Design Aids

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  • Design Aid J.1-1 Areas of Reinforcing Bars

    Design Aid J.1-2 Approximate Bending Moments and Shear Forces for Continuous Beams and One-way Slabs

    Design Aid J.1-3 Variation of with Net Tensile Strain in Extreme Tension Steel t and c / dt

    Grade 60 Reinforcement and Prestressing Steel

    Design Aid J.1-4 Simplified Calculation of As Assuming Tension-Controlled Section and Grade 60 Reinforcement

    Design Aid J.1-5 Minimum Number of Reinforcing Bars Required in a Single Layer

    Design Aid J.1-6 Maximum Number of Reinforcing Bars Permitted in a Single Layer

    Design Aid J.1-7 Minimum Thickness h for Beams and One-Way Slabs Unless Deflections are

    Calculated

    Design Aid J.1-8 Reinforcement Ratio t for Tension-Controlled Sections Assuming Grade 60 Reinforcement

    Design Aid J.1-9 Simplified Calculation of bw Assuming Grade 60 Reinforcement and = 0.5 max

    Design Aid J.1-10 T-beam Construction

    Design Aid J.1-11 Values of Vs = Vu - Vc (kips) as a Function of the Spacing, s

    Design Aid J.1-12 Minimum Shear Reinforcement Av, min / s

    Design Aid J.1-13 Torsional Section Properties

    Design Aid J.1-14 Moment of Inertia of Cracked Section Transformed to Concrete, Icr

    Design Aid J.1-15 Approximate Equation to Determine Immediate Deflection, i, for Members Subjected to Uniformly Distributed Loads

    Design Aids J.2 Two-Way Slabs Direct Design method, includes the following:

    Conditions for Analysis by the Direct Design Method

    Definitions of Column Strip and Middle Strip

    Definition of Clear Span, Design Moment Coefficients used with the Direct Design Method

    Effective Beam and Slab Sections for Computation of Stiffness Ratio, f

    Computation of Torsional Stiffness Factor, t, for T- and L-Sections

    Moment Distribution Constants for Slab-Beam Members without Drop Panels

    Stiffness and Carry-Over Factors for Columns

  • DESIGN AID J.1-1 Areas of Reinforcing Bars

    Total Areas of Bars (in.2)

    Bar Size

    Number of Bars 1 2 3 4 5 6 7 8 9 10

    No. 3 0.11 0.22 0.33 0.44 0.55 0.66 0.77 0.88 0.99 1.10 No. 4 0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60 1.80 2.00 No. 5 0.31 0.62 0.93 1.24 1.55 1.86 2.17 2.48 2.79 3.10 No. 6 0.44 0.88 1.32 1.76 2.20 2.64 3.08 3.52 3.96 4.40 No. 7 0.60 1.20 1.80 2.40 3.00 3.60 4.20 4.80 5.40 6.00 No. 8 0.79 1.58 2.37 3.16 3.95 4.74 5.53 6.32 7.11 7.90 No. 9 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00 9.00 10.00 No. 10 1.27 2.54 3.81 5.08 6.35 7.62 8.89 10.16 11.43 12.70 No. 11 1.56 3.12 4.68 6.24 7.80 9.36 10.92 12.48 14.04 15.60

    Areas of Bars per Foot Width of Slab (in.2/ft)

