PROJECT: RECONSTRUCTION OF ROB AT KM 0/2
DrgNo:
Design Loadings : INPUT VALUES REV case NORMAL
Type of Bearing Fixed Bearing R0 Date 27/01/2014
V-max. = max. vertical imposed load KN 5750.0 KN
V-min. = min. vertical imposed load KN 3900.0 KN
H-L (N) = Horizontal longitudinal load KN 450 KN
H-Q (N) = Horizontal Transverse load KN 0 KN
Tan - phi = tilting angle ( Radians) 0.003 rad
H-For (N) = Horizontal force KN 575.00 KN
PAGE 28a
PROJECT: RECONSTRUCTION OF ROB AT KM 0/2
DrgNo:
Type of Bearing Fixed Bearing
Notation Unit Value
Dia of Elastomer/cylinder di mm 600 V max 5750 kN
Elastomer height he mm 44 Qnty 1 Nos
width of mating interface (no X1 mm 7
width of mating interface (co X2 mm 11 Bending moment calculation
Eff. Contact width we mm 5
X2 mm BOTTOM
thickness of cylinder wall bp mm 54 Pedestal Dia 1200 mm
height of cylinder wall hc mm 55
Overall diameter of pot DRA mm 708 Dia of Ela De 600 mm
Overall diameter of pot bott D-B mm 736 Overall di LDA - Initial 760 mm 736.000
thickness of pot base plate TT mm 34 L1 80
thickness of pot bottom TB mm 89 W 12.675 N/mm2
Dia. Of dispersion width (supDPC mm 760 BM 40560.2625 N-mm
Flange thickness of pot cove TU mm 40 TT -cal 32.93 mm
Thickness of pot cover TD mm 58 thickness TT-Provided 34.00 mm
Dia. Of dispersion width (pe DWA mm 736
No.of bolts N nos 4 Soffit DIA 900 mm
Dia of bolt DB mm 20 Loaded Dia top 800 mm
effective area of bolts Ab mm² 247 600 mm
Dia of the sleeve DS mm 50
length of sleeve LS mm 250 Dia. Of bolPCD -pitch circle di 800 mm
Permissible stress of bolt FB N / mm² 190
fck, sub st N / mm² 35 W1 11.439 N/mm2
fck, sup st N / mm² 40 L2 100
A1, B mm² 1130973 BM1 57196.1739 N/mm
A2, B mm² 453646
AA, B 1.00 1.58 TU-Cal 39.11 mm
A1, T mm² 636173 TU-Provided 40.00 mm
A2, T mm² 502655
AA, T 1.00 1.13 Check dispersion as per IRC :83(Part III)-2002
Thickness of lug LT mm 20 Clause:926.3.1.1.6.1 Fig27
Length of lug LG mm 60 Pedestal side
For calculation of anchor De+4*TT 736 mm
Sleeve dimensions
fck ,pier st N / mm² 35 Soffit of Girder
DE+4*TU 760 mm
POT BOTTOM 340 N/mm2
POT COVER 340 N/mm2 For calculation of anchor
Sleeve dimensions Value
fck ,super N / mm² 40
PAGE 29a
PROJECT: RECONSTRUCTION OF ROB AT KM 0/2
DrgNo: 0
Type of Bearing Fixed Bearing
Notation Unit Permissible value Calculated Value Checks
Elastomer
Safe elastomer sts ce Centre N / mm² 35 20.34 Ok
Safe elastomer stsce1 edge N / mm² 40 23.99 Ok
Pot Bottom/Pot cover Cast steel)
su (ultimate tensilesu
strength of the steel N / mm² of piston / cylinder)
material 440 249.48 Ok
sat N / mm² 204 187.19 Ok
bending stress at sbt N / mm² 224.4 186.92 Ok
lvm N / mm² 153 43.19 Ok
se N / mm² 306 201.33 Ok
sp,(Hertz) N / mm² 255 134.58 Ok
Pier/Sub structure
Perm.stress in co s C, Bot N / mm² 11.55 0.57 Ok
in pedestal/substr s CC, Bot N / mm² 8.750 5.08 Ok
sComb, Bot N / mm² 1 0.631 Ok
Soffit /Super Structure
Perm.stress in co s C, Top N / mm² 13.2 1.11 Ok
in superstructure s CC, Top N / mm² 10.000 9.04 Ok
sComb, Top N / mm² 1 0.988 Ok
Anchor
SR-Friction kN 780
SR-Perm kN 188
H resu kN 575 968 Ok
BS - Con- Aver N / mm² 13.2 3.75
BS - P con N / mm² 13.20 11.25 Ok
S-NL N / mm² 153 119.79 Ok
DRA-OLD DPC-NEW
266 270
BP-OLD BP-NEW
28 30
Sleeve length 135mm
M16 8.8Gr
Elastomer
N / mm² 5.00 13.79 Ok
PAGE 30a
Type of Bearing : Fixed Bearing
Data :
V-max. Maximum vertical imposed load 5750 KN Clause Ref
V - min. Minimum vertical imposed load 3900 KN
H-L Horizonatal longitudinal force 450 KN
H-Q Horizontal transverse force 0 KN
H-R Frictional force ( 0.05 * V - max.) 0 KN
TanØ Tilting angle ( radians) 0.003 rad
H Horizontal force 575 KN
Design of Elastomer :
sce Safe elastomer stress, centre 35 N/mm² 926.2.3.2.
