15.00 %. For Class-A. (Ref. Cl. 208.1 IRC 6:2017). = 10 %. 70R Tracked. = 25 %. 70r Wheeled viii Thickness of wearing coat. = 75 mm ix Carriage way width. =.
DESIGN CALCULATION OF BRIDGE SUPERSTRUCTURE AT CH:444/150
DESIGN OF DECK-SLAB 1.0
INTRODUCTION :
The Bridge Deck essentially consists of concrete slab monolithically cast over longitudinal girder so that the T-beam effect prevails.To improve transverse stiffness to the deck ,crossgirders or diaphragms are provided at regular intervals. The number of longitudinal girders depends on the width of road. For analysis purpose the deck slab is modelled over STAAD-Pro as simply supported over two sides with over-hang on each side.After Application of Vehicular load as per IRC the deck is designed for most critical combination. DESIGN DATA:
2.0
3.0
i ii iii iv v vi vii
Density of concrete Grade of concrete Grade of steel Reinforcement Span Deck width Impact Factor
viii ix x xi
Thickness of wearing coat
Carriage way width No of Lanes to be considered Footpath REFERENCES: i. IRC: 6 - 2017 ii. IRC: 112 - 2011
= = = = = = = = = = = = =
3
2.50 t/m M- 35 Fe- 500 HYSD bars conforming to IS: 1786 24 m 16 m 15.00 % For Class-A 10 % 70R Tracked 25 % 70r Wheeled 75 mm 11 m 3 1.5 m
(Ref. Cl. 208.1 IRC 6:2017)
15000 500
C/L Carriageway
200 130 2166
2030 0.325
625 2700
625 2650
625 2650
625 2650
625 2650
2700
(Ref: IRC 6:2017 Table B.2,Table B.3) Load Case
Partial Safety Factor for verification of structural Strength
Partial Safety Factor for verification of Serviceability Limit State
QuassiBasic Accidental Normal Rare Frequent permanent Combinatio Combinatio Combinatio Combinatio Combinatio Combinatio n n n n n n
Dead load SIDL Surfacing Live Load Braking
1.35 1.35 1.75 1.5 1.5
1.00 1.00 1.00 0.75 0.75
1.00 1.00 1.00 1.00 1.00
1.00 1.00 1.20 1.0 1.5
1.00 1.00 1.20 0.75 0.75
1.00 1.00 1.20 0.00 1.00
E.P. due to backfill Pressure
1.50
1.00
1.00
1.00
1.00
1.00
C.F Force
1.50
0.75
1.00
1.00
0.75
0.00
Wind Water Current
1.50 1.00
0.00 1.00
1.00 1.00
1.00 1.00
0.60 1.00
0.00 0.00
4.0
DESIGN OF THE CANTILIVER SLAB PORTION Dead load bending moment and shear force: 500 0
1 1887.5 mm 5 0 mm 200 mm 130 mm
2 3 4
2387.5 mm
330 mm
Beam edge
Component
Dead Load shear force/ meter run(t/m) Railing (1) 1.2 Footpath(2) 0x1 x2.3875x2.5= 0.000 Slab Rectangular(3) 0.2x2.3875x1x2.5= 1.194 Slab triangular(4) (0.13x2.3875x1x2.5)1/2= 0.388 Wearing coat(5) 0.075x1.8875x1x2.5= 0.008 Total 1.590 t
Distance of C.G.(m) 2.054 1.888 1.194 0.796 0.944
Bending moment(t-m/m) 2.465 0.000 1.425 0.309 0.008 4.206 t-m
Live load bending moment and shear force: The minimum clear distance of 70 R vehicle edge from footpath edge is 1.2m,As available lear distance of Cantilever is Only 1887.5 mm,Class 70R loading cannot be considered on cantilever portion. How ever Class A loading can be cnsidered.For Calculating the effective effective length and effective width of dispersion average thickness can be considered. Cantiliver Portion (Ref.Annexure B-3 of IRC: 112-2011) The over hang Portion is succeptable to only Footpath Load Intensity of live load (P)
