beam slab design

LARSEN & TOUBRO LIMITED ECC Division - GES

DATE

TITLE: HOSPITAL BUILDING - DESIGN OF SECOND FLOOR BEAMS & SLABS

DESIGNED

1861B-CS-05-00320DOCUMENT NO

CSR/MDS

(AT SECOND FLOOR LEVEL IN TOWER BLOCK OF HOSPITAL BUILDING)

SIDRA MEDICAL AND RESEARCH CENTER,QATAR

RVR / UMA

2.0 BEAM SLAB DESIGN

PROJECT:01/07/09

CHECKED SHEET

(AT SECOND FLOOR LEVEL IN TOWER BLOCK OF HOSPITAL BUILDING)


DOCUMENT NO DATE

1861B-CS-05-00320CHECKED SHEET

DESIGN OF BEAM SLABS

In this section the design of slab for beam slab portion of part -3 is presented. This portion consist of oneway slabs and twoway slabs supported by main beams and secondary beams. Slab thickness considered is 200 mm. Analysis and design carried out as per BS 8110.

Unit weight of the concrete = kN/m3

Loads ConsideredSuperimposed Dead load = kN/m2

Live load = kN/m2

CSR/MDSHOSPITAL BUILDING - DESIGN OF SECOND FLOOR BEAMS &

SLABS

1/7/09

5.54

25

PROJECT:

TITLE:

SIDRA MEDICAL & RESEARCH CENTER, DOHA

DESIGNED

RVR / UMA


DOCUMENT NO DATE


Design of slab panels S7,S8 AND S10,S11

The design moments & shear forces are arrived based on clause 3.5.2.4 of BS 8110 Part 1 provisions by considering 1m wide strip of the one way slab.Loads are as follows.

Slab thickness = 200 mmSelf weight = 5 kN/m2

Super imposed dead load = 5.5 kN/m2

(a) Total Dead load (DL) = 10.5 kN/m2

(b) Live load (LL) = 4 kN/m2

Design factored load (Fu) =1.4DL+1.6LL = 21.1 kN/m2

Load for serviceability condition, (Fs) =DL+LL = 14.5 kN/m2

Moment and Shear coefificients (Table 3.12, pg 37) of BS8110

RVR/UMA

PROJECT: SIDRA MEDICAL & RESEARCH CENTER, DOHA

TITLE:HOSPITAL BUILDING - DESIGN OF SECOND FLOOR BEAMS &

SLABSDESIGNED

1/7/09

CSR/MDS

0 S7 S8 -0.063

.L19= L18=

(a) Moment coefficients

S7 0.6 S8 0.5

L19= L18=

(b) Shear coefficients

0.075 0.063

5.2m

0.46

5.2m

5.2m

-0.086

5.2m


DOCUMENT NO DATE


RVR/UMA



SLABSDESIGNED

1/7/09

CSR/MDS

Bending moment and shear force diagram

(a) Strength case

Bending moment = (FuxL) x L x moment coefficient

(a) Bending Moment(kN-m)

Shear Force = (FuxL) x shear coefficient

65.376(b) Shear Force(kN)

65.450.12

35.4

-35.4

54.48

42.2

-48

(b) Shear Force(kN)

(b) Seviceability case

Bending moment = (FsxL) x L x moment coefficient


Design for Flexure

Slab section is designed for maximum moment from the above calculation.Grade of Concrete, fcu = 40 N/mm2

Yield Strength of Steel, fy = 420 N/mm2

Cover to reinforcement = 30 mmSlab thickness, D = 200 mm

(a) Top Reinforcement (main bars)Maximum Hogging moment = 48.4 kN-mEffective depth, d = 162 mmBreadth, b = 1000 mm

29.0 24.4

-24.4-33


DOCUMENT NO DATE


RVR/UMA



SLABSDESIGNED

1/7/09

CSR/MDS

K = (Mu / fcub * d2 ) = 0.05 < K' (0.156)Z = Min[0.95d, d{0.5 + sqrt(0.25-K/0.9)}] = 153.2 mm

Area of Steel required, (Mu/(0.87fy*z) = 864 mm2

Req %Pt = 0.53 % Min. Ast required (0.13%) = 211 mm2

Ast provided = 1340 mm2

Provide mm dia bar at mm C/C as Top reinforcement (main bars)

(b) Bottom Reinforcement (main bars)Maximum Sagging moment = 42.2 kN-mEffective depth, d = 162 mm

Breadth, b = 1000 mmK = (Mu / fcub * d2 ) = 0.04 < K' (0.156)

Z = Min[0.95d, d{0.5 + sqrt(0.25-K/0.9)}] = 153.9 mmArea of Steel required, (Mu/(0.87fy*z) = 750 mm2



