Deck Slab Design Report 300719 R1

REHABILITATION AND UPGRADATION OF 2 LANE ROAD WITH PAVED SHOULDERS OF MANGRULPIR TO MAHAN [DESIGN KM. 75/000 TO KM. 107/500] (TOTAL LENGTH = 32.5 KM) NH 161A IN THE STATE OF MAHARASHTRA ON EPC BASIS MODE

OWNER :

:

PUBLIC WORKS DEPARTMENT NH DIVISION, MAHARASHTRA

CONTRACTOR CLIENT

:

SHRI SWAMI SAMARTH ENGINEERS & ISC PROJECTS JV

AUTHORITY'S ENGINEER :

PROOF CONSULTANT

:

C. V. KAND CONSULTANTS PRIVATE LIMITED

SAFETY CONSULTANT

:

PAVETECH CONSULTANTS

DESIGN CONSULTANT

:

ATUL ENGINEERING CONSULTANCY SERVCIES PVT. LTD.

DESIGN OF DECK SLAB OF MJB @ CH. 106+541

DESIGN NOTE NO

:

XXX/MSM/MJB/DC/DECK/DN01

PAGES

:

1 + 10

=

11

REV.

MODIFICATIONS / PURPOSE OF ISSUE

PREPARED

No.

Details

Initials

18/06/19

R0

FOR REVIEW

SO

30/07/19

R1

Steel reduced as per PC's comments

SO

CHECKED

APPROVED

DATE Signature

Initials

Signature

Initials

Signature

DESIGN OF DECK SLAB OF MJB @ CH. 106+541

TITLE:

Sr. No. Description 1

General Features

2

Loads considered in Analysis of Deck slab

3

Partial Safety factors for Deck Slab

4

Design check for Ultimate Limit State

5

Design check for Serviceability Limit State

Note No: Designed SO

XXX/MSM/MJB/DC/DECK/DN01 Date

30/07/19

Checked Sheet No.

Page

XXX/MSM/MJB/DC/DECK/DN01 Date

Designed SO

30/07/19

Checked

0.45

Sheet No.

1.500

16.000 m

0.45

Note No:

0.45

DESIGN OF DECK SLAB OF MJB @ CH. 106+541

0.45

TITLE:

1.500

0.250

1.500

0.5 0.020

1.600

3.200

3.200

3.200

3.200

Input Data Span of the Superstructure (c/c of EJ) Width of the Superstructure Footpath to be provided (both side) Thickness of Crash Barrier Thickness of Hand Rail Clear Carriageway width Depth of the Superstructure Thickness of wearing coat c/s Area of the Crash Barrier c/s Area of the Hand Rail Deck system adopted No. of Girders Nos. of Bearing (per span) Type of Bearing

= = = = = = = = = =

17.000 m 16.000 m 1.500 m 0.450 m 0.450 m 11.200 m 1.500 m 75 mm m2 0.450 m2 0.200

= RCC Girder and slab = 5 = 10 = Elastomeric

Depth of Deck Slab at Cantiliver edge = Depth of Slab at face of the girder web = Clear Cover for Main Reinforcement =

250 250 40

mm mm mm

Material properties and Design parameters Unit weight of Concrete = Unit weight of Steel girders = Unit weight of Wearing coat = Grade of Concrete = Grade of Reinforcement =

2.500 7.800 2.200

t/m3 t/m3 t/m3

M 40 Fe 500D

40 Characteristic Compressive Strength of Concrete, fck = Mpa Secant modulus of Elasticity of Concrete, Ecm = 33345.764 Mpa 50 Mean Compressive Strength of Concrete, fcm = Mpa Mean axial tensile Strength of Concrete, fctm =

3.00

Mpa

1.600

DESIGN OF DECK SLAB OF MJB @ CH. 106+541

TITLE:

Note No:

XXX/MSM/MJB/DC/DECK/DN01 Date

Designed SO

Mean flexural tensile Strength of Concrete, fctm,fl h fctm,fl for Top Slab Design Compressive strength of Concrete, fcd Where, α γm So, fcd

Sheet No.