=
P' Span(L)
= =
P Intensity of live load per meter width of Road
= =
P'-(40L - 300)/9 2 0.4 t/m 21 m 2 0.34 t/m 0.51 t/m
0.51 t 943.75 200 130
330 2387.5
Bending moment owing to live load
=
0.51x943.75
=
0.481 t-m
Load Combination for verification of Structural Strength Design Bending moment Basic Combination 1.35x4.206+1.5x0.481 = 6.400 Accidental Combination 1x4.206+0.75x0.481 = 4.567 Normal Combination 1x4.206+1x0.481 = 4.687 Design shear Basic Combination 1.35x1.58978125+1.5x0.51 = 2.911 Accidental Combination 1x1.58978125+0.75x0.51 = 1.972 Normal Combination 1x1.58978125+1x0.51 = 2.100 Load Combination for verification of Serviceability Limit State Design Bending moment Rare Combination 1x4.206+1x0.481 = 4.687 Frequent Combination 1x4.206+0.75x0.481 = 4.567 Quassi-permanent Combination 1x4.206+0x0.481 = 4.206 Design shear Rare Combination 1x1.58978125+1x0.51 = 1.972 Frequent Combination 1x1.58978125+0.75x0.51 = 1.590 Quassi-permanent Combination 1x1.58978125+0x0.51 = 2.100
t-m/m t-m/m t-m/m t/m t/m t/m
t-m/m t-m/m t-m/m t/m t/m t/m
OUTER GIRDER End Section Precast Section : 2
3
4
0.075
0.15
5 2.023
0.625
Zone Mark 2 3 4 5 Zone Mark 2 3 4 5
Width
Height
Type
Area
0.15 0.325 0.15 0.325
0.075 0.075 0.075 2.023
t r t r
0.005625 0.024375 0.005625 0.657475
Iz 1.76E-06 1.14E-05 1.76E-06 0.224228
CG from top 0.025 0.0375 0.025 1.0865
h
Ah2
1.007379 0.994879 1.007379 -0.05412
0.005708 0.024126 0.005708 0.001926
Ki 0.229 0.285 0.229 0.3
2.11E-05 3.91E-05 2.11E-05 0.020834
IY 7.03E-06 0.000215 7.03E-06 0.005787
IJ
Location of CG from top Location of CG from bottom Location of CG upto bottom of flenge
= = =
1.032379 m -1.06562 m 1.032379 m
Area of Section
=
2 0.6931 m
Moment of inertia about j axis
=
4 0.020915 m
Moment of inertia about y axis
=
Moment of inertia about z axis
=
Section Modulus about Z top
=
Section Modulus about z bottom
=
3 0.253503 m 3 -0.2456 m
Section Modulus about z bottom of top flange Unit Weight per unit length
= =
3 0.253503 m -1.73275 t/m
4 0.006016 m 4 0.261711 m
PROPERTIES OF COMPOSITE SECTION : 2.700
1.325 0.3
5
Zone Mark Deck Slab Precast section Zone Mark Deck Slab Precast section
Width
Height
Type
Area
4.025
0.3
r
1.2075 0.693
Iz 0.009056 0.261711
CG from top 0.15 1.332
0.431 0.027169 -0.751 1.2304
Ki
IY 1.63 0.0060
Ah2
h
IJ
0.318 0.034559 0.020915
Location of CG from top Location of CG from bottom
= =
Area of Section
=
0.581 m -1.517 m 2 1.901 m
Moment of inertia about j axis
=
4 0.055474 m
Moment of inertia about y axis
=
4 1.636016 m
Moment of inertia about z axis
=
4 0.270768 m
Section Modulus about Z top
=
3 0.46589 m
Section Modulus about z bottom Unit Weight per unit length
