3 Slab Design

32
Chapter two Slab design 42 3 Slab design A B C D 1' 2' 3' 4' 1 2 3 4 A' B' C' D' R0.28m 0.57m 0.40m 0.40m 5.00m 7.00m 5.50m 2.50m 0.57m R0.28m 0.40m 0.40m 2.00m 1.10m 1.65m 0.40m 0.40m 7.0 m 5.0 m 5.0 m 15.0 m 22.0 m E E' S1 S2 S3 S4 S5 S6 S7 S8 S9 S10 S11 S12

description

slab design

Transcript of 3 Slab Design

  • Chapter two Slab

    design

    42

    3 Slab design

    AB

    CD

    1' 2' 3' 4'

    1 2 3 4

    A'

    B'

    C'

    D'

    R0.28m

    0.57m

    0.40m0.40m

    5.00m

    7.00m

    5.50m

    2.50m

    0.57mR0.28m

    0.40m

    0.40m

    2.00m

    1.10m1.65m

    0.40m

    0.40m

    7.0 m

    5.0 m 5.0 m

    15.0 m

    22.0 m

    E E'

    S1 S2 S3

    S4 S5 S6

    S7 S8 S9

    S10 S11 S12

  • Chapter two Slab

    design

    43

    Figure (2-1) plan of slab and notations.

    In multistory building, there isnt rectangular reinforced concrete

    beam in whole frame; all beams are T-shape or L-shape.

    Figure (2-2) T-beam and L-beam.

    Design of two way slabs

    There are several methods for analysis and design of two way slab systems;

    more useful methods include:

    1. Direct Design Method DDM.

    2. Equivalent Frame Method EFM.

    3. Yield Line Theory YLT.

    4. Coefficient method.

    The ACI code 13.5.1.1 specifies two methods for designing two-way slabs for

    gravity loads, its Direct Design Method and Equivalent Frame Method.

    1. Direct Design Method

    The code 13.6 provides a procedure with which a set of moment coefficients

    can be determined. The method in effect ,involves a single cycle moment

    distribution analysis of the structure based on (a) the estimated flexural

    stiffness of the slabs, beams(if any) and columns (b) the torsional stiffnesses of

    the slabs and beams(if any) transverse to the direction in which flexural

    h

    be

    t

    h

    bw

    be

    t

    bw

  • Chapter two Slab

    design

    44

    moments are being determined. Some types of moment coefficients have been

    used statistically for many years for slab design. They do not, however, give

    very satisfactory results for slabs with unsymmetrical dimensions and loading

    patterns.

    Limitations of DDM:

    1. There shall be minimum of three continuous spans in each direction.

    The panels shall be rectangular, with the ratio of longer to shorter spans within

    a panel not greater than 2.

    3. The successive span lengths in each direction shall not differ by more than

    one third the longer span.

    4. Columns may be offset a maximum of 10 percent of the span in the direction

    of the offset from either axis between centerlines of successive columns.

    5. All loads must be due gravity and uniformly distributed, the live load shall

    not exceed 2 times of dead load.

    6. If beams are used on the columns lines, the relative stiffness of the beams in

    the tow perpendicular directions, given by the ratio

    , must be between

    0.2 and 5.

    2. Equivalent Frame Method

    In this method a portion of the structure is taken out by itself, the same

    stiffness values used for direct design method are used for equivalent frame

    method. This latter method, which is very satisfactory for symmetrical frames

    as well as for those with unusual dimensions or loadings.

    The only difference between the DDM and the EFM is in the determination of

    the longitudinal moments in the spans of the equivalent rigid frame. Whereas

    the DDM involves one cycle moment distribution, the EFM involves a normal

    moment distribution of several cycles. The design moments obtained by either

    method are distributed to column and middle strips in the same fashion. There

    are no such limitations (as in DDM) on EFM. This is a very important matter

  • Chapter two Slab

    design

    45

    because so many floor systems do not meet the limitations specified for the

    DDM.

    3. Yield Line Theory

    Although the yield line theory not included in the ACI code slab analysis by this

    method may be useful in providing the needed information for understanding

    the behavior of irregular or single panel with various boundary condition.