= Max {[1.6-(h/1000)]*fctm , fctm} = Total depth of member 3.00 = Mpa = α * fck / γm 0.67 = 1.50 = For Basic & Seismic Comb 17.87 = Mpa

Characteristic Strength of Reinforcement, fyk = Design Yield Strength of Reinforcement, fyd = Modulus of Elasticity of Steel, Es = Permissible Compressive Stress in Concrete Permissible Compressive Stress in Concrete Permissible Tensile Stress in Steel Condition of Exposure Limiting Crack width Limiting Crack width

30/07/19

Checked

500 434.78 200000

Mpa Mpa for Basic Comb Mpa

19.20 = Mpa for Rare Comb 14.40 = Mpa for Quasi Permanent comb 300 = Mpa = Moderate 0.3 = mm for Quasi Permanent Comb 0.2 = mm for Frequent Comb

Idaelization of the Deck slab for transverse analysis The Deck slab has been modeled in STAAD pro as a line element by considering 1.0m strip at mid span, providing supports representing the I girders supporting the deck slab.

Schematic diagram of STAAD Pro Model

1

2

3

4

5

6

7

8

9

10 11 12

13

14 15 16

17

Qualitative diagram for division of Deck slab for STAAD modeling

18 19

20

21

TITLE:

DESIGN OF DECK SLAB OF MJB @ CH. 106+541

Note No:

XXX/MSM/MJB/DC/DECK/DN01 Date

Designed SO

30/07/19

Checked Sheet No.

1. Dead loads- Self weight is calculated based upon unit weight mentioned below: Unit weight of Steel girder = Unit weight of RCC Concrete = Unit weight of wearing coat =

3 78.00 kN/m 3 25.00 kN/m 3 22.00 kN/m

2. Super Imposed Dead loads are calculated as mentioned below: Load due to Crash Barrier = 0.45 * 25 = 11.250 kN/m Load due to Crash Barrier = 0.2 * 25 = 5.000 kN/m Load due to wearing coat = MAX(0.075*22 , 2) kN/m2 = 2.000

3. Vehicular Live Loads are considered for vehicles like Class A, Class 70R wheeled, Class 70R Tracked and Class 70R Boggie specified in IRC: 6 - 2017 for various combinations having possibilities of producing worst forces (shear force and Bending moments) in the deck slab of superstructure inclusive of the Impact factor. These considered combinations of vehicles' wheel loads have been dispersed in transverse as well as longitudinal direction according to IRC: 112-2011. So, ultimately Point loads due to wheels have been converted to dispersed Uniformly distributed loads and these UDLs have been run across the width of the superstructure.

Typical Calculation to evaluate dispersed Load due to wheel load of Vehicle Class A - wheeled on Continuous Span beff = 1.2 * a +b1 = α * a ( 1-(a/lo) ) + b1 Where, beff α a lo b b1

= = = = = = =

For Cantilever Span For one way span (supported @ both ends)

Effective width of the slab on which load acts Constant based upon b/lo Distance of CG of concerntrated load from nearer Support Effective span Width of the slab Breadth of the concentrated/contact area Dimension of Tyre + 2*(Thickness of WC) Size of the wheel b1 b lo b/lo α

= = = = = =

Max Wheel Load, P = Dist from Max Loaded Wheel = Impact Factor =

500 x 250 400 mm 16.00 m 3.20 m 5.000 2.60

5.70 T 1.80 m 1.49 (Ref: IRC: 6 - 2017_Clause:208)

Location of the Wheel in Transverse direction Location of the Wheel along the vehicle movement Distance from face of left girder web, aLeft Distance from face of right girder web, aRight Distance from nearest support, a

= = = = =

8.000 3.500 1.890 1.290 1.290

m m m m m

Dispersion width in Transverse direction, beff 1 = (2.6*1.29*(1-(1.29/3.2)))+(400/1000) = 2.402 m Load dispersed in Transverse direction, Q = P / beff = 4.041 T Dispersion width in Longitudinal direction, beff 2 = 500 + 2*75 + 2*250 = 1150 mm Load dispersed in along the vehicle movement = 4.041 / 1.15 = 3.5139 T/m

Note No: TITLE:

DESIGN OF DECK SLAB OF MJB @ CH. 106+541 Designed SO

XXX/MSM/MJB/DC/DECK/DN01

Checked

Date Sheet No.

