PCI 6th Edition

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PCI 6th Edition

• Connection Design

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Presentation Outline

• Structural Steel Design
• Limit State Weld Analysis
• Strut Tie Analysis for Concrete Corbels
• Anchor Bolts
• Connection Examples

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Changes

• New method to design headed studs (Headed
  Concrete Anchors - HCA)
• Revised welding section
• Stainless Materials
• Limit State procedure presented
• Revised Design Aids (moved to Chapter 11)
• Structural Steel Design Section
• Flexure, Shear, Torsion, Combined Loading
• Stiffened Beam seats
• Strut Tie methodology is introduced
• Complete Connection Examples

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Structural Steel Design

• Focus on AISC LRFD 3rd Edition
• Flexural Strength
• Shear Strength
• Torsional Strength
• Combined Interaction
• Limit State Methods are carried through examples

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Structural Steel Details

• Built-up Members
• Torsional Strength
• Beam Seats

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Steel Strength Design

• Flexure
• fMp fFyZs
• Where
• fMp Flexural Design Strength
• Fy Yield Strength of Material
• Zs Plastic Section Modulus

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Steel Strength Design

• Shear
• fVn f(0.6Fy)Aw
• Where
• fVp Shear Design Strength
• Aw Area subject to shear

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Steel Strength Design

• Torsion (Solid Sections)
• fTn f(0.6Fy)aht2
• Where
• fTp Torsional Design Strength
• a Torsional constant
• h Height of section
• t Thickness

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Torsional Properties

• Torsional Constant, a
• Rectangular Sections

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Steel Strength Design

• Torsion (Hollow Sections)
• fTn 2f(0.6Fy)?t
• Where
• fTp Torsional Design Strength
• ? Area enclosed by centerline of walls
• t Wall thickness

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Torsional Properties

• Hollow Sections
• ? wd

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Combined Loading Stress

• Normal Stress
• Bending Shear Stress
• Torsion Shear Stress

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Combined Loading

• Stresses are added based on direction
• Stress Limits based on Mohrs circle analysis
• Normal Stress Limits
• Shear Stress Limits

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Built-Up Section Example
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Example
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Determine Neutral Axis Location, y

• Tension Area Compression Area
• Tension Compression

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Define Plastic Section Modulus, Zp

• Either Tension or Compression Area x Distance
  between the Tension / Compression Areas Centroids

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Determine Centroid Locations

• Tension
• Compression

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Calculate Zp
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Beam Seats

• Stiffened Bearing
• Triangular
• Non-Triangular

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Triangular Stiffeners

• Design Strength
• fVnfFyzbt
• Where
• fVn Stiffener design strength
• f Strength reduction factor 0.9
• b Stiffener projection
• t Stiffener thickness
• z Stiffener shape factor

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Stiffener Shape Factor
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Thickness Limitation
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Triangular Stiffener Example

• Given
• A stiffened seat connection shown at right.
  Stiffener thickness, ts 3/8 in.
• Fy 36 ksi
• Problem
• Determine the design shear resistance of the
  stiffener.

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Shape Factor
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Thickness Limitation
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Design Strength
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Weld Analysis

• Elastic Procedure
• Limit State (LRFD) Design introduced
• Comparison of in-plane C shape
• Elastic Vector Method - EVM
• Instantaneous Center Method ICM

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Elastic Vector Method (EVM)

• Stress at each point calculated by mechanics of
  materials principals

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Elastic Vector Method (EVM)

• Weld Area ( Aw ) based on effective throat
• For a fillet weld
• Where
• a Weld Size
• lw Total length of weld

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Instantaneous Center Method (ICM)

• Deformation Compatibility Solution
• Rotation about an Instantaneous Center

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Instantaneous Center Method (ICM)

• Increased capacity
• More weld regions achieve ultimate strength
• Utilizes element vs. load orientation
• General solution form is a nonlinear integral
• Solution techniques
• Discrete Element Method
• Tabular Method

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ICM Nominal Strength

• An elements capacity within the weld group is
  based on the product of 3 functions.
• Strength
• Angular Orientation
• Deformation Compatibility

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Strength, f
Aw - Weld area based on effective throat
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Angular Orientation, g

• Weld capacity increases as the angle of the force
  and weld axis approach 90o

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Deformation Compatibility, h

