1. Headed Concrete Anchors (HCA)
PCI 6th Edition
Headed Concrete Anchors (HCA)

2. Presentation Outine Research Background Steel Capacity
Concrete Tension Capacity
Tension Example
Concrete Shear Capacity
Shear Example
Interaction 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 research
The 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 tension
Section D.4.2 of ACI specifically permits alternate procedures, providing the test results met a 5% fractile criteria
The 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 Principles
Performance based on the location of the stud relative to the member edges
Shear design capacity can be increased with confinement reinforcement
In tension, ductility can be provided by reinforcement that crosses the potential failure surfaces

8. HCA Design Principles Designed to resist
Tension
Shear
Interaction of the two
The design equations are applicable to studs which are welded to steel plates or other structural members and embedded in unconfined concrete

9. HCA Design Principles
Where feasible, connection failure should be defined as yielding of the stud material
The groups strength is taken as the smaller of either the concrete or steel capacity
The minimum plate thickness to which studs are attached should be ½ the diameter of the stud
Thicker plates may be required for bending resistance or to ensure a more uniform load distribution to the attached studs

10. Stainless Steel Studs
Can be welded to either stainless steel or mild carbon steel
Fully annealed stainless steel studs are recommended when welding stainless steel studs to a mild carbon steel base metal
Annealed stud use has been shown to be imperative for stainless steel studs welded to carbon steel plates subject to repetitive or cyclic loads

11. Stud Dimensions
Table
Page 6-12

12. Steel Capacity Both Shear and Tension governed by same basic equation
Strength reduction factor is a function of shear or tension
The 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 capacity
Ns = nominal tensile strength steel capacity
n = number of headed studs in group
Ase = nominal area of the headed stud shank
fut = ultimate tensile strength of the stud steel

14. Material Properties Adapted from AWS D1.1-02 Table 6.5.1.1 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 anchors
In 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 cracked
All equations contain adjustment factors for cracked and un-cracked concrete
Typical un-cracked regions of members
Flexural compression zone
Column or other compression members
Typical precast concrete
Typical cracked regions of members
Flexural tension zones
Potential of cracks during handling
The 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 expected
Capacity
5% Failures
Test strength

18. The 5% fractile
This allows us to say with 90 percent confidence that 95 percent of the test actual strengths exceed the equation thus derived
Determination of the coefficient κ, associated with the 5 percent fractile (κσ)
Based on sample population,n number of tests
x the sample mean
σ 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 reinforcement
f = 0.75 with reinforcement
f = 0.70 with out reinforcement
It is highly recommended that such confinement be provided around all concrete controlled headed stud connections.

21. Notation Definitions Edges Stud Layout Critical Dimensions
de1, de2, de3, de4
Stud Layout
x1, x2, …
y1, y2, …
X, Y
Critical Dimensions
BED, SED

22. Concrete Tension Failure Modes
Design tensile strength is the minimum of the following modes:
Breakout
fNcb: usually the most critical failure mode
Pullout
fNph: function of bearing on the head of the stud
Side-Face blowout
fNsb: studs cannot be closer to an edge than 40% the effective height of the studs
Each of these possible modes must be checked when a stud connection is designed

23. Concrete Tension Strength
fNcb: Breakout
fNph: Pullout
fNsb: Side-Face blowout
fTn = Minimum of

24. Concrete Breakout Strength
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

25. Effective Embedment Depth
hef = effective embedment depth
For 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 35o
AN - calculated, or empirical equations are provided in the PCI handbook
Critical edge distance is 1.5hef

27. No Edge Distance Restrictions
For a single stud, with de,min > 1.5hef

28. Side Edge Distance, Single Stud
de1 < 1.5hef

29. Side Edge Distance, Two Studs
de1 < 1.5hef
By adding an additional stud, the length of the projected area increases by “X”

30. Side and Bottom Edge Distance, Multi Row and Columns
de1 < 1.5hef
de2< 1.5hef
By adding an additional row, the height of the projected area increases by “Y”

31. Edge Distance Modification
Yed,N = modification for edge distance
de,min = minimum edge distance, top, bottom, and sides
PCI 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 Loaded
When the load application cannot be logically assumed concentric.
Where:
e′N = eccentricity of the tensile force relative to the center of the stud group
e′N ≤ s/2

35. Pullout Strength Nominal pullout strength Where
Abrg = bearing area of the stud head
= area of the head – area of the shank
Ccrp = cracking coefficient (pullout)
= 1.0 uncracked
= 0.7 cracked
The 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)
Where
Nsb = Nominal side-face blowout strength
de1 = Distance to closest edge
Abrg = 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 Blowout
For multiple headed anchors located close to an edge (de1 < 0.4hef)
Where
so = spacing of the outer anchors along the edge in the group
Nsb = 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 plate
Nominal stud length = 8 in
f′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

41. Solution Steps Step 1 – Determine effective depth
Step 2 – Check for edge effect
Step 3 – Check concrete strength of stud group
Step 4 – Check steel strength of stud group
Step 5 – Determine tension capacity
Step 6 – Check confinement steel

42. Step 1 – Effective Depth

43. Step 2 – Check for Edge Effect
Design aid, Case 4
X = 16 in.
Y = 8 in.
de1 = 4 in.
de3 = 6 in.
de1 and de3 > 1.5hef = 12 in.
Edge effects apply
de,min = 4 in.

