2 Presentation Outine Research Background Steel Capacity Concrete Tension CapacityTension ExampleConcrete Shear CapacityShear ExampleInteraction Example
3 Background for Headed Concrete Anchor Design Anchorage to concrete and the design of welded headed studs has undergone a significant transformation since the Fifth Edition of the Handbook.“Concrete Capacity Design” (CCD) approach has been incorporated into ACI Appendix D
4 Headed Concrete Anchor Design History The shear capacity equations are based on PCI sponsored researchThe Tension capacity equations are based on the ACI Appendix D equations only modified for cracking and common PCI variable names
5 Background for Headed Concrete Anchor Design PCI sponsored an extensive research project, conducted by Wiss, Janney, Elstner Associates, Inc., (WJE), to study design criteria of headed stud groups loaded in shear and the combined effects of shear and tensionSection D.4.2 of ACI specifically permits alternate procedures, providing the test results met a 5% fractile criteriaThe tension equations are as shown in the ACI code, except for the cracking coefficients. The shear provisions are based on the PCI sponsored tests. Equations derived from those tests meet the “5% fractile” criterion discussed above. For combined shear and tension, the PCI sponsored tests did not find significant variance from the ACI code recommendations.
6 Supplemental Reinforcement Appendix D, Commentary“… supplementary reinforcement in the direction of load, confining reinforcement, or both, can greatly enhance the strength and ductility of the anchor connection.”“Reinforcement oriented in the direction of load and proportioned to resist the total load within the breakout prism, and fully anchored on both side of the breakout planes, may be provided instead of calculating breakout capacity.”
7 HCA Design PrinciplesPerformance based on the location of the stud relative to the member edgesShear design capacity can be increased with confinement reinforcementIn tension, ductility can be provided by reinforcement that crosses the potential failure surfaces
8 HCA Design Principles Designed to resist TensionShearInteraction of the twoThe design equations are applicable to studs which are welded to steel plates or other structural members and embedded in unconfined concrete
9 HCA Design PrinciplesWhere feasible, connection failure should be defined as yielding of the stud materialThe groups strength is taken as the smaller of either the concrete or steel capacityThe minimum plate thickness to which studs are attached should be ½ the diameter of the studThicker plates may be required for bending resistance or to ensure a more uniform load distribution to the attached studs
10 Stainless Steel StudsCan be welded to either stainless steel or mild carbon steelFully annealed stainless steel studs are recommended when welding stainless steel studs to a mild carbon steel base metalAnnealed stud use has been shown to be imperative for stainless steel studs welded to carbon steel plates subject to repetitive or cyclic loads
12 Steel Capacity Both Shear and Tension governed by same basic equation Strength reduction factor is a function of shear or tensionThe ultimate strength is based on Fut and not Fy
13 Steel Capacity fVs = fNs = f·n·Ase·fut Where f = steel strength reduction factor= 0.65 (shear)= 0.75 (tension)Vs = nominal shear strength steel capacityNs = nominal tensile strength steel capacityn = number of headed studs in groupAse = nominal area of the headed stud shankfut = ultimate tensile strength of the stud steel
14 Material Properties Adapted from AWS D1.1-02 Table 184.108.40.206 page 6-11 shows the current minimum tensile and yield strengths for headed studs
15 Concrete Capacity ACI 318-02, Appendix D, “Anchoring to Concrete” Cover many types of anchorsIn general results in more conservative designs than those shown in previous editions of this handbook
16 Cracked Concrete ACI assumes concrete is cracked PCI assumes concrete is crackedAll equations contain adjustment factors for cracked and un-cracked concreteTypical un-cracked regions of membersFlexural compression zoneColumn or other compression membersTypical precast concreteTypical cracked regions of membersFlexural tension zonesPotential of cracks during handlingThe PCI handbook method assumes that the majority of the precast member anchorages are in uncracked regions.This is reasonable because many precast members are prestressed and most of the anchorages designed for precast concrete are located where cracking is unlikely. Therefore, all of the tension and shear design equations in the handbook are written as “uncracked” equations. There is thus an additional cracked concrete factor, Ccrb for concrete breakout, or Ccrp for pullout, which reduces the headed stud capacity due to cracking.
