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Topics DOI: 10.1002/best.200710107
Ronald A. Cook Rolf Eligehausen Jörg J. Appl
Overview: Behavior of Adhesive Bonded Anchors This paper presents an overview of a behavioral model to predict the failure load of anchorage systems with adhesive bonded anchors loaded in tension. The development and complete behavioral model was presented by Eligehausen, Cook, and Appl in the November-December 2006 edition of the American Concrete Institute Structural Journal.
1 Introduction Connections to concrete include both cast-in-place and post-installed anchors. Post-installed anchors are either mechanical or bonded anchors. Fig. 1 shows the typical types of anchors. The purpose of this paper is to present a behavioral model to predict the failure load of anchorage systems with adhesive bonded anchors loaded in tension. This model was first presented in Eligehausen, Cook, and Appl [1] and this paper simply provides an overview of the information previously published. For detailed information please refer to Eligehausen, Cook, and Appl [1] and other references provided in this paper. The behavioral model is based on extensive numerical and experimental work that provides a foundation for incorporating design provisions for adhesive bonded anchorage systems into building codes and standards.
2 Description of adhesive bonded anchors An adhesive bonded anchor is a steel element (threaded rod or deformed bar) inserted into a drilled hole in hardened concrete with a structural adhesive acting as a bonding agent between the concrete and the steel (Fig. 1). For adhesive anchors, the diameter of the drilled hole is typically not larger than 1.5 times the diameter of the steel element. Adhesive anchors are available in glass or foil capsule systems using organic compounds and in injection systems using organic or inorganic compounds or a mixture of the two in either pre-packaged cartridge systems or bulk injection systems.
3 Background The design strength of anchorages to concrete is either controlled by the strength of the anchor steel or by the strength associated with the embedment of the anchors into the concrete. The design provisions regarding failure of the anchor steel in both tension and shear provided in current building codes and standards appear to be applic-
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Fig. 1. Types of anchors [1]
able to adhesive bonded anchors. The behavior of cast-inplace and post-installed mechanical anchors associated with embedment failure has been extensively studied [2], [3] and embedment design provisions for these types of anchors are incorporated in current building codes and design standards. The embedment shear strength provisions of current building codes and design standards appear to be applicable to adhesive bonded anchors. This paper is concerned with the behavior of adhesive bonded anchors loaded in tension and arranged in groups and/or with free edges near the anchors where the strength is limited by embedment failure. The nominal bond strength of adhesive bonded anchors to be used in the design is dependent on the mean bond strength of anchors installed in accordance with manufacture’s guidelines, adjusted for scatter of the product’s test results, and for the product’s sensitivity to installation and in-service conditions. As discussed in Cook et al. [4] and Meszaros [5] the bond strength of properly installed bonded anchor products varies quite considerably. Based on tests of twenty adhesive anchor products, Cook et al. [4] found that the mean bond strength at the adhesive/anchor interface for individual products ranged from 2.3 MPa to 19.5 MPa. Results of tests performed by Meszaros [5] using three products indicated that the mean bond strength decreases as the anchor diameter increases. In addition to the large variations in the mean bond strength for bonded anchors installed according to manufacture’s recommendations, each bonded anchor product is influenced differently by other conditions. These condi-
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tions include sensitivity to the hole cleaning procedure, hole drilling method (e.g., hammer drilling or diamond core drilling), and moisture presence in the concrete at installation, temperature effects, and creep under sustained loads. The implementation of the behavioral model presented in this paper is dependent on the acceptance of a comprehensive product evaluation standard that establishes a product’s nominal bond strength. The following provides the current information regarding the behavior of adhesive anchors loaded in tension in uncracked concrete. Information on the effects of concrete cracks on the strength of adhesive bonded anchors is provided in Eligehausen and Balogh [3] and Meszaros [5].
