 4.500 249.89 B 112
312 55.53 1.500 83.30 312
512 55.53 -1.500 -83.30 512
712 55.53 -4.500 -249.89 222.12 0.00 712
A 102 18.92 4.500 85.14 A 102
302 6.70 1.500 10.05 302
502 6.70 -1.500 -10.05 502
702 18.92 -4.500 -85.14 51.24 0.00 702
B 112 18.92 4.500 85.14 B 112
312 6.70 1.500 10.05 312
512 6.70 -1.500 -10.05 512
712 18.92 -4.500 -85.14 51.24 0.00 712A 102 74.45 4.500 335.03 A 102
302 62.23 1.500 93.35 302
502 62.23 -1.500 -93.35 502
702 74.45 -4.500 -335.03 273.36 0.00 702
B 112 74.45 4.500 335.03 B 112
312 62.23 1.500 93.35 312
512 62.23 -1.500 -93.35 512
712 74.45 -4.500 -335.03 273.36 0.00 712
DeadLoad(Pre
Girder)
TOTALDEADLOAD
TOTALDEADLOAD+
SIDL
1SIDL
DeadLoad(Deck
S
lab)
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3.2 Synopsis of Bearing Reaction due to Live Load (with Impact)
27.59 m c/c EJ
26 m
3.00 m
1.5 m
C/L of Bridge
1.5 m
3.00 m
Fig. 6.1 Bearing Node Numbering
(Not to Scale)
NODE Load LOAD Support Node Force-Y Total Total
List CASE No. (t) V (t) MT (tm)
A 102 44.27 4.500 199.22s . 2 D
Distance
from C/L of
Brid e m
Ass ociated
MT (tm)
102
302
A
502
702
112
312
B
512
712
302 48.53 1.500 72.80
502 3.57 -1.500 -5.36
702 -1.83 -4.500 8.24 94.54 274.89
B 112 10.81 4.500 48.65
312 5.85 1.500 8.78
512 4.04 -1.500 -6.06
712 -1.15 -4.500 5.18 19.55 56.54
Load Load LOAD Support Node Force-Y Total Total
Case List CASE No. (t) V (t) MT (tm)A 102 16.96 4.500 76.32
302 59.84 1.500 89.76
502 18.54 -1.500 -27.81
702 -0.81 -4.500 3.65 94.53 141.92
B 112 7.70 4.500 34.65
312 5.43 1.500 8.15
512 5.10 -1.500 -7.65
712 1.32 -4.500 -5.94 19.55 29.21
Load Load LOAD Support Node Force-Y Total Total
Case List CASE No. (t) V (t) MT (tm)
A 102 41.63 4.500 187.34
302 37.69 1.500 56.54
502 15.16 -1.500 -22.74
702 -1.50 -4.500 6.75 92.98 227.88B 112 10.48 4.500 47.16
312 6.60 1.500 9.90
512 4.23 -1.500 -6.35
712 -0.21 -4.500 0.95 21.10 51.66
LiveLoadReaction
coexistentwithMa
ReactionatNode3
atSupportA
34
Distance
from C/L of
Ass ociated
MT (tm)
70RWHEELPLACE
MOST
ECCENTRICALLY
LiveLoadR
eactions
coexistentw
ithMax.
ReactionatNode302
atSupportA
230
CLASSA2LANE
PLACEDMOST
ECCENTRICALLY
LiveLoadReactions
coexistentwithMax.
ReactionatNode302at
SupportA
133
Distance
from C/L of
Ass ociated
MT (tm)
70RWHEELPLACED
CENTRALLYIN
CARRIAGEWAY
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3.2 Synopsis of Bearing Reaction due to Live Load (with Impact)
27.59 m c/c EJ
26 m
3.00 m
1.5 m
C/L of Bridge
1.5 m
3.00 m
Fig. 6.1 Bearing Node Numbering
(Not to Scale)
102
302
A
502
702
112
312
B
512
712
Load Load LOAD Support Node Force-Y Total Total
Case List CASE No. (t) V (t) MT (tm)
A 102 26.29 4.500 118.31
302 40.98 1.500 61.47ctions
Max.
de302
A ANE
ALLY
WAY
Distance
from C/L of
Ass ociated
MT (tm)
. - . - .