= =
3 -0.17851 m -4.7515 t/m
MID SPAN SECTION Precast Section 2
3
4
0.15
0.3 1.548 5
0.2 6
7
0.15
8 0.625
Zone Mark 1 2 3 4 5 6 7 8
Width
Height
Type
0.625 0.3 0.325 0.3 0.325 0.2 0.2 0.625
0 0.15 0.15 0.15 1.548 0.15 0.15 0.25
r t r t r t t r
0.25
CG from top 0 0 0.0225 0.05 0.04875 0.075 0.0225 0.05 0.5031 0.924 0.015 1.798 0.015 1.798 0.15625 1.973 Area
h 1.063711 1.013711 0.988711 1.013711 0.139711 -0.73429 -0.73429 -0.90929
2
Ah
0 0.023121 0.047656 0.023121 0.00982 0.008088 0.008088 0.129189
Zone Mark 1 2 3 4 5 6 7 8
Iz 0 2.81E-05 9.14E-05 2.81E-05 0.100465 1.88E-05 1.88E-05 0.000814
Ki
IY 0 0.000113 0.000429 0.000113 0.004428 3.33E-05 3.33E-05 0.005086
0.333 0.229 0.237 0.229 0.289 0.18 0.18 0.25
IJ 0 0.000338 0.00026 0.000338 0.015357 0.000225 0.000225 0.002441
Location of CG from top Location of CG from bottom
= =
Area of Section
=
1.063711 m -1.03429 m 2 0.7831 m
Moment of inertia about j axis
=
0.019184 m
4
Moment of inertia about y axis
=
0.010235 m
4
Moment of inertia about z axis
=
0.350546 m
4
Section Modulus about Z top
=
3 0.32955 m
Section Modulus about z bottom Unit Weight per unit length
= =
3 -0.33892 m -1.95775 t/m
PROPERTIES OF COMPOSITE SECTION
2.700
1.325 0.3
Zone Mark Deck Slab Precast section
Zone Mark Deck Slab Precast section
Width
Height
Type
4.025
0.3
r
Iz 0.009056 0.7831
IY 1.63 0.0102
CG from h Ah2 top 1.2075 0.15 0.477473 0.275286 0.7831 1.3637 -0.73624 0.424477
Area
Ki 0.318 0.034559 0.019184
IJ
Location of CG from top Location of CG from bottom
= =
Area of Section
=
Moment of inertia about j axis
=
Moment of inertia about y axis
=
Moment of inertia about z axis
=
Section Modulus about Z top
=
Section Modulus about z bottom Unit Weight per unit length
= =
0.627473 m -1.47053 m 2 1.9906 m 4 0.053742 m 4 1.640235 m 4 1.491919 m 3 2.377664 m 3 -1.01455 m -4.9765 t/m
WEB WIDENING SECTION Precast Section
2
3
4
0.1125
0.075 0.475
1.5855
5 0.075 6
7
0.15
8 0.625
Zone Mark 2 3 4 5 6 7 8
Width 0.075 0.475 0.075 0.475 0.075 0.075 0.625
Height 0.1125 0.1125 0.1125 1.5855 0.15 0.15 0.25
0.25
Type
Area
t r t r t t r
0.004219 0.053438 0.004219 0.753113 0.005625 0.005625 0.15625
CG from top 0.0375 0.05625 0.0375 0.90525 1.798 1.798 1.973
h
Ah2
0.994153 0.975403 0.994153 0.126403 -0.76635 -0.76635 -0.94135
0.00417 0.050841 0.00417 0.012033 0.003303 0.003303 0.138458
Zone Mark 2 3 4 5 6 7 8
Iz 2.97E-06 5.64E-05 2.97E-06 0.157765 7.03E-06 7.03E-06 0.000814
Ki
IY 1.32E-06 0.001005 1.32E-06 0.01416 1.76E-06 1.76E-06 0.005086
IJ
0.196 1.58E-05 0.284 0.000192 0.196 1.58E-05 0.27 0.045879 0.229 2.11E-05 0.229 2.11E-05 0.25 0.002441
Location of CG from top Location of CG from bottom
= =
Area of Section
=
Moment of inertia about j axis
=
Moment of inertia about y axis
=
Moment of inertia about z axis
=
Section Modulus about Z top
=
Section Modulus about z bottom Unit Weight per unit length
= =
