Concrete Slabs Design Example

  • View
    221

  • Download
    0

Embed Size (px)

Text of Concrete Slabs Design Example

  • 8/11/2019 Concrete Slabs Design Example

    1/31

  • 8/11/2019 Concrete Slabs Design Example

    2/31

    Types of Slab

    One-way slab Two-way slabOne-way slab

    Flat plate slab Flat slab Grid slab

  • 8/11/2019 Concrete Slabs Design Example

    3/31

    Think well need some additional framing members???

    Load Path / Framing Possibilities

    Ln = 4.4 m

    Ln = 8.2 m

    Ln = 3.2 m

    Ln = 3.6 m

  • 8/11/2019 Concrete Slabs Design Example

    4/31

    Plan

    Framing Concepts

    Lets use a simple example

    for our discussion

    Think about relating it to your

    design project.

    Column spacing 8 m c-c

  • 8/11/2019 Concrete Slabs Design Example

    5/31

    Framing Concepts

    We can first assume that

    well have major girders

    running in one direction

    in our one-way system

  • 8/11/2019 Concrete Slabs Design Example

    6/31

    Framing Concepts

    We can first assume that

    well have major girders

    running in one direction

    in our one-way system

    If we span between girders

    with our slab, then we have

    a load path, but if the spans

    are too long

  • 8/11/2019 Concrete Slabs Design Example

    7/31

    But we need to support the

    load from these new beams,

    so we will need additional

    supporting members

    Framing Concepts

    We will need to shorten up

    the span with additional beams

  • 8/11/2019 Concrete Slabs Design Example

    8/31

    We again assume that well

    have major girders running in

    one direction in our one-way

    system.

    Framing Concepts

    Now lets go back through with

    a slightly different load path.

    This time, lets think about

    shortening up the slab span by

    running beams into our girders.

    Our one-way slab will transfer our load to the beams.

  • 8/11/2019 Concrete Slabs Design Example

    9/31

    Two Load Path Options

  • 8/11/2019 Concrete Slabs Design Example

    10/31

    Framing Concepts - Considerations

    For your structure:

    Look for a natural load path

    Assume walls are not there for structural support, but

    consider that the may help you in construction (forming)

    Identify which column lines are best suited to having

    major framing members (i.e. girders)

  • 8/11/2019 Concrete Slabs Design Example

    11/31

    ExampleExample

    Condo Floor PlanCondo Floor Plan

  • 8/11/2019 Concrete Slabs Design Example

    12/31

    1.0m

    L S

    Main reinforcement

    One-way Slab

    Design of one-way slabs is like design of parallel 1m beams.

  • 8/11/2019 Concrete Slabs Design Example

    13/31

    Design of One-way Slab (L > 2S)

    S

    L 1 m

    1

    S

    w

    Minimum Thickness (ACI)

    Simply

    supported

    One end

    continuous

    Both ends

    continuous Cantilever

    L/20 L/24 L/28 L/10

    *

    multiplied by 0.4 + fy/7,000 for steel other than SD40

  • 8/11/2019 Concrete Slabs Design Example

    14/31

    ACI Design ProvisionACI Design Provision

    Shrinkage and temperature reinforcement

    Spacing 5 t 45 cm

    Main Steel (short direction):As 6 mm

    Max. Spacing 3 t 45 cm

    Min. Spacing f main steel 4/3 max agg. 2.5 cm

    For structural slabs only; not intended for soil-supported slabs on grade

    Ratio of reinforcement As to gross concrete area Ag : As/Ag

    RB24 (fy = 2,400 ksc) . . . . . . . . . . . . . . . . . 0.0025

    DB30 (fy = 3,000 ksc) . . . . . . . . . . . . . . . . . 0.0020

    DB40 (fy = 4,000 ksc) . . . . . . . . . . . . . . . . . 0.0018

    DB (fy > 4,000 ksc) . . . . . . . . . . . . . . . . . . . 0.0018 4,000 0.0014yf

  • 8/11/2019 Concrete Slabs Design Example

    15/31

    Effect of column width

    b b

    L

    b/212

    2wL

    2

    wL

    A

    b/2

    B

    w

    Moment atA:

    ( )

    +=

    +=

    8412

    2

    2/

    2212

    22

    22

    wbwLbwL

    bwbwLwL

    ( )

    +=

    =

    1261212

    222 wbwLbwLbLwM

    IfAandBare fiexed against rotation,

    B

    12

    2wL

    2

    wL

  • 8/11/2019 Concrete Slabs Design Example

    16/31

    Typical reinforcement in a oneTypical reinforcement in a one--way slabway slab

    Exterior span

    Bottom bars

    Top bars at

    exterior beams

    Top bars at

    exterior beams

    Interior span

    Temperature bars

    (a) Straight top and bottom bars

    Exterior span

    Bottom bars

    Bent bar Bent bars

    Interior span

    Temperature bars

    (b) Alternate straight and bent bars

  • 8/11/2019 Concrete Slabs Design Example

    17/31

    3@8m=

    24m

    4 @ 12 m = 48 m

    G1

    A AS1 S2 S3

    Example: Design one-way slab as shown below to carry the live

    load 500-kg/m2 fc= 210 kg/cm2,fy = 2,400 kg/cm

    2

    0.4 + 2400/7000 = 0.74

    min h = 400(0.74)/24 = 12.3 cm

    USE h = 13 cm

    DL = 0.132400 = 312kg/m2

    wu = 1.4(312) + 1.7(500) = 1,286.8 kg/m2

    clear span = 4 - 0.3 = 3.7 m

    Mu = (1,286.8)(3.7)2/10 = 1,762 kg-m

    max = 0.75b = 0.75(0.0454) = 0.0341

  • 8/11/2019 Concrete Slabs Design Example

    18/31

    USE RB9 with 2 cm covering: d= 13-2-0.45 = 10.55 cm

    ksc6.1755.101009.0

    100176222

    =

    ==

    bd

    MR un

    0077.085.0

    211

    85.0'