Fuchs et al. [2] proposed the behavioral model for concrete breakout failure currently accepted for use in building codes and design standards. This model was created to predict the failure loads of cast-in-place headed anchors and post-installed mechanical anchors loaded in tension or in shear that exhibit concrete breakout failure. According to Fuchs et al. [2], the mean concrete breakout capacity for single cast-in-place anchors and post-installed mechanical anchors in uncracked concrete is given by the following equations: Cast-in-place anchors: (N)
— 1.5 Nb = 13.5 兹苵 fc苵chcf
(1a)
(N)
(1b)
The concrete breakout capacity of anchor groups and anchors located near free edges with a tension load applied — concentrically to the anchors is given by Eq. (2) where Nb is taken from Eq. (1): Nch =
A Nc ψ N (N) A Nc0 ed,N b
(2a)
where ψ ed,N = 0.7 + 0.3
3.1 Cast-in-place and post-installed mechanical anchors
— 1.5 Nb = 15.5 兹苵 fc苵chef
Post-installed mechanical anchors:
ca1 if ca1 < ccr ccr
(2b)
Fig. 2 provides information on how ANco and ANc are to be determined. For cast-in-place and post-installed mechanical anchors, the critical spacing, scr, is 3.0hef and the critical edge distance, ccr, is 1.5hef.
3.2 Single adhesive anchors Fig. 3 presents the embedment failure modes observed for single adhesive anchors. In Fig. 4 the transfer of load at the steel/mortar and mortar/concrete bond interfaces is shown. The mortar is the adhesive bonding agent used to connect the anchor with the concrete. As shown in Fig. 4, a tension load is transferred by mechanical interlock from the threaded rod into the mortar and by adhesion and/or
Fig. 2. Calculation of effective areas ANc0 and ANc [1]
Fig. 3. Potential embedment failure modes of bonded anchors, Cook et al. [7]
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load given by Eq. (1). This is shown in Fig. 5. In this figure, failure loads and failure modes of adhesive anchors with constant embedment depth but varying diameter are given. According to these test results, the failure load of adhesive anchors is limited to the concrete breakout failure load of post-installed mechanical anchors as given by Eq. (1b). By equating Eq. (1b) with Eq. (3), the upper limit on the bond strength that can be utilized for single anchors can be determined (Eq. (4)). τmax =
0.5 h 0.5 4.3 fcc ef (MPa) d
(4)
4 Numerical investigation Fig. 4. – Mechanism of load transfer of a bonded anchor, Eligehausen et al. [6]
micro interlock (due to the roughness of the drilled hole) from the mortar into the concrete. Experimental studies discussed in Eligehausen et al. [6], indicate that the actual bond stress distribution along the embedment length at peak load is non-linear with lower bond stresses at the concrete surface and higher bond stresses at the embedded end of the anchor. However, in Cook et al. [7] a comparison of suggested behavioral models to a worldwide data base for single adhesive anchors indicates that their failure load is best described by a uniform bond stress model incorporating the nominal anchor diameter (d) with the mean bond stress (τ-) associated with each product. This is confirmed by experimental and numerical studies of Meszaros [5] and McVay et al. [8]. The uniform bond stress model for adhesive anchors is given by Eq. (3). This equation is valid for 4 ≤ hef/d ≤ 20, d ≤ 50 mm, and a bond area πdhef ≤ 58,000 mm2. — Nτ = τ- πdhef
(N)
(3)
According to Eligehausen et al. [6] and based on information presented in Cook et al. [7], the failure load of single bonded anchors is limited by the concrete breakout failure