Provide mm dia bar at mm C/C as Bottom reinforcement (main bars)16 150

16 150

Provide mm dia bar at mm C/C as Bottom reinforcement (main bars)(c) Secondary reinforcement

Minimum reinforcement shall be provided both top and bottom secondary reinforcemetMin Percentage of Ast = 0.13 % Ast min = 211 mm2


Provide mm dia bar at mm C/C on as secondary bars both at top and bottom

Check for Shear

Allowable shear stress in concrete (using Table 3.8, pg 30 BS8110 part1)

vc = 0.79[100As/(bvd)]1/3 (400/d)1/4/γm

(multiplication factor for concrete grade > 25 = (fcu/25)1/3 ) vc = N/mm2

(where, As = , bv = 1000 d = , γm = 1.25)Maximum shear, v = Vu/bd

(Vu = 65 kN, b=1000, d= ) v = N/mm2

< vc Hence Safe

Check for deflection (Cl 3.4.6.3 of BS8110 part 1)

Basic span/effective depth ratio from table 3.9 = 26

Modification factors(a) For Tension reinforcement (Using Table 3.10 of the code)

162

162

0.40

16 150

13400.87

10 150


DOCUMENT NO DATE


RVR/UMA



SLABSDESIGNED

1/7/09

CSR/MDS

Design service stress, fs = 2fyAs req/(3As prov βb)

= 131 N/mm2

where, As req = mm2

As prov = mm2

βb = for 20%redistribution

Mu/bd2 = 1.61

Modification factor = 0.55 + (477-fs) / [120(0.9+Mu/bd2] < 2.0= 1.70 < 2.0

(b) For Compression reinforcement (Using Table 3.11 of the code)

As`prov = mm2 100As`prov/bd = Modification factor = 1 + (100As`prov/bd) / (3+ 100As`prov/bd) < 1.5

= < 1.5Allowable span/effective depth ratio = 26 x 1.7 x 1.22

= 53.8Actual ratio = 5.164 x 1000 / 162 = 31.9 Hence safe against deflection

1.22

13401.2

750

1340 0.83

Check for crack width

Crack width is calculated and and attached seperately


DOCUMENT NO DATE


Design of slab panels S12,S13,S14

The design moments & shear forces are arrived based on clause 3.5.2.4 of BS 8110 Part 1 provisions by considering 1m wide strip of the one way slab.Loads are as follows.

Slab thickness = 200 mmSelf weight = 5 kN/m2


(a) Total Dead load (DL) = 10.5 kN/m2

(b) Live load (LL) = 4 kN/m2

Design factored load (Fu) =1.4DL+1.6LL = 21.1 kN/m2

Load for serviceability condition, (Fs) =DL+LL = 14.5 kN/m2

Moment and Shear coefificients (Table 3.12, pg 37)

1/7/09


SLABSDESIGNED

RVR/UMA CSR/MDS


S14 S13 -0.086 S12

.L21= L22= 2.78m L23=

(a) Moment coefficients

S14 S13 0.6 S12

L21= L22= 2.78m L23=

(b) Shear coefficients

-0.063

0.5

3.2m

0.46

-0.04

0.063 0.063 0.075

2.90m

2.90m

3.2m


DOCUMENT NO DATE


1/7/09


SLABSDESIGNED

RVR/UMA CSR/MDS


Bending moment and shear force diagram

(a) Strength case

Bending moment = (FuxL) x L x moment coefficient

-51

10.24(a) Bending Moment(kN-m)

Shear Force = (FuxL) x shear coefficient


-7.1

13.3

28

13.4

36.729.28

-13.41 -15.3

54.92


(b) Seviceability case

Bending moment = (FsxL) x L x moment coefficient

-10.5


Design for Flexure

Slab section is designed for maximum moment from the above calculation.Grade of Concrete, fcu = 40 N/mm2



(a) Top Reinforcement (main bars)Maximum Hogging moment = 50.5 kN-mEffective depth, d = 162 mmBreadth, b = 1000 mm

9.2 9.1

-9.21 -4.9

7.03

-35


DOCUMENT NO DATE


1/7/09


SLABSDESIGNED

RVR/UMA CSR/MDS


K = (Mu / fcub * d2 ) = 0.05 < K' (0.156)Z = Min[0.95d, d{0.5 + sqrt(0.25-K/0.9)}] = 152.8 mm

Area of Steel required, (Mu/(0.87fy*z) = 905 mm2



Provide mm dia bar at mm C/C as Top reinforcement (main bars)

(b) Bottom Reinforcement (main bars)Maximum Sagging moment = 13.4 kN-mEffective depth, d = 162 mm


Z = Min[0.95d, d{0.5 + sqrt(0.25-K/0.9)}] = 153.9 mmArea of Steel required, (Mu/(0.87fy*z) = 238 mm2