    '

    =

    =

    c

    n

    y

    c

    f

    R

    f

    f < max OK

    As = bd = 0.0077(100)(10.55) = 8.16 cm2/m

    Select RB9@0.07 (As = 9.28 cm2/m)

    Temp. steel = 0.0025(100)(13) = 3.25 < 9.28 cm2/m OK

    Select RB9@0.18 (As = 3.53 cm2/m)

  • 8/11/2019 Concrete Slabs Design Example

    19/31

    Detailing of one-way slab

    3

    1L

    4

    1L

    8

    1L

    L1

    Temp. steel

    4.0 .

    .13 .

    1.0 . 1.3 .

    RB9@0.10

    RB9@0.18 RB9@0.07

    4.0 .

    .13 .

    1.0 . 1.3 .RB9@0.07

    RB9@0.18 RB9@0.14

  • 8/11/2019 Concrete Slabs Design Example

    20/31

    Design of Two-way Slab (L < 2S)

    L

    S

    Min. Thickness:

    t 9 cm Perimeter/180 = 2(L+S)/180

    Reinforcement Steel:

    As 6 mm Temp. steel

    Max. Spacing 3 t 45 cm

    Min. Spacing main steel 4/3 max agg. 2.5 cm

  • 8/11/2019 Concrete Slabs Design Example

    21/31

    Load transfer from two-way Slab

    45o 45o

    45o 45o

    A

    D C

    B

    S

    L

    Short span (BC):

    Floor load = w kg/sq.m

    Tributary area = S2/4 sq.m

    Load on beam = wS/4 wS/3 kg/m

    Long span (AB): Span ratio m = S/L

    Tributary area = SL/2 - S2/4 = sq.m

    Load on beam kg/m

    m

    mS 2

    4

    2

    2

    3

    3

    2mwS

  • 8/11/2019 Concrete Slabs Design Example

    22/31

    Moment Coefficient Method

    S/4

    S/4

    S/2

    L/4 L/2 L/4

    -Ms

    -Ms

    +Ms+ML

    -ML -ML

    Middle strip moment: MM = CwS2

    Column strip moment: MC = 2MM/3

  • 8/11/2019 Concrete Slabs Design Example

    23/31

    ( C)

    m

    --

    1.0 0.9 0.8 0.7 0.6 0.5

    0.033-

    0.025

    0.040-

    0.030

    0.048-

    0.036

    0.055-

    0.041

    0.063-

    0.047

    0.083-

    0.062

    0.033-

    0.025

    --

    0.0410.0210.031

    0.0480.0240.036

    0.0550.0270.041

    0.0620.0310.047

    0.0690.0350.052

    0.0850.0420.064

    0.0410.0210.031

    -

    -

    0.0490.025

    0.037

    0.0570.028

    0.043

    0.0640.032

    0.048

    0.0710.036

    0.054

    0.0780.039

    0.059

    0.0900.045

    0.068

    0.0490.025

    0.037

  • 8/11/2019 Concrete Slabs Design Example

    24/31

    ( C)

    m

    --

    1.0 0.9 0.8 0.7 0.6 0.5

    0.0580.0290.044

    0.0660.0330.050

    0.0740.0370.056

    0.0820.0410.062

    0.0900.0450.068

    0.0980.0490.074

    0.0580.0290.044

    -

    -

    -0.033

    0.050

    -0.038

    0.057

    -0.043

    0.064

    -0.047

    0.072

    -0.053

    0.080

    -0.055

    0.083

    -0.033

    0.050

  • 8/11/2019 Concrete Slabs Design Example

    25/31

    Bar detailing in slab

    L1 L2

    L1/7 L1/4

    L1/3

    L2/4

    L2/3

    Bar detailing in beam

    L1 L2

    L1/8

    L1/3 L2/3

    L1/8

  • 8/11/2019 Concrete Slabs Design Example

    26/31

    L/5

    L/5

    L =

  • 8/11/2019 Concrete Slabs Design Example

    27/31

    Example: Design two-way slab as shown below to carry the live

    load 300-kg/m2 fc= 240 kg/cm2,fy = 2,400 kg/cm2

    3.80

    4.00

    4.805.00

    Floor plan

    0.10

    0.50

    0.20 0.20

    Cross section

    Min h = 2(400+500)/180 = 10 cm

    DL = 0.10(2,400) = 240 kg/m2

    wu = 1.4(240)+1.7(300) = 846 kg/m2

    m = 4.00/5.00 = 0.8

    As,min = 0.0018(100)(10) = 1.8 cm2/m

  • 8/11/2019 Concrete Slabs Design Example

    28/31

    Short span

    Moment coeff. C

    -M() +M -M()

    0.032 0.048 0.064

    Max.M= C w S2 =

    0.064 846 4.02

    = 866 kg-m/1 m width

    d= 10 - 2(covering) - 0.5(half of DB10) = 7.5 cm

    22 286,600 17.11 kg/cm0.9 100 7.5

    un MR

    bd= = =

    0.85 21 1 0.0045

    0.85

    c n

    y c

    f R

    f f

    = =

    As = 0.0045(100)(7.5) = 3.36 .2 > As,min

    DB10@0.20 (As=3.90

    .2)

  • 8/11/2019 Concrete Slabs Design Example