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SEISMIC DESIGN OF REINFORCED CONCRETE STRUCTURES

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SEISMIC DESIGN OF REINFORCED CONCRETE STRUCTURES Powered By Docstoc
					       SEISMIC DESIGN OF
REINFORCED CONCRETE STRUCTURES




     Instructional Material Complementing FEMA 451, Design Examples   Design for Concrete Structures 11 - 1
     NEHRP Recommended Provisions
      Concrete Design Requirements
• Context in the NEHRP Recommended
    Provisions
•   Concrete behavior
•   Reference standards
•   Requirements by Seismic Design Category
•   Moment resisting frames
•   Shear walls
•   Other topics
•   Summary

          Instructional Material Complementing FEMA 451, Design Examples   Design for Concrete Structures 11 - 2
    Context in NEHRP Recommended
               Provisions
Design basis: Strength limit state

Using NEHRP Recommended Provisions:
 Structural design criteria:     Chap. 4
 Structural analysis procedures: Chap. 5
 Components and attachments:     Chap. 6
 Design of concrete structures:  Chap. 9
                                 and
                                 ACI 318
        Instructional Material Complementing FEMA 451, Design Examples   Design for Concrete Structures 11 - 3
     Seismic-Force-Resisting Systems
                     Reinforced Concrete
Unbraced frames (with
rigid “moment resisting” joints):
   Three types
        Ordinary
        Intermediate
        Special
R/C shear walls:
      Ordinary
      Special
Precast shear walls:
      Special
      Intermediate
      Ordinary
           Instructional Material Complementing FEMA 451, Design Examples   Design for Concrete Structures 11 - 4
 NEHRP Recommended Provisions
        Concrete Design

• Context in the Provisions
• Concrete behavior




      Instructional Material Complementing FEMA 451, Design Examples   Design for Concrete Structures 11 - 5
Unconfined Concrete Stress-Strain Behavior
               20000
                                                                              4500 psi
               18000                                                          8800 psi
               16000                                                          13,500 psi
               14000                                                          17,500 psi
 Stress, psi




               12000
               10000
                8000
                6000
                4000
                2000
                   0
                       0              0.001             0.002             0.003             0.004
                                                 Strain, in./in.

                           Instructional Material Complementing FEMA 451, Design Examples      Design for Concrete Structures 11 - 6
                         Idealized Stress-Strain Behavior
                             of Unconfined Concrete
              6000

              5000

              4000
Stress, psi




              3000                                                                 ⎡ 2ε ⎛ ε ⎞2 ⎤
                                                                          fc = fc' ⎢ c − ⎜ c ⎟ ⎥
                                                                                   ⎢ εo ⎝ εo ⎠ ⎥
                                                                                   ⎣           ⎦
              2000
                                                                                2fc'
                                                                          εo =
              1000                                                               Et
                                                                          Et = 1.8 x106 + 460fc' , psi
                0
                     0    0.0005 0.001 0.0015 0.002 0.0025 0.003 0.0035 0.004
                                                                Strain
                           Instructional Material Complementing FEMA 451, Design Examples   Design for Concrete Structures 11 - 7
 Confinement by Spirals or Hoops
          Asp                                           fyhAsp



                                  ds


                                                      fyhAsp

Confinement                       Forces acting                           Confinement
from spiral or                    on 1/2 spiral or                        from square
circular hoop                     circular hoop                           hoop


         Instructional Material Complementing FEMA 451, Design Examples   Design for Concrete Structures 11 - 8
                          Confinement




Rectangular hoops                        Confinement by                     Confinement by
  with cross ties                        transverse bars                    longitudinal bars


         Instructional Material Complementing FEMA 451, Design Examples   Design for Concrete Structures 11 - 9
Opened 90° hook on hoops




 Instructional Material Complementing FEMA 451, Design Examples   Design for Concrete Structures 11 - 10
Confined Concrete Stress-Strain Behavior

                8000                                                           no confinement
                                                                               4.75 in.
                7000                                                                     Pitch of
                                                                               3.5 in.
                                                                                         ¼ in. dia.
                6000                                                           2.375 in.
                                                                                         spiral
                                                                               1.75 in.
  Stress, psi




                5000
                4000
                3000
                                                                                            Tests of
                2000                                                                        6 in. x 12 in.
                1000                                                                        cylinders

                   0
                       0             0.01               0.02               0.03         0.04
                            Average strain on 7.9 in. gauge length
                       Instructional Material Complementing FEMA 451, Design Examples   Design for Concrete Structures 11 - 11
                 Idealized Stress-Strain Behavior of
                         Confined Concrete
                                           Kent and Park Model
                                                                                                   No Hoops
                4500                                                                               4 in.
                4000                                                                               6 in.
                                                                                                   9 in.
                3500
                                                                                                   12 in.
                3000
  Stress, psi




                2500
                2000
                1500
                1000
                 500
                   0
                       0               0.004                 0.008                 0.012            0.016

Confined Area 12” x 16”                               Strain, in./in.

                           Instructional Material Complementing FEMA 451, Design Examples   Design for Concrete Structures 11 - 12
Reinforcing Steel Stress-Strain Behavior

               100

                                                       Grade 75
               80
 Stress, ksi




                                                             Grade 60
               60                                                                       rupture~10-12%


                                                                             Grade 40
               40
                                                                              strain hardening~ 1-3%
                               E = 29,000 ksi                                 rupture ~18-20%
               20



                         1000       2000       3000       4000        5000       6000    7000        8000
                                                        Microstrain


                     Instructional Material Complementing FEMA 451, Design Examples     Design for Concrete Structures 11 - 13
       Reinforced Concrete Behavior


        steel
        yields                                                               failure

Load
                                              cracked-inelastic
                     cracked-elastic

           uncracked

                    Mid-Point Displacement, Δ

          Instructional Material Complementing FEMA 451, Design Examples   Design for Concrete Structures 11 - 14
Behavior Up to First Yield of Steel

           b
                                                  εc                    fc
                            c

d                                            φ
          As
                                                                                εsEs < fy
                                     εs
                                    Strain                            Stress


     Instructional Material Complementing FEMA 451, Design Examples    Design for Concrete Structures 11 - 15
    Behavior at Concrete Crushing
      b                               ε c,max                          f'c
                     c                                                                                   C

d                                    φ                                            jd

     As
                                                                             fy                           Asfy
                            εs >εy
                            Strain                           Stress                    Forces

                                   Mn = Asfyjd
          Instructional Material Complementing FEMA 451, Design Examples          Design for Concrete Structures 11 - 16
                  Typical Moment Curvature Diagram
            700
                          w/ strain hardening
            600                                                                                       f’c = 4 ksi
                                                                                                      fy = 60 ksi
            500
M, in-kip




                                         w/o strain hardening
                                                                                                      b = 8 in
            400                                                                                       d = 10 in
            300                                                                                       ρ = 0.0125

            200

            100

             0
                  0                  100                            200                      300

