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Design Concepts for Anchorage | Concrete
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Design Concepts for Reinforcement Anchorage
Over the past 10 years Reid™ Construction Systems have carried out research into the most accurate formula, based on embedment depth and concrete strength, for the pullout capacity of headed anchors in concrete. This research has resulted in the refinement of Reid’s™ Threaded Inserts to ensure that in a minimum 30MPa concrete they are capable of breaking the reinforcing, ensure minimum slippage and have sufficient bearing area to prevent concrete crushing. The following table presents the information of Reid™ Insert Capacity based on the Haeussler formula and non cracked concrete.
Why use a Reid
Threaded Insert or Footplate when hooked and bent bars have always been used?
Is a common question asked by structural engineers when presented with the Reidbar™ system for the first time.
To answer this question some explanation is required:
Hooked bars and bent bars have been the standard method of providing anchorage for reinforcing steel in concrete construction where the standard bond length for a straight bar cannot be achieved. Concrete design codes account for this shorter bond length by specifying a minimum length, L
from the back of the bend, or hook, to the critical surface. The minimum length equation considers the effect of concrete strength, f`
, and steel yield strength f y
RB12 500E 82 78 56.5 97 92 79 108
RBA16 500E 110 103 100.6 130 122 140.8 126
RB20 500E 137 129 157.0 162 153 219.9 156
RB25 500E 171 161 245.5 203 191 343.7 199
RB32 500E 219 206 402.0 260 244 562.9 -
Note 1: The adoption of embedment depth L
will ensure that the failure mechanism will be ductile rather than by brittle shear cone pullout. See note 3
Note 2: Embedment depth is calculated using the formulas developed by Haeussler. The general form is given as P = 0.972 x L
where: P = pullout capacity of shear cone in Newtons L = effective embedment depth in mm B = concrete compressive strength in MPa
Note 3: Screw in plastic nail plates recess the insert by 8mm
With modern design and construction practices, where thinner sections are used and anchorages are required in concrete Threaded Insert capacity in concrete
Minimum embedment depths for threaded inserts & footplate in 25Mpa and 30Mpa concrete Table 31. Product Code
25Mpa 30Mpa 25Mpa 30Mpa
Char Min Yield Strength
Depth to develop Char Max Ult Strength
Char Max Ult Strength
Threaded Insert Length plus 8mm
Depth to develop Min Yield Strength
tension zones that can be micro cracked, the above formula requires modification to represent the reduction in strength that will occur. While this is possible with the Haeussler approach, research in NZ has focused on an alternative formula for the prediction of cone pullout capacity which accommodates anchor centre, edge distances, material property variations and construction tolerances. Known as the q method, it is this design approach that is presented here to be consistent with NZ research.
(Test results have shown that pull out calculated with Haeussler will be about 15% conservative) (P.T. 2001)
Standard 90° or 180° hook
As designers and constructors become more familiar with the use of tilt-up and precast methods normal conservatism can be pushed to the limit. This is especially true with the current trend towards increasingly slimmer wall panels where the provision of an effective base anchorage for cantilever action is still required. Although bent starter bars are still widely used for this function it is not always possible to meet code requirements for minimum anchorage length in thin panels.
The Design Code NZS 3101 2006 and the previous code both draw attention to the issues related to concrete cone pullout of shallow embedment anchorage of hooked bars. The minimum development length of 150 mm is removed from clause 7.3.14.2 and two new clauses added
“The development length, L
, calculated using eqn 7-
11 shall apply when there is no likelihood of a failure mode of a pullout of a concrete cone from the volume of concrete in which the bar is anchored” 3 part 1 p3
“If a cone of concrete pullout is likely then a rational analysis or suitable testing shall account for the proximity of the anchored bars to other loaded elements and to edges of elements”
Essentially these amendments say that one should not use hooked bars to develop full bar capacity unless
concrete cone pullout capacity exceeds the bar strength.
Detail 36.
© Copyright Reid™ Construction Systems 2007. All rights reserved. Moral rights asserted.
So how do I calculate concrete cone pullout ?
In 1993, NZ University of Canterbury research by Restrepo-Posada and Park
showed that the q-method can be used to predict the concrete cone capacity of hooked bar and headed stud type anchorages, provided that the correct embedment depth is defined. This design approach accounts for the influence of edge distance, bar spacing and micro cracking in tension zones, by applying reduction factors to the calculated concrete cone pull out capacity of the anchorage. To reduce the probability of premature brittle failures the approach also incorporates factors in the formula to account for likely variations in material strengths and construction tolerances.