    Bar Size

    Bar Spacing (in.) 6 7 8 9 10 11 12 13 14 15 16 17 18

    No. 3 0.22 0.19 0.17 0.15 0.13 0.12 0.11 0.10 0.09 0.09 0.08 0.08 0.07 No. 4 0.40 0.34 0.30 0.27 0.24 0.22 0.20 0.18 0.17 0.16 0.15 0.14 0.13 No. 5 0.62 0.53 0.46 0.41 0.37 0.34 0.31 0.29 0.27 0.25 0.23 0.22 0.21 No. 6 0.88 0.75 0.66 0.59 0.53 0.48 0.44 0.41 0.38 0.35 0.33 0.31 0.29 No. 7 1.20 1.03 0.90 0.80 0.72 0.65 0.60 0.55 0.51 0.48 0.45 0.42 0.40 No. 8 1.58 1.35 1.18 1.05 0.95 0.86 0.79 0.73 0.68 0.63 0.59 0.56 0.53 No. 9 2.00 1.71 1.50 1.33 1.20 1.09 1.00 0.92 0.86 0.80 0.75 0.71 0.67 No. 10 2.54 2.18 1.91 1.69 1.52 1.39 1.27 1.17 1.09 1.02 0.95 0.90 0.85 No. 11 3.12 2.67 2.34 2.08 1.87 1.70 1.56 1.44 1.34 1.25 1.17 1.10 1.04

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    pfs314 Design Aid

  • PositiveMoment

    NegativeMoment

    Shear

    n n n n

    Prismatic members

    n

    nuw nuw nuw

    nuw avgnuw avgnuw nuw nuwSpandrelSupport

    ColumnSupport

    nuw

    nuw nuwnuw nuwnuw nuw

    nuw

    nnavgn

    Note A nuw avgnuw avgnuw nuw nuw

    Two or more spans

    Uniformly distributed load wu (L/D 3)

    nuw

    DESIGN AID J.1-2

    pfs314 Design Aid

  • DESIGN AID J.1-3

    pfs314 Design Aid

  • DESIGN AID J.1-4

    Simplified Calculation of sA Assuming Tension-Controlled Section and Grade 60 Reinforcement

    cf (psi) sA (in.2)

    3,000 d

    M u84.3

    4,000 d

    M u00.4

    5,000 d

    M u10.4

    uM is in ft-kips and d is in inches

    In all cases, d

    MA us 4= can be used.

    Notes:

    d

    ff

    f

    MA

    c

    yy

    us

    =

    '85.05.0

    1

    For all values of < 0.0125, the simplified As equation is slightly conservative. It is recommended to avoid > 0.0125 when using the simplified As equation.

    pfs314 Design Aid

  • DESIGN AID J.1-51

    Assumptions:

    yf

    cc

    sf

    Bar Size

    Beam Width (in.)

    Minimum number of bars, nmim:

    1)5.0(2

    sdcb

    n bcwmin

    where

    s

    cs

    f

    cf

    s

    000,4012

    5.2000,4015

    1 Alsamsam, I.M. and Kamara, M. E. (2004). Simplified Design Reinforced Concrete Buildings of Moderate Size and Heights, EB104, Portland Cement Association, Skokie, IL.

    db

    pfs314 Design Aid

  • DESIGN AID J.1-61

    Assumptions:

    yf

    sc

    Bar Size

    Beam Width (in.)

    Maximum number of bars, nmax:

    1space)(Clear

    )(2

    b

    sswdrdcb

    nmax

    1 Alsamsam, I.M. and Kamara, M. E. (2004). Simplified Design Reinforced Concrete Buildings of Moderate Size and Heights, EB104, Portland Cement Association, Skokie, IL.

    db

    pfs314 Design Aid

  • 1 2 3

    5.18/1h 21/2h 8/3h

    1 2 3

    24/1h 28/2h 10/3hSolid One-way Slabs

    Applicable to one-way construction not supporting or attached to partitions or other construction likely to be damaged by large deflections.

    Values shown are applicable to members with normal weight concrete ( 145cw lbs/ft3) and Grade 60

    reinforcement. For other conditions, modify the values as follows:

    For structural lightweight having cw in the range 90-120 lbs/ft3, multiply the values by

    .09.1005.065.1 cw

    For yf other than 60,000 psi, multiply the values by .000,100/4.0 yf

    For simply-supported members, minimum slabsway -one ribbedor beamsfor 16/

    slabsway -one solidfor 20/h

    Beams or Ribbed One-way Slabs

    DESIGN AID J.1-7h

    pfs314 Design Aid

  • DESIGN AID J.1-8

    Reinforcement Ratio t for Tension-Controlled Sections Assuming Grade 60 Reinforcement

    cf (psi) t when t = 0.005 t when t = 0.004

    3,000 0.01355 0.01548

    4,000 0.01806 0.02064

    5,000 0.02125 0.02429 Notes:

    1. ( )bcfC c 1'85.0 = ys fAT =

    ( ) ysc fAbcfTC == 1'85.0

    a. When t = 0.005, c/dt = 3/8. ( ) ystc fAbdf =83'85.0 1

    y

    c

    t

    st f

    f

    bdA )8

    3(85.0 1 ==

    b. When t = 0.004, c/dt = 3/7.