                                            φ x 10-5 in-1
                      Instructional Material Complementing FEMA 451, Design Examples   Design for Concrete Structures 11 - 17
              Influence of Reinforcement Ratio
            5000
                                                                                                  f’c = 4 ksi
            4000
                                                                                                  fy = 60 ksi
                                                                                                  b = 10 in
M, in-kip




            3000
                                                                                                  d = 18 in
            2000

                                                                                                   ρ = 2.5%
            1000
                                                                                                   ρ = 1.5%
                                                                                                   ρ = 0.5%
              0
                   0          100                   200                  300             400

                                       φ x 10-5 in-1

                       Instructional Material Complementing FEMA 451, Design Examples   Design for Concrete Structures 11 - 18
   Influence of Compression Reinforcement

          1600                                                             Beam              ρ                 ρ'
                                                                             1            0.0375            0.0250
                                                                             2            0.0375            0.0125
                                                                         1   3            0.0375               0
          1200                                    2                          4            0.0250            0.0125
                                       3                                     5            0.0250               0
                                                                             6            0.0125            0.0125
           800                                    5                       4 7             0.0125               0
 M
    lb / in2
bd2                                                                               6
           400                                                             7


               0
                   0                0.008               0.016             0.024
                                                   φ
                       Instructional Material Complementing FEMA 451, Design Examples   Design for Concrete Structures 11 - 19
        Moment-Curvature
      with Confined Concrete
                                      ε c,max                                f'c
                   c

                                      φ
As
                                                                                   fy
                          εs >εy
                          Strain                                  Stress

 Instructional Material Complementing FEMA 451, Design Examples   Design for Concrete Structures 11 - 20
                 Moment-Curvature with Confined
                           Concrete
               35000

               30000

               25000
Moment, in-k




               20000                              Beam - 24 in. x 36 in.
                                                  Tension Steel - 12 ea. #10
               15000                              Compression Steel - 5 ea. #8
                                                  Confining Steel - #4 hoops at 4 in. c-c
               10000

               5000
                                                       without confining                    with confining
                  0
                       0                     500                    1000                     1500                   2000
                                               curvature, microstrain/in.
                           Instructional Material Complementing FEMA 451, Design Examples       Design for Concrete Structures 11 - 21
                 Plastic Hinging



l
                                                                                     idealized
                      M                                              φ
                                                                                     actual


                                   lp                                                plastic
                                                                                     rotation
                                                 φu −φy
                  Mu                                φu



    Instructional Material Complementing FEMA 451, Design Examples   Design for Concrete Structures 11 - 22
 Strategies to Improve Ductility

• Use low flexural reinforcement ratio
• Add compression reinforcement
• Add confining reinforcement




      Instructional Material Complementing FEMA 451, Design Examples   Design for Concrete Structures 11 - 23
    Other Functions of Confining Steel

• Acts as shear reinforcement
• Prevents buckling of longitudinal
    reinforcement
•   Prevents bond splitting failures




          Instructional Material Complementing FEMA 451, Design Examples   Design for Concrete Structures 11 - 24
    Structural Behavior
          Frames




Story Mechanism                                 Sway Mechanism



  Instructional Material Complementing FEMA 451, Design Examples   Design for Concrete Structures 11 - 25
         Story Mechanism




Instructional Material Complementing FEMA 451, Design Examples   Design for Concrete Structures 11 - 26
        Structural Behavior - Walls
                                                                                Δs


                             H                    V


                                                                                                N       V
                 H                                                          V
                                                                                          V         N
    V      C                                                            V
T

Flexural             Horizontal                     Sliding on                         Sliding on
 failure              tension                    flexural cracks                      construction
                                                                                          joint

           Instructional Material Complementing FEMA 451, Design Examples       Design for Concrete Structures 11 - 27
         Structural Behavior
                Walls

  Vu                                              Vu             Compression               Vu

                            1
     2                                                                                 1
                                        hw
                                                   2
                                                                                       45

  lw




Instructional Material Complementing FEMA 451, Design Examples     Design for Concrete Structures 11 - 28
                                          Structural Behavior
                                                                                                           14 in square
                                               Columns                                                     4-#11 bars
                                                                                                           f' c = 4 ksi
                                                                                                           f y = 45 ksi
                                Ultimate
                     1000
                                yield
                      800
Axial load, P, kip




                      600                                                        1.75”                bending axis


                      400


                      200


                        0
                            0   400         800         1200        1600          0.002                 0.001                       0
                                Moment, M, in-kip                                                 Curvature, φ, rad/in
                                 Instructional Material Complementing FEMA 451, Design Examples       Design for Concrete Structures 11 - 29
Influence of Hoops on Axial Strength
                       Gross column                                Confined concrete
                       Area = A g                                  Area = A core




  Before spalling-                             After spalling-
    P = Agf’c                                    P = Acore(f’c + 4 flat)

          After spalling ≥ Before spalling

        Instructional Material Complementing FEMA 451, Design Examples   Design for Concrete Structures 11 - 30
                                                  Column with
                                                Inadequate Ties




Instructional Material Complementing FEMA 451, Design Examples   Design for Concrete Structures 11 - 31
 Well Confined Column




Instructional Material Complementing FEMA 451, Design Examples   Design for Concrete Structures 11 - 32
Hysteretic Behavior of Well Confined
              Column

                             M 1.0
                             Mu
                               0.5


 -4                                                                                      4

                                               -0.5                    Drift, %

                                                -1.0

      Instructional Material Complementing FEMA 451, Design Examples    Design for Concrete Structures 11 - 33
               Structural Behavior
                    Columns
        Δ
                                                     M1                M1                         V
                                       V

L
                                        V

                                                    M2        M2
                                                             P
   M1 + M2 2Mu
V=        =
      L     L                              Range
                                           of P
                                                                                               M
                                                                       Mo             Mu
      Instructional Material Complementing FEMA 451, Design Examples        Design for Concrete Structures 11 - 34
      Column Shear Failure




Instructional Material Complementing FEMA 451, Design Examples   Design for Concrete Structures 11 - 35
              Structural Behavior
                    Joints



           V

    fc                  T
             ft
h
                        Cc
                             Cs

                     Max. shear force
                     Vj = T- V




    Instructional Material Complementing FEMA 451, Design Examples   Design for Concrete Structures 11 - 36
Hysteretic Behavior of Joint with Hoops

              1.0
       M
       Mu
              0.5



            -1                                               5 6
                                                          Drift, %
                           -0.5

      Instructional Material Complementing FEMA 451, Design Examples   Design for Concrete Structures 11 - 37
Hysteretic Behavior of Joint with No Hoops

                      1.0
               M
               Mu
                      0.5



                    -1                                            5 6
                                                               Drift, %
                                  -0.5



        Instructional Material Complementing FEMA 451, Design Examples   Design for Concrete Structures 11 - 38
Joint Failure – No Shear Reinforcing