702 0.54 -4.500 -2.43 92.99 139.58
B 112 8.10 4.500 36.45
312 6.42 1.500 9.63
512 5.02 -1.500 -7.53
712 1.56 -4.500 -7.02 21.10 31.53
Load Load LOAD Support Node Force-Y Total Total
Case List CASE No. (t) V (t) MT (tm)
A 102 41.01 4.500 184.55
302 38.69 1.500 58.04
502 41.32 -1.500 -61.98
702 18.45 -4.500 -83.03 139.47 97.58
B 112 9.92 4.500 44.64
312 8.84 1.500 13.26
512 7.43 -1.500 -11.15
712 5.46 -4.500 -24.57 31.65 22.19
Load Load LOAD Support Node Force-Y Total Total
Case List CASE No. (t) V (t) MT (tm)
A 102 28.96 4.500 130.32
302 40.78 1.500 61.17
502 40.78 -1.500 -61.17
702 28.96 -4.500 -130.32 139.48 0.00
B 112 7.66 4.500 34.47
312 8.16 1.500 12.24
512 8.16 -1.500 -12.24712 7.66 -4.500 -34.47 31.64 0.00
Distance
from C/L of
Ass ociated
MT (tm)
Live
LoadReactions
coexistentwithMax.
ReactionatNode302
atSupportA
527
CL
ASSA3LANE
PLACEDCENTRALLY
INCARRIAGEWAY
LiveLoadRea
coexistentwit
ReactionatNo
atSupport
329
CLASSA2L
PLACEDCENT
INCARRIAGE
Distance
from C/L of
Ass ociated
MT (tm)
LiveLoadReactions
coexistentwithMa
x.
ReactionatNode5
02
atSupportA
428
CLASSA3LANE
PLACEDMOST
ECCENTRICALLY
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3.2 Synopsis of Bearing Reaction due to Live Load (with Impact)
27.59 m c/c EJ
26 m
3.00 m
1.5 m
C/L of Bridge
1.5 m
3.00 m
Fig. 6.1 Bearing Node Numbering
(Not to Scale)
102
302
A
502
702
112
312
B
512
712
Load Load LOAD Support Node Force-Y Total Total
Case List CASE No. (t) V (t) MT (tm)
A 102 37.35 4.500 168.08
302 9.14 1.500 13.71ctions
Max.
de702
B ANE
ST
LLY
LLY
Distance
from C/L of
Ass ociated
MT (tm)
. - . - .
702 37.35 -4.500 -168.08 92.98 0.00
B 112 5.97 4.500 26.87
312 4.58 1.500 6.87
512 4.58 -1.500 -6.87
712 5.97 -4.500 -26.87 21.10 0.00LiveLoadRea
coexistentwit
ReactionatNo
atSupport
923
CLASSA2L
PLACEDM
ECCENTRIC
BUT
SYMMETRIC
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4 Sumamry of Bm & Shear Force
The Diaphrgam, down stand and support at top of shear key is modeled in STAAD.