Table: 3.2 Partial Safety Factors for Verification of Structural Strength (To be checked for Internal failure or excessive deformation) Load specifications

Sr. No. A

Basic Accidental Seismic Combinatio Combinatio Combinatio ns (B) ns (C) ns (S) Permanent Loads

1

Dead Load, SIDL (Except Surfacing), Snow Load

a

Adding to the effect of Variable loads

1.35

1.00

1.35

b

Relieving the effect of Variable loads

1.00

1.00

1.00

2

Surfacing (Wearing Coat)

a

Adding to the effect of Variable loads

1.75

1.00

1.75

b

Relieving the effect of Variable loads

1.00

1.00

1.00

Variable Loads

B 1

CWLL, FPLL, Braking and Centrifugal force

a

Leading Load

1.50

0.75

0.00

b

Accompanying Load

1.15

0.20

0.20

c

Construction live load

1.35

1.00

1.00

Table: 3.3 Partial Safety Factors for Verification of Serviceability Limit State (To be checked to have control on Stress, deflection, vibration, crack width, settlement and Creep & Shrinkage effects) Load specifications

Sr. No.

Permanent Loads

A 1

Dead Load, SIDL (Including Surfacing), Snow Load, Weight of Backfill, Creep and Shrinkage effect, Earth pressure due to Backfill

1.00

1.00

a Leading Load

1.00

0.75

b Accompanying Load

0.75

0.20

1.00

Variable Loads

B 1

Rare Frequent Quasi-Per Combinatio Combinatio Combinatio ns (R) ns (F) ns (Q)

CWLL, FPLL, Braking and Centrifugal force 0.00

30/07/19

Note No: TITLE:

DESIGN OF DECK SLAB OF MJB @ CH. 106+541

XXX/MSM/MJB/DC/DECK/DN01 Date

Designed SO

30/07/19

Checked Sheet No.

Forces Summary for Basic Combination for ULS Check Member Deck Slab

Location

Bending Moment Memb Shear Hogging Sagging number Force (kN) (kN*m) (kN*m) 1,4,17,20 172.137 99.8529 36.84825 4 To 17 215.899 57.518 51.262

Section

Cantilever Simply supported

A B

Design of Section

(Ref: IRC: 112-2011 Cl: 16.5.1.1)

Min Ast,req = Max (0.26 * (fctm/fyk) * b * d , 0.0013 * b * d) Max Ast = 0.025 * Ac For Tension Reinf. Other than laps = 0.04 * Ac For Tension + Comprssion Reinf at any section Xu = (0.87 * fyk * Ast) / (0.362 * fck *b) Leverarm, z = d - (0.416 * xu) Ast,req = M / (0.87 * fyk * z) Xu, max = (0.0035 / (0.0055 + fy/1.15Es) ) * d Width, b = 1000 mm h = Overall depth of member in mm d = Effective depth of member in mm Section A B

Sagging Moment 36.848 51.262

h 250 250

Reinforcement Dia Spacing Dia Spacing

12 10

200 200

0 10

200 200

d

Ast,prov

Ast,min

204 205

565.49 785.40

318.24 319.80

Ast,m ax 6250 6250

Check Ast,range

Xu

Xu,max

OK OK

16.988 23.594

93.042 93.499

Check Check z Ast, Req Ast,req Xu OK 196.9 430.139 OK OK 195.2 603.754 OK

Hogging Section Moment A 99.853 B 57.518

h 250 250

Reinforcement

d

Ast,prov

Ast,min

202 204

1398.01 958.19

315.12 318.24

Dia Spacing Dia Spacing

16 12

200 200

200 200

10 10

Ast,m Check Ast,ran ax ge 6250 OK 6250 OK

Xu

Xu,max

41.998 28.785

92.130 93.042

Check Check z Ast, Req Ast,req Xu OK 184.5 1243.963 OK OK 192 688.584 OK

Calculation for distribution Reinforcement As per Clause: 16.6.1.1 (3), The minimum secondary transverse reinforcement should be 20% of main reinforcement. Asec, min = 0.2 * 785.398 = 0.2 * 958.186 = 0.2 * 1398.009