The method and corresponding formula are set out in this manual in the form of a flow diagram on page 114 and is followed by a design example that compares the design of a “L” shaped hooked anchorage to that of a comparable sized Reid
Threaded Insert anchor for a wall panel to foundation connection. (page 115.)
Importance of ductile failure The importance of ductile failure should be appreciated, as it is essential to ensure that a brittle failure mechanism does not occur before a ductile failure, taking into account the possible material over strengths that can exist. In the design example it is shown that brittle failure of the anchorage will occur for both situations but in the case of the Threaded Insert it has enough capacity to ensure that the wall stem will have a ductile failure before cone pullout and thus provide a safe connection. Anchorage slip The q-method does not address slippage of the anchor. With hooked bars the inside of the hook causes local crushing of the concrete as the bar tries to straighten under load. Higher slippage of the reinforcing can occur compared to a headed anchor where the bearing stress under the head can be accommodated in the design of the product to minimize crushing.
Research at NZ University of Auckland by Maureen
Ma in 1999 into Methods of Joining Precast Concrete components to form Structural Walls
highlighted the performance of Reid™ Threaded Inserts compared to that of conventional hooked bar construction. The diagram below shows the test comparison between the two forms of anchorage in a wall panel to footing connection when subject to cyclic loading. It can be seen that the threaded inserts performed significantly better.
Detail 37.
Applied Load vs Displacement at the Load Point RB12 FOOTPLATES
– LOAD +
RB12FP
Detail 38.
Detail 40.
Detail 41.
Detail 39.
Design Process for Cone Pullout
hooked bars possible
Hooked Bar effective depth h
Definition of Spacing Parameters used by the q-method.
Can full development length Ldh and cover be achieved in the wall thickness
12mm dia – 214mm min thickness
16mm dia – 275mm min thickness
required for 30 Mpa concrete and 500 grade steel
Use Reid
RB12TI – 120mm
RBA16TI – 140mm
Do starter bars need site bending for access?
Do starter bars need bending for transport?
Still want to use hooked bar anchorages?
ldh ~ 30mm
Threaded Insert effective depth he
Calculate Concrete Cone Pullout from:
` ⎟
- to determine the effective embedment to yield the steel
f f ξ - to determine maximum steel stress without inducing cone pullout
f characteristic concrete strength – Mpa
f characteristic steel yield strength - MPa
f steel stress – Mpa
d nominal steel diameter – mm
h effective anchor embedment – mm
cy cx sy sx CR R
ϕ ϕ ϕ ϕ ϕ ξ = - overall reduction factor
Where: 75 . 0 =
ϕ for cone area in cracked section
= 1.00 in any other case.
ϕ ϕ & spacing reduction factor
( )( ) ( ) 1 / / 1 1 ≤ − + =
x CR x x sx
n S S n ϕ
n number of anchors in x direction
S centre to centre spacing in x direction
h S 3 =
ϕ as for sx
ϕ with subscript y in place of x.
ϕ ϕ & edge reduction factors
( ) { } 1 5 . 1 / 7 . 0 3 . 0 ≤ + =
h cx ϕ
cy = edge distance in y direction
ϕ as for cx
ϕ with subscript x in place of y
Use normal limit
state for design of
Use elastic design
of joint capacity
Example calculation of typical base fixing for Threaded Insert Connection and Hooked Bar Connection
Material Properties MPa 10
Pa := kN 10
N := kNm kN m · := GPa 10
30MPa := f
500MPa := | 0.85 :=
Concrete modulus of Elasticity E
3320 MPa · f'
· 6900MPa + ( ) := Steel Modulus of Elasticity E
200GPa :=
Wall Panel Properties
120mm :=
Unit width of
B 1000mm :=
Wall panel flexural strength
Reinforcing - bar diameter d
12mm := centres c
300mm := top cover
Area of reinforcing per unit length
:= a 7.392 mm = |M
· := |M
9 kNm =
Nominal tensile capacity of section M
0.6 f'
· := M
7.9kNm =
Over strength - cl. 2.6.5.5 (b) iii)
1.35 · f
15MPa + ( ) · B ·
6.65 mm =
· := |Mover
14.4 kNm =
Foundation to wall panel connection:
D 300mm :=
Starter bars/ inserts of diameter d
12mm := at spacing of
s 300mm :=
Hooked bar pullout cone capacity Threaded Insert pullout cone capacity
@300c/c
@ 300c/c
RB12TI
Effective embedment depth of hooked bar
with cover to starter = 30mm
Effective embedment depth of threaded insert
with cover to insert = 12mm ( galvanised)
Bar height ht
170mm := Insert height ht
170mm :=
e_bar
~ 30mm ~ := h
72mm = h
108mm := h
Reduction factor for cracked section
cr_bar
0.75 :=
cr_insert
Critical Spacing for embedment depth Critical Spacing for embedment depth
216 mm = s
324 mm =
Spacing reduction factors therefore are Spacing reduction factors therefore are
sx_insert
sy_insert
sx_bar
1 := q
sy_bar
Edge reduction factors are Edge reduction factors are
cy_bar
· + := q
cy_insert
1.402 = q
cx_bar
1.035 = q
cx_insert
Total reduction factors to apply Total reduction factors to apply
· := ç
R_insert
0.75 = ç
:= h'
0.23 d'
MPa · := f
158 MPa = f
268.8MPa =
Yielding of the reinforcement cannot be achieved
before pullout failure will occur.