1.031653 m -1.06635 m 2 0.982488 m 4
0.048586 m 4 0.020257 m 4
0.158655 m 3 0.153787 m 3 -0.14878 m -2.45622 t/m
PROPERTIES OF COMPOSITE SECTION
2.700
1.325 0.3
Zone Mark Deck Slab Precast section
Zone Mark Deck Slab Precast section
Width
Height
Type
4.025
0.3
r
Iz 0.009056 0.048586
IY 1.63 0.1538
CG from h Ah2 top 1.2075 0.15 0.477473 0.275286 0.982488 1.3317 -0.7042 0.487186 Area
Ki 0.318 0.034559 0.158655
IJ
Location of CG from top Location of CG from bottom
= =
0.680121 m 0.680121 m
Area of Section
=
2.189988 m
Moment of inertia about j axis
=
Moment of inertia about y axis
=
4 0.193214 m 4 1.783787 m
Moment of inertia about z axis
=
Section Modulus about Z top
=
0.820114 m 3 1.205835 m
Section Modulus about z bottom Unit Weight per unit length
= =
1.205835 m 0.328498 t/m
2
4
3
CROSS GIRDERS 1.042 0
1.698
0.3
Zone Mark Top flange web
Width
Height
Type
Area
1.042 0.3
0 1.698
r r
0 0.5094
Zone Mark Top flange web
Iz 0 0.122392
IY 0 0.003821
CG from top 0 0.849
h
Ah2
-0.849 0
0 0
Ki 0.333 0.296
IJ 0 0.01357
Section Property Area
=
2 0.5094 m
CG from top
=
0.8490 m
Moment of inertia about z axis
=
4 0.1224 m
Torsional moment of inertia
=
0.0136 m
4
5.0 STEEL CALCULATIONS OF THE CANTILIVER SLAB PORTION The Section is checked for Ultimate Limit State (Refer: Clause 7.6.4. IRC 112-2011) Charecterstic Compressive Strength of Concrete fck = 35 Mpa Charecterestic Tensile Strength of Reinforcement fy = 500 Mpa Design Moment per unit width = Overall Depth Clear Cover Diameter of Main Rods Diameter of Distribution Rods Effective Cover = 50 + 12 / 2 Effective Depth, d = 330 - 56 Width of Slab Considered
6.3996 t-m/m = = = = = = =
330 50 12 10 56 274 1000
mm mm mm mm mm mm mm
Depth check for Cantiliver portion Mu = 6.3996 t-m/m (Mu/R.b)0.5 0.165 x fck 5.775 dreq. = 105.27 mm Limiting moment of resistsnce : dreq. = R =
Mulim
274 mm
0.165 x fck x b x d2 43.35639 t-m/m
= =
Ast req
OK
6.3996 t-m/m
`
OK
[1-(1-4.6Mu/(fck b d2)0.5]
0.5 x fck x b x d fy 2 553.145 mm
=
Minimum required tensile steel
=
553.145+10.048
2 563.193 mm
=
Minimum Reinforcement area for each face of Slab
=
0.0013 x Ac
(Cl. 16.3.1 IRC : 112-2011)
= = =
mm2/m 429 0.13 % of b d ( 0.13 / 100 ) x 274 x 1000
fctm fyk
= = =
0.26 fctm/fyk .bd
=
Asmin
=
2 429 mm /m 2.8 500.00 2 398.944 mm /m 2 429 mm /m
Horizontal Reinforcement at top face of cantilever edge in Transverse direction : Provide T-
12 @
Area of Steel Provided Provide T0@
150 mm c/c =
In LAYER I
( π / 4 )12^2 x 1000 / 150 = 135 mm c/c In LAYER II
Area of Steel provided = Total area of Longitudinal Steel Provided,Ast
2 0 mm
( π / 4 )0^2 x 1000 / 135 = 754 + 0 =
2 754 mm
2 754 mm /m
2 2 Therefore, Ast = 754 mm /m > 563.193 mm /m Horizontal Distribution Reinforcement Minimum Horizontal reinforcement (Cl. 16.3.2 of IRC:112-2011)
1)
maximum of
2)
Spacing between two adjacent bar should not be more than 2h
Provide TTherefore, Ast_trans