The summary of BM 7 Shear forces are given as hereunder:-
4.1 Sumamry of Design BM & Shear Forces for Horizontal Bending
Beam L/C Node Fx Mton Fy Mton Fz Mton Mx MTon- My MTon- Mz MTon-
Max Fx 6007 1 7 0 0 11.773 0.791 19.52 0
Min Fx 6007 1 7 0 0 11.773 0.791 19.52 0
Max Fy 6007 1 7 0 0 11.773 0.791 19.52 0
Min Fy 6007 1 7 0 0 11.773 0.791 19.52 0
Max Fz 6007 1 7 0 0 11.773 0.791 19.52 0
Min Fz 6035 1 83 0 0 6.618 0.365 14.52 0
Max Mx 6007 1 7 0 0 11.773 0.791 26.80 0
Min Mx 6070 1 178 0 0 8.93 0.24 12.46 0
Max My 6007 1 8 0 0 11.773 0.791 26.80 0
Min My 6070 1 178 0 0 8.93 0.24 12.46 0
Max Mz 6007 1 7 0 0 11.773 0.791 19.52 0Min Mz 6007 1 7 0 0 11.773 0.791 19.52 0
Max 11.773 26.8
Spacing between horizontal members = 0.19 m
Design BM for Plan bending = 26.8
0.19
Design BM for Plan bending = 141 tm per m
Design BM for Plan Shear = 11.773
0.19
Design SF for Plan bending = 62 t per m
4.2 Sumamry of Design BM & Shear Forces for Vertical Bending
Beam L/C Node Fx Mton Fy Mton Fz Mton x MTon- y MTon- Mz MTon-m
Max Fx 181 1 111 0 0 22 -0.043 15.19 0
Min Fx 181 1 111 0 0 18.39 -0.043 15.19 0
Max Fy 181 1 111 0 0 18.39 -0.043 15.19 0
Min Fy 181 1 111 0 0 18.39 -0.043 15.19 0
Max 22 15.19
Spacing between Vertical members = 0.1175 m
Design BM for Vertical Bending = 15.19
0.1175
Design BM for Vertical bending = 129 tm per m
Design BM for Vertical Shear = 22
0.1175
Design SF for Vertocal bending = 187 t per m
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4.0 Design of End Diaphragm for Longitudinal Seismic Forces
The Longitudinal Seismic Forces are considered due to Dead load and SID only and seismic forces due to live shall not be considered as
er clause 222.7 of IRC:6-2000
Total Dead Load = 2 x 222.12 = 444.25 t
(Sum of DL Reactions for Four Bearings)
Total SIDL = 2 x 51.24 = 102.48 t
(Sum of SIDL Reactions for Four Bearings)
Longitudinal Seismic Force due to DL = 0.18 x 444.25 = 79.96 t
= =
.
. .
Total Longitudinal Seismic Force = 79.96 + 18.45 = 98.41 t
Say 99.00 t
As per cl 222.11 of IRC:6-2000, the reaction blocks should be designed for twice the seismic forces.
Design Seismic Force = 2 x 99.00 = 198.00 t
No of Longitudinal girder = = 4
Shear Force = = 99.00 t
Design of Diaphragm at Section 'B" :
owever as t e se sm c restra ners are es gne to prevent s o gement o superstructure
The in plane stiffness of deck slab is very high and the distribution of longitudinal seismic forces may be uniform among precast girders.
The BM cause plan bending of diaphragm.
Thickness of Diaphragm D = = 0.60 m
Effective cover = = 0.07 m
Effective depth d = = 0.53 m
Depth of Diaphragm b = = 1.74 m
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For M 45 Grade Concrete End Diaphragm at
fck = 45 MPa
fy = 400 MPa
As per IS:456-2000,
Moment of Resistance w.r.t. concrete
MuR = 0.36.fck.b.xu(d-0.416xu)
Where xumax/d = 0.48
=umax .
MuR = 270 tm
> 222.75 tm OK
Proposed tensile Reinforcement on vertical Face of Diaphragm
As = 11 Nos Tor 32 + 11 Nos Tor 25
As = 14246 mm pt = 1.74 %
Actual xu = 0.87 fy As
. . c . .