= = =

157.080 mm2 in Bottom. 191.637 mm2 in Top Sim Supp. 279.602 mm2 in Top Cantilever.

Provide 10 mm φ bar at Provide 10 mm φ bar at Provide 10 mm φ bar at

300 mm c/c = 300 mm c/c = 200 mm c/c =

Check for Shear Reinforcement Required

261.799 mm2 …OK 261.799 mm2 …OK 392.699 mm2 …OK

Ref: IRC: 112-2011: CL 10.3.2

Ved = The design shear force Vrdc = Max(0.12 * k * (80 * p1 * fck)^(0.33) + 0.15 * σcp) * bw*d, (Vmin + 0.15 *σcp) * bw * d) Design shear resistance of the member without shear reinforcement k = Min(1+√200/d, 2) Ned = Design value of applied axial force σcp = Is mean compressive stress, Minimum of (Ned / Ac ), (0.2 * fcd) p1 = Minimum of ((Ast / bwd), 0.02) Vmin = 0.031 * k^(3/2) * fck^(1/2), Used in calculating Vrdc β = αv/2*d, Is the ratio of the longitudinal force in the new concrete and the total longitudinal force av = 0.5 * d < αv < 2 * d, Where av is distance from the edge of a support

Section

Ved

A B

172.137 215.899

Dist

av

0.250 0.250 0.250 0.250

β

β*Ved

d

k

Ast,prov

p1

Vmin

Ned

σcp

0.61 0.61

105.476 131.646

204 205

1.990 1.988

1398.009 958.186

0.0069 0.0047

0.55 0.55

0.000 0.000

3.573 3.573

Vrdc

Check Ved

245.710 SR not Reqd 230.358 SR not Reqd

Design Shear Reinforcement Asw fywd z αcw γ Adopted θ Vrdmax

= = = = = = =

Ref: IRC: 112-2011: CL 10.3

Is the cross sectional area of shear reinforcement = 434.783 Mpa fyk/γm, Is the design yield strength of the shear reinforcement 0.9 * d, Lever arm for R.C section Is a coefficient taking account of the state of the stress in the compression chord, 1, (Where σcb = 0) (0.6 * (1 - (fck / 310)), Is strength reduction factor for concrete cracked in shear = 0.542 45 , Adopted θ for calculation of Vrdmax (αcw * bw * z * γ * (fcd//(cotθ+tanθ))) The design value of maximum shear force which can be sustained by the member limited by crushing of te compression struts

Vrds = (Asw/S) * z * fywd * cotθ The design value of the shear force which can be sustained by the yielding shear reinforcement Vns = Net design shear force (algebraic sum of Ved, Vccd and Vtd) θ = 0.5 * sin^(-1)*((2 * Vns / (αcw * bw * z * v1 * fcd)), Inclination angle of concrete compressive truss Vrd = For member with vertical shear reinf, the shear resistance Vrd is smaller value of "Vrdmax" and "Vrds" Section

Ved

A B

172.137 215.899

Reinf Dia Spacing 0 200 0 200

Asw

z

αcw

Vrdmax

θ

Vrds

Vrd

Check Ved
0.00 0.00

183.60 184.50

1.200 1.200

1066.63 1071.86

4.64 5.81

0.0 0.0

0.0 0.0

OK OK

Check for Shear Capacity Section

Ved

b

d

A B

172.137 215.899

1000 1000

204 205

Check, 0.5 * b * d * γ Ved<0.5*b*d * fcd *γ*fcd

987.62 992.46

OK OK

Check for Additional Shear Ref: IRC: 112-2011: Mrd = 0.87 * fyk * Ast * (d - 0.416 * xu), Design moment required ∆Fd = (0.5 * Ved * cotθ), ∆Fd is additional tensile force in the longitudinal reinforcement