20% of Main reinforcement =
10
0.2x754
200 mm c/c ( π / 4 ) x 10^2 x 1000 / 200
Therefore, Ast_trans
=
2 393 mm / m
Reinforcement at bottom face Provide T10
@
Therefore, Ast-Vertical
=
Provide
T-
10
Therefore, Ast_trans
=
200
= = = =
ƥ1
=
ƥ1
=
0.003
K
= = = = = =
1+(200/d)0.5 1.854 35 Mpa 15.633 Mpa 0N 0
fck fcd NED ϭcp
Asl/(bw.d)
,OK
2 524 mm / m ,OK
=
mm c/c as Transverse R/F
( π / 4 ) x 10^2 x 1000 / 200
Design of shear Reinforcement: (Ref: Cl. 10.3.3 of IRC:112-2011) Check for shear: Shear force Overall depth of Section Effective depth of the section width of the Section
660 mm & 250 mm
mm c/c Horizontally along Road
( π / 4 ) x 10^2 x 1000 / 150 @
2 150.8 mm
=
=
@ =
150
,OK
0.02
0.2911205 t Hence shear reinforcement not Required ok ∆Ftd = 0.5 VED(cotϴ-cotα) = 0.5x2911.2046875x(cot21.8-cot90) = 4368.817 N 4.369 KN =
4368.817/400
=
2 10.048 mm /m
7.0
DESIGN OF THE GIRDER DESIGN DATA: i) Density of concrete ii) Grade of concrete iii) Grade of steel iv) Reinforcement v) Live Load
=
= 2.50 0.475 = M- 35 = Fe- 500 HYSD bars conforming to IS: 1786
a) Class A x 3 Lanes
b) One Class 70R(T) + Class A c) One Class 70R(W) + Class A vi) Impact Factor
(Ref. Cl. 208.1 IRC 6:2017)
For Class-A 70R Tracked 70r Wheeled vii) viii) ix) x) x)
= = = = = = = =
Effective span Overall span C/c spacing of L.girder Thickness of wearing coat C/c spacing of C.girder
15 10 25 21 24 2.65 75 10.5
% % % m m m mm M
Deck slab and Girder Arrangement: 15 0.5
C/L Carriageway
2.50%
2.50%
0.2 0.13
0.33 1.3
0.4 625 2.7
625 2.65
2.65
2.65
2.65
Load Calculation: For dead load and live load analysis Software STAAD Pro is used and moments and shear force are find out. Dead Load: Maximum Structural Strength Serviceability Limit Un- factored Check State Check B M(t-m) L. Girder 199.830 269.77 199.83 C. Girder 31.797 42.93 31.797 S F(t- m) L. Girder 33.831 45.67 33.831 C. Girder 13.664 18.45 13.664
Live Load: No. of Lanes Loading Class :
=
3 Lanes
One lane of Class 70R for Every two lanes with one lane of Class A for the remaining lanes, If any ,OR one lane of Class A for each Lane. (Ref. Cl. 205 IRC:6-2017) Reduction in Longitudinal effecton Bridges = 10 %
Maximum Shear(t)
Results from STAAD-Pro
BM(t-m)
Longitudinal Girder
Un-factored Factored
109.09
112.91
25.627
26.52
b) One Class 70R(T) + 1 Class A
144.39
146.19
35.072
35.51
c) One Class 70R(W) + 1 Class A
157.72
166.79
35.32
37.35
Maximum Shear(t)
Results from STAAD-Pro
BM(t-m) Un-factored Factored
Cross Girder
Un-factored Factored
a) Class A x 3 Lanes
Un-factored Factored
a) Class A x 3 Lanes
14.2
14.70
6.843
7.08
b) One Class 70R(T) + 1 Class A
26.4
26.73
7.86
7.96
c) One Class 70R(W) + 1 Class A
27.86
29.46
11.845
12.53
Design Live load with Load Combination Factor : a) Class A x 3 Lanes
L. Girder C. Girder b) One Class 70R(T) + 1 Class A L. Girder C. Girder c) One Class 70R(W) + 1 Class A L. Girder C. Girder