= 4957725.38
25168.05= 197 mm
< xumax
Therefore section is Under reinforced, and Moment of Resistance is given by
MuR = 0.87fy.As(d-0.42.xu)
= 222 tm
> 222.75 tm OK
Check for Shear
Max. Shear Force = 99 x 1.00E+04
V = 9.90E+05 N
Shear stress = 9.90E+051545 x 530
= 1.21 MPa
< 3.9 MPa O.K
For pt= 1.5 % ( Taken on lower side)
Tc < 0.792 MPa
Vs = 9.90E+05 -0.792 x 1545 x 530
= 3.41E+05 N
Shear Reinforcement
Adopting spacing s = 200 mm
Asv = 3.41E+05 x 200
0.87 x 400 x 530
= 370 mm
Min Asv = 0.4 x 1545 x 200
0.87 x 400
= 355 mm (Governing)
Provide 4-Legged stirrups of 12 mm dia @ 200 mm c/c
Asv = 452 mm > 355 mm
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5.2 Design of Diaphragm for Vertical Bending & Shear
For M 45 Grade Concrete End Diaphragm at
The BM cause plan bending of diaphragm.
Thickness of Diaphragm D = 0.60 m
Assuming 70 mm rff cover d = 0.53 mLength of Diaphragm, b = 1 m
fck = 45 MPa
As per IS:456-2000,
Moment of Resistance w.r.t. concrete
MuR = 0.36.fck.b.xu(d-0.416xu)
Where x d = 270 0848umax .
xumax = 143.1449 m
MuR = 175 tm per m
> 129 tm per m OK
Proposed tensile Reinforcement on vertical Face of Diaphragm
As = 10 Nos Tor 32 + 0 Nos Tor 32
As = 8042 mm2
t = 1.52 %
Actual xu = 0.87 fy As
0.362.fck.b.
= 3498478
16290
= 215 mm< xumax
Therefore section is Under reinforced, and Moment of Resistance is given by
MuR = 0.87fy.As(d-0.42.xu)
= 154 tm
> 129 tm OK
5.1.1 Check for Shear
V = 1.9E+06 N
Shear stress =
1000 x 530
= 3.53 MPa
< 3.9 MPa O.K
1.87E+06
For pt= 1.5 % ( Taken on lower side)
Tc < 0.792 MPa
Vs = 1.9E+06 -0.792 x 1000 x 530
= 1.5E+06 N
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Shear Reinforcement
Adopting spacing s = 100 mm
Asv = 1.5E+06 x 100
0.87 x 415 x 530
= 759 mm2
Provide 6-Legged stirrups of 16 mm dia @ 100 mm c/c
=2
>
759 mm2
O.K
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5.0 Design of Longitudinal Sesmic Restrainer
Shear key is designed as a corbel to cater for the longitudinal forces from End diaphragm.
Reference: "Practical Design against Shear & Torsion and Design of of Short Cantilevers and Deep Beams" from
"Concrete Bridge Practice-Analysis , Design and Economic" by Dr. V. K Raina
Hus
Longitudinal Seismic Restrainer
Vu
Longitudinal/Traffic Direction
a
Pier Cap Top Level
d'
h
Vu = 198 t (After multiplying by 2)
Hu = 0 t
h = 500 mm
s = 500 mm
b = 2400 mm
a = 225 mm
fck = 45 MPa
fsy = 500 MPa (For main reinforcement calculations) 80% OF PERMISSIBLE S
fsy = 415 MPa (For shear reinforcement calculations)
= 1.4 (For Concrete placed monol ithical ly across interface)
p = 150 mm ( Pitch of Horizontal stuirrups)
fc' = 0.8 x 45
= 36 MPa
Eff cover = 80 mm
d' = 500 -80
= 420 mm
Step-1: Ensure s/d' > 0.5
s/d' = 500 / 420 = 1.19
> 0.50 OK
Step-2: Ensure Vu/(bd) < 0.15 fc'
d = 0.8 d' = 336 mm
0.15 fc' = 0.15 x 360 = 54.0 kg/cm 2
Shear Stress = Vu / bd
= 198000 / 8064 = 24.55 kg/cm^2
< 54.0 OK
Step-3: Calculate Shear Friction Reinforcement : Avf
Avf = Vu / 0.85.fsy.