Safe elastomer stress, edge 40 N/mm² 926.2.3.2.
di Elastomer diameter 600 mm
he Elastomer height 44 mm
sce1,cal Elastomer stress, centre
V.max x 4 5750 x 4 x 1000 20.34 N / mm²
di² x π 600 ²x π Ok
Safety factor Alpha N - factor dependent on di 600 13.64 926.2.3.6
he 44
Strain in elastomer
di x tanØ <0.15 600 x 0.003 0.0205 926.2.3.4
he eff x 2 40 x 2 Ok
Restoring Moment 1.3
Induced moments M.ed = di³ x (k1 Up + k2 U v)
Up 0.003 x 0.8 x 1.3 = 0.0031 K1 and K2 as per table (1) di/he K1 K2
Uv 0.003 x 0.2 x 1.3 = 0.00078 (Intermediate values may be 15 2.2 101
obtained by linear interpolation) 13.64 1.98 78.09
K1 1.98 k2 78.09 12.5 1.8 59
10 1.5 30.5
600 ³ x( 0.006183 + 0.0609109 14492343 Nmm
M.rd 0.2 x di x H 926.1.5.2
2
0.2 x 600 x 575000 34500000 Nmm
2
M-Sum M.rd + M.ed = Total induced Moment 48992343.27273 Nm 926.1.5.3
W-eatx π x di³ π x 600 ^3 21205750.41 mm3
32 32
Moment due to horizontal loads = (HХ x a1 )/ W eat-x 1.34
Where a1 = [(X2/2)+he] 49.5
sce2 cal Elastomer stress due to Rotation and Horizontal force
M-Sum
W-eatx
48992343.272727 2.31 N/mm² Ok
21205750.411731
Total stress on elastomer
sce1,cal + sce2 cal 20.34 + 2.31 + 1.34 23.99 N/mm² Ok
Min. Average stress in Elastomer 5.00 N / mm² 926.2.3.3
V.min x 4 3900 x 4 x 1000 13.79 N / mm²
di² x π 600 ² x π Ok
PAGE 31a
Pressure between Ring and Cover
su (ultimate tensile strength of the steel material of piston / cylinder) 440 N/mm²
sp( safe steel stress ) N /mm ² 255 N/mm²
Parabolic load distribution factor = 1.50 926.3.1.1.7.2
X1 1.5x di x tanØ+ 6 1.5 x 600 x 0.003 + 6 7.35 mm
2 2
X1 (adopted ) mm 7 mm
X2 di x tanØ+ 10 600 x 0.003 + 10 10.9 mm
2 2
X 2 ( adopted ) mm 11 mm
sp Permissible bearing stress of steel( 0.75*fy) 255 N/mm²
we = 1.3 x H 1.3 x 575 x 1000 4.89 mm
dn x sp 599 x 255
dp Diameter of pistion =di-0.75 599.25 mm
dc Diameter of cylinder 600 mm
sp,cal 1.3 x H /dp x s 1.3 x 575 x 10³ 249.48 N/mm²
599.25 x 5 926.3.1.3.1
Curved contact surface between Piston and cylinder shall be designed 926.3.1.3.2
We Effective contact width of contact surface in 15mm
s ( adopted min.value 5.00 mm) In case s >15 ,then recalculate S and X - 2 5.00 mm
Hoop tensile stress in the cross section of the cylinder wall due to clause Ref
sat1 Fluid pressure (di x he x sce)/(2x bp xhc) 926.3.1.1.7.1
at2 Horizontal force H/(2x bp xhc)
sat = Permissible stress in axial tension 204 N/mm²
sat, cal = Tensional stress in ring sat1+sat2
bp = Thickness of cylinder wall 54 mm
hc = height of cylinder wall he + x2 44 + 11 55.00 mm
Tension stress in ring from horizontal forces.