To understand the behavior of adhesive anchors under tension loading, three-dimensional non-linear finite element analyses were performed with the program MASA developed by Ozˇbolt [9]. In this program, the concrete behavior is simulated by the microplane model described in detail in Ozˇbolt et al. [10]. To avoid steel failure, elastic behavior of the anchor steel was assumed. The bond behavior of the mortar was modeled in different ways. In Meszaros [5] and Li et al. [11], [12], an interface model was used that only transfers shear stress. The shear strength is influenced by compression and tension stresses in the concrete perpendicular to the anchor. In recent studies performed at the University of Stuttgart [13], the threads of the threaded rod were modeled and the mortar behavior was simulated using the microplane model with a proper calibration of the model parameters to represent the measured macroscopic mortar properties. The loading on the anchors was introduced under deformation control by applying incremental displacements to the anchor at the concrete surface. In the concrete breakout failure mode of cast-inplace and post-installed mechanical anchors the critical anchor spacing (scr) has been determined to be 3.0hef and the critical edge distance (ccr) to be 1.5hef. Results of the numerical investigation shown in Fig. 6 and Fig. 7 indicated that the embedment length (hef) was not an important
Fig. 5. Failure loads of single adhesive anchors as a function of anchor diameter, Eligehausen et al. [6]
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Based on the above considerations the failure load of adhesive anchor groups and/or anchorages located near edges can be calculated by Eq. (2) with Nb replaced by Nτ from Eq. (3) and using scr and ccr determined from Eq. (5). However, a further strength adjustment factor related to anchorages with adhesive anchors closely located should be accounted for. This proposed strength adjustment factor is presented in Eligehausen, Cook, and Appl [1] and will always be greater than or equal to 1.0.
5 Experimental investigation
Fig. 6. Principal compression stresses in concrete. Single adhesive anchors d = 12 mm, Appl and Eligehausen [14]
Fig. 8 shows the types of failures observed during the testing of quadruple groups of adhesive anchors [15]. In the two figures shown on the left side of Fig. 8, the embedment depth was kept constant and the anchor spacing was increased. The failure mode changed from a concrete breakout starting at the base of the anchors to a pullout failure with a shallow cone at a large spacing. The three figures shown on the right side of Fig. 8 are valid for anchor groups with a ratio s/hef = 1 but increasing embedment depth. The failure mode changes from a concrete breakout starting at the base of the anchors over a common partial concrete cone to an individual anchor pullout with shallow cones at the surface. The change in failure mode occurs because the load that can be introduced by bond into the concrete increases linearly with hef while the concrete breakout strength increases in proportion to 1.5 hef . Note that the numerically obtained failure modes agree with those observed in the experiments. However, the critical spacing scr evaluated from the experimental results differ from that obtained numerically (Eq. (5)). Based on the experimental results, the critical spacing scr should be approximated by Eq. (6). ⎛ τ ⎞ 0.5 scr = 2ccr = 20 d ⎜ ⎟ (mm) ⎝ 10 ⎠
Fig. 7. Principal compression stresses in concrete. Single adhesive anchor, d = 24 mm, hef = 20d, Appl and Eligehausen [14]
parameter in the definition of the critical spacing (scr) or critical edge distance (ccr) but that the bond strength of the adhesive and anchor diameter were significant factors. To determine the critical spacing, (scr) a large numerical parametric study with anchor groups was performed at the University of Stuttgart [14]. The parameters varied included anchor diameter, embedment depth, concrete strength, bond strength, and anchor spacing. In each individual numerical test series the anchor diameter, embedment depth, and bond strength were kept constant and the anchor spacing was varied. The critical spacing (scr) resulting from the numerical analysis is best described by Eq. (5). The critical edge distance (ccr) may be taken as one half of the critical spacing. ⎛ τ⎞ scr = 2ccr = 14.7 d ⎜ ⎟ (mm) ⎝ 10 ⎠
(5)
(6)