    A yield line analysis uses rigid plastic theory to compute the failure loads

    corresponding to given plastic moment resistances in various parts of the slab.

    It does not give any information about deflections or about the loads at which

    yielding first starts.

    K.W Johansson 1948 developed modern yield line theory. These types of

    analysis are widely used for the design in the Scandinavian countries. Although

    the concepts of YLT was first presented by Ingerslev 1921-23. For solving the

    yield line problems two methods are available

    Figure (2-3) mode of failure of a slab.

    For designing two way slabs (continuous system) all supports are assumed to be fixed and several

    modes of failure are taken into consideration to find the ultimate capacity of the slab.

    1.Equilibrium Method 2.Virtual Work Method

  • Chapter two Slab

    design

    46

    4. Coefficient method:

    (Method 3 of the ACI-code 1963 (Marcos method).

    Limitation of coefficient method:

    1. The method is applicable for slabs supported of the edges by required

    concrete walls, steel beams or monolithic concrete beams having total

    depth, h3 hf.

    2. The design is based on coefficient from tables for the middle strip of the

    slab.

    3. The moment at the discontinuous edge is taken as 1/3 of the positive

    moment.

    4. The moments at the column strip are taken as 2/3 of that at the middle

    strip.

    Slab design calculation:

    The slabs in the our project are designed by coefficient method.

    For slab(1) with panels (7*5).

    1. slab thickness:

    i. Perimeter= 2*(5+7)=24 m.

    t primary=

    =133.33 mm.

    t provided by architecture =180 mm not economic.

    ii. finding t by DDM.

    600

    150

    1300 mm

    400mm

    850mm

    150mm

    400mm

    h=6

    00 mm

  • Chapter two Slab

    design

    47

    Figure (2-3) dimension of beam cross-sections.

    beT-section=bw+2(h-t)bw+8t

    beL-section=bw+ (h-t)bw+4t

    kf1= (

    ) (

    t

    hf ) (

    t

    hf (

    t

    hf)

    ) (

    t

    hf )

    (

    ) (

    t

    hf )

    KfL-beam=1.388

    KfT-beam=1.642

    Ib T-beam=

    =11.822*109 mm4

    Ib L-beam=

    =9.993*109 mm4

    Is:

    Sec 1 Is=2500*

    =0.703*109 mm4

    Sec 2 Is=3500*

    =0.984*109 mm4

    Sec 3 Is=5000*

    =1.406*109 mm4

    Sec 4 Is=7000*

    =1.968*109 mm4

    Sec 5 Is=2500*

    =0.703*109 mm4

    Sec 6 Is=6250*

    =1.758*109 mm4

    =

    1=14.214

    2=10.155

    1From Chu-kia Wang , Charles G. Salmon, Jose A. Pincheira, Reinforced concrete design,7th ed.,2007,John Wiley & sons inc., page 632.

  • Chapter two Slab

    design

    48

    3=8.408

    4=6.0

    5=14.214

    6=6.724

    m for each panel:

    panel A m=

    =9.694

    panel B m=

    =8.242

    panel C m=

    =8.836

    panel D m=

    =7.385

    panel E m=

    =9.0175

    panel F m=

    =7.566

    *For all panels m >2.0 Use ACI eq.9.13

    tmin=

    c=

    =1.434

    for critical panel A,B ln=7000-400=6600mm

    tmin=

    =141.68 mm use 150mm

  • Chapter two Slab

    design

    49

    2. Weights:

    L.L= 4 KPa

    Selfweight=([0.05+0.02]*23)+(0.15*

    24)+(0.02*14)

    Self weight= 5.49 KPa use 5.5 KPa.

    Wu= 1.2 Wud.l+1.6 Wul.l2

    Wud=1.2*5.5=6.6 KPa.

    Wul=1.6*4=6.4 KPa.

    Wu=6.6+6.4=13.0 KPa.

    3. Using coefficient method to determining factored moments:

    la and lb are clear spans.

    la=shorter span length, m.

    lb=longer span length, m.

    la=5.0-0.4=4.6 m

    lb=7-0.4=6.6 m

    m=la

    l =

    =0.6969 0.7

    from appendix(B), table (B-1,2,3,4) case 4 for one end continuous in each

    direction may be critical case for slabs (multi-bays).