      Instructional Material Complementing FEMA 451, Design Examples   Design for Concrete Structures 11 - 39
      Anchorage Failure in
      Column/Footing Joint




Instructional Material Complementing FEMA 451, Design Examples   Design for Concrete Structures 11 - 40
   Summary of Concrete Behavior
• Compressive Ductility
  – Strong in compression but brittle
  – Confinement improves ductility by
     • Maintaining concrete core integrity
     • Preventing longitudinal bar buckling
• Flexural Ductility
  – Longitudinal steel provides monotonic ductility at low
    reinforcement ratios
  – Transverse steel needed to maintain ductility through
    reverse cycles and at very high strains (hinge
    development)

         Instructional Material Complementing FEMA 451, Design Examples   Design for Concrete Structures 11 - 41
   Summary of Concrete Behavior

• Damping
  – Well cracked: moderately high damping
  – Uncracked (e.g. prestressed): low damping
• Potential Problems
  – Shear failures are brittle and abrupt and must be
    avoided
  – Degrading strength/stiffness with repeat cycles
     • Limit degradation through adequate hinge
       development


         Instructional Material Complementing FEMA 451, Design Examples   Design for Concrete Structures 11 - 42
NEHRP Recommended Provisions
       Concrete Design

 • Context in the Provisions
 • Concrete behavior
 • Reference standards




    Instructional Material Complementing FEMA 451, Design Examples   Design for Concrete Structures 11 - 43
                                                         ACI 318-05




Instructional Material Complementing FEMA 451, Design Examples   Design for Concrete Structures 11 - 44
     Use of Reference Standards
• ACI 318-05
  – Chapter 21, Special Provisions for Seismic Design
• NEHRP Chapter 9, Concrete Structures
  – General design requirements
  – Modifications to ACI 318
  – Seismic Design Category requirements
  – Special precast structural walls
  – Untopped precast diaphragms (Appendix to Ch.9)



         Instructional Material Complementing FEMA 451, Design Examples   Design for Concrete Structures 11 - 45
    Detailed Modifications to ACI 318

•   Modified definitions and notations
•   Scope and material properties
•   Special moment frames
•   Special shear walls
•   Special and intermediate precast walls
•   Foundations
•   Anchoring to concrete



          Instructional Material Complementing FEMA 451, Design Examples   Design for Concrete Structures 11 - 46
    NEHRP Recommended Provisions
           Concrete Design

•   Context in the Provisions
•   Concrete behavior
•   Reference standards
•   Requirements by Seismic Design Category




       Instructional Material Complementing FEMA 451, Design Examples   Design for Concrete Structures 11 - 47
Design Coefficients - Moment Resisting Frames
  Seismic Force                  Response                                   Deflection
    Resisting                   Modification                               Amplification
     System                     Coefficient, R                              Factor, Cd

   Special R/C
                                              8                                     5.5
  Moment Frame

 Intermediate R/C
                                              5                                     4.5
  Moment Frame

   Ordinary R/C
                                              3                                     2.5
  Moment Frame


          Instructional Material Complementing FEMA 451, Design Examples     Design for Concrete Structures 11 - 48
               Design Coefficients
          Shear Walls (Bearing Systems)
    Seismic Force                        Response                             Deflection
      Resisting                         Modification                         Amplification
       System                           Coefficient, R                        Factor, Cd


  Special R/C Shear
                                                  5                                     5
        Walls

    Ordinary R/C
                                                  4                                     4
    Shear Walls

 Intermediate Precast                             4                                     4
      Shear Walls


Ordinary Precast Walls                            3                                     3


            Instructional Material Complementing FEMA 451, Design Examples   Design for Concrete Structures 11 - 49
               Design Coefficients
           Shear Walls (Frame Systems)

 Seismic Force                       Response                                 Deflection
   Resisting                        Modification                             Amplification
    System                          Coefficient, R                            Factor, Cd
  Special R/C Shear
                                                  6                                      5
        Walls

    Ordinary R/C
                                                  5                                    4.5
    Shear Walls

 Intermediate Precast                             5                                    4.5
      Shear Walls


Ordinary Precast Walls                            4                                      4


            Instructional Material Complementing FEMA 451, Design Examples    Design for Concrete Structures 11 - 50
            Design Coefficients
     Dual Systems with Special Frames

 Seismic Force                   Response                                  Deflection
   Resisting                    Modification                              Amplification
    System                      Coefficient, R                             Factor, Cd
Dual System w/
                                           8 (7)                             6.5 (5.5)
 Special Walls
Dual System w/
                                              6                                      5
Ordinary Walls

(ASCE 7-05 values where different)


         Instructional Material Complementing FEMA 451, Design Examples    Design for Concrete Structures 11 - 51
                                  Frames
Seismic                           Minimum                                   ACI 318
 Design                          Frame Type                               Requirements
Category

                                                                         Chapters 1 thru
 A and B                            Ordinary
                                                                           18 and 22

                                                                         ACI 21.2.1.3 and
    C                           Intermediate
                                                                           ACI 21.12
                                                                         ACI 21.2.1.4 and
D, E and F                            Special                             ACI 21.2, 21.3,
                                                                          21.4, and 21.5

        Instructional Material Complementing FEMA 451, Design Examples      Design for Concrete Structures 11 - 52
   Reinforced Concrete Shear Walls

Seismic                           Minimum                                 ACI 318
 Design                             Wall                                Requirements
Category                            Type


                                                                       Chapters 1 thru
A, B and C                         Ordinary
                                                                         18 and 22


                                                                       ACI 21.2.1.4 and
D, E and F                           Special
                                                                       ACI 21.2 and 21.7



      Instructional Material Complementing FEMA 451, Design Examples      Design for Concrete Structures 11 - 53
     Precast Concrete Shear Walls

Seismic                             Minimum                                 ACI 318
 Design                             Wall Type                             Requirements
Category
                                                                         Chapters 1 thru
 A and B                             Ordinary
                                                                           18 and 22

                                                                         ACI 21.2.1.3 and
    C                            Intermediate
                                                                           ACI 21.13

                                                                         ACI 21.2.1.4 and
D, E and F                             Special
                                                                          ACI 21.2, 21.8


        Instructional Material Complementing FEMA 451, Design Examples      Design for Concrete Structures 11 - 54
Additional Provisions Requirements

    • Category C
      – Discontinuous members
      – Plain concrete
            • Walls
            • Footings
            • Pedestals (not allowed)




      Instructional Material Complementing FEMA 451, Design Examples   Design for Concrete Structures 11 - 55
    NEHRP Recommended Provisions
           Concrete Design

•   Context in the Provisions
•   Concrete behavior
•   Reference standards
•   Requirements by Seismic Design Category
•   Moment resisting frames




        Instructional Material Complementing FEMA 451, Design Examples   Design for Concrete Structures 11 - 56
 Performance Objectives
• Strong column
  – Avoid story mechanism
• Hinge development
  – Confined concrete core
  – Prevent rebar buckling
  – Prevent shear failure
• Member shear strength
• Joint shear strength
• Rebar development