lvm safe steel shear stress 153 N/mm²
sat1 Fluid pressure di x he xsce 600 x 44 x 20.34 90.38 N/mm²
2x bp xhc 2 x 54 x 55
sat2 Horizontal force H 575 x 1000 96.80 N/mm²
2x bp xhc 2 x 54 x 55
sat, cal = sat1 + sat2 90.38 + 96.80 187.19
Ok
The effect of the HERTZ Stress at the mating interface shall be calculated using following
0.6 x √[{(H x Es/We x dc)} x ( 1-dn/dc)]
sp( Hertz Stress) allowable 0.75 x fy 255 N/mm² 926.3.32.2.1
0.6 x √[ 575000 x 210000 x ( 1 - ### )]
5 x ### ###
0.6 √( 40250000 x 0.0012 ) 134.58 N/mm²
Ok
sp( Hertz Stress) allowable > sp( Hertz Stress) cal
PAGE 32a
Ring turned completely :
Shear stress at cylinder wall and base interface calculated considering clause Ref
1 mm radial slice of cylinder due to 926.3.1.1.7.2
1 lvm1, Fluid pressure he x sce 44 x 20.34 16.570 N/mm2
bp 54
2 lvm2 Horizontal force 1.5 x H 1.5 x 575000 26.620 N/mm2
di x bp ### x 54
lvm , Permissible shear stress of (0.45*fy) 153 N/mm2 926.2.2.3
lvm total lvm1 + lvm2 16.570 + 26.620 43.191
Ok
Bending stress at cylinder and base interface calculated considering 926.3.1.1.7.3
1mm radial slice of cy;inder due to
1 Fluid pressure,sbt1
6 x sce x he² 6 x 20.34 x 44 ² 40.506 N / mm2
2 x bp² 2 x 54 ²
2 Horizontal force sbt2 1.5 x 6 x H x ha
di x bp²
ha Height of application of design horizontal force from cylinder above base interface in mm
he + X2 44 + 11 49.5 mm
2 2
1.5 x 6 x 575000 x 49.5 146.412 N/mm2
### x 54 ^2
sbt, Permissible bending stress (0.66*fy) 224 N/mm2 926.2.2.2
sbt,cal sbt1+sbt2 40.506 + 146.412 186.9 N/mm2
Ok
Equivalent stress due to combined bending and shear shall be checked in 926.3.1.1.7.4
accordance with
permissible equivalent stress in steel =0.9 xfy) ### N/mm2 926.2.2.5
se √(sbt² + 3 x lvm²)
se ,cal. √( 186.9 ²+ 3 x 43.19 ²) 201.33 N/mm²
Hence , (secal<se ) N mm ² Ok
Pot Bottom :
Thickness of base plate ( TT ) of the pot must be atleast 2.5% of piston diameter and in any
case shall not be less than 12 mm.
T T = ( thickness of base plate ) = di * 2.5% 15.00 mm
Adopted value of TT mm ( if T T is < 12 mm adopt 12 mm ) 34 mm
TB =(thickness of pot bottom) TT + he + x2 34 + 44 + 11 89 mm
POT COVER :
TU Flange thickness of cover 40 mm
TD Thickness of cover TD + X1 + X2 40 + 7 + 11 58 mm
TD min TD 58.0 58 mm
PAGE 33a
Concrete Pressure Abutment side / Support side
LDA = Final value De + 4 x TT ### + 4 x ### 1200 mm
WAT =resistance moment LDA³ x π 1200 ³x π 169646003 mm3
32 ###
scc , cal Calculated direct compressive stress
1 Vmax x 4 5750 x 10³ x 4 5.08 N/mm²
LDA² xπ 1200 ²x π
sc , cal = Calculated compressive flexural stress
2 TT + he + x2 x H 34 + 44 + 11 x 575000 0.28 N/mm²
2 WAT 2 169646003
Stresses on concrete due to due to rotation.