    Negative moments:

    For m=0.7

    Ca=0.081

    Cb=0.019

    Ma=Ca Wu la2=0.081*13.0*4.62

    =22.28 kN.m

    Mb=Cb Wu lb2

    2 From ASCE 7-05, page 5.

    Tile

    Plastering (gypsum) R.C slab

    Mortar

    15 cm

    2

    5

    2

    figure(2-4)slab layers. 7.0m

    5.0m

    Mb

    Ma

    These slab moments

    becomes torsion (tu) on the beams.

  • Chapter two Slab

    design

    50

    =0.019*13.0*6.62=10.76 kN.m

    Positive moments:

    Dead positive moments:

    Ca=0.046

    Cb=0.011

    Ma=0.046*6.6*4.62=6.42 kN.m

    Mb=0.011*6.6*6.62=3.16 kN.m

    Live load positive moments:

    Ca=0.057

    Cb=0.014

    Ma=0.057*6.4*4.62=7.72 kN.m

    Mb=0.014*6.4*6.62=3.90 kN.m

    Total positive moments:

    Ma total=MaL+MaD

    Ma total=6.42+7.72=14.14 kN.m

    Mb total=MbL+MbD

    Mb total=3.16+3.9=7.06 kN.m

    4. Determining Reinforcement:

    In two way slab the main reinforcement placed in two directions.

    Reinforcement can be determining according to (7.12) ACI 318M-08:

    i. Slab with grade 50 (350 MPa) or less min=0.002.

    ii. Slab with grade 60 (420 MPa) min=0.0018.

    iii. Slab with grade more than 60 min=0.0018*

    f but min should not

    less than 0.0014.

    Use fy=350 MPa, fc=21 MPa.

    min=0.002

    The down main reinforcement is along shorter span.

    Negative moments:

    Short direction reinforcement:

    Figure (2-5) panel (1,3)

  • Chapter two Slab

    design

    51

    d= 150-20-

    =123.65 mm.

    Ma=22.28 kN.m

    =

    m(1-

    mR

    f )

    m=f

    f c ; R=

    u

    d

    m=

    =19.6 ; R=

    =1.619140

    =

    (1-

    )=0.004858 > min=0.002 ok.

    As= bd=0.004858*1000*123.65=600.609 mm2/m

    Use 13 Ab=129 mm2

    No. of bars=

    =4.65588 bars/m

    Spacing=

    =214.78 mm

    Smax=2h=2*150=300 mm Sprovided=214.78mm Ok.

    Use S=200 mm

    Use No. 13@200 mm.

    Long direction reinforcement:

    d= 150-20-

    -12.7=110.95 mm.

    Mb=10.76 kN.m

    =

    m(1-

    mR

    f )

    m=f

    f c ; R=

    u

    d

    m=

    =19.6; R=

    =0.971153

  • Chapter two Slab

    design

    52

    =

    (1-

    )=0.002855 > min=0.002 ok.

    As= bd=0.002855*1000*110.95=316.719 mm2/m

    Use 13 Ab=129 mm2

    No. of bars=

    =2.455 bars/m

    Spacing=

    =407.33 mm

    Smax=2h=2*150=300 mm Sprovided=407.33 mm not Ok.

    Use S=300 mm

    Use No. 13@300 mm.

    Positive moment reinforcements (mid span reinforcement):

    Short direction reinforcement:

    d= 150-20-

    =123.65 mm.

    Ma=14.14 kN.m

    =

    m(1-

    mR

    f )

    m=f

    f c ; R=

    u

    d

    m=

    =19.6 ; R=

    =1.02759

    =

    (1-

    )=0.003026 > min=0.002 ok.

    As= bd=0.003026*1000*123.65=374.125 mm2/m

    Use 13 Ab=129 mm2

    No. of bars=

    =2.9 bars/m

    Spacing=

    =344.8 mm

  • Chapter two Slab

    design

    53

    Smax=2h=2*150=300 mm Sprovided=344.8mm not ok.