Structural Strength(t-m) BM SF 169.362 39.786 22.046 10.624 BM SF 219.292 53.266 40.095 11.937 BM SF 250.183 56.026 44.188 44.188
Design Bending Moment for L.Girder for Structural Strength : = 269.7705+250.18335 = Design Bending Moment for L.Girder for Serviceability Check : = 199.83+166.7889 = Design Shear force for L.Girder for Structural Strength : = 45.67185+56.02635 = Design Shear force for L.Girder for Serviceability Check : = 33.831+37.3509 = Design Bending Moment for C.Girder for Structural Strength : = 42.925545+44.18816625 = Design Bending Moment for C.Girder for Serviceability Check : = 31.7967+29.4587775 = Design Shear force for C.Girder for Structural Strength : = 18.4464+44.18816625 = Design Shear force for C.Girder for Serviceability Check : = 13.664+12.5260875 =
Serviceability Check(t-m) BM SF 112.908 26.524 14.697 7.083 BM SF 146.195 35.510 26.730 7.958 BM SF 166.789 37.351 29.459 12.526
519.954 t-m 366.619 t-m
101.698 t 71.182 t
87.11 t-m 61.26 t-m
62.63 t 26.19 t
7.1
DESIGN OF LONGITUDINAL GIRDER FOR MAXIMUM REACTION FORCE
Depth of Girder
= = = = = = =
Dia. of top main bar clear cover Dia. of bottom main bar Dia. of stirrups Effective cover = (50 + 32 + 32+32/2) Effective depth
2.03 20 50 32 12 130 1.9
= = = = =
fyk fcd
αcc β1 β2
500 Mpa 15.633 Mpa 0.67 0.8 0.4
beff Depth of Girder Effective depth of Girder
= =
b bw
= =
2.03 1.9 2650 325
m m
beff,1
beff,2
mm mm bw
Effective width of flanged beam (Ref: cl. 7.6.1.2 of IRC:112-2011) beff ∑beff , I + bw = beff,i 0.2bi + 0.1Lo =
≤
beff,i
≤
bi
L0
=
0.7*effective span
b1
=
b2
=
beff,1
=
beff,2
=
So, beff
=
b neutral axis depth
1012.5 1012.5 1672.5 1672.5
14700 mm
=
mm mm
<
Simplified rectangular stress block to be considered : x/d
=
fyk x Ast β1 x fcd x b x d
500x8042 0.8x15.633x2650x1900
=
Xu
=
194.4418 mm
Xu
0.2 x 1855 mm
mm mm mm mm
0.87*fy*Ast
=
0.36*fck*b*Xu
Xu
=
0.87*fy*Ast/0.36*fck*b
Xu
68.67335 mm (Ref: Eq. 16.4 and 16.5 of IRC:112-2011)
Ƥw
Asw/(s.bwsinα) = = 0.003551173 Minimum shear reinforcement ratio for Beams Ƥwmin (0.072/fck)/fyk = = 0.000851915 < Additional tensile steel due to shear ∆Ftd 0.5 VED(cotϴ-cotα) =
(Ref: Eq. 10.20 of IRC:112-2011) 0.003551
= =
0.5x626345.6625x(cot21.8-cot90) 939951.031 N
=
939951.031/400
,OK (Ref: Eq. 10.16 of IRC:112-2011)
=
2 2161.887 mm /m
CRACKWIDTH CALCULATION FOR L.BEAM Parameters Overal depth of the section Width of the section Clear cover Effective cover cover Effective depth
(h) (W) (Cmin) (C) (d)
= = = = =
2030.00 475.00 50 130 1900
mm mm mm mm mm
Grade of concrete
=
2 35 N/mm
Grade of steel Maximum Serviceablility Case moment
= =
2 500 N/mm 366.62 kNm
=
(M)
fcm
2
Es
=
45 N/mm 2 200000 N/mm
Ecm Dia. Of Bar Φ1 n1
= = =
2 32308.25 N/mm 32 mm 5
Φ2
=
n2
32
=
= 200000/32308.25 6.19036933 95 mm 2 12063.00 mm /m width
=
804 mm /m width
Allowable crack width Wmax
=
0.3 mm
Crack width Wk
=
Modular Ratio (m) m Bar spacing Ast