  Instructional Material Complementing FEMA 451, Design Examples   Design for Concrete Structures 11 - 57
     Frame Mechanisms
“strong column – weak beam”




Story mechanism                                Sway mechanism




   Instructional Material Complementing FEMA 451, Design Examples   Design for Concrete Structures 11 - 58
         Required Column Strength


                                                ∑ Mnc ≥ 1.2∑ Mnb
               M nc1



M nb1                                                   M nb2



                  M nc2


        Instructional Material Complementing FEMA 451, Design Examples   Design for Concrete Structures 11 - 59
               Hinge Development

• Tightly Spaced Hoops
  – Provide confinement to increase concrete strength
    and usable compressive strain
  – Provide lateral support to compression bars to
    prevent buckling
  – Act as shear reinforcement and preclude shear
    failures
  – Control splitting cracks from high bar bond stresses



         Instructional Material Complementing FEMA 451, Design Examples   Design for Concrete Structures 11 - 60
     Hinge Development

                                                                 Before
                                                                 spalling




                                                                 After
                                                                 spalling




Instructional Material Complementing FEMA 451, Design Examples    Design for Concrete Structures 11 - 61
      Hinge Development

                                           Bidirectional cracking




                                                      Spalled cover


Instructional Material Complementing FEMA 451, Design Examples   Design for Concrete Structures 11 - 62
ACI 318-05, Overview of Frames:
 Beam Longitudinal Reinforcement
                                            200           ≤ ρ ≤ 0 .025
                                                     fy
                                          At least 2 bars continuous
                                          top & bottom


                                         Joint face Mn+ not less than 50% Mn-
                                         Min. Mn+ or Mn- not less than
                                         25% max. Mn at joint face


                                          Splice away from hinges and
                                          enclose within hoops or spirals


     Instructional Material Complementing FEMA 451, Design Examples   Design for Concrete Structures 11 - 63
 ACI 318-05, Overview of Frames:
      Beam Transverse Reinforcement
                                         Closed hoops at hinging regions
                                         with “seismic” hook

                                         135º hook, 6dh ≥ 3” extension

                                         Maximum spacing of hoops:
                                         d/4           8db           24dh 12”

                                            Longitudinal bars on perimeter
                                            tied as if column bars
2d
min                                         Stirrups elsewhere, s ≤ d/2

        Instructional Material Complementing FEMA 451, Design Examples   Design for Concrete Structures 11 - 64
             ACI 318-05, Overview of Frames:
                        Beam Shear Strength
                1.2D + 1.0L + 0.2S
Mpr1                                                               Mpr2
                                                                                 Mpr = Mn            with

                                                                                 fs = 1.25fy ,           φ = 1 .0
       Ve1                 ln                                  Ve2

                    Mpr1 + Mpr 2           w ul n
             Ve =                        ±                  ≥ Ve           by analysis
                           ln                2

If earthquake-induced > 1 V
                           e
           shear force  2
                                                                  then Vc = 0
                                               '
                                          A f
                      and Pu <
                                             g c

                                           20
                Instructional Material Complementing FEMA 451, Design Examples       Design for Concrete Structures 11 - 65
    ACI 318-05, Overview of Frames:
                 Beam-Column Joint

      Vcol
                                                      Vj = T + C − Vcol
T                                          C


                                                     T = 1.25fy A s, top
       Vj

                                                     C = 1.25fy A s, bottom


        Instructional Material Complementing FEMA 451, Design Examples   Design for Concrete Structures 11 - 66
     ACI 318-05, Overview of Frames:
                    Beam-column Joint
                          ⎧20⎫
                          ⎪ ⎪
                     Vn = ⎨15 ⎬ f 'c A j
                          ⎪12 ⎪
                          ⎩ ⎭
•   Vn controls size of columns
•   Coefficient depends on joint confinement
•   To reduce shear demand, increase beam depth
•   Keep column stronger than beam


           Instructional Material Complementing FEMA 451, Design Examples   Design for Concrete Structures 11 - 67
   ACI 318-05: Overview of Frames:
   Column Longitudinal Reinforcement

        M nc1

                                                           0.01 ≤ ρ ≤ 0.06
M nb1                               M nb2
                                                          ∑ Mnc ≥ 1.2∑ Mnb
                                                       At joints
         M nc2                              (strong column-weak beam)
               Mnc based on factored axial force,
               consistent with direction of lateral forces

        Instructional Material Complementing FEMA 451, Design Examples   Design for Concrete Structures 11 - 68
       ACI 318-05, Overview of Frames:
 Column Transverse Reinforcement at Potential
              Hinging Region

    Spirals                                                                  Hoops
          ⎛ Ag     ⎞ f 'c                                           ⎛     f 'c ⎞⎛ A g    ⎞
ρs = 0.45⎜      − 1⎟                                A sh      ≥ 0 .3⎜ sbc      ⎟⎜     − 1⎟
          ⎜A
          ⎝ ch
                   ⎟f
                   ⎠ yt
                                                                    ⎜
                                                                    ⎝     fyt ⎟⎜ A ch
                                                                               ⎠⎝
                                                                                         ⎟
                                                                                         ⎠
and                                                 and
           f 'c                                                         f 'c
ρs ≥ 0.12                                           A sh      ≥ 0.09sbc
           fyt                                                          fyt



            Instructional Material Complementing FEMA 451, Design Examples     Design for Concrete Structures 11 - 69
   ACI 318-05, Overview of Frames:
Column Transverse Reinforcement at Potential
             Hinging Region
                                   hx                  hx




                                     ⎛ 14 − h x ⎞
                            so = 4 + ⎜          ⎟
                                     ⎝ 3 ⎠
Spacing shall not exceed the smallest of:
              b/4 or 6 db or so (4” to 6”)
Distance between legs of hoops or crossties, hx ≤ 14”
        Instructional Material Complementing FEMA 451, Design Examples   Design for Concrete Structures 11 - 70
    ACI 318-05, Overview of Frames:
                Potential Hinge Region

•   For columns supporting stiff members such as
    walls, hoops are required over full height of column
    if
                                              f 'c A g
                                 Pe >
                                                  10
•   For shear strength- same rules as beams (concrete
    shear strength is neglected if axial load is low and
    earthquake shear is high)
•   Lap splices are not allowed in potential plastic
    hinge regions


            Instructional Material Complementing FEMA 451, Design Examples   Design for Concrete Structures 11 - 71
                                                    Splice in Hinge
                                                        Region

                                                                 Terminating
                                                                 bars




Instructional Material Complementing FEMA 451, Design Examples    Design for Concrete Structures 11 - 72
ACI 318-05, Overview of Frames:
        Potential Hinge Region