    Use S=300 mm

    Use No. 13@300 mm.

    Long direction reinforcement:

    d= 150-20-

    -12.7=110.95 mm.

    Mb=7.06 kN.m

    =

    m(1-

    mR

    f )

    m=f

    f c ; R=

    u

    d

    m=

    =19.6 ; R=

    =0.0.6372

    =

    (1-

    )=0.0018544 < min=0.002 use min.

    As= bd=0.002*1000*110.95=221.9 mm2/m

    Use 13 Ab=129 mm2

    No. of bars=

    =1.720 bars/m

    Spacing=

    =581.343 mm

    Smax=2h=2*150=300 mm Sprovided=581.343 mm not Ok.

    Use S=300 mm

    Use No. 13@300 mm.

    5. Check for shear:

    Also by coefficient method [appendix (B-4)].

    m=la

    l =0.7

    Wa=0.81

    Wb=0.19

  • Chapter two Slab

    design

    54

    Wa,Wb Both direction is checked.

    Vushort=Wa

    =

    =24.22 kN

    Vulong=W

    =

    =8.15 kN

    Strength of slab:

    =0.75

    Vc=f c

    *b*d

    Vc=

    *1000*123.65

    Vc=94.439 kN

    Vc=70.83 kN

    Vc=70.83 >24. 22 Ok. for shear.

    Design of slab (7) with panel 5.5*5.0:

    la=5.0-0.4=4.6 m

    lb=5.5-0.4=5.1 m

    m=la

    l =

    =0.9

    from appendix(B), table (B-1,2,3,4) case 9 for three end continuous may be

    critical case for slabs (multi-bays).

    Negative moments:

    For m=0.9

    Ca=0.068

    Cb=0.025

    Ma=Ca Wu la2

    =0.068*13.0*4.62=18.71 kN.m

    Mb=Cb Wulb2

    =0.025*13.0*5.12=8.453 kN.m

    Positive moments:

    Dead positive moments:

    Ca=0.026

    Cb=0.015

    Ma=0.026*6.6*4.62=3.63 kN.m

    5.0 m

    5.5

    m

    Figure (2-6) panel (7).

  • Chapter two Slab

    design

    55

    Mb=0.015*6.6*5.12=2.58 kN.m

    Live load positive moments:

    Ca=0.036

    Cb=0.022

    Ma=0.036*6.4*4.62=4.88 kN.m

    Mb=0.022*6.4*5.12=3.66 kN.m

    Total positive moments:

    Ma total=MaL+MaD

    Ma total=3.63+4.88=8.51 kN.m

    Mb total=MbL+MbD

    Mb total=2.58+3.66=6.24 kN.m

    6. Determining Reinforcement:

    Short direction reinforcement:

    Negative reinforcement:

    d= 150-20-

    =123.65 mm.

    Ma=18.71 kN.m

    =

    m(1-

    mR

    f )

    m=f

    f c ; R=

    u

    d

    m=

    =19.6 ; R=

    =1.3597

    =

    (1-

    )=0.004045 > min=0.002 ok.

    As= bd=0.004045*1000*123.65=500.191 mm2/m

    Use 13 Ab=129 mm2

    No. of bars=

    =3.878 bars/m

    Spacing=

    =257.9 mm

  • Chapter two Slab

    design

    56

    Smax=2h=2*150=300 mm Sprovided=257.9mm ok.

    Use S=250 mm

    Use No. 13@250 mm.

    Long direction reinforcement:

    d= 150-20-

    -12.7=110.95 mm.

    Mb=8.45 kN.m

    =

    m(1-

    mR

    f )

    m=f

    f c ; R=

    u

    d

    m=

    =19.6 ; R=

    =0.7708

    =

    (1-

    )=0.002252 > min=0.002 ok.

    As= bd=0.002242*1000*110.95=249.87 mm2/m

    Use 13 Ab=129 mm2

    No. of bars=

    =1.937 bars/m

    Spacing=

    =516.27 mm

    Smax=2h=2*150=300 mm Sprovided=516.27 mm not ok.