3 MSum 48992343.27 0.29 N/mm²
WAT 169646003
Grade of concrete M 35 N /mm² clause Ref
sco = 0.25 * fck 8.75 N/mm² 926.2.1.1
scc=Average Permissible direct bearing pressure in concrete .
PD = Pedestal Diameter 1200 mm
A1 = Dispersed concentric area = ( PD^2 x π ) / 4 1130973.36 mm²
A2 = Loaded area =( LDA² x π) /4 1130973.36 mm²
scc=sco√ (A1 / A2) <= 2 1.00
Calculate concrete stress for Ok
sc = Allowable compressive flexural stress in concrete
sc = 0.33 x fck (Permissible compressive flexural stress in cponcrete) 11.55 N/mm² 926.2.1.2
scc = 0.25 x fck x sqrt (A1 / A2) ( Allow direct bearing stress) 8.75 N/mm²
scc, cal = 1 5.08 N/mm²
s c, cal = 2 +3 0.57 N/mm²
Calculate concrete stress for coexisting direct and flexural compressive stresses on the adjacent 926.2.1.3
concrete structure , following criteria should be satisfied :
scc, cal + sc, cal 5.08 + 0.57
<= 1
scc sc 8.75 11.55 0.631
Ok
Concrete Pressure. Bridge Underside: Superstructure side
LDA = loaded diameter ### + 4 x 75 900 mm
WAT =resistance moment LDA³ x π 900 ³x π 71569407.6 mm3
32 ###
scc , cal = Calculated direct compressive stress
1 Vmax x 4 5750 10 ³ x 4 9.04 N/mm²
LDA² xπ 900 ²x π
sc , cal = Calculated compressive flexural stress
2 TD - x2 x H 58 - ### x 575 0.42 N/mm²
2 WAT 2 71569407.6
Stresses on concrete due to due to rotation.
3 MSum 48992343.27 0.68 N/mm²
WAT 71569407.64
PD1 = Minimum required dia in soffit 900 mm
A1 = Dispersed concentric area = PD1^2 636417.00 mm²
A2 = Loaded area =LDA1 Dia LDA1² x π /4 636417.00 mm²
PAGE 34a
√ (A1 / A2) <= 2 1.00 Ok
Calculate for stresses
s c = 0.33 x fck (all comp flexural stress) 13.20 N/mm²
s cc = 0.25 x fck x √(A1 / A2) (Allow average direct compressive stress in concrete) 10.00 N/mm²
scc, cal = 1 9.04 N/mm²
s c, cal = 2 + 3 0.42 + 0.68 1.11 N/mm²
Calculate concrete stress for coexisting direct and flexural compressive stresses 926.2.1.3
on the adjacent concrete structure , following criteria should be satisfied :
scc, cal + sc, cal 9.04 + 1.11 0.99
<= 1
scc sc 10.00 13.20 Ok
Anchor Bolts
The total resistive force against shifting of the bearing, Due to firction
H perm 1 = min of ( u x Nmin / FOS)
where - u 0.20 coeff of friction between steel & concrete
Hperm 1 0.2 x 3900 780.0 kN
780 kN
Due to shear resistance of bolts, H perm 2 = ( n x Ab x, permis stress) / 1000
n = no of bolts: Grade of bolt : 10.90 4 nos
Dia of bolt 20 mm
Ab = effective area of bolts 247 mm²
Perm stress gr 4.60 80
gr 8.80 ###
gr 10.90 ###
H perm 2 188 kN
H perm = H perm1 + H perm 2 188 + 780 968 kN
Anchor Sleeve Ok
L - length of sleeve 250 mm
D - Dia of the sleeve 50 mm
Average bearing stress in concrete, s cav = (Ab x perm stress) / (L x D) 3.75 N/mm²
Considering triangular distribution, bearing stress in concrete,
σctr = 2.0 x s - cav 7.50 N/mm²
Considering incremental factor, sp = 1.50 , peak stress,
σpeak = 1.50 x s - ctr 11.25 N/mm²
σ peak < 0.330 x fck Grade concrete on Superstructure M 40 13.2 N/mm² Ok
Lugs
Thickness of lug - LT 20 mm
Length of lug - LG 60 mm
Effective area of lug ,Eal 60 x 20 1200 mm²
Horizontal force on each lug , S-NL = H or H res / No of bolts
575 / 4 143.75 kN
119.79 N/mm²
143.75 x 1000 ok
1200
PAGE 35a