                    ⎧      d       ⎫
                    ⎪              ⎪
                    ⎪              ⎪
                    ⎪ clear height ⎪
                    ⎪              ⎪
               lo ≥ ⎨       6      ⎬
                    ⎪              ⎪
                    ⎪     18"      ⎪
                    ⎪              ⎪
                    ⎪
                    ⎩              ⎪
                                   ⎭

    Instructional Material Complementing FEMA 451, Design Examples   Design for Concrete Structures 11 - 73
                      Moment Frame Example
                  A         A’       B        C        C’        D                 N
                                                                        1

                                                                        2
7 @ 30’ = 210’


                                                                         3

                                                                        4

                                                                        5

                                                                        6

                                                                         7

                                                                         8
                         5 @ 20’ = 100’
                 Instructional Material Complementing FEMA 451, Design Examples   Design for Concrete Structures 11 - 74
                       Frame Elevations
A   A’   B       C       C’       D
                                                             A       A’   B       C        C’        D




                                       11 @ 12.5'




                                                                                                          11 @ 12.5'
                                       15' 18'




                                                                                                          15' 18'
Column Lines 2 and 7                                             Column Lines 3 to 6
         Instructional Material Complementing FEMA 451, Design Examples   Design for Concrete Structures 11 - 75
                  Story Shears:
                 Seismic vs Wind
                                                                  seismic E-W
                                                                  seismic N-S
                                                                  wind E-W
                                                                   wind N-S




Instructional Material Complementing FEMA 451, Design Examples   Design for Concrete Structures 11 - 76
 Story Shears: E-W Loading

                                                   frame 1
                                                   frame 2
                                                                                               1
                                                   frame 3
                                                                                               2

                                                                                               3




            includes shearwall

0
Instructional Material Complementing FEMA 451, Design Examples   Design for Concrete Structures 11 - 77
            Story Shears: 25% rule
                                                                               Frame 1
                                                                               25% Frame 1




                                                 w/ walls
w/o walls




      Instructional Material Complementing FEMA 451, Design Examples   Design for Concrete Structures 11 - 78
    Layout of Reinforcement

                           4




                                                                 28.6”
                                                                         29.6”
                                                                                 32”
                          22.5”
                          30”


Instructional Material Complementing FEMA 451, Design Examples   Design for Concrete Structures 11 - 79
           Bending Moment Envelopes:
                 Frame 1 Beams
A                  A’                             B               C         C
                                                                   L
                        4708                          4515

                                                                                 Seismic

                                                      715

                                                                                 Dead

    5232                 5834                          5761          492

                                                                                 Combined:
                                                                    834
4122                4222                          4149
                                                                            1.42D +0.5 L + E
                                                                            0.68D - E
                                                                            1.2D + 1.6L

           Instructional Material Complementing FEMA 451, Design Examples   Design for Concrete Structures 11 - 80
             Beam Reinforcement:
                Longitudinal

Max negative Mu = 5834 in-kips
 b = 22.5” d = 29.6” f’c = 4 ksi fy = 60 ksi
                Mu          5834
                   φ             0 .9
A s req'd =            =                  = 4.17in2
            fy (0.875d) 60 ⋅ 0.875 ⋅ 29.6

Choose: 2 #9 and 3 #8 As = 4.37 in2
ρ = 0.0066 < 0.025 OK
φMn = 6580 in-kips OK


       Instructional Material Complementing FEMA 451, Design Examples   Design for Concrete Structures 11 - 81
             Beam Reinforcement:
            Longitudinal (continued)

Positive Mu at face of column = 4222 in-kips
         (greater than ½(5834) = 2917)
b for negative moment is the sum of
the beam width (22.5 in.) plus 1/12 the
span length (20 ft x 12 in./ft)/12,
b = 42.5 in.
                  Mu                           4222
                    φ            0.9 = 2.94in2
A s req'd   =          =
              fy (0.9d) 60 ⋅ 0.9 ⋅ 29.6

        Instructional Material Complementing FEMA 451, Design Examples   Design for Concrete Structures 11 - 82
        Beam Reinforcement:
       Longitudinal (continued)

Choose 2 #7 and 3 #8 As = 3.57 in2
φMn = 5564 in-kips OK

Run 3 #8s continuous top and bottom
φMn = 3669 in-kips
This moment is greater than:
     25% of max negative Mn = 1459 in-kips
     Max required Mu = 834 in-kips


     Instructional Material Complementing FEMA 451, Design Examples   Design for Concrete Structures 11 - 83
                     Beam Reinforcement:
                      Preliminary Layout


  A           A'                       B                        C                    C'                         D
       2 #8            2 #9                 3 #8                                             2 #8
                                                                       2 #9




2 #7          2 #7                  3 #8                     3 #8                       2 #7




              Instructional Material Complementing FEMA 451, Design Examples   Design for Concrete Structures 11 - 84
        Moments for Computing Shear
                                                                    Hinging mechanism

B                          C                                 C'
                9697                               8999

                                                                             Plastic
                                                                             moments
    10085
               9.83'
                                  10085
                                 10.5'
                                                                             (in-kips)
       20.0'                             20.0'

                      150.4
                                                                  Girder and
       94.2                                 90.9
                                                                  column shears
                                                                  (kips)
                      150.4
            Instructional Material Complementing FEMA 451, Design Examples   Design for Concrete Structures 11 - 85
                        Joint Shear Force

              150.5 kip


355.5 kip                                      355.5 kip
                                            T = 1.25fy A s,top = 355.5 kips
            560.5 kip
                                           C = 1.25fy A s,bot = 355.5 kips
                                            Vj = T + C − Vcol = 560.5 kips
                                             v j = 15 f 'c = 949 psi
                                            Vn = v j A j = 949 ⋅ 30 ⋅ 30 = 854 kips
                                            φVn = 0.85 ⋅ 854 = 726 kips > 560.5 kips


            Instructional Material Complementing FEMA 451, Design Examples   Design for Concrete Structures 11 - 86
                                Beam Shear Force
 A                    A’                               B                                  C
         79.4                         82.7                            82.7

                                                                                              Seismic shear


         75.6                         79.4                            82.7
                  29.5                            29.5                             29.5
                                                                                              Factored
                                                                                              gravity shear
  29.5                     29.5                           29.5
                108.9                         112.2                               112.2
 49.9                     53.2                            53.2
                                                                                              Design shear
                 46.1                            49.9                              53.2
105.1                    108.9                          112.2
                 Instructional Material Complementing FEMA 451, Design Examples       Design for Concrete Structures 11 - 87
        Beam Reinforcement:
            Transverse

Vseismic > 50% Vu therefore take Vc = 0
82.7 kips = 73%(112.2)

Use 4 legged #3 stirrups
                                     A v fy d
                          Vs =
                                         s
At ends of beam s = 5.5 in.
Near midspan s = 7.0 in.


  Instructional Material Complementing FEMA 451, Design Examples   Design for Concrete Structures 11 - 88
             Beam Reinforcement:
                 Transverse

• Check maximum spacing of hoops within
 plastic hinge length (2d)
  – d/4 = 7.4 in.
  – 8db = 7.0 in.
  – 24dh = 9.0 in.