Section

∆Fd

A B

86.068 107.949

Check for Sagging Moment Check for Hogging Moment Sagging (Med/z) + (Med/z) + Check, Mrd/z > Hogging Check, Mrd/z > z Mrd Mrd/z z Mrd Mrd/z (Med/z)+Fd Moment (Med/z)+Fd Moment ∆Fd ∆Fd 36.848 196.9 86.255 48.443 245.987 OK 99.853 184.5 86.609 112.218 608.134 OK 51.262 195.2 108.212 66.684 341.648 OK 57.518 192 108.249 80.038 416.811 OK

Note No: TITLE:

DESIGN OF DECK SLAB OF MJB @ CH. 106+541

Forces Summary for SLS Check Member

Location

Section

Memb number

Deck Slab

Cantilever Simply supported

A B

1,4,17,20 4 To 17

Rare Combination Shear Bending Moment Force Hogging Sagging (kN) kNm kNm 116.262 68.049 24.506 144.475 38.597 34.375

XXX/MSM/MJB/DC/DECK/DN01

Designed SO

Checked

Quasi Combination Shear Bending Moment Force Hogging Sagging (kN) kNm kNm 19.415 15.124 0.357 12.559 4.988 3.361

Modular Ratio 'm' = Es/Ecm' <Ecm' is Modulus of Elasticity steel For long term loading From CL.6.4.2.5 point no.4 IRC:112-2011, Ecm can be modified by a factor (1/(1+ф )) accounting for long term creep effect where ф is the creep co-efficient defined by Eq.6.9 and the table 6.9. The development of creep with time may be taken as ф(t,to) = β(t,to).ф(ȸ,to) Notational size of member "ho" = 2Ac/u Ac = Cross sectional Area in mm2 u = Perimeter in contact with atmosphere in mm where β(t,to) t t to

= = = = = (t-to) = = βH =

[(t-to)/(βH+(t-to))]^0.3 is the age of concrete in days at the time considered. 25550 days is the age of concrete in days at the time of loading. 90 days is the actual duration of loading in days. 25460 days is the coefficient depending on the relative humidity(RH in percent) and the notation member size (ho in mm)

Stress Calculation in Concrete and Reinforcement m = Modular ratio As = Area of steel provided b = Breadth of structure d = Depth of the structure provided Xu = Depth of Neutral Axis INA = Moment of Inertia 3 INA (UnCracked) = bh /12 3 2 INA (Cracked) = b *xu /3 + m* As *(d-xu)

Date Sheet No.

30/07/19

Compressive Stress in concrete σc = MRARE* Xu / INA Tensile Stress in steel σst = m* MRARE* (d - Xu ) / INA Flexural comressive strength, fctm,fl = Max

1.6 −

h fctm; fctm 1000

(IRC:112, Cl.6.4.2.3, Eq.6.6)

fctm,fl = Mean Flexural Tensile Strength of solid beam h = Total depth of member in mm fctm = Mean axial tensile strength from table 6.5 Width of the member, b = 1000 d = Effective depth of member in mm Stress Check for SLS Load Combinations SLS (R Comb)

Sagging Moment

h

d

Ast, Provided

Section

kNm/m

mm

mm

mm

A B

24.51 34.38

250 250

204 205

565.49 785.40

SLS (R Comb)

Hogging Moment

h

d

Ast, Provided

Section

kNm/m

mm

mm

mm2

A B

68.05 38.60

250 250

202 204

1398.01 958.19

SLS (QP Comb)

Sagging Moment

h

d

Ast, Provided

2

2

Section

kNm/m

mm

mm

mm

A B

0.36 3.36

250 250

204 205

565.49 785.40

SLS (QP Comb)

