chapter 3 slab - skyscrapers slab 16 3.3 design of one-way slab step 1: estimation of slab thickness

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  • CHAPTER 3

    SLAB

    3.1 INTRODUCTION

    Reinforced concrete slabs are one of the most widely used structural elements. In many structures, in addition to providing a versatile and economical method of supporting gravity loads, the slab also forms an integral portion of the structural frame to resist lateral forces. Usually a slab is a broad, flat plate, with top and bottom surfaces parallel or nearly so. It may be supported by reinforced concrete beams, by masonry or reinforced concrete walls, by structural steel members, directly by columns, or continuously by the ground.

    3.2 TYPES OF SLAB

    • One-way slab : Independent of support condition. (Figure 3.1a 3.1b)

    2

    1

    l l

    > 2;

    • Two-way slab : Depends on support condition. (Figure 3.1c)

    2

    1

    l l

    ≤ 2

    (a) One- way slab

    Figure 3.1: Types of slab

    2

    1 l

    l >2

    1l 2l

    2

    1

    l l > 2

  • SLAB

    15

    Two-way slabs are classified as:

    • Two-way edge supported slab or slab with beams. ( Figure 3.1d ) • Two-way column supported slab or slab without beams. ( Figure 3.1e,3.1f, 3.1g )

    (f) Flat slab (Column supported slab)

    (d) Slab with beams (Edge supported slab)

    (b) One- way slab

    (g) Grid slab (Column supported slab)

    (e) Flat plate (Column supported slab)

    (c) Two- way slab

    1l 2l

    1l2l

    Figure 3.1: Types of slab (continued)

  • SLAB

    16

    3.3 DESIGN OF ONE-WAY SLAB

    Step 1: Estimation of Slab Thickness (h)

    Slab thickness is determined according to ACI Code 9.5.2 as given in Table 3.1

    Table 3.1: Minimum thickness of non-prestressed one- way slab

    Members wc = 145 pcf

    fy = 60.000 psi

    wc =90∼120 pcf fy 60.000 psi

    Rounding up the thickness

    Simply supported l/20

    One end continuous l/24

    Both end continuous l/28

    Cantilever l/10

    Multiply by (1.65-0.005wc) but > 1.09

    Multiply by

    0.4 + 000,100 yf

    (1) h≤6 in next higher ¼ in

    (2) h > 6 in next higher ½ in

    # Span length l is in inches, as defined by ACI Code 8.7 given in Fig. 3.2(a), (b), & (c)

    Step 2 : Calculation of Factored Load (wu)

    wu = 1.4 D+ 1.7 L psf

    Dead load, D = wc x 12 h psf

    wc = Unit weight of concrete (145 ~ 150 pcf for normal weight concrete )

  • SLAB

    17

    Step 3: Determination of Design Moment

    Design moment is determined by using ACI Moment Coefficient (ACI Code 8.3.3) as given in Table 3.4.

    Step 4 : Checking the Design Thickness

    d = )59.01(

    c

    y y

    u

    f f

    bf

    M

    ′ − ρφρ

    putting ρ = ρmax = 0.75ρb.

    Where, ρ b = 0.85*β 1 y

    c

    f f /

    * yf+87000

    87000

    Values of β 1 is given in Table 3.2

    Table3.2 : Values of β 1 (ACI Code 10.2.7.3)

    f c / ≤ 4000 psi β 1 = 0.85

    f c / > 4000 psi β 1 shall be reduced at a rate of 0.05 for each 1000 psi of strength

    in excess of 4000 psi.

    0.65 ≤ β 1≤ 0.85

    Table 3.3: Clear cover for slab ( ACI Code 7.7.1)

    No 14 & No 18 bars .................................... .... 1 1/2 in No 11 bar & smaller .................................... ¾ in

  • SLAB

    18

    t

    al

    h

    (a) Slabs not built integrally with the support (ACI Code 8.7.1)

    l= la + h ≤ la + t t

    al

    h

    l= la + t

    (b) Slabs are continuous (ACI Code 8.7.2)

    t al

    Figure 3.2 : Span length

    (c) Slabs built integrally with support

    If (d + clear cover) < h; Design is ok.