    Use S=300 mm

    Use No. 13@300 mm.

    Positive moment reinforcements (mid span reinforcement):

    Short direction reinforcement:

    d= 150-20-

    =123.65 mm.

  • Chapter two Slab

    design

    57

    Ma=8.51 kN.m

    =

    m(1-

    mR

    f )

    m=f

    f c ; R=

    u

    d

    m=

    =19.6 ; R=

    =0.61844

    =

    (1-

    )=0.001799 < min=0.002 not ok.

    As= bd=0.002*1000*123.65=247.3 mm2/m

    Use 13 Ab=129 mm2

    No. of bars=

    =1.9171 bars/m

    Spacing=

    =521.63 mm

    Smax=2h=2*150=300 mm Sprovided=463.55mm not ok.

    Use S=300 mm

    Use No. 13@300 mm.

    Long direction reinforcement:

    d= 150-20-

    -12.7=110.95 mm.

    Mb=6.24 kN.m

    =

    m(1-

    mR

    f )

    m=f

    f c ; R=

    u

    d

    m=

    =19.6 ; R=

    =0.5632

    =

    (1-

    )=0.001635 < min=0.002 not ok.

  • Chapter two Slab

    design

    58

    As= bd=0.002*1000*110.95=221.9 mm2/m

    Use 13 Ab=129 mm2

    No. of bars=

    =1.72 bars/m

    Spacing=

    =581.34 mm

    Smax=2h=2*150=300 mm Sprovided=581.34 mm not Ok.

    Use S=300 mm

    Use No. 13@300 mm.

    7. Check for shear:

    Also by coefficient method [appendix (-)].

    m=la

    l =0.9

    Wa=0.75

    Wb=0.25

    Wa,Wb Both direction is checked.

    Vushort=Wa

    = 7

    =22.43 kN

    Vulong=W

    =

    =8.29 kN

    Strength of slab:

    =0.75

    Vc=f c

    *b*d

    Vc=

    *1000*123.65

    Vc=94.44 kN

    Vc=70.83 kN

    Vc=70.83 >22.43 Ok. for shear.

    Design of cantilever slab (12):

    All slabs are (5*2.5)

    la=2.5-.2=2.3 m

    lb=5-0.4=4.6 m

  • Chapter two Slab

    design

    59

    m=la

    l =

    =0.5

    from appendix(B), table(B-1) case 4 for one end continuous in each

    direction may be critical case for slabs (multi-bays).

    Negative moments:

    For m=0.5

    Ca=0.094

    Cb=0.060

    Ma=Ca Wu la2=0.094*13*2.32

    =6.46 kN.m

    Mb=Cb Wu lb2

    =0.006*13.0*4.62=1.65 kN.m

    *Cantilever slab there isnt positive moment.

    Finding reinforcement:

    Short direction reinforcement:

    d= 150-20-

    =123.65 mm.

    Ma=6.46 kN.m

    =

    m(1-

    mR

    f )

    m=f

    f c ; R=

    u

    d

    m=

    =19.6 ; R=

    =0.4694

    =

    (1-

    )=0.00136 < min=0.002 use =0.002 .

    As= bd=0.002*1000*123.65=247.3 mm2/m

    Use 13 Ab=129 mm2

    No. of bars=

    =1.917 bars/m

    2.5

    m

    5.0 m

    figure (2-7) panel(10,12).

  • Chapter two Slab

    design

    60

    Spacing=

    =521.63 mm

    Smax=2h=2*150=300 mm Sprovided=521.63mm not ok.

    Use S=300 mm

    Use No. 13@300 mm.

    Long direction reinforcement:

    d= 150-20-

    -12.7=110.95 mm.

    Mb=1.65 kN.m

    =

    m(1-

    mR

    f )

    m=f

    f c ; R=

    u

    d

    m=

    =19.6 ; R=

    =0.1489

    =

    (1-

    )=0.0004273 < min=0.002 NOT

    As= bd=0.002*1000*110.95=221.9 mm2/m

    Use 13 Ab=129 mm2

    No. of bars=

    =1.72 bars/m

    Spacing=

    =581.34 mm

    Smax=2h=2*150=300 mm Sprovided=581.34 mm OK.