    ( ) ystc fAbdf =73'85.0 1

    y

    c

    t

    st f

    f

    bdA )7

    3(85.0 1 ==

    2. 1 is determined according to 10.2.7.3.

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    pfs314 Design Aid

  • DESIGN AID J.1-9

    Simplified Calculation of wb Assuming Grade 60 Reinforcement and max= 5.0

    cf (psi) wb (in.)*

    3,000 26.31

    d

    M u

    4,000 27.23

    d

    M u

    5,000 20.20

    d

    M u

    * uM is in ft-kips and d is in inches

    In general:

    ( ) 211 2143.01600,36

    df

    Mb

    c

    uw

    =

    where max= / , cf is in psi, d is in inches and uM is in ft-kips and

    003.0004.0003.085.0 1+

    =

    y

    cmax f

    f (10.3.5)

    pfs314 Design Aid

  • 1s

    fhh =

    +

    +

    +

    2443

    612lengthSpan

    121

    1

    1

    1sbb

    hb

    b

    b

    ww

    w

    w

    e

    1eb

    2s 1wb 2wb

    2eb

    ++

    +

    +

    242

    164lengthSpan

    21312

    22ssbbb

    hbb

    www

    we

    3wb

    2w

    fbhh =

    wb

    we bb 4

    Isolated T-beam

    DESIGN AID J.1-10 T-beam Construction

    8.12

    pfs314 Design Aid

  • DESIGN AID J.1-11

    Values of cus VVV = (kips) as a Function of the Spacing, s*

    s No. 3 U-stirrups No. 4 U-stirrups No. 5 U-stirrups d/2 19.8 36.0 55.8

    d/3 29.7 54.0 83.7

    d/4 39.6 72.0 111.6 * Valid for Grade 60 ( 60=ytf ksi) stirrups with 2 legs (double the tabulated values for

    4 legs, etc.).

    In general:

    sdfA

    V ytvs

    = (11.4.7.2)

    where ytf used in design is limited to 60,000 psi, except for welded deformed wire reinforcement, which is limited to 80,000 psi (11.4.2).

    pfs314 Design Aid

  • DESIGN AID J.1-12

    Minimum Shear Reinforcement */, sA minv

    cf (psi) sA minv,

    in.in.2

    500,4 wb00083.0

    5,000 wb00088.0

    * Valid for Grade 60 ( 60=ytf ksi) shear reinforcement.

    In general:

    yt

    w

    yt

    wc

    minv

    fb

    fb

    fs

    A 5075.0, = Eq. (11-13)

    where ytf used in design is limited to 60,000 psi, except for welded deformed wire reinforcement, which is limited to 80,000 psi (11.4.2).

    pfs314 Design Aid

  • DESIGN AID J.1-13 Torsional Section Properties

    Section* Acp pcp Aoh phEdge

    bwh + behf 2(h + bw + be) x1y1 2(x1 + y1)

    x1 = bw - 2c - dsy1 = h - 2c - ds

    Interior

    bw(h - hf) + behf 2(h + be) x1y1 2(x1 + y1)

    x1 = bw - 2c - dsy1 = h - 2c - ds

    L-shaped

    b1h1 + b2h2 2(h1 + h2 + b2) x1y1 + x2y2 2(x1 + x2 + y1)x1 = b1 - 2c - dsy1 = h1 + h2 - 2c - dsx2 = b2 - b1y2 = h2 - 2c - ds

    Inverted tee