6 Behavioral model As a result of numerical and experimental work, a behavioral model was developed that best describes the failure loads of anchorages with adhesive anchors loaded in tension where the effects of anchor groups and/or edges needs to be accounted for. The behavioral model incorporates both the potential concrete breakout failure mode and potential bond failure mode. Both values are determined in accordance with the following and the lessor of the two represents the expected failure of the adhesive bonded anchors. The concrete breakout strength is determined by Eq. (2) using Eq. (1b) for Nb and with scr = 3.0hef and ccr = 1.5hef when calculating ANc and ANo. The bond pullout strength is determined by Eq. (2) using Eq. (3) for Nb with bond strength limited by Eq. (4) and with scr and ccr determined from Eq. (6) when calculating ANc and ANo. For design, appropriate capacity reduction factors or partial safety factors and nominal strengths must be addressed in developing code provisions to implement the findings of this research. It is suggested that the 5 % fractile of the bond strength be used for the design of adhesive
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Fig. 8. Failure modes of groups of adhesive anchors observed in tests, Lehr [15]
bonded anchors which should be adjusted to consider several influencing factors on adhesive anchor performance such as sensitivity to hole cleaning procedures and increased temperature as well as behavior under long term loads and in cracked concrete. The proposed behavioral model presented in Eligehausen, Cook, and Appl [1] agrees very well with the results of 415 group tests contained in a worldwide data base. Based on a comparison to 133 tests with single anchors close to an edge, the behavioral model is conservative for anchorages located very near to an edge. As discussed above, one particular strength adjustment factor that is always greater than or equal to 1.0 is not discussed in this paper and the reader should refer to Eligehausen, Cook, and Appl [1] for the full behavioral model.
7 Conclusion and acknowledgment In summary, this paper presents an overview of a behavioral model for adhesive bonded anchors loaded in tension presented in Eligehausen, Cook, and Appl [1]. We wish to express gratitude and sincere appreciation to the manufacturers and individuals contributing to the extensive numerical and experimental work necessary to develop this model. Sponsoring manufacturers were (in alphabetical order): fischerwerke, Hilti AG, and Würth KG. Dr. P. Pusill-Wachtsmuth of Hilti AG and Dr. R. Mallée of fischerwerke deserve special recogonition for their contributions over the years. Dr. B. Lehr, Dr. J. Meszaros, Dr. H. Spieth all deserve credit for this.
Notation ANco projected concrete failure area of a single anchor, for calculation of strength in tension if not limited by edge distance or spacing, mm2 ANc projected concrete failure area of a single anchor or group of anchors, for calculation of strength in tension, mm2 ccr edge distance where the strength of the anchor is not influenced by the free edge, mm d diameter of the anchor, mm d0 diameter of the hole, mm 20
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fcc hef — Nb — Ncb — Nτ scr ττ-max ψed,N
concrete compressive strength, measured on 200 mm cubes, MPa effective embedment depth of an anchor, mm mean basic concrete breakout strength in tension of a single anchor in uncracked concrete, N mean concrete breakout strength in tension of a single anchor at an edge or of a group of anchors in uncracked concrete, N mean bond pullout strength in tension of a single adhesive anchor in uncracked concrete, N anchor spacing where the anchor strength is not influenced by other anchors, mm mean uniform bond strength at the steel/mortar interface, MPa maximum mean uniform bond strength at the steel/mortar interface, MPa factor used to modify tensile strength of anchors based on proximity to edges of concrete member