    Use S=300 mm

    Use No. 13@300 mm.

    Check for shear:

    Also by coefficient method [appendix (-)].

  • Chapter two Slab

    design

    61

    m=la

    l =0.5

    Wa=0.94

    Wb=0.06

    Wa,Wb Both direction is checked.

    Vushort=Wa

    =

    =14.05 kN

    Vulong=W

    =

    =1.79 kN

    Strength of slab:

    =0.75

    Vc=f c

    *b*d

    Vc=

    *1000*123.65

    Vc=94.439 kN

    Vc=70.83 kN

    Vc=70.83 >14.05 Ok. for shear.

    Design of slab 6:

    Panel 6 can be divided into three one-way slab systems.

    Slab 1

    la

    l =

    =0.27 < 0.5 one way slab

    Slab 2

    la

    l =

    =0.457 < 0.5 one way slab

    Slab 3

    la

    l =

    =0.428 < 0.5 one way slab

    7.0 m

    5.4 m

    1.6m

    5.0 m

    1.5m 3.5 m

    3.5m

    1.5m

    2

    1

    3

  • Chapter two Slab

    design

    62

    Design of slab1 @ panel 6:

    Wu=13.0 kN.m

    1. Check depth for moment and shear:

    a. Check for moment:

    Mucantilever =Wu l

    Mu= fy b d (1-

    7 f c)

    Mucantilever =

    =14.63 kN.m

    14.63*10=0.9*350*0.01*1000*d *(1-

    )

    d=71.75 mm < 123.65 ok.

    b. Check for shear:

    Vu=Wu.l= 13.0* 1.5=19.5 kN

    VuVc

    Vc=

    bd

    19.5=0.75*

    *

    d=34.04 mm < 123.65 mm ok.

    2. Finding reinforcement:

    Mu= As fy z

    Assume z=0.925 d

    d=123.65 mm

    14.63*10=0.9*As*350*0.925*123.65

    As=406.067 mm

    Number of bars=As

    A =

    =3.1478 bars

    Spacing=

    o of ars=

    7 =317.68 mm

    Smax=3h=3*150=450 mm

  • Chapter two Slab

    design

    63

    Smax=450 mm

    Smax=

    f -2h=

    -2*20=412.38 mm

    Smax=

    =

    =360 mm

    S provided=317.68 < all Smax

    Use No. 13@300 mm

    Design of slab2 @ panel 6:

    Wu=13.0 kN.m

    1. Check depth for moment and shear:

    a. Check for moment:

    Mucantilever =Wu l

    Mu= fy b d (1-

    7 f c)

    Mucantilever =

    =16.64 kN.m

    16.64*10=0.9*350*0.01*1000*d *(1-

    )

    d=76.53 mm < 123.65 ok.

    b. Check for shear:

    Vu=Wu.l= 13.0* 1.6=20.8 kN

    VuVc

    Vc=

    bd

    20.8=0.75*

    *

    d=36.31 mm < 123.65 mm ok.

    2. Finding reinforcement:

    Mu= As fy z

    Assume z=0.925 d

  • Chapter two Slab

    design

    64

    d=123.65 mm

    16.64*10=0.9*As*350*0.925*123.65

    As=461.856 mm

    Number of bars=As

    A =

    =3.58 bars

    Spacing=

    o of ars=

    =279.31 mm

    Smax=3h=3*150=450 mm

    Smax=450 mm

    Smax=

    f -2h=

    -2*20=412.38 mm

    Smax=

    =

    =360 mm

    S provided=279.31 < all Smax

    Use No. 13@275 mm

    Design of slab3 @ panel 6:

    Wu=13.0 kN.m

    3. Check depth for moment and shear:

    c. Check for moment:

    Mucantilever =Wu l

    Mu= fy b d (1-

    7 f c)

    Mucantilever =

    =14.63 kN.m

    14.63*10=0.9*350*0.01*1000*d *(1-

    )

    d=71.75 mm < 123.65 ok.

    d. Check for shear:

    Vu=Wu.l= 13.0* 1.5=19.5 kN

    VuVc

    Vc=

    bd

  • Chapter two Slab

    design

    65

    19.5=0.75*

    *

    d=34.04 mm < 123.65 mm ok.