Using elastic analysis for an opening moment on
m' 7.973 =
m 7.973 =
:= A'
· := A'
na' 100mm :=
na' ~ ( ) · ~
Find na' ( ) := d'
29.1 mm = na 100mm :=
na ~ ( ) · ~
Find na ( ) := d
29.1 mm =
stress in the steel is f
158 MPa = stress in the steel is f
Total force in reinforcing bars is F
· := Total force in reinforcing bars is
moment will be M
· := moment will be M
Hooked bar opening moment capacity: Reid Threaded Insert opening moment capacity:
9.5kNm = M
16.2 kNm =
The hooked bar base connection is an unsafe design with brittle failure of the connection likely to occur before the
yielding of the wall panel. M
9.5kNm = compared to possible wall strength of |Mover
On the otherhand the Reid threaded Insert connection is safe because yielding in the wall panel is likely to occur
before cone failure in the foundation connection.
16.2 kNm = compared to possible wall strength of |Mover
1) NZS:3101:Part 1:1995 Concrete Structures Standard The Design of Concrete
2) NZS:3101:Part 2:1995 Commentary on The Design of Concrete Structures
3) NZS:3101:Part 2:1995 Amendment No1 December 1998
4) Tensile Capacity of Steel Connectors with Short Embedment Lengths in
Concrete - Restrapo- Prosada and Park August 1993
5) Tensile Capacity of Hooked Bar Anchorages with Short Embedment Lengths
in Concrete - Nigel Watts University of Canterbury September 1996
6) Methods of Joining Precast Concrete components to formStructural Walls-
Maureen Ma University of Auckland 1999
7) The Design and Construction of Tilt-up Reinforced Concrete Buildings -
Restrepo, Crisafulli and Park. University of Canterbury 1996
8) The Performance of Reidbar Couplers in Seismic Resistant Frame Structures -
BassimBahr-Aliloom University of Auckland Feb 1997
9) Assessing the Seismic Performance of Reinforcement Coupler Systems -
Anselmo Bai University of Auckland Feb 1997
10) Tensile Capacity of Headed Anchors with Short Embedment Lengths in
Concrete - Barry Magee University of Canterbury September 1996
NOTE: Software for wall/base calculation is available on Reids Resource Disc or direct from Reids Engineering Manager Ph 09 920 4346
ANCHORS & FASTENERS REIDBAR & FITTINGS
Detail 40. Higher slippage of the reinforcing can occur compared to a headed Bar Slip anchor where the bearing stress under the head can be accommodated in the design of the product to minimize crushing. This design approach accounts for the influence of edge distance.
Wall Panel RB12@300
Detail 38. (page 115. The diagram below shows the test comparison between the two forms of anchorage in a wall panel to footing connection when subject to cyclic loading. It can be seen that the threaded inserts performed significantly better. provided that the correct embedment depth is defined.
Detail 37. In the design example it is shown that brittle failure of the anchorage will occur for both situations but in the case of the Threaded Insert it has enough capacity to ensure that the wall stem will have a ductile failure before cone pullout and thus provide a safe connection. With hooked bars the inside of the hook causes local crushing of the concrete as the bar tries to straighten under Local Ldh crushing load.COMPANY BACKGROUND
Reid™ Design Concepts for Reinforcement Anchorage
The -method does not address slippage of the anchor.
MODULAR WALL CASTING SYSTEM
Detail 39. NZ University of Canterbury research by Restrepo-Posada and Park4 showed that the -method can be used to predict the concrete cone capacity of hooked bar and headed stud type anchorages.)
