Deep Beam Check

8/12/2019 Deep Beam Check

1/10

Subject :

Title

Drg.No:

Data

Width of beam B = 1100 mm

Depth of beam D = 8000 mm

Clear cover to reinforcement at top and bottom = 50 mm

Clear cover to reinforcement at sides = 50 mm

Diameter of main reinforcement = 16 mm

Diameter of Stirrup = 0 mm

Effective Span = 13.8 mm

Effective depth beam Deep Beam d = 7918 mm

Lever arm Z = 2402.76 mm

Characteristic strength of concrete fck = 40 N/mm2

Characteristic strength of reinforcement fy = 500 N/mm2

Characteristic strength of Shear reinforcement fy = 415 N/mm2

Design Moments, tors ion & s hear

Sl.No.Shear Force

(T)

1 -

2 -

3 507.94

3 0.00

Design of Top Reinforcement : - Refer Secti on 41.3 of IS:456-2000

At end support

Support Moment + Torsion :-

Maximum equivalent support moment, Me1= Mu+ MT

If MT > Muthen Me2= MT - Muacting opposite to sense of Me1

MT= Equivalent Bending moment due to torsion

MT= Tu (( 1+D/b)/1.7) = 249.15 T.M

Maximum equivalent support moment Me1

= 2691 T.m

Me2 = 0.0 T.m

Limiting Moment capacity of the section Mulimit = 36689 T.m

Mu2 = 0.00 T.m

Mtop/(B*d2) = 0.390 N/mm

2

Mulimt/Bd2 = 5.320 N/mm

2

Percentage of steel correspong to limiting moment Ptlimit = 1.510 %

Percentage of tensile steel pt-top = 0.329 %

Reinforcement required at top Ast = 28659.4 mm2

Minimum reinforcement

Percentage of Reinforcement required pt, min = 0.21 %

Minimum Reinforcement required Ast, min = 17855.09 mm2

Diameter of main bar at (top Thru bars) = 32 mm

Number of Bars provided at top (Thru) = 30 Nos

Reinforcement provided @ top thru Zone 1 = 24127.43 mm2

Moment (T.M)Staad Memb

No. / LoadDescription

-

64.233

2441.503

Torsion (T.M)

51.20

60.65

51.20

Support Moment +

Torsion (maxside)

Beam25 -

LC160

Project :

Client :

Job :

SEG deep beam at retrieval shaft Prepared : Project Code :

Retrieval shaft portion grid 19 to 21 Checked : Job Code :

Date: Rev :

Span Moment + TorsionBeam9080 -

LC91

Shear Force + Torsion Beam25 -LC160

Support Moment +

Torsion on (other end)Beam - LC - 0.00


2/10

Subject :

Title

Drg.No:

Project :

Client :

Job :



Date: Rev :