    4. Finding reinforcement:

    Mu= As fy z

    Assume z=0.925 d

    d=123.65 mm

    14.63*10=0.9*As*350*0.925*123.65

    As=406.067 mm

    Number of bars=As

    A =

    =3.1478 bars

    Spacing=

    o of ars=

    7 =317.68 mm

    Smax=3h=3*150=450 mm

    Smax=450 mm

    Smax=

    f -2h=

    -2*20=412.38 mm

    Smax=

    =

    =360 mm

    S provided=317.68 < all Smax

    Use No. 13@300 mm

    Smax=

    =

    =360 mm

    S provided=255 < all Smax

    Use No. 13@250 mm

    Other holes and openings can be neglected because all panels remain two-

    way system.

  • Chapter two Slab

    design

    66

    Table of moments, ,As, and spacing of the floor panels:

    Negative parameters:

    fc=21 MPa; fy=350 Mpa

    by using 13mm(Ab=129 mm2)

    min=0.002 for fy

  • Chapter two Slab

    design

    67

    Positive parameters:

    fc=21 MPa; fy=350 Mpa

    by using 13mm(Ab=129 mm2)

    min=0.002 for fy

  • Chapter two Slab

    design

    68

    Design of over roof slab:

    7.00

    5.00

    0.30

    0.30

    PARAPET

    SLAB

    0.30

    ? 1

    d

    d

    ? 2

    By using yield line method we can find moment of the slab:

    W=Wu*[(

    *5*

    *

    )+(

    *(

    )2 *

    *2 )+( 2*

    *

    *)]

    =Wu*(2.0833+2.0833+2.5)*

    W=6.667**Wu ..(1)

    1=2=

    M=(Mn+Mp)*5*1+(Mn+Mp)*7*2

    M=(Mn+Mp)*5*

    +(Mn+Mp)*7*

    M=4.8*(Mn+Mp)*

    Assume Mn=2Mp

    M=14.4*Mp* (2)

    By equating (1) and (2) we get the slab moments:

    M=W

    2

    1

    Figure (3-9) detail of parapet slab.

  • Chapter two Slab

    design

    69

    Wu=(1.2D.L+1.6L.L)

    LL=1.5 KPa for parapet.

    Wu=(1.2*5.5)+(1.6*1.5)=9.0 KN/m2

    6.667*9=14.4*Mp

    Mp=4.166 KN.m

    Mn=2*4.166=8.33KN.m

    Design for negative reinforcement:

    Using fy=350 MPa, fc=21 MPa.

    min=0.002

    d= 150 -20-

    =123.65 mm (using 13mm).

    =

    m(1-

    mR

    f )

    m=f

    f c ; R=

    u

    d

    m=

    =19.6 ; R=

    =0.60536

    =

    (1-

    )=0.0017599 < min=0.002

    Use min=0.002

    As= bd=0.002*1000*123.65=247.3 mm2/m

    Use 13 Ab=129 mm2

    No. of bars=

    =1.917bars/m

    Spacing=

    =521.63 mm

    Smax=2h=2*150=300 mm Sprovided=521.63mm NOT OK.

  • Chapter two Slab

    design

    70

    Use S=300 mm ;Use No. 13@300 mm.Other direction and positive

    reinforcement also minimum control.

    Use 13mm@300mm c/c.

    Table (2-1) distribution of the reinforcement for the floor panels.