Hogging Moment

h

d

Ast, Provided

Section

kNm/m

mm

mm

mm2

A B

15.12 4.99

250 250

202 204

1398.01 958.19

Ecm'

Moment of Inertia, I

MPa

mm

4

Y/2

σc

(Stress

fctm,fl

mm

MPa

MPa

14163.66 7.07E+08 14163.66 7.18E+08

125 125

4.33 5.99

3.00 3.00

Ecm'

Moment of Inertia, I

Y/2

σc (Stress)

fctm,fl

MPa

mm4

mm

MPa

MPa

14163.66 6.87E+08 14163.66 7.07E+08

125 125

12.38 6.82

3.00 3.00

Moment of Inertia, I

Y/2

Ecm' MPa

4

σc

(Stress

fctm,fl

Crack/Uncra Modula cked r Ratio

Cracked Cracked

14.12 14.12

Crack/Uncra Modula cked r Ratio

Cracked Cracked

14.12 14.12

Crack/Uncra Modula cked r Ratio

N.A depth (xu)

INA

mm

mm

4

17.0 3E+08 23.6 4E+08 N.A depth (xu)

INA

mm

mm4

42.0 5E+08 28.8 4E+08

N.A depth (xu)

INA mm

4

mm

MPa

MPa

mm

14163.66 7.07E+08 14163.66 7.18E+08

125 125

0.06 0.59

3.00 Uncracked 14.12 3.00 Uncracked 14.12

17.0 1E+09 23.6 1E+09

Ecm'

Moment of Inertia, I

Y/2

σc (Stress)

fctm,fl

MPa

mm4

mm

MPa

125 125

2.75 0.88

mm

14163.66 6.87E+08 14163.66 7.07E+08

Crack/Uncra Modula cked r Ratio

N.A depth (xu)

INA

MPa

mm

mm4

3.00 Uncracked 14.12 3.00 Uncracked 14.12

42.0 1E+09 28.8 1E+09

Compre Max C. ssive Stress Stress MPa MPa

1.5 2.2

14.40 14.40

Compre Max C. ssive Stress Stress MPa MPa

5.39 2.62

14.40 14.40

Compre Max C. ssive Stress Stress MPa MPa

0.00 0.06

10.80 10.80

Compre Max C. ssive Stress Stress MPa MPa

0.49 0.11

10.80 10.80

Check

OK OK Check

Tensile Max T. Stress Stress MPa

MPa

230.4 238.4

300 300

Tensile Max T. Stress Stress MPa

MPa

OK OK

290.0 225.6

300 300

Check

Tensile Stress MPa

OK OK

0.7 6.6

Check

Tensile Stress MPa

OK OK

26.2 9.5

Check

OK OK Check

OK OK

SLS CRACK WIDTH CHECK (QUASI PERMANENT LOAD COMBINATION) 1) CHECK Ast,min for crack control Minimum area of reinforcement may be calculated as follows As,min = kc k fct,eff Act/σs As,min A ct σs fct,eff

(as per IRC-112 Eq 12.1)

= = = =

is the minimum area of reinforcing steel within the tensile zone is the area of concrete within the tensile zone. = b*(h-xu) 500 Mpa is the absolute value of maximum stress permitted= is the mean value of the tensile strength of the concrete. 2.9 Mpa or fctm fct,eff should be taken as the grater of k = is the coefficient which allows for the effect of non-linear self -equilibrating stresses, which leads to a reduction of restraint forces = 1.0 for webs with h< 300 mm flange width less then 300 mm = 0.65 for webs with h> 800 mm flange width less then 800 mm kc = is the coefficient which takes account of the stress distribution within the section. For Rectangular sections and webs of box sections and T sections σ Kc = 0.4 1 − ℎ c ≤1 𝑘1 ∗ fct,eff ℎ σc = is the mean stress of the concrete acting on the part of the section under consideration. σc =