Diameter of main bar at (top Extra bars) = 20 mm 25 mm

Number of Bars provided at top (Extra) = 60 Nos 0 Nos

Reinforcement provided @ top Extra Zone 2 = 18849.56 mm2

Total Reinforcement @TOP = 42977.0 mm2

Reinforcement provided is adequate

Design of B ottom Reinforcement :-

At mid span

Maximum Span Moment + Torsion :-

Maximum equivalent support moment, Me1= Mu+ MT

If MT > Muthen Me2= MT - Muacting opposite to sense of Me1

MT= Equivalent Bending moment due to torsion

MT= Tu (( 1+D/b)/1.7) = 295.16 T.M

Maximum equivalent support moment Me1 = 359.39 T.m

Me2 = 230.92 T.m

Limiting Moment capacity of the section Mulimit = 36688.95 T.m

Mu2 = 0.00 T.m

Mbot/(B*d2) = 0.052 N/mm

2

Mulimt/Bd2 = 5.320 N/mm2

Percentage of steel correspong to limiting moment Ptlimit = 1.510 %

Additional % of tensile steel for balancing in DR beam pt2 = 0.000 %

Percentage of tensile steel ptbottom = 0.015 %

Percentage of compression steel pt-top = 0.03 %

Reinforcement required at bottom Ast-bottom = 1287.7 mm2

Minimum re in forcement

Minimum % of Reinforcement required pt, min = 0.21 %

Minimum Reinforcement required Ast, min = 17855.09 mm2

Diameter of main bar at (bottom Thru bars) = 32 mm

Number of Bars provided at bottom (Thru) = 10 Nos

Reinforcement provided @ bottom thru = 8042.48 mm2

Diameter of main bar at (bottom Extra bars) = 32 mm 25 mm

Number of Bars provided at bottom (Extra) = 0 Nos 0 Nos

Reinforcement provided @ bottom Extra = 0.00 mm2

Total Reinforcement = 8042.48 mm2


Check for Shear Reinforcem ent :-

Maximum Shear Force + Torsion :-

Maximum equivalent Shear Force Ve= Vu+ 1.6(Tu/b) Ve = 582.42 T

Nominal Shear stress tv = 0.67 N/mm2

% of Reinforcement provided pt, provided = 0.59 %

Shear strength of concrete tc = 0.54 N/mm2

Provide Shear reinforcement

Refer Sect ion 41.4.3 of IS:456-2000

Shear Reinforcement required Asv = Tu + Vu mm2/mm

sv b1*d1*0.87*fy 2.5*d1*0.87*fy

b1 = 1000 mm

d1 = 7900 mm

Asv/Sv = 0.892 mm2/mm

+

+


3/10

Subject :

Title

Drg.No:

Project :

Client :

Job :



Date: Rev :

Diameter of shear link provided = 20 mm 0 mm

Number of legs provided = 2 No's + 0 No's

Spacing of shear reinforcement provided = 150 mm 150 mm



Check for Minimum Shear Reinforcement:- Refer Cl ause 26.5.1.6 of IS:456-2000

Min.Shear reinforcement required

Asv =

sv Asv/Sv = 0.38 mm2/mm

Diameter of shear link provided = 16 mm

Number of legs provided = 4 No's

Spacing of shear reinforcement provided = 150 mm



Side face Reinforcement : -

% of side face Reinforcement required pt = 0.05 %

Reinforcement required Ast, min = 4354.90 mm2

Diameter of side face reinforcement = 16 mm

Number of bars provided as side face reinforcement = 22 Nos

Summary

Provide Y - 32 nos(thru) & Y - 20+ Y - 25 nos(extra) as Top reinforcement

Provide Y32 - 10 nos(thru) & Y32 - 0+ Y25 - 0 nos(extra) as bottom reinforcement

Provide 2L-Y 20+ 0L-Y0@150 mm c/c outer ring and 4L-Y16@150mm c/cas Shear reinforcement

Provide Y16 - 22nos as Side face reinforcement on each face

0.87*fy

(tv- tc)*b


4/10

Contract UAA01Design and Construction of Underground Stations and Associated Tunnels

7.0 SLAB LATERAL DESIGN CHECK

7.1 Deep Beam design check

Support reaction = 1244*6.3/2 = 3920 kN

3920 kN

1244 kN/m

3.4

8

m

12 m

Clear span , l = 12 m

depth, D = 8 m

Effective span, leff = 13.8 m

Moment at mid span = 15061 kNm (sagging)

Moment at face = 36555 kNm (hogging)

leff/ D = 1.725 < 2.5

hence design as deep beam in accordance with Section 29

of IS 456 : 2000

Reinforcement

(for continuous beams where 1 < l/D < 2)

lever arm, z = 0.2(l+1.5D)

= 5.16 m

Design for hogging close to the ends (supports)