17 The 5% fractile ACI 318-02, Section D.4.2 states, in part: “…The nominal strength shall be based on the 5 percent fractile of the basic individual anchor strength…”Statistical concept that, simply stated,if a design equation is based on tests, 5 percent of the tests are allowed to fall below expectedCapacity5% FailuresTest strength
18 The 5% fractileThis allows us to say with 90 percent confidence that 95 percent of the test actual strengths exceed the equation thus derivedDetermination of the coefficient κ, associated with the 5 percent fractile (κσ)Based on sample population,n number of testsx the sample meanσ is the standard deviation of the sample set
19 The 5% fractile Example values of κ based on sample size are:
20 Strength Reduction Factor Function of supplied confinement reinforcementf = 0.75 with reinforcementf = 0.70 with out reinforcementIt is highly recommended that such confinement be provided around all concrete controlled headed stud connections.
22 Concrete Tension Failure Modes Design tensile strength is the minimum of the following modes:BreakoutfNcb: usually the most critical failure modePulloutfNph: function of bearing on the head of the studSide-Face blowoutfNsb: studs cannot be closer to an edge than 40% the effective height of the studsEach of these possible modes must be checked when a stud connection is designed
24 Concrete Breakout Strength Where:Ccrb = Cracked concrete factor, 1 uncracked, 0.8 CrackedAN = Projected surface area for a stud or groupYed,N =Modification for edge distanceCbs = Breakout strength coefficient
25 Effective Embedment Depth hef = effective embedment depthFor headed studs welded to a plate flush with the surface, it is the nominal length less the head thickness, plus the plate thickness (if fully recessed), deducting the stud burnoff lost during the welding process about 1/8 in.
26 Projected Surface Area, An Based on 35oAN - calculated, or empirical equations are provided in the PCI handbookCritical edge distance is 1.5hef
27 No Edge Distance Restrictions For a single stud, with de,min > 1.5hef
29 Side Edge Distance, Two Studs de1 < 1.5hefBy adding an additional stud, the length of the projected area increases by “X”
30 Side and Bottom Edge Distance, Multi Row and Columns de1 < 1.5hefde2< 1.5hefBy adding an additional row, the height of the projected area increases by “Y”
31 Edge Distance Modification Yed,N = modification for edge distancede,min = minimum edge distance, top, bottom, and sidesPCI also provides tables to directly calculate fNcb, but Cbs , Ccrb, and Yed,N must still be determined for the in situ condition
32 Determine Breakout Strength, fNcb The PCI handbook provides a design guide to determine the breakout area
33 Determine Breakout Strength, fNcb First find the edge condition that corresponds to the design condition
34 Eccentrically LoadedWhen the load application cannot be logically assumed concentric.Where:e′N = eccentricity of the tensile force relative to the center of the stud groupe′N ≤ s/2
35 Pullout Strength Nominal pullout strength Where Abrg = bearing area of the stud head= area of the head – area of the shankCcrp = cracking coefficient (pullout)= 1.0 uncracked= 0.7 crackedThe nominal pullout strength is a function of the bearing of the stud head against the concrete. The strength is:
36 Side-Face Blowout Strength For a single headed stud located close to an edge (de1 < 0.4hef)WhereNsb = Nominal side-face blowout strengthde1 = Distance to closest edgeAbrg = Bearing area of head
37 Side-Face Blowout Strength If the single headed stud is located at a perpendicular distance, de2, less then 3de1 from an edge, Nsb, is multiplied by:Where:
38 Side-Face BlowoutFor multiple headed anchors located close to an edge (de1 < 0.4hef)Whereso = spacing of the outer anchors along the edge in the groupNsb = nominal side-face blowout strength for a single anchor previously defined
39 Example: Stud Group Tension Given:A flush-mounted base plate with four headed studs embedded in a corner of a 24 in. thick foundation slab(4) ¾ in. f headed studs welded to ½ in thick plateNominal stud length = 8 inf′c = 4000 psi (normal weight concrete)fy = 60,000 psi
40 Example: Stud Group Tension Problem:Determine the design tension strength of the stud group
49 Step 5 – Tension Capacity The controlling tension capacity for the stud group is Breakout Strength
50 Step 6 – Check Confinement Steel Crack plane area = 4 in. x 8 in. = 32 in.2Design confinement reinforcement by shear-friction, (See PCI handbook Section 4.3.6:)