44. Step 2 – Edge Factor

45. Step 3 – Breakout Strength

46. Step 3 – Pullout Strength

47. Step 3 – Side-Face Blowout Strength
de,min = 4 in. > 0.4hef
= 4 in. > 0.4(8) = 3.2 in.
Therefore, it is not critical

48. Step 4 – Steel Strength

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.2
Design 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 testing
The in-place strength should be taken as the minimum value based on computing both the concrete and steel

54. Front Edge Shear Strength, Vc3

55. Corner Edge Shear Strength, Modified Vc3

56. Side Edge Shear Strength, Vc1

58. Front Edge Shear Strength
Where
Vco3 = Concrete breakout strength, single anchor
Cx3 =X spacing coefficient
Ch3 = Member thickness coefficient
Cev3 = Eccentric shear force coefficient
Cvcr = Member cracking coefficient
This condition represents a majority of shear loaded connections. The shear force is applied perpendicular to the front edge de3
Notice all factors have a subscript 3 to indicate the Front Edge failure mode
Vco3 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 factor
BED = distance from back row of studs to
front edge

60. X Spacing factor Where: X = Overall, out-to-out dimension of outermost
studs in back row of anchorage
nstuds-back= Number of studs in back row

61. Thickness Factor
Where:
h = Member thickness

62. Eccentricity Factor Where
e′v = Eccentricity of shear force on a group of anchors
distance between point of shear force application and geometric centroid of group of anchors

63. Cracked Concrete Factor
Uncracked concrete
Cvcr = 1.0
For cracked concrete,
Cvcr = 0.70 no reinforcement or
reinforcement < 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 Edge
distance (SED) as
shown
The 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 coefficient
Cvcr = Member cracking coefficient
Cc3 = Corner influence coefficient
Note the 3 still indicated loading toward to the de3 edge for a edge 3 failure mode
Note that there is no Cx3 factor when computing a corner capacity.

66. Corner factor
For 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, de1
Research determined that the corner influence can be quite large, especially in thin panels
If 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 values
A 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 stud
CX1 = X spacing coefficient
CY1 = Y spacing coefficient
Cev1 = Eccentric shear coefficient
Note 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 direction
nsides Factor = 1 or 2, I.E. 2 for a column in which connection is placed equidistant from each side

71. X Spacing Factor
For 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 capacity
Proper 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 strength
Pry-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 an
eccentricity of
1 ½ in from the
centerline. The
panel has #5
confinement bars.
Example Page 6-21

78. Example
Problem:
Determine the design shear strength of the stud group.

79. Solution Steps Step 1 – Check corner condition
Step 2 – Calculate steel capacity
Step 3 – Front Edge Shear Strength
Step 4 – Calculate shear capacity coefficients
Step 5 – Calculate shear capacity

80. Step 1 – Check Corner Condition
Not a Corner Condition

81. Step 2 – Calculate Steel Capacity
fVns = f·ns·An·fut
= 0.65(4)(0.20)(65) = 33.8 kips

82. Step 3 – Front Edge Shear Strength

83. Step 4 – Shear Capacity Coefficient
Concrete Breakout Strength, Vco3

84. Step 4 – Shear Capacity Coefficient
X Spacing Coefficient, Cx3

85. Step 4 – Shear Capacity Coefficient
Member Thickness Coefficient, Ch3

86. Step 4 – Shear Capacity Coefficient
Eccentric Shear Force Coefficient, Cev3

87. Step 4 – Shear Capacity Coefficient
Member Cracking Coefficient, Cvcr
Assume uncracked region of member
#5 Perimeter Steel

88. Step 5 – Shear Design Strength
fVcs = f·Vco3·Cx3·Ch3·Cev3·Cvcr
= 0.75(47.0)(0.93)(0.53)(0.94)(1.0)
= 16.3 kips

89. Interaction
Trilinear Solution
Unity curve with a 5/3 exponent

90. Interaction Curves

91. Combined Loading Example
Given:
A ½ in thick plate with headed studs for attachment of a steel bracket to a column as shown at the right
Problem:
Determine if the studs are adequate for the connection

92. Example Parameters f′c = 6000 psi normal weight concrete λ = 1.0
(8) – 1/2 in diameter studs
Ase = 0.20 in.2
Nominal stud length = 6 in.
fut = 65,000 psi (Table )
Vu = 25 kips
Nu = 4 kips
Column size: 18 in. x 18 in.

93. Provide ties around vertical bars in the column to ensure confinement: f = 0.75
Determine effective depth
hef = L + tpl – ths – 1/8 in
= – – = 6.06 in

94. Solution Steps Step 1 – Determine applied loads
Step 2 – Determine tension design strength
Step 3 – Determine shear design strength
Step 4 – Interaction Equation

95. Step 1 – Determine applied loads
Determine net Tension on Tension Stud Group
Determine net Shear on Shear Stud Group
The 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

96. Step 2 – Concrete Tension Capacity

97. Step 2 – Steel Tension Capacity

98. Step 2 – Governing Tension

99. Step 3 – Concrete Shear Capacity
For concrete shear strength, it is apparent that “side edge” breakout will be critical:

100. Step 3 – Steel Shear Capacity
For concrete shear strength, it is apparent that “side edge” breakout will be critical:

101. Step 3 – Governing Shear

102. Step 4 – Interaction
Check if Interaction is required

103. Step 4 – Interaction

104. Questions?