Mu = 0.87 fy As z = 2.2446 As

= 36555 kNm

As (hogging) = 16286 mm2

0.5 (leff/ D-0.5) proportion of the above reinforcement should be

placed close to the tension face

Beam Design check

at 2.6m d eep po rt ion

239042087.xlsx.ms_office

Deep Beam Design

_______________________________________________________________________________________________7/21/2014


5/10


61 %= 9975 mm2

ThisR/f shall be provided in 0.2D from top as = 1.6 m

Refering Section 5 from our reinforcement drawing number

TTA/465/SEG/1275423

The Reinforcment provided in top 1.5m zone is

Bar mark b1, b4 is provided for lateral load resistance

b1 = 9-Y32 = 7238.2 mm2

b4 = 9-Y25 = 4417.9 mm2

mm2

Also slab reinforcement b7 and b9 has been provided

b7 = 8-Y25 = 3927 mm2

b9 = 8-Y20 = 2513 mm

2

Total R/f in 1.3m zone = 18096 mm2

Area of R/f provided = 18096 mm2

Remaining = 6311 mm2

to be provided in the zone 0.3D on either side of the mid depth

of beam

0.3D = 2.40 m

Distribution reinforcement in this zone is Y-16 @150 c/c

at both top and bottom faces

Total Number of Top bars = 16.00

Total Number of Bottom bars = 16.00

Total bars in this zone = 32

Area of R/f provided = 6434 mm2

hence ok

hence ok


Deep Beam Design

_______________________________________________________________________________________________7/21/2014


6/10


Design for sagging at mid span

As (sagging) = 6709.9 mm2

placed within a distance 0.25D-0.05 l i.e. 1.31 m

Reinforcement in this zone is Y-20 @150 c/c at both top

and Y-25 @150 at bottom faces

Total Number of Top bars = 9

Total Number of Bottom bars = 9

Area of R/f provided 7031 mm2

Note: In addition to this an additional face bar of 7-Y25 has

been provided i.e. 3436 mm2 area

36555

kN-m

5628

kN-m

13217 kN-m

15061 kN-m

(@ 8m from the face of the temp opening)

hence ok

Bending Moment Diagram for given loading


Deep Beam Design

_______________________________________________________________________________________________7/21/2014


7/10


Design of deep beam is presented above

For the portion of 2.75m depth, between permanent and temporary

opening following sections are taken

1. Hogging B.M. at support

2. Sagging B.M. at the face of permanent opening


Deep Beam Design

_______________________________________________________________________________________________7/21/2014


8/10

Contract UAA01

Design and Construction of Underground Stations and Associated Tunnels__________________________________________________________________________

7.2 Beam Design ch eck at 2.6m deep po rt ion

7.2.1 Design Load CalculationsUOM

Section Number 1 2

STAAD Output

a) Factored Max. B.M.from STAAD (ULS) kN-m 5628 13217

a.i) Load case for Max. B.M. from STAAD ULS

b) Factored Max. B.M.from STAAD (SLS) kN-m 4329 10167

b.i) Load case for Max. B.M. from STAAD SLS

c) Factored Max. S.F. from STAAD (ULS) kN 7528 7528

c.i) Load case for Max. S.F. from STAAD ULS

d) Axial Compression ULS (Pu) kN

e) Axial Compression SLS kN

7.2.2 Load Combinations1) 1.5*(DL+IL+EP)SERVICE STAGE kN-m 5628 13217

DESIGN LOADS (Mu) kN-m 5628 13217

ii) SLS Load Combinations (B.M.)

1)1.0*(DL+IL+EP)SERVICE STAGE kN-m 4329 10167

SLS MOMENTS (MSLS) kN-m 4329 10167

iii) ULS Load Combinations (S.F.)

1) 1.5*(DL+IL+EP)SERVICE STAGE kN 7528 7528

DESIGN LOADS (Vu) kN 7528 7528


design of Beam bet. openings

_____________________________________________________________________________


9/10

Contract UAA01

Design and Construction of Underground Stations and Associated Tunnels___________________________________________________________________________

7.2.3 Calculations of Flexural Reinforcement (ULS Design)UOM

Section Number 1 2

Design Parameters

Actual Clear Cover (c ) mm 75 75

Nominal cover (Cnom) (For Calculating Crack Width) mm 45 45

Width of Section (b) mm 1000 1000

Concrete Grade (fck) N/mm 40 40

Main R/f Steel Grade (fy) N/mm 500 500

Stirrup Steel Grade (fys) N/mm 415 415

Dia of each leg of stirrup provided mm 12 12

Maximum Permissible Crack Width mm 0.3 0.3

Modulus of Elasticity of Steel (Es) N/mm 2E+05 2E+05

Xu(max)/ d 0.456 0.456

Total Depth of Section (D) mm 2600 2600Distance of compression face to point of crack (a) mm 2570 2570