Provide mm dia bar at mm C/C as Bottom reinforcement (main bars)16 150

16 150

Provide mm dia bar at mm C/C as Bottom reinforcement (main bars)(c) Secondary reinforcement




Check for Shear


vc = 0.79[100As/(bvd)]1/3 (400/d)1/4/γm



(Vu = 55 kN, b=1000, d= ) v = N/mm2

< vc Hence Safe


Basic span/effective depth ratio from table 3.9 = 26


16 150

10 150

0.871340 162

162 0.34


DOCUMENT NO DATE


1/7/09


SLABSDESIGNED

RVR/UMA CSR/MDS



= 42 N/mm2

where, As req = mm2

As prov = mm2

βb = for 20%redistribution

Mu/bd2 = 0.51


(b) For Compression reinforcement (Using Table 3.11 of the code)

As`prov = mm2 100As`prov/bd = Modification factor = 1 + (100As`prov/bd) / (3+ 100As`prov/bd) < 1.5

= < 1.5Allowable span/effective depth ratio = 26 x 2 x 1.22

= 63.2Actual ratio = 3.176 x 1000 / 162 = 19.6 Hence safe against deflection

1340 0.83

1.22

23813401.2


Crack width is calculated and and attached seperately


DOCUMENT NO DATE


Design of slab panel S15

The design moments & shear force are arrived by taking the slab as a cantilever slab considering 1m wide strip of the one way slab.Design loads are as follows.

Slab thickness = 250 mmSelf weight = 6.25 kN/m2


Curtain wall load = 5 kN/m(a) Total Dead load (DL) per meter width = 16.75 kN/m(b) Live load (LL) per meter width = 4 kN/m

Design factored load (Fu) =1.4DL+1.6LL = 29.85 kN/mLoad for serviceability condition, (Fs) =DL+LL = 20.75 kN/m

Clear span, L = 1.517 mEffective Span = 1.84 mMaximum Support moment, Mu = FuL

2/2 = 51 kN-mMaximum Shear force, Vu = FuL = 55 kN

1/7/09

CSR/MDSRVR / UMA



SLABSDESIGNED

Moment under serviceability condition, Mu = FsL2/2 = 35 kN-m

Design for Flexure

Slab section is designed for maximum moment.Grade of Concrete, fcu = 40 N/mm2



(a) Top Reinforcement (main bars)Maximum Hogging moment = 51 kN-mEffective depth, d = 212 mm


Z = Min[0.95d, d{0.5 + sqrt(0.25-K/0.9)}] = 201 mmArea of Steel required, (Mu/(0.87fy*z) = 687 mm2



Provide mm dia bar at mm C/C as Top reinforcement (main bars)(b) Bottom reinforcement

16 150


DOCUMENT NO DATE


1/7/09

CSR/MDSRVR / UMA



SLABSDESIGNED

Min Percentage of Ast = 0.13 % Ast min = 276 mm2


Provide mm dia bar at mm C/C on as Bottom reinforcement (main bars)(c) Secondary reinforcement




Check for Shear


vc = 0.79[100As/(bvd)]1/3 (400/d)1/4/γm



(Vu = 55 kN, b=1000, d= ) v = N/mm2

10 150

16 150

1340 212

212 0.26

0.74

( u 55 kN, b 1000, d ) v< vc Hence Safe


Basic span/effective depth ratio from table 3.9 = 7(for cantilever condition)



= 143 N/mm2

where, As req = mm2

As prov = mm2

βb =Mu/bd2 = 1.12


(b) For Compression reinforcement (Using Table 3.11 of the code)As`prov = mm2 100As`prov/bd =

Modification factor = 1 + (100As`prov/bd) / (3+ 100As`prov/bd) < 1.5

= < 1.5Allowable span/effective depth ratio = 7 x 1.92 x 1.17

= 15.8

0.26

6871340

1

1340 0.63

1.17


DOCUMENT NO DATE


1/7/09

CSR/MDSRVR / UMA



SLABSDESIGNED

Actual ratio = 1.84 x 1000 / 212 = 8.7 Hence safe against deflection


Crack width is calculated and and attached seperately.

LARSEN & TOUBRO LIMITED ECC Division – EDRC

PROJECT : SIDRA MEDICAL AND RESEARCH CENTER,QATAR DOCUMENT NO. DATE

1861B-CS-05-00320TITLE : HOSPITAL BUILDING - DESIGN OF SECOND FLOOR BEAMS & SLABS DESIGNED CHECKED PAGE

As per BS 8110 : Part 1 : 1997 RVR / UMA CSR / MDS OFClear cover : 30 mmGrade of conc: 40 N/mm2 DESIGN OF TWO WAY SLAB NAMED AS S1, S2, S3, S4 & S5Grade of steel: 420 N/mm2