• Where the ultimate element deformation Du is

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Element Force

• Where r and q are functions of the unknown
  location of the instantaneous center, x and y

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Equations of Statics
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Tabulated Solution

• AISC LRFD 3rd Edition, Tables 8-5 to 8-12
• fVn CC1 Dl
• Where
• D number of 16ths of weld size
• C tabulated value, includes f
• C1 electrode strength factor
• l weld length

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Comparison of Methods

• Page 6-47

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Corbel Design

• Cantilever Beam Method
• Strut Tie Design Method
• Design comparison
• Results comparison of Cantilever Method to Strut
  Tie Method
• Embedded Steel Sections

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Cantilever Beam Method Steps

• Step 1 Determine maximum allowable shear
• Step 2 Determine tension steel by cantilever
• Step 3 Calculate effective shear friction
  coeff.
• Step 4 Determine tension steel by shear
  friction
• Step 5 Compare results against minimum
• Step 6 Calculate shear steel requirements

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Cantilever Beam Method

• Primary Tension Reinforcement
• Greater of Equation A or B
• Tension steel development is critical both in the
  column and in the corbel

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Cantilever Beam Method

• Shear Steel
• Steel distribution is within 2/3 of d

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Cantilever Beam Method Steps

• Step 1 Determine bearing area of plate
• Step 2 Select statically determinate truss
• Step 3 Calculate truss forces
• Step 4 Design tension ties
• Step 5 Design Critical nodes
• Step 6 Design compression struts
• Step 7 Detail Accordingly

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Strut Tie Analysis Steps

• Step 1 Determine of bearing area of plate

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Strut Tie Analysis Steps

• Step 2 Select statically determinate truss

AC I provides guidelines for truss angles,
struts, etc.
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Strut Tie Analysis Steps

• Step 3 Determine of forces in the truss members

Method of Joints or Method of Sections
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Strut Tie Analysis Steps

• Step 4 Design of tension ties

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Strut Tie Analysis Steps

• Step 5 Design of critical nodal zone

where ßn 1.0 in nodal zones bounded by
structure or bearing areas 0.8 in nodal zones
anchoring one tie 0.6 in nodal zones
anchoring two or more ties
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Strut Tie Analysis Steps

• Step 6 Check compressive strut limits based on
  Strut Shape

The design compressive strength of a strut
without compressive reinforcement fFns
ffcuAc where f 0.75 Ac width of corbel
width of strut
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Strut Tie Analysis Steps Compression Strut
Strength

• From ACI 318-02, Section A.3.2
• Where
• bs function of strut shape / location
• 0.60l, bottle shaped strut
• 0.75, when reinforcement is provided
• 1.0, uniform cross section
• 0.4, in tension regions of members
• 0.6, for all other cases

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Strut Tie Analysis Steps

• Step 7 Consider detailing to ensure design
  technique

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Corbel Example

• Given
• Vu 80 kips
• Nu 15 kips
• fy Grade 60
• f'c 5000 psi
• Bearing area 12 x 6 in.
• Problem
• Find corbel depth and reinforcement based on
  Cantilever Beam and Strut Tie methods

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Step 1CBM Cantilever Beam Method (CBM)

• h 14 in
• d 13 in.
• a ¾ lp 6 in.
• From Table 4.3.6.1

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Step 2CBM Tension Steel

• Cantilever Action

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Step 3CBM Effective Shear Friction Coefficient
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Step 4CBM Tension Steel

• Shear Friction

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Step 5CBM As minimum

• As based on cantilever action governs
• As 1.18 in2

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Step 6CBM Shear Steel

• Use (2) 3 ties (4) (0.11 in2) 0.44 in2
• Spaced in top 2/3 (13) 8 ½ in

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Step 1ST Strut - Tie Solution (ST)

• Determination of bearing plate size and
  protection for the corner against spalling
• Required plate area
• Use 12 by 6 in. plate, area 72 in2 gt 25.1 in2

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Step 2ST Truss Geometry

• tan qRNu / Vu (15)/(80) 0.19
• l1 (h - d) tanqR aw (hc - cc)
• (14 - 13)(0.19) 6 (14 - 2.25)
• 17.94 in.
• l2 (hc - cc) ws/2
• (14 - 2.25) - ws/2
• 11.75 - ws/2