Dia.of 1st layer of tension R/f Provided (1t) mm 25 32

Number of bars of 1st Layer tension of Reinforcement (n1t) 7 7

Dia.of 2nd layer of tension R/f Provided (2t) mm 20 32

Number of bars of 1st Layer tension of Reinforcement (n2 t) 7 7

Dia.of 3rd layer of tension R/f Provided (3t) mm 0 32

Number of bars of 1st Layer tension of Reinforcement (n3 t) 7 7

CG. Of Steel from Bottom = Effective Cover (h)BOTTOM mm 118 167

Effective Depth of Section from Bottom (deff)BOTTOM mm 2482 2433

Dia.of 1st layer of compression R/f Provided (1C) mm 0 0

Number of bars of 1st Layer of compression Reinforcement (n1c) 150 150

Dia.of 2nd layer of compression R/f Provided (2c) mm 0 0

Number of bars of 1st Layer of compression Reinforcement (n2 c) 150 150

Dia.of 3rd layer of compression R/f Provided (3c) mm 0 0

Number of bars of 1st Layer of compression Reinforcement (n2 c) 150 150

CG. Of Steel from Top = Effective Cover (h)TOP mm 0 0

Factored Moment on Section = Mu kN-m 5628 13217

Limiting Moment of Resistance = Mu(lim) kN-m 32703 31425

Type of Section Singly R/f Singly R/f

Ast,required mm 5359 13425

Ast,provided mm 5635 16889

Asc, required= 0.87*fy*( Asc)reqd/ (fsc- 0.46*fck) mm 0 0

Asc, provided mm 0 0



______________________________________________________________________________


10/10

Contract UAA01

Design and Construction of Underground Stations and Associated Tunnels_____________________________________________________________________________

7.2.4 Servicibility ChecksUOM

Section Number 1 2

Modular Ratio (m) = 280 / fck 7.00 7.00

Percent Reinforcement prov.(p) = (Ast)provided/ (b*d) 0.23% 0.69%

Calculating neutral Axis Depth by WSM (n*d) mm 405 649

7.2.5 Crack Width Check

Maximum Permissible Crack Width mm 0.3 0.3

Moment (SLS Normal Case) kN-m 4329 10167

In Tension Steel (fst) kN/m 327326 271585

Strain at the centroid of tension steel (e)=fst/ Es= 1.6E-03 1.4E-03

Strain at the Tension Face (e1) = 1.7E-03 1.5E-03

7.2.6 Crack Width As Per IS-456 / BS-8110Reduction in strain due to tension stiffning (e2) =

b*(D-x)*(a-x)

(3* Es*Ast*(d-x))

Avg. steel strain at level considered (em) = e1-e2 = 1.0E-03 1.3E-03

Crack Width (Wcr) =

3*acr*em

(1+2*(acr-Cnom)/(D-x))

* Negative Crack Width indicates absence of Cracking

7.2.7 Calculations of Shear ReinforcementUOM

Section Number 1 2

tc,max= 0.62*(fck)0.5

(Approximately) N/mm 3.92 3.92

tc,max (Approximately) kN/m 3921 3921

Shear Stresses ( tv) = Vu/ (b*d) kN/m 3033 3094

Check for Adequacy of Section in Shear O.K. O.K.

Design Shear Strength of Concrete = (tc) * k* kN/m 359 583

maximum Vertical stirrup spacing as per caluse 26.5.1.5 mm 300 300

Spacing of Stirrups Provided mm 150 150

Total width of beam mm 1000 1000No. of Legs of Shear Stirrups-1 Provided in total length 4 4

Dia of each leg of stirrup-1 provided mm 20 20

No. of Legs of Shear Stirrups-2 Provided in total length 0 0

Dia of each leg of stirrup-2 provided mm 0 0

Actual Asv(Required) / m width mm 1111 1043

Total Shear R/f Provided Asv(Provided) /m width mm 1257 1257

Note:

As per Cl.22.6.1 of IS-456, Critical Section for B.M. should be at the face of support for monolithic construction

As per Cl 22.6.2.1 of IS-456, Critical Section for SF should be at a distance 'd' from face of support

2.1E-04

0.293

6.8E-04

mm 0.245



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Deep Beam Check