Importance of ductile failure
The importance of ductile failure should be appreciated. Research at NZ University of Auckland by Maureen Ma in 1999 into Methods of Joining Precast Concrete components to form Structural Walls6 highlighted the performance of Reid™ Threaded Inserts compared to that of conventional hooked bar construction. To reduce the probability of premature brittle failures the approach also incorporates factors in the formula to account for likely variations in material strengths and construction tolerances. The method and corresponding formula are set out in this manual in the form of a flow diagram on page 114 and is followed by a design example that compares the design of a “L” shaped hooked anchorage to that of a comparable sized ReidTM Threaded Insert anchor for a wall panel to foundation connection.
270 70 150
Detail 41. taking into account the possible material over strengths that can exist.
Base Block 70
Hook Bar 300
© Copyright Reid™ Construction Systems 2007. by applying reduction factors to the calculated concrete cone pull out capacity of the anchorage. Moral rights asserted. All rights reserved. as it is essential to ensure that a brittle failure mechanism does not occur before a ductile failure. bar spacing and micro cracking in tension zones.
23db⎟ ⎝ ⎠
f c` = characteristic concrete strength – Mpa f y = characteristic steel yield strength .5db
© Copyright Reid™ Construction Systems 2007.to determine maximum steel stress without inducing cone pullout ⎜ 0.
spacing reduction factor
Hooked Bar effective depth he
sy cx
= ( + (n x − 1)(S x / S CR ))/ n x ≤ 1 1 n x = number of anchors in x direction S x = centre to centre spacing in x direction S CR = 3he
= as for
sx with subscript y in place of x.5he ) ≤ 1 0 }
cx with subscript x in place of y
cy n =4 x sy
y x ny= 2
Use normal limit state for design of joint capacity
is f s < f y
Use elastic design of joint capacity
Definition of Spacing Parameters used by the -method. All rights reserved.00 in any other case.
. Moral rights asserted.to determine the effective embedment to yield the steel
fs = ξR
⎛ h ⎞ 1. wall thickness RB12TI – 120mm RBA16TI – 140mm
Do starter bars need site bending for access? Do starter bars need bending for transport?
Use Reid™ Threaded Inserts
⎛ fy he = ⎜ ` ⎜ξ ⎝ R fc
⎞3 d ⎟ b ⎟ 4/3 ⎠
.overall reduction factor
= 0.TM
12mm dia – 214mm min thickness 16mm dia – 275mm min thickness required for 30 Mpa concrete and 500 grade steel
Conventional hooked bars possible
Use ReidTM Threaded Inserts Min.3 + (0.MPa f s = steel stress – Mpa d b = nominal steel diameter – mm he = effective anchor embedment – mm
ldh he
1.5 f c` ⎜ e ⎟ .75 for cone area in cracked section
= edge reduction factors
= { .7cx / 1.
bar diameter d r := 12mm centres cr := 300mm wallt d r cover := Area of reinforcing per unit length 2 2 As := a := dr
REIDBAR & FITTINGS
As = 377 mm wallt 2
4 cr As fy 0.9 kNm
acom = 6.85 f' c + 6900MPa
kN := 10 N
kNm := kN m
GPa := 10 Pa
Concrete modulus of Elasticity Ec := 3320 MPa
Steel Modulus of Elasticity Es := 200GPa
Wall thickness wallt := 120mm Unit width of B := 1000mm top cover
Reinforcing .COMPANY BACKGROUND
f' c := 30MPa MPa := 10 Pa fy := 500MPa := 0.cl.392 mm
Mn :=
As fy B wallt 6
0.5 (b) iii) acom := As 1.6 f' c Over strength .4 kNm Overstrength factor Mover ncom Mn
= 1. All rights reserved. Moral rights asserted.
.35 fy 0.65 mm
Mover ncom := ( As 1.5.5
M n = 9 kNm
Nominal tensile capacity of section M t := 0. 2.85 f' c B
a = 7.35fy)
Moverncom = 14.6
Foundation depth D := 300mm Starter bars/ inserts of diameter d b := 12mm at spacing of s := 300mm
Hooked bar pullout cone capacity
120 12diam @ 300c/c
Threaded Insert pullout cone capacity
120 12diam @ 300c/c RB12TI
12diam @ 300c/c
© Copyright Reid™ Construction Systems 2007.85 ( f' c + 15MPa ) B wallt 2 acom 2
M t = 7.6.