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Step 2ST Truss Geometry

• Find ws
• Determine compressive force,
• Nc, at Node p
• ?Mm 0
• Vul1Nud Ncl20 Eq. 1
• (80)(17.94) (15)(13) Nc(11.75 0.5ws) 0
• Eq. 2

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Step 2ST Truss Geometry

• Maximum compressive stress at the nodal zone p
  (anchors one tie, ßn 0.8)
• fcu 0.85bnfc 0.85(0.8)(5) 3.4 ksi
• An area of the nodal zone
• bws 14ws

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Step 2ST Determine ws , l2

• From Eq. 2 and 3
• 0.014Nc2 - 11.75Nc - 1630 0
• Nc 175 kips
• ws 0.28Nc (0.28)(175) 4.9in
• l2 11.75 - 0.5 ws
• 11.75 - 0.5(4.9) 9.3

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Step 3ST Solve for Strut and Tie Forces

• Solving the truss mnop by statics, the member
  forces are
• Strut op 96.0 kips (c)
• Tie no 68.2 kips (t)
• Strut np 116.8 kips (c)
• Tie mp 14.9 kips (t)
• Tie mn 95.0 kips (t)

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Step 4ST Critical Tension Requirements

• For top tension tie no
• Tie no 68.2 kips (t)
• Provide 2 8 1.58 in2 at the top

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Step 5ST Nodal Zones

• The width ws of the nodal zone p has been
  chosen in Step 2 to satisfy the stress limit on
  this zone
• The stress at nodal zone o must be checked
  against the compressive force in strut op and
  the applied reaction, Vu
• From the compressive stress flow in struts of the
  corbel, Figure 6.8.2.1, it is obvious that the
  nodal zone p is under the maximum compressive
  stress due to force Nc.
• Nc is within the acceptable limit so all nodal
  zones are acceptable.

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Step 6ST Critical Compression Requirements

• Strut np is the most critical strut at node
  p. The nominal compressive strength of a strut
  without compressive reinforcement
• Fns fcuAc
• Where
• Ac width of corbel width of strut

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Step 6ST Strut Width

• Width of strut np

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Step 6ST Compression Strut Strength

• From ACI 318-02, Section A.3.2
• Where - bottle shaped strut, bs 0.60l
• 161 kips 116.8 kips OK

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Step 7ST Surface Reinforcement

• Since the lowest value of bs was used, surface
  reinforcement is not required based on ACI 318
  Appendix A

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Example Conclusion
Strut-and-Tie Method
Cantilever Beam Method
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Embedded Steel Sections
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Concrete and Rebar Nominal Design Strengths

• Concrete Capacity

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Concrete and Rebar Nominal Design Strengths

• Additional Tension Compression Reinforcement
  Capacity

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Corbel Capacity

• Reinforced Concrete

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Steel Section Nominal Design Strengths

• Flexure - Based on maximum moment in section
  occurs when shear in steel section 0.0
• Where
• b effective width on embed, 250 x Actual
• f 0.9

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Steel Section Nominal Design Strengths

• Shear
• where
• h, t depth and thickness of steel web
• f 0.9

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Anchor Bolt Design

• ACI 318-2002, Appendix D, procedures for the
  strength of anchorages are applicable for anchor
  bolts in tension.

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Strength Reduction Factor

• Function of supplied confinement reinforcement
• f 0.75 with reinforcement
• f 0.70 with out reinforcement

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Headed Anchor Bolts
No CbsANCcrbYed,N

• Where
• Ccrb Cracked concrete factor,
• 1 uncracked, 0.8 Cracked
• AN Projected surface area for a stud or group
• Yed,N Modification for edge distance
• Cbs Breakout strength coefficient

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Hooked Anchor Bolts
No 126fcehdoCcrp

• Where
• eh hook projection 3do
• do bolt diameter
• Ccrp cracking factor (Section 6.5.4.1)

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Column Base Plate Design

• Column Structural Integrity requirements 200Ag

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Completed Connection Examples

• Examples Based
• Applied Loads
• Component Capacity
• Design of all components
• Embeds
• Erection Material
• Welds
• Design for specific load paths

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Completed Connection Examples

• Cladding Push / Pull
• Wall to Wall Shear
• Wall Tension
• Diaphragm to Wall Shear

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Questions?