𝑁𝐸𝑑 𝑏ℎ

NEd = is the axial force at the serviceability limit state acting on the part of the cross-section under consideration. k1 = is a coefficient considering the effects of axial forces on the stress distribution. k1 = 1.5 if NEd is a compressive force k1 = 2h*/3h if Ned is a tensile force h*= h for h < 1.0 m h*= 1.0 m for h >= 1.0 m For Sagging Moment QP h d Comb Section mm mm A 250 204 B 250 205

Act

Mean Stress 'σc'

mm2 187012 181405.5

Mpa 0.00 0.00

h* 0.25 0.25

fct,eff 3.00 3.00

k 1.00 1.00

kc

As,min

0.33 0.40

mm2 368.04 435.37

As,provid Check ed mm2 565.49 OK 785.40 OK

For Hogging Moment Mean Act=b*(hQP h d Stress 'σc' Comb xu) 2 Section mm mm Mpa mm A 250 202 160001.8 0.00 B 250 204 175214.7 0.00

h* 0.25 0.25

fct,eff 3.00 3.00

k 1 1

kc

As,min

0.40 0.40

mm2 384.00 420.52

As,provid Check ed mm2 1398.01 OK 958.19 OK

2) CHECK FOR MAXIUM SPACING b/w bars For Sagging Moment Bar Max SLS Dia Dia (QP Comb) фeq фeq Sectio mm mm A 12 32 B 10 32

Spacing b/w bars Provided Required mm mm 200 300.00 200 300.00

Check

OK OK

For Hogging Moment Bar Max SLS Dia Dia (QP Comb) фeq фeq Sectio mm mm A 16 32 B 12 32

Spacing b/w bars Provided Required mm mm 200 300.00 200 300.00

Check

OK OK

3) CHECK FOR CRACK WIDTH 1) Crack width varies between the reinforcement bar depanding upon the spacing of the bars. The crack width, Wk, may be calculated from (IRC-112 Eq.12.5) Wk = Sr,max(εsm-εcm) Sr,max = Maximum crack spacing For pure bending,

Sr,max = 3.4𝑐 +

0.17ф

ρρeff

ρPeff = As/Ac,eff As = Area of steel provided Ac,eff = effective area of concrete in tension surrounding the reinforcement, of depth hc,eff, where hc,eff is lesser of 2.5(h-d);(h-x)/3;or h/2 εsm = mean stran in the reinforcement under the relevant combination of loads. εcm = is the mean strain in the concrete between cracks. εsm-εcm may be calculated form: εsm-εcm = [σsc-kt fct,eff (1+αeρρ,eff)/ρρ,eff]/Es]>,0.6σsc/Es (IRC-112 Eq.12.6) kt = factor dependent on the duration of laod which may be taken as 0.5 αe = ratio of Es/Ecm'

For Sagging Moment QP Comb Section

A B

hc,eff

Ac,eff=b*hc,

As Provided

ρρeff

eff

mm 77.671 75.469

mm2 77670.66 75468.5

mm2 565.49 785.40

0.007281 0.010407

As Provided

ρρeff

Dia

Cover, c фeq mm 12 10

mm 40 40

Sr,max

INA

σsc

mm mm4 MPa 416.1978 3E+08 3.4 299.3521 4E+08 23.3

xu

mm 17.0 23.6

kt

αe

εsm-εcm

Wk

Check

0.5 0.5

14.12 14.12

0.0000 0.0001

0.0042 0.0209

OK OK

kt

αe

εsm-εcm

Wk

Check

0.5 0.5

14.12 14.12

0.0002 0.0001

0.0590 0.0286

OK OK

For Hogging Moment QP Comb Section

A B

hc,eff

Ac,eff=b*hc, eff

mm 69.334 73.738

mm2 69333.94 73738.24

mm2 1398.01 958.19

0.020163 0.012994

Dia

Cover, Sr,max INA σsc c фeq mm mm mm mm4 MPa 16 50 304.8978 5E+08 64.5 12 50 326.9904 4E+08 29.2

xu

mm 42.0 28.8