SLAB Depth Span Slab

ID D short long short long Ratio βbAs

Prov.fs mf l/d dreqd Id

( mm) lx ly lx ly ly/lx Dead S. W. Live Total short long -ve +ve -ve +ve -ve +ve -ve +ve -ve +ve -ve +ve -ve +ve mm2 -ve +ve -ve +ve Support Span Support Span mm2 N/mm2 mm

S1, S5 200 4.392 5.796 5.092 6.496 1.28 5.500 5.000 4.000 21.100 One long edge discontinuous 162 146 0.061 0.046 0.037 0.028 33.12 25.05 20.24 15.32 0.156 0.032 0.024 0.024 445 399 302 260 589 445 399 302 Y- 16 @ 150 Y- 16 @ 150 Y- 16 @ 150 Y- 16 @ 150 1.00 1340 93 2.00 26 97.9 S1, S5

S2,S4 200 4.528 6.830 5.228 7.530 1.44 5.500 5.000 4.000 21.100 Interior panel 162 146 0.051 0.038 0.032 0.024 29.53 22.04 18.45 13.84 0.156 0.028 0.021 0.022 359 333 250 260 481 359 333 260 Y- 16 @ 150 Y- 16 @ 150 Y- 16 @ 150 Y- 16 @ 150 1.00 1340 75 2.00 26 100.5 S2,S4

S3 200 5 062 5 780 5 562 6 480 1 17 5 500 5 000 4 000 21 100 I t i l 162 146 0 040 0 031 0 032 0 024 26 27 19 98 20 89 15 67 0 156 0 025 0 019 0 024 325 377 283 260 428 325 377 283 Y 16 @ 150 Y 16 @ 150 Y 16 @ 150 Y 16 @ 150 1 00 1340 68 2 00 26 107 0 S3

short span long span short span long spanhort spa long span

Ast req. in mm2 spacing of bars ( mm ) spacing of bars ( mm ) Check for Deflection

short span long span short span long span short span ong spa

As As, min

1/7/2009

Clear Span (m) Eff. Span ( m )Un fact. Load in kN/m2

Boundary conditions/TypeEff. Depth

(mm)

Moment coefficients Fac. B. M. ( kN-m )K'

K=Mu/bd2fcu

S3 200 5.062 5.780 5.562 6.480 1.17 5.500 5.000 4.000 21.100 Interior panel 162 146 0.040 0.031 0.032 0.024 26.27 19.98 20.89 15.67 0.156 0.025 0.019 0.024 325 377 283 260 428 325 377 283 Y- 16 @ 150 Y- 16 @ 150 Y- 16 @ 150 Y- 16 @ 150 1.00 1340 68 2.00 26 107.0 S3

Designed By Checked By


Calculation for crack width (For slab panal - S7)

Moment due to service load = kNmWidth of slab (b) =Overall depth of slab (h) =Area of steel provided (As) = mm2

Clear cover to tension steel provided (c) =Diameter of bar provided on the tension face (φ) =Effective depth of slab (d) = 200-30-16/2 =Spacing of steel (s) = mm c/cAs per BS8110-2:1985 Design Surface Crack Width

Wcr = 3acrεm/(1+2(acr-Cmin)/(h-x))Where

x = depth of neutral axis. = mmfs = the tensile stress in the reinforcement.

M(d )/I 2

61.6

150

30 mm16 mm162 mm

33.31000 mm200 mm1340

TITLE: Hospital Building - Crack width calculation DESIGNED CHECKED SHEET

RVR/UMA CSR/MDS

PROJECT: SIDRA MEDICAL AND RESEARCH CENTER,QATAR DOCUMENT NO DATE1861B-CS-05-00320 1/7/09

= M(d-x)/I = N/mm2

ε1 = Strain at the level considered, calculated ignoringthe stiffening of the concrete in the tension zone.ε1 = (h-x)fs/Es(d-x) =

εm = average steel strain at the level considered,ε1 - b(h-x)(a-x)/(3EsAs(d-x)) =

a = distance from the compression face to the point atwhich crack width is being calculated, and =

Actual crack width:

acr = distance from the point considered to the surfaceof the nearest longitudinal bar = mm

Wcr = Crack width = mm

Allowable crack width = mm

HENCE SAFE

76.1

0.133

0.300

175

0.00121

0.00097

200 mm







M(d )/I 2



RVR/UMA CSR/MDS

35.11000 mm250 mm134030 mm16 mm212 mm150

72.6

= M(d-x)/I = N/mm2




Actual crack width:




HENCE SAFE

140

0.00089

0.00061

250 mm

76.1

0.091

0.300







M(d )/I 2



RVR/UMA CSR/MDS

35.11000 mm200 mm134030 mm16 mm162 mm150

61.6

= M(d-x)/I = N/mm2




Actual crack width:




HENCE SAFE

185

0.00128

0.00104

200 mm

76.1

0.142

0.300

beam slab design

Documents