       Instructional Material Complementing FEMA 451, Design Examples   Design for Concrete Structures 11 - 89
                Column Design Moments
A                  A'                            B
                       7311

                                                               Girder moments
                                                               (Level 7)
           6181

                                           ∑ Mnc = 1.2(7311 + 6181)
                                                             = 16190 in − k

    8095
                                      8095
                                                          Column moments
                                                          (Level 7)


           Instructional Material Complementing FEMA 451, Design Examples   Design for Concrete Structures 11 - 90
    Column Design Moments

                                  f 'c A g
           if        Pu >
                                 10
           ∑ Mnc              > 1.2∑ Mnb

Distribute relative to stiffness of columns
above and below:

Mnc = 8095 in-kips (above)
Mnc = 8095 in-kips (below)

   Instructional Material Complementing FEMA 451, Design Examples   Design for Concrete Structures 11 - 91
                      Design Strengths

    Design Aspect                                           Strength Used

   Beam rebar cutoffs                                        Design strength
                                                         Maximum probable
Beam shear reinforcement
                                                             strength
   Beam-column joint                                     Maximum probable
       strength                                              strength
Column flexural strength                         1.2 times nominal strength
                                                         Maximum probable
 Column shear strength
                                                             strength

        Instructional Material Complementing FEMA 451, Design Examples   Design for Concrete Structures 11 - 92
    Column Transverse Reinforcement
                        ⎛     f 'c ⎞ ⎡⎛ A g ⎞ ⎤
          A sh     = 0.3⎜ sbc      ⎟ ⎢⎜
                                      ⎜ A ⎟ − 1⎥
                        ⎜
                        ⎝     fyt ⎟ ⎢⎝ ch ⎟ ⎥
                                   ⎠⎣       ⎠ ⎦
          and
                                        f 'c
          A sh = 0.09sbc
                                        fyt

  Ag = gross area of column
  Ach = area confined within the hoops
  bc = transverse dimension of column core
        measured center to center of outer legs
Second equation typically governs for larger columns

        Instructional Material Complementing FEMA 451, Design Examples   Design for Concrete Structures 11 - 93
 Column Transverse Reinforcement

Maximum spacing is smallest of:
  •One quarter of minimum member dimension
  •Six times the diameter of the longitudinal bars
  •so calculated as follows:

                            14 − h x
                   so = 4 +
                               3

hx = maximum horizontal center to center spacing
     of cross-ties or hoop legs on all faces of the
     column, not allowed to be greater the 14 in.


     Instructional Material Complementing FEMA 451, Design Examples   Design for Concrete Structures 11 - 94
        Column Transverse Reinforcement

   For max s = 4 in.
            ⎛     f 'c ⎞ ⎡⎛ A g ⎞ ⎤         ⎛            4 ⎞⎛ 900 ⎞
A sh   = 0.3⎜ sbc      ⎟ ⎢⎜
                          ⎜A ⎟  ⎟ − 1⎥ = 0.3⎜ 4 ⋅ 26.5 ⋅ ⎟⎜      − 1⎟
            ⎜     fyt ⎟ ⎢⎝ ch ⎠ ⎥           ⎝           60 ⎠⎝ 702 ⎠
            ⎝          ⎠⎣            ⎦
A sh = 0.60 in2
and
                 f 'c                      4
A sh   = 0.09sbc      = 0.09 ⋅ 4 ⋅ 26.5 ⋅    = 0.64 in2
                 fyt                      60

         Use 4 legs of #4 bar – Ash = 0.80 in2

             Instructional Material Complementing FEMA 451, Design Examples   Design for Concrete Structures 11 - 95
    Determine Seismic Shear

                                                                         Mpr,top
Mpr,1                                Mpr,2                                         Vseismic


                                              ln


                                                                                 Vseismic
Mpr,3                                 Mpr,4
                                                                          Mpr,bottom

        Instructional Material Complementing FEMA 451, Design Examples     Design for Concrete Structures 11 - 96
         Column Transverse Reinforcement
         Shear Demand from Mpr of Beams

         Mpr, 1 = 9000 in-k (2 #9 and 3 #8)
         Mpr,2 = 7460 in-k (2 #7 and 3 #8)
Assume moments are distributed equally above and below joint
                       8230 ⋅ 2
       Vseismic   =                  = 139 kips
                    (12.5 ⋅ 12) − 32
         Note Vseismic~100%Vu
                                       f 'c Ag
        Vc = 0, if Pmin <                            = 180 kips
                                          20
         For 30 in. square column
         Pmin = 266 kips OK
            Instructional Material Complementing FEMA 451, Design Examples   Design for Concrete Structures 11 - 97
       Column Transverse Reinforcement
       Shear Demand from Mpr of Beams

φVc = φ2λ f 'c bd = 0.75 ⋅ 2 ⋅ 0.85 4000 ⋅ 30 ⋅ 27.5 = 66.5 kips
φVs,required = 139 − 66.5 = 72.5 kips
                   A v fy d            4 ⋅ 0.2 ⋅ 60 ⋅ 29.6
φVs,provided = φ                = 0.75                     = 266.4 kips
                       s                         4


         Hoops                                              4 legs #4
                                                            s = 4”

              Instructional Material Complementing FEMA 451, Design Examples   Design for Concrete Structures 11 - 98
      Column Reinforcement
                         A'




     7 @ 4"
                                                      #4 hoops:
           5"

     8 @ 6"

        5"
     7 @ 4"                                          12 #8 bars




Instructional Material Complementing FEMA 451, Design Examples   Design for Concrete Structures 11 - 99
   Levels of Seismic Detailing for Frames

        Issue                         Ordinary                  Intermediate               Special
Hinge development and
                                                                      minor                    full
     confinement
    Bar buckling                                                      lesser                   full

    Member shear                                                      lesser                   full

     Joint shear                         minor                        minor                    full

   Strong column                                                                               full

 Rebar development                       lesser                       lesser                   full

    Load reversal                        minor                        lesser                   full



          Instructional Material Complementing FEMA 451, Design Examples   Design for Concrete Structures 11 - 100
    NEHRP Recommended Provisions
           Concrete Design

•   Context in the Provisions
•   Concrete behavior
•   Reference standards
•   Requirements by Seismic Design Category
•   Moment resisting frames
•   Shear walls



         Instructional Material Complementing FEMA 451, Design Examples   Design for Concrete Structures 11 - 101
      Performance Objectives

• Resist axial forces, flexure and shear
• Boundary members
  – Where compression strains are large, maintain
    capacity
• Development of rebar in panel
• Discontinuous walls: supporting columns
  have full confinement




       Instructional Material Complementing FEMA 451, Design Examples   Design for Concrete Structures 11 - 102
                  Design Philosophy