    Slab No. Short Long

    Top Bottom Top Bottom

    Right 13@200 mm c/c 13@600 mm c/c 13@300 mm c/c 13@600 mm c/c

    S1 Mid .. 13@300 mm c/c .. 13@300 mm c/c

    Left 13@200 mm c/c 13@600 mm c/c 13@300 mm c/c 13@600 mm c/c

    Right 13@225 mm c/c 13@600 mm c/c 13@250 mm c/c 13@600 mm c/c

    S2 Mid ..... 13@300 mm c/c .. 13@300 mm c/c

    Left 13@225 mm c/c 13@600 mm c/c 13@250 mm c/c 13@600 mm c/c

    Right 13@200 mm c/c 13@600 mm c/c 13@300 mm c/c 13@600 mm c/c

    S3 Mid .. 13@300 mm c/c .. 13@300 mm c/c

    Left 13@200 mm c/c 13@600 mm c/c 13@300 mm c/c 13@600 mm c/c

    Right 13@200 mm c/c 13@600 mm c/c 13@300 mm c/c 13@600 mm c/c

    S4 Mid .. 13@300 mm c/c .. 13@300 mm c/c

    Left 13@200 mm c/c 13@600 mm c/c 13@300 mm c/c 13@600 mm c/c

    Right 13@225 mm c/c 13@600 mm c/c 13@300 mm c/c 13@600 mm c/c

    S5 Mid .. 13@300 mm c/c .. 13@300 mm c/c

    Left 13@225 mm c/c 13@600 mm c/c 13@300 mm c/c 13@600 mm c/c

    S6-1 13@300mm c/c 13@300 mm c/c

    S6 S6-2 13@275mm c/c 13@300mm c/c

    S6-3 13@300 mm c/c 13@300 mm c/c

    Right 13@250 mm c/c 13@600 mm c/c 13@300 mm c/c 13@600 mm c/c

    S7 Mid .. 13@300 mm c/c .. 13@300 mm c/c

    Left 13@250 mm c/c 13@600 mm c/c 13@300 mm c/c 13@600 mm c/c

    Right 13@300 mm c/c 13@600 mm c/c 13@300 mm c/c 13@600 mm c/c

    S8 Mid .. 13@300 mm c/c .. 13@300 mm c/c

    Left 13@300 mm c/c 13@600 mm c/c 13@300 mm c/c 13@600 mm c/c

    Right 13@250 mm c/c 13@600 mm c/c 13@300 mm c/c 13@600 mm c/c

    S9 Mid .. 13@300 mm c/c .. 13@300 mm c/c

    Left 13@250 mm c/c 13@600 mm c/c 13@300 mm c/c 13@600 mm c/c

    Right 13@300 mm c/c 13@600 mm c/c 13@300 mm c/c 13@600 mm c/c

    S10 Mid .. 13@300 mm c/c .. 13@300 mm c/c

    Left 13@300 mm c/c 13@600 mm c/c 13@300 mm c/c 13@600 mm c/c

    Right 13@300 mm c/c 13@600 mm c/c 13@300 mm c/c 13@600 mm c/c

    S11 Mid .. 13@300 mm c/c .. 13@300 mm c/c

    Left 13@300 mm c/c 13@600 mm c/c 13@300 mm c/c 13@600 mm c/c

    Right 13@300 mm c/c 13@600 mm c/c 13@300 mm c/c 13@600 mm c/c

  • Chapter two Slab

    design

    71

    S12 Mid .. 13@300 mm c/c .. 13@300 mm c/c

    Left 13@300 mm c/c 13@600 mm c/c 13@300 mm c/c 13@600 mm c/c

  • Chapter two Slab

    design

    72

    12 3 4

    A

    B

    C

    D

    E

    5.005.005.00

    7.00

    7.00

    5.50

    2.50

    22.20

    15.46

    4.60

    1.30

    4.60

    1.30

    2.90

    1.28

    3.40

    1.30

    a

    bc

    d

    e

    f

    a:13mm@600mmc/cBOT

    b:13mm@600mmc/c BOT

    c:13mm@200mmc/c TOP

    d:13mm@600mmc/cBOT

    e:13mm@600mmc/c BOT

    f:13mm@250mmc/c TOP

    g

    g:213mm@bottom&top

    @ all open corners

    90

    h

    h:313mm@bottom&top

    @ all corners

  • Chapter two Slab

    design

    73

    Cutoff point for bars:

    L1 L2

    L1/7 L1/5 L2/4 L2/4

    L2/3 L2/3L1/3L1/5

    15cm

    minimum

    L1 L2

    L1/8 L2/8 L2/8

    L2/3 L2/3L1/3L1/4

    15cm

    minimum