Moral rights asserted.402 1
= 1. All rights reserved.3 + 0.5
d'b :=
db mm h'e
h'e :=
h e := he
f' c MPa
Effective embedment depth of threaded insert with cover to insert = 12mm ( galvanised) Insert height htinsert := 170mm
Effective embedment depth of hooked bar with cover to starter = 30mm Bar height htbar := 170mm 3 db
30mm h e_bar = 72 mm 2 Reduction factor for cracked section cr_bar := 0.75 Critical Spacing for embedment depth scr_bar := 3 h e_bar scr_bar = 216 mm
h e_bar := wallt
h e_insert := 108mm
h e_insert = 108 mm
Reduction factor for cracked section cr_insert := 0.5 h e_insert
cx_insert :=
= 1. Using elastic analysis for an opening moment on the connection: Modular ratio Es m := Ec
m' = 7.5 4
fs_bar :=
fs_insert :=
.75 h e_bar mm fc f' c MPa d'b := db mm
m = 7.8 MPa
Yielding of the reinforcement cannot be achieved before pullout failure will occur.035
cy_bar :=
cy_insert := 1 Total reduction factors to apply
Total reduction factors to apply
htbar 1.23 d'b fs_bar = 158 MPa
fs_bar := fs_bar MPa
fs_insert := fs_insert MPa
fs_insert = 268.75 Critical Spacing for embedment depth scr_insert := 3 h e_insert scr_insert = 324 mm
Spacing reduction factors therefore are
sx_bar :=
Spacing reduction factors therefore are s sx_insert := sy_insert := 1 scr_insert Edge reduction factors are
cy_insert :=
Edge reduction factors are
0. Using elastic analysis for an opening moment on the connection: Modular ratio Es m' := Ec d'1 := htbar na' := 100mm A' st := db 4
Yielding of the reinforcement cannot be achieved before pullout failure will occur.69 h e_insert mm
1.23 d'b
0.3 + 0.973
A' st = 377 mm
d 1 := htinsert
Ast = 377 mm
© Copyright Reid™ Construction Systems 2007.5 h e_bar
htinsert 1.
Barry Magee University of Canterbury September 1996
© Copyright Reid™ Construction Systems 2007.5 kNm
Reid Threaded Insert opening moment capacity: Me_insert = 16.Restrapo.Nigel Watts University of Canterbury September 1996 6) Methods of Joining Precast Concrete components to form Structural WallsMaureen Ma University of Auckland 1999 7) The Design and Construction of Tilt-up Reinforced Concrete Buildings Restrepo.
.4 kNm On the otherhand the Reid threaded Insert connection is safe because yielding in the wall panel is likely to occur before cone failure in the foundation connection.COMPANY BACKGROUND
Given na'
m' A'st 2 B
( d'1
na' ) = 0
d'na := Find( na' )
d'na = 29.2 kNm
The hooked bar base connection is an unsafe design with brittle failure of the connection likely to occur before the yielding of the wall panel. Moral rights asserted.4 kNm
1) NZS:3101:Part 1:1995 Concrete Structures Standard The Design of Concrete Structures 2) NZS:3101:Part 2:1995 Commentary on The Design of Concrete Structures 3) NZS:3101:Part 2:1995 Amendment No1 December 1998 4) Tensile Capacity of Steel Connectors with Short Embedment Lengths in Concrete .2 kNm compared to possible wall strength of Moverncom = 14. M e_bar = 9. M e_insert = 16.1 mm
na := 100mm Given na d na := Find( na)
m Ast 2 B
na) = 0
d na = 29.Prosada and Park August 1993 5) Tensile Capacity of Hooked Bar Anchorages with Short Embedment Lengths in Concrete .5 kNm compared to possible wall strength of Mover ncom = 14.8 MPa Total force in reinforcing bars is Fs_insert := fs_insert Ast moment will be M e_insert := Fs_insert d 1 d na 3
moment will be Me_bar := Fs_bar d'1
Hooked bar opening moment capacity: M e_bar = 9. University of Canterbury 1996 8) The Performance of Reidbar Couplers in Seismic Resistant Frame Structures Bassim Bahr-Aliloom University of Auckland Feb 1997 9) Assessing the Seismic Performance of Reinforcement Coupler Systems Anselmo Bai University of Auckland 2003 Feb 1997 10) Tensile Capacity of Headed Anchors with Short Embedment Lengths in Concrete . Crisafulli and Park. All rights reserved.1 mm
stress in the steel is fs_bar = 158 MPa Total force in reinforcing bars is Fs_bar := fs_bar A' st d'na 3
stress in the steel is fs_insert = 268.
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