    Otherwise redesign the thickness.

  • SLAB

    19

    3. Discontinuous ends are

    Table 3.4 : ACI moment coefficient

    Support Condition

    1 9

    1 1 1

    0 0

    Moment Coefficent

    For two span:

    1. Discontinuous ends are

    1 2 4

    1 9

    1 1 4

    1 1 4

    0 11 0

    1 1 1

    1 1 1

    1 2 4

    1 1 0

    1 1 4

    1 2 4

    1 9

    1 1 6

    1 1 4

    1 1 6

    1 9

    1 9

    1 1 4

    unrestrained

    built integrally with support 2. Discontinuous ends are

    (spandrel beam or girder)

    1 1 6

    1 1 1

    1 1 1

    1 1 6

    1 1 1

    1 1 1

    1 1 1

    1 1 4

    1 1 6

    1 1 6

    1 1 0

    1 1 1

    1 1 1

    1 1 1

    built integrally with support (when support is a column only)

    For continuous Span: 1. Discontinuous ends are unrestrained.

    (spandrel beam or girder) built integrally with support 2. Discontinuous ends are

    3. Discontinuous ends are built integrally with support

    (when support is a column only)

    w = Total factored load per unit length of beam or per unit area of slab

    l = Clear span for positive moment and the average of two adjacent clear spans for negative moment.

    1. Shear in end members at first interior support

    2. Shear at all other supports 1.15 w2

    w 2

    1 9

    1 1 1

  • SLAB

    20

    Step 5 : Determination of Steal Area (As)

    Reinforcement for 1 ft. strip towards shorter distance is calculated by Iteration. Details shown in Figure 3.3 (here b = 12 in)

    Figure 3.3: Iteration process to determine the steel area

    Calculate a for next trial with (As) corrected

    (a) corrected = bf fA

    c

    ys

    ′′′85.0

    (As) trial = ( )2adf M

    y

    u

    −φ

    (As) corrected

    A corrs , ≈

    As, trial

    Yes

    OK

    Assume a (hints: a = 0.3d)

    No

  • SLAB

    21

    Generally # 3 or # 4 bars are used for slab main reinforcement.

    Spacing: ACI Code 7.6.5 specifies that

    Spacing ≤ 3h or 18 in, whichever is smaller

    but > 1.5 h

    Finding out bar spacing: Let us chose # 3 bar (0.11 2in )

    Spacing = sA

    12*11.0 in c/c

    Step 6 : Temperature and Shrinkage Reinforcement

    Reinforcement is provided normal to main reinforcements. ACI Code 7.12.2.1 provides required area of temperature and shrinkage reinforcement as given in Table 3.5.

    Table 3.5 : Minimum ratio of temperature and shrinkage reinforcement in slabs.

    Slabs where grade 40 or 50 deformed bars are used

    0.0020

    Slabs where grade 60 deformed bars or welded wire fabric are used

    0.0018

    Slabs where reinforcement with yield strength exceeding 60,000 psi measured at a yield strain of 0.35 percent is used

    yf 000,600018.0 ×

    But should be:

    ρ > 0.0014

    Required steel area, As = ρbh 2in per 1 ft. strip

  • SLAB

    22

    Spacing: ACI Code 7.12.2.2 specifies that

    Spacing ≤ 5h

    or ≤ 18 in , whichever is smaller

    Using # 3 or # 4 bar required spacing can be obtained.

    Step 7 : Shear Check

    According to ACI shear coefficient given in Table 3.2

    Shear at end members at first interior support is 2

    15.1 nulw

    Critical shear at a distance d from support, Vu = (1.15 122 dWlW unu − )

    Design strength for shear, φ Vc = φ ′cf2 bd ; φ = 0.85

    If φVc > Vu, slab design for shear is OK

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