= = =
Asc
5
2
Srmax(εsm - εcm)
Calculation of Sr.max :
(Eq. 12.5 of IRC:112-2011)
(max. crack spacing)
Depth of neutral axis : Transformed area of compression steel = (6.19 - 1 ) x 804
=
2 4173.057 mm
= (6.19x12063 ) -ASES +√ (AS ES )2 + 2bAsEsEc,eff d
=
2 74674.43 mm
Transformed area of tension steel dc
=
b Ec,eff dc
(-12063x200000)+√(12063x200000)^2+(2x475x12063x200000x32308.25x1900) 475x32308.25 dc = 631.530293 mm
If Spacing ≤ 5(c+Φ/2)
Sr.max
=
3.4 c + 0.425 k1 k2 Φ ρ ρ,eff
S M CONSULTANTS,BHUBANESWAR
(Ref. Eq.12.8 of IRC 112-2011)
Sr.max
else, Φ
=
1.3 (h-x)
2
n1 Φ1 + n2Φ
=
(Ref. Eq.12.12 of IRC 112-2011)
2
=
n1 Φ1 + n2 Φ2 Φ 5(C + Φ/2)
hc,eff = Lesser of
= =
330
k1
=
K2
=
> Bar Spacing = Hence Eq. 12.8 is valid. 0.8 for deformed bars
95 mm
0.5 for bending
a. 2.5 x (h-d) = b. (h-x)/3 = c. h/2 =
2.5 x(2030-1900) (2030-631.53)/3 (2030/2 )
=
Ac ,eff
=
475x325
рр,eff
= =
2 154375 mm AS / Ac.eff =
рр,eff
= =
5x32+5x32
32
hc,eff
Sr.max
5x32^2 +5x32^2
= = =
325 mm 466.1566 mm 1015 mm
325
12063/154375 (Ref. Eq, 12.7 of IRC 112-2011)
0.0781
3.4 c + 0.425 k1 k2 Φ
(Ref. Eq, 12.8 of IRC 112-2011)
ρ ρ,eff Sr.max
=
3.4 x50+0.425 x0.8x0.5x32
=
239.654 mm
0.0781 Calculation of ԑsm & ԑcm cracked Moment of Inertia Which gives Moment of Inertia Ix = 1/3 x475 x631.53^3 +74674.425 x1268.47 ^2 4 = 160032278293.803 mm Stress in steel is given by fs = m x M (d-x)/Ix = 6.19 x (366618900 x (1900 - 631.53) ) /160032278293.803 0.8fyk = 17.989 Mpa < = 400 Strain in tension steel =fs/Es = 17.989 /200000 = 0.00009 Zs = 160032278293.803/(1900-631.53) = 126161687.1
Zs
S M CONSULTANTS,BHUBANESWAR
=
160032278293.803/(631.53)
=
253403961.9
The Concrete Stres at top of section : σc MED Ecff / Zc ES = = = 0.6 x σs / Es = (εsm - εcm)
(366618900x32308.25)/(126161687.112x200000) 0.36fck = 0.469 < 12.6 Mpa (Ref: Cl. 12.2.1 of IRC: 112-2011) 5.4E-05
σSC - kt( fct,eff / рp,eff)(1+ ɑ e рp,eff )
=
≥
0.6 x σs / Es
ES (Ref: Eq. 12.6 of IRC: 112-2011) fct,eff
=
fctm
=
2.9 0.259(fck)2/3
Modular ratio = ɑe =
6.19
Kt
0.5
=
(εsm - εcm)
=
(εsm - εcm)
=
Crack Width WK
=
2.771268
17.989-0.5x(2.9/0.0781)(1+6.19x0.0781) 200000 -0.00005 =< 5.4E-05 = = =
S M CONSULTANTS,BHUBANESWAR
Srmax(εsm - εcm) 239.654 x -0.00005 -0.0119827
Main Reinforcement along Long span : Provide T-
12 @
Area of Steel Provided Provide T0@
2 1340 mm /m 1243.738 mm /m 2
150 mm c/c =
,OK
In LAYER I 2 754 mm
( π / 4 )12^2 x 1000 / 150 = 150 mm c/c In LAYER II
2 0 mm
Area of Steel provided = ( π / 4 )0^2 x 1000 / 150 Total area of Longitudinal Steel Provided,Ast = 754 + 0 = 2 754 mm /m
Therefore, Ast =
>
Design of shear Reinforcement: (Ref: Cl. 10.3.3 of IRC:112-2011) Check for shear: Shear force Overall depth of Section Effective depth of the section width of the Section
= = = =
ƥ1
=
Asl/(bw.d)
ƥ1
=
0.005
K
= = = = =
1+(200/d)0.5 1.857 35 Mpa 15.633 Mpa 0N
fck fcd NED
2 754 mm /m 2 628.8321 mm /m