• Flexural yielding will occur in predetermined
    flexural hinging regions
•   Brittle failure mechanisms will be precluded
    – Diagonal tension
    – Sliding hinges
    – Local buckling




           Instructional Material Complementing FEMA 451, Design Examples   Design for Concrete Structures 11 - 103
     ACI 318-05, Overview of Walls:
         General Requirements
                lw
                                              ρt = parallel to shear plane

                                              ρl = perpendicular
hw                                                  to shear plane

                                                  Shear plane, Acv =
                                                     web thickness x
                                                     length of wall

       Instructional Material Complementing FEMA 451, Design Examples   Design for Concrete Structures 11 - 104
     ACI 318-05, Overview of Walls:
         General Requirements
•   ρl and ρt not less than 0.0025
       unless
                      Vu < A cv f 'c
     then as allowed in 14.3
•   Spacing not to exceed 18 in.
•   Reinforcement contributing to Vn
    shall be continuous and distributed
    across the shear plane

        Instructional Material Complementing FEMA 451, Design Examples   Design for Concrete Structures 11 - 105
       ACI 318-05, Overview of Walls:
           General Requirements

•   Two curtains of reinforcing required
    if:
             Vu > 2A cv f 'c
•   Design shear force determined from
    lateral load analysis



         Instructional Material Complementing FEMA 451, Design Examples   Design for Concrete Structures 11 - 106
       ACI 318-05, Overview of Walls:
           General Requirements
•   Shear strength:
                                     (
              Vn = A cv α c f 'c + ρ t fy                                 )
       αc = 3.0 for hw/lw≤1.5
       αc = 2.0 for hw/lw≥2.0
       Linear interpolation between

•   Walls must have reinforcement in two
    orthogonal directions

         Instructional Material Complementing FEMA 451, Design Examples       Design for Concrete Structures 11 - 107
      ACI 318-05, Overview of Walls:
          General Requirements
• For axial load and flexure, design like a
  column to determine axial load – moment
  interaction       P
                                                         M




         Instructional Material Complementing FEMA 451, Design Examples   Design for Concrete Structures 11 - 108
ACI 318-05, Overview of Walls:
     Boundary Elements

                                       For walls with a high
                                       compression demand
                                       at the edges – Boundary
                                       Elements are required



                             Widened end with confinement

                             Extra confinement and/or
                             longitudinal bars at end
 Instructional Material Complementing FEMA 451, Design Examples   Design for Concrete Structures 11 - 109
       ACI 318-05, Overview of Walls:
            Boundary Elements
•   Boundary elements are required if:
                          lw
                    c≥
                          ⎛ δu ⎞
                       600⎜
                          ⎝   hw ⎟
                                 ⎠
δu = Design displacement
c = Depth to neutral axis from strain
     compatibility analysis with loads
     causing δu
         Instructional Material Complementing FEMA 451, Design Examples   Design for Concrete Structures 11 - 110
     ACI 318-05, Overview of Walls:
          Boundary Elements
• Where required, boundary elements must
 extend up the wall from the critical section a
 distance not less than the larger of:

                           lw         or Mu/4Vu




        Instructional Material Complementing FEMA 451, Design Examples   Design for Concrete Structures 11 - 111
      ACI 318-05: Overview of Walls
           Boundary Elements
• Boundary elements are required where the
 maximum extreme fiber compressive stress
 calculated based on factored load effects,
 linear elastic concrete behavior and gross
 section properties, exceeds 0.2 f’c

• Boundary element can be discontinued
 where the compressive stress is less than
 0.15f’c


        Instructional Material Complementing FEMA 451, Design Examples   Design for Concrete Structures 11 - 112
        ACI 318-05: Overview of Walls
             Boundary Elements
• Boundary elements must extend horizontally
    not less than the larger of c/2 or c-0.1lw
•   In flanged walls, boundary element must
    include all of the effective flange width and at
    least 12 in. of the web
•   Transverse reinforcement must extend into
    the foundation




           Instructional Material Complementing FEMA 451, Design Examples   Design for Concrete Structures 11 - 113
                 Wall Example
                  A       A’       B        C       C’       D




Instructional Material Complementing FEMA 451, Design Examples
                                                                 11 @ 12.5'
                                                                 15' 18'
                                                                              Design for Concrete Structures 11 - 114
                  Wall Cross-Section

                                      17’-6”=210”
      30”                                                                                        30”
30”                                                                                                       30”
            12”




            Instructional Material Complementing FEMA 451, Design Examples   Design for Concrete Structures 11 - 115
                     Story Shears
                     E-W Loading
                                                   frame 1
                                                   frame 2
                                                                                                1
                                                   frame 3
                                                                                                2

                                                                                                3




            includes shearwall

0
Instructional Material Complementing FEMA 451, Design Examples   Design for Concrete Structures 11 - 116
         Boundary Element Check
Required if: fc > 0.2 fc' based on gross concrete section
Axial load and moment are determined based on
factored forces, including earthquake effects

At ground Pu = 5550 kip

Mu from analysis is 268,187 in-kip

The wall has the following gross section properties:
       A = 4320 in2                            S = 261,600 in3
fc = 2.3 ksi = 38% of f’c = 6 ksi

        ∴ Need boundary element

        Instructional Material Complementing FEMA 451, Design Examples   Design for Concrete Structures 11 - 117
               Boundary Element Design
Determine preliminary reinforcing ratio in boundary elements
by assuming only boundary elements take compression
                                    M = 268,187 in-k

                     M
                                    P = 5550 k
         P                              P   M
                                    B1 =  +   = 3892 kip
 B2                   B1
                                        2 240
                                        P   M
                                    B2 = −    = 1658 kip
                                        2 240

      Need                                          [
             0 . 8Po = 0 . 8 (0 . 7 ) A g 0 . 85 fc' (1 − ρ ) + ρ f y > 3892 kip       ]
      For Ag = 30(30) = 900 in2
      For fc’ = 4 ksi ⇒ ρ = 7.06% Too large
      For fc’ = 6 ksi ⇒ ρ = 4.18% Reasonable; 24 #11
             Instructional Material Complementing FEMA 451, Design Examples   Design for Concrete Structures 11 - 118
  Boundary Element Confinement

Transverse reinforcement in boundary elements is to be
designed essentially like column transverse reinforcement

                           fc'
      A sh   = 0 . 09 sb c     = 1 . 08 in at s = 4 "
                                          2
                           fy


                 4 legs of #5




         Instructional Material Complementing FEMA 451, Design Examples   Design for Concrete Structures 11 - 119
          Shear Panel Reinforcement

Vn = A cv ⎛ 2 λ
          ⎜             fc' + ρ t f y ⎞
                                      ⎟
          ⎝                           ⎠
Vu = 539 kips (below level 2)                                   ρl                  Panel ⊥ to Acv

φ = 0.6 (per ACI 9.3.4(a))
                                               Acv                                                                 ρt
ρt = 0.0036 for fy = 40 ksi