= 198000 / 5950 = 33.28 cm 2
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Step-4: Calculate Direct Tension Reinforcement : At
Hu < 0.2 Vu = 39.6 t
At = Hu / 0.85.fsy
= 39600 / 4250 = 9.32 cm^2
Step-5: Calculate Flexure Tension Reinforcement : Af
Af = Vu.a+Hu.(h-d') / 0.85.fsy.d
= 4771800 / 142800 = 33.42 cm 2
Step-6: Compute Total Primary Reinforcement : As
As 6.35 cm^2 OK
Min. Development Length= 50 x 10
= 500 mm
in each of 6 165mm c/c
Step 8 Provide Horizontal Stirrups, Av
Av = / fsy.d
Vc = 10.b.d. kg = 106464 kg
Av = 0.05837 cm 2
Provide 2 L-10mm Horizontal Planes spaced at
for full height of shear key.
in each of 5 296mm c/c
0.50 ( Vu-Vc).p
Ah Provided = 7.85 cm^2
> 0.06 cm^2 OK
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6.0 Design of Pedastal for Transverse Sesmic Forces
Downstand from diphragm is designed to as a corbel to cater for the Transverse forces from Superstructure
Transverse Direction
Hu
s
Bearing
a
Vu Downstand from Diaphragm acts
as Tranvserse Stopeer against Pedestal
Pier Cap Top Level d'
d'
C/c distance between girders = 3000 mm
Dimension of Pedestal in transverse direction = 700 mmDimension of Pedestal in Longitudinal direction = 600 mm
Depth of Pedestal at G3 (On conservative side) = 550 mm
Thickness of Bearing = 80 mm
Depth of bottom rectangular & traingular haunch = 360 mm
Gra e o concrete o Diap ragm = 40 Mpa
Grade of Steel = 500 Mpa
Vertical Loads of One Span:
Total DL = = 444.2 t
Total SIDL = = 102.5 t
Total Live Load = = 83.1 t
( 50% of (3 x 55.4) t for 3 Lanes of Class "A")
Transverse Seismic Force due toDL = 0.18 x 444 = 79.96 t
SIDL = 0.18 x 102 = 18.45 t
50% Live Load = 0.18 x 83 = 14.96 t
113.37 t
The above forces is to be shared by two end end diaphragms of a span.
Transverse seismic Force at each end of Diaphragm
HT = 56.68452 t
Vu = 113.36904 t (After multiplying by 2)
Hu = 0 t
h = 700 mm
s = 700 mm
b = 600 mm
a = 275 mm (Acting at half the depth of pedestal from top of pier cap)
Cover = 80 mm
fck = 40 MPa
fsy = 500 MPa
= 1.4 (For Concrete placed monolithically across interface)
p = 150 mm ( Pitch of Horizontal stuirrups)
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fc' = 0.8 x 40 = 32.00 MPa
d' = 700 -80 = 620 mm
Step-1: Ensure s/d' > 0.5
s/d' = 700 / 620 = 1.13
> 0.5 OK
Step-2: Ensure Vu/(bd) < 0.15 fc'
d = 0.8 d' = 496 mm.
0.15 fc' = = 48.0 kg/cm 2
Shear Stress = Vu / bd
= 113369 / 3720 = 30.48 kg/cm 2
< 48.0 OK
Step-3: Calculate Shear Friction Reinforcement : Avf
= . . .
= 113369.04 / 5950 = 19.05 cm 2
Step-4: Calculate Direct Tension Reinforcement: At
Hu < 0.2 Vu
= 22.673808 t
At = Hu / 0.85.fsy
= 22673.808 / 4250 = 5.34 cm^2
Step-5: Calculate Flexure Tension Reinforcement: Af
Af =
= 3299039.1 / 210800 = 15.65 cm 2
Step-6: Compute Total Primary Reinforcement: As
As