References [1] Eligehausen R., Cook, R. A., and Appl. J.: “Behavior and Design of Adhesive Bonded Anchors”, ACI Structural Journal, American Concrete Institute (ACI), V. 103, No. 83, November- December 2006, pp. 822–831. [2] Fuchs , W., Eligehausen, R., and Breen, J. E.: “Concrete Capacity Design (CCD) Approach for Fastening to Concrete,” ACI Structural Journal, V. 92, No. 1, January–February 1995, pp. 73–94. [3] Eligehausen, R., and Balogh, T.: “Behavior of Fasteners Loaded in Tension in Cracked Reinforced Concrete”, ACI Structural Journal, V. 92, No. 3, May–June 1995, pp. 365–379. [4] Cook, R. A., and Konz, R. C., “Factors Influencing Bond Strength of Adhesive Anchors”, ACI Structural Journal, V. 98, No. 1, January–February 2001, pp. 76–86. [5] Meszaros, J.: “Tragverhalten von Verbunddübeln im ungerissenen und gerissenen Beton” (Load-bearing behavior of bonded anchors in uncracked and cracked concrete). Doctoral thesis, University of Stuttgart, 1999. [6] Eligehausen, R., Appl, J. J., Lehr, B., Meszaros, J., and Fuchs, W.: “Tragverhalten und Bemessung von Befestigungen mit Verbunddübeln unter Zugbeanspruchung, Part 1: Einzeldübel mit großem Achs- und Randabstand” (Load-bearing Behavior and Design of Fastenings with Adhesive Anchors
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under Tension Loading – Part 1: Single Anchors with Large Axial and Edge Spacing), Beton und Stahlbetonbau 99, No. 7, July 2004, pp. 561–571. [7] Cook, R. A., Kunz, J., Fuchs , W., and Konz, R. C.: “Behavior and Design of Single Adhesive Anchors under Tensile Load in Uncracked Concrete”, ACI Structural Journal, V. 95, No. 1, January–February 1998, pp. 9–26. [8] McVay, M., Cook, R. A., and Krishnamurthy, K.: “Pullout Simulation of Post-installed Chemically Bonded Anchors”, Journal of Structural Engineering, ASCE, V. 122, No. 9, September 1996, pp. 1016–1024. [9] Ozˇbolt, J.: “MASA-Finite Element Program for Nonlinear Analysis of Concrete and Reinforced Concrete Structures”, Research Report, Institute of Construction Materials, University of Stuttgart, 1998, 74 pp. [10] Ozˇbolt, J.; Li, Y.-J., and Kozar, I.: “Microplane Model for Concrete with Relaxed Kinematic Constraint”, International Journal of Solids and Structures, V. 38, 2001, pp. 2683–2711. [11] Li, Y.-J., Eligehausen, R., Ozˇbolt, J., and Lehr, B.: “Numerical Analysis of Quadruple Fastenings with Bonded Anchors”, ACI Structural Journal, V. 99, No. 2, March–April 2002, pp. 149–156. [12] Li, Y.-J., and Eligehausen, R.: “Numerical Analysis of Group Effect of Bonded Anchors with Different Bond Strengths”, RILEM Proceedings PRO 21, Connections between Steel and Concrete, RILEM Publications, http://www.rilem.net/pro21.php, 2001, pp. 699–707. [13] Appl, J., Eligehausen R.: “Gruppenbefestigungen mit Verbunddübeln – Bemessungskonzept”, (Adhesive Anchor Groups – Design Concept –), Report No. 03/27-2/55, Institute of Construction Materials, University of Stuttgart, 2003 (in German). [14] Appl, J., Eligehausen R.: “Gruppenbefestigungen mit Verbunddübeln – Numerische Untersuchung”, (Adhesive Anchor Groups – Numerical Investigations –), Report No. 05/072/66, Institute of Construction Materials, University of Stuttgart, 2005 (in German).
[15] Lehr, R.: “Tragverhalten von Verbunddübeln im ungerissenen unter zentrischer Belastung im ungerissenen Beton – Gruppenbefestigungen und Befestigungen am Bauteilrand“ (Load-Bearing Behavior of Adhesive Anchors under Axial Tension in uncracked concrete – Anchor Groups and Anchors close to an edge). Doctoral thesis, University of Stuttgart, 2003 (in German).
Prof. Ronald A. Cook, P.E University of Florida Department of Civil Engineering 365 Weil Hall Gainesville, FL 32607, USA
[email protected]
Prof. Dr.-Ing. Rolf Eligehausen University of Stuttgart Institute of Construction Materials Pfaffenwaldring 4 70550 Stuttgart, Germany
[email protected]
Dipl.-Ing. Jörg J. Appl Engineering Office Eligehausen & Asmus Hauptstraße 4 70563 Stuttgart, Germany
[email protected]
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