51 Step 6 – Confinement Steel Use 2 - #6 L-bar around stud group.These bars should extend ld past the breakout surface.
52 Concrete Shear Strength The design shear strength governed by concrete failure is based on the testingThe in-place strength should be taken as the minimum value based on computing both the concrete and steel
58 Front Edge Shear Strength WhereVco3 = Concrete breakout strength, single anchorCx3 =X spacing coefficientCh3 = Member thickness coefficientCev3 = Eccentric shear force coefficientCvcr = Member cracking coefficientThis condition represents a majority of shear loaded connections. The shear force is applied perpendicular to the front edge de3Notice all factors have a subscript 3 to indicate the Front Edge failure modeVco3 is unaffected by connection or member geometry (lbs)Cx3 =X spacing coefficient for overall X spacing of a connection with two or more X rows for a de3 type anchorage
59 Single Anchor Strength Where:λ = lightweight concrete factorBED = distance from back row of studs tofront edge
60 X Spacing factor Where: X = Overall, out-to-out dimension of outermost studs in back row of anchoragenstuds-back= Number of studs in back row
62 Eccentricity Factor Where e′v = Eccentricity of shear force on a group of anchorsdistance between point of shear force application and geometric centroid of group of anchors
63 Cracked Concrete Factor Uncracked concreteCvcr = 1.0For cracked concrete,Cvcr = 0.70 no reinforcementorreinforcement < No. 4 bar= 0.85 reinforcement ≥ No. 4 bar= 1.0 reinforcement. ≥ No. 4 bar and confined within stirrups with a spacing ≤ 4 in.
64 Corner Shear Strength A corner condition should be considered when: where the Side Edgedistance (SED) asshownThe corner is considered to be a special case of the front edge loaded anchorage. If the shear force is applied perpendicular to the front edge, and the anchorage is located close to the corner, a different concrete breakout mode occurs
65 Corner Shear Strength Where: Ch3 = Member thickness coefficient Cev3 = Eccentric shear coefficientCvcr = Member cracking coefficientCc3 = Corner influence coefficientNote the 3 still indicated loading toward to the de3 edge for a edge 3 failure modeNote that there is no Cx3 factor when computing a corner capacity.
66 Corner factorFor the special case of a large X-spacing stud anchorage located near a corner, such that SED/BED > 3, a corner failure may still result, if de1 ≤ 2.5BED
67 Side Edge Shear Strength In this case, the shear force is applied parallel to the side edge, de1Research determined that the corner influence can be quite large, especially in thin panelsIf the above ratio is close to the 0.2 value, it is recommended that a corner breakout condition be investigated, as it may still control for large BED valuesA connection loaded in shear parallel to a side edge results in a concrete breakout failure that does not affect the front edge. All failure mode is to the edge.
68 Side Edge Shear Strength Where:Vco1 = nominal concrete breakout strength for a single studCX1 = X spacing coefficientCY1 = Y spacing coefficientCev1 = Eccentric shear coefficientNote the 1 subscript failure mode
69 Single Anchor Strength Where:de1 = Distance from side stud to side edge (in.)do = Stud diameter (in.)
70 X Spacing Factor Where: nx = Number of X-rows x = Individual X-row spacing (in.)nsides =Number of edges or sides that influence the X directionnsides Factor = 1 or 2, I.E. 2 for a column in which connection is placed equidistant from each side
71 X Spacing FactorFor all multiple Y-row anchorages located adjacent to two parallel edges, such as a column corbel connection, the X-spacing for two or more studs in the row:Cx1 = nx
72 Y Spacing Factor Where: ny = Number of Y-rows Y = Out-to-out Y-row spacing (in) = Sy (in)
73 Eccentricity Factor Where: ev1 = Eccentricity form shear load to anchorage centroid
74 Back Edge Shear Strength Under a condition of pure shear the back edge has been found through testing to have no influence on the group capacityProper concrete clear cover from the studs to the edge must be maintained
75 “In the Field” Shear Strength When a headed stud anchorage is sufficiently away from all edges, termed “in-the-field” of the member, the anchorage strength will normally be governed by the steel strengthPry-out failure is a concrete breakout failure that may occur when short, stocky studs are used
76 “In the Field” Shear Strength For hef/de ≤ 4.5 (in normal weight concrete)Where:Vcp = nominal pry-out shear strength (lbs)
77 Front Edge Failure Example Given:Plate with headed studs as shown, placed in a position where cracking is unlikely. The 8 in. thick panel has a 28-day concrete strength of 5000 psi. The plate is loaded with aneccentricity of1 ½ in from thecenterline. Thepanel has #5confinement bars.Example Page 6-21
78 ExampleProblem:Determine the design shear strength of the stud group.
95 Step 1 – Determine applied loads Determine net Tension on Tension Stud GroupDetermine net Shear on Shear Stud GroupThe eccentric shear force, Vu, is resolved by the force couple shown in the sketch at the right, assuming that the tensile force is resisted by the top two rows of studs, with breakout planes as shown. Note: assumptions for load distribution are a matter of engineering judgment