Min ρl (and ρt) = 0.0025

2 curtains if
                      Vu > 2                  '
                                             fc A cv

                Instructional Material Complementing FEMA 451, Design Examples   Design for Concrete Structures 11 - 120
    Shear Panel Reinforcement

Select transverse and longitudinal reinforcement:

   longitudin al :
                 0 .2 ⋅ 2
    # 4 @ 12" ⇒           = 0.0028 > 0.0025
                12 ⋅ 12
    transverse :
               0 .2 ⋅ 2
    # 4 @ 9" ⇒          = 0.0037 > 0.0036
               12 ⋅ 9


       Instructional Material Complementing FEMA 451, Design Examples   Design for Concrete Structures 11 - 121
                            Check Wall Design
                30000
                                                                                     Nominal
                25000
                                                                                     Factored
                                                                                     Combinations
Axial Load, k




                20000


                15000


                10000


                5000


                   0
                        0     20000      40000       60000      80000 100000 120000 140000
                                                    Moment, k-ft


                    Instructional Material Complementing FEMA 451, Design Examples       Design for Concrete Structures 11 - 122
                        Shear Wall Reinforcement
     B                      C             B                    C                 B                     C
R                                   8                                      3
                                                                                          24 #10


12                                  7                                      2                                  fc’ = 6 ksi
                                                                                      #4@12" ver. E.F.
                                                  24 #9
                                                                                      #4@6" hor. E.F.


11                                  6
            12 #9
                                                                           G
                                                                                         24 #11
10                                  5
                                                                                         #5 @ 4"

         #4@18" ver. E.F.
                                                                           B
         #4@16" hor. E.F.
9                                   4         #4@12"
                                              E.W. E.F.

                                                   #4 @ 4"
8                                   3
                                                                    fc’ = 4 ksi

                     Instructional Material Complementing FEMA 451, Design Examples       Design for Concrete Structures 11 - 123
     NEHRP Recommended Provisions
            Concrete Design
•   Context in the Provisions
•   Concrete behavior
•   Reference standards
•   Requirements by Seismic Design Category
•   Moment resisting frames
•   Shear walls
•   Other topics



          Instructional Material Complementing FEMA 451, Design Examples   Design for Concrete Structures 11 - 124
        Members Not Part of SRS
• In frame members not designated as part of
 the lateral-force-resisting system in regions
 of high seismic risk:
  – Must be able to support gravity loads while subjected
    to the design displacement
  – Transverse reinforcement increases depending on:
             Forces induced by drift
             Axial force in member




         Instructional Material Complementing FEMA 451, Design Examples   Design for Concrete Structures 11 - 125
                            Diaphragms
                                                      Diaphragm

                                                      Shear walls
                                              Collectors, if req’d to transfer force
                                              from diaphragm to shear walls
                                          Load from analysis in accordance
                                          With design load combinations
Check:
• Shear strength and reinforcement (min. slab reinf.)
• Chords (boundary members)
      - Force = M/d Reinforced for tension
      (Usually don’t require boundary members)

          Instructional Material Complementing FEMA 451, Design Examples   Design for Concrete Structures 11 - 126
                Struts and Trusses
            performance objectives

• All members have axial load (not flexure), so
  ductility is more difficult to achieve

• Full length confinement




         Instructional Material Complementing FEMA 451, Design Examples   Design for Concrete Structures 11 - 127
          Precast performance objectives




Field connections                               Field connections
at points of low                                must yield
stress
Strong connections                                  Ductile connections
• Configure system so that hinges                   • Inelastic action at field splice
occur in factory cast members
away from field splices


              Instructional Material Complementing FEMA 451, Design Examples   Design for Concrete Structures 11 - 128
                    Quality Assurance
                    Rebar Inspection
• Continuous
  – Welding of rebar
• Periodic
  – During and upon completion of placement for special
    moment frames, intermediate moment frames and
    shear walls




         Instructional Material Complementing FEMA 451, Design Examples   Design for Concrete Structures 11 - 129
Shear panel reinforcement cage




 Instructional Material Complementing FEMA 451, Design Examples   Design for Concrete Structures 11 - 130
Instructional Material Complementing FEMA 451, Design Examples   Design for Concrete Structures 11 - 131
Instructional Material Complementing FEMA 451, Design Examples   Design for Concrete Structures 11 - 132
         Quality Assurance:
 Reinforcing Inspection - Prestressed

• Periodic
  – Placing of prestressing tendons (inspection required
    upon completion)
• Continuous
  – Stressing of tendons
  – Grouting of tendons




       Instructional Material Complementing FEMA 451, Design Examples   Design for Concrete Structures 11 - 133
     Quality Assurance:
Concrete Placement Inspection

• Continuous
  – Prestressed elements
  – Drilled piers
  – Caissons
• Periodic
  – Frames
  – Shear walls



   Instructional Material Complementing FEMA 451, Design Examples   Design for Concrete Structures 11 - 134
            Quality Assurance:
        Precast Concrete (plant cast)

• Manufacturer may serve as special inspector
    if plant’s quality control program is approved
    by regulatory agency
•   If no approved quality control program,
    independent special inspector is required




         Instructional Material Complementing FEMA 451, Design Examples   Design for Concrete Structures 11 - 135
             Quality Assurance:
          PCI Certification Program

• Review of plant operations
  – Scheduled and surprise visits
  – Qualified independent inspectors
  – Observed work of in-plant quality control
  – Check results of quality control procedures
  – Periodic – specific approvals requiring renewal




         Instructional Material Complementing FEMA 451, Design Examples   Design for Concrete Structures 11 - 136
        Quality Assurance:
     ACI Inspector Certification

• Specialized training available for:
  – Laboratory and in situ testing
  – Inspection of welding
  – Handling and placement of concrete
  – Others




     Instructional Material Complementing FEMA 451, Design Examples   Design for Concrete Structures 11 - 137
              Quality Assurance:
             Reinforcement Testing
• Rebar
  – Special and intermediate moment frames
  – Boundary elements
• Prestressing steel
• Tests include
  – Weldability
  – Elongation
  – Actual to specified yield strength
  – Actual to specified ultimate strength

        Instructional Material Complementing FEMA 451, Design Examples   Design for Concrete Structures 11 - 138
                   Quality Assurance:
                    Concrete Testing

• Sample and test according to ACI 318-05
  – Slump
  – Air content
  – 7 and 28 day strengths
  – Unit weight
• Rate
  – Once per day per class



         Instructional Material Complementing FEMA 451, Design Examples   Design for Concrete Structures 11 - 139
    NEHRP Recommended Provisions:
           Concrete Design

•   Context in the Provisions
•   Concrete behavior
•   Reference standards
•   Requirements by Seismic Design Category
•   Moment resisting frames
•   Shear walls
•   Other topics
•   Summary

         Instructional Material Complementing FEMA 451, Design Examples   Design for Concrete Structures 11 - 140

				
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posted:11/17/2011
language:English
pages:140