Prying of a Large Span Base Plate Undergoing a Moment Load Applied by a Round Pier

Transcription

1 Prying of a Large Span Base Plate Undergoing a Moment Load Applied by a Round Pier by Anastasia Wickeler A thesis submitted in conformity with the requirements for the degree of Masters of Applied Science and Engineering Graduate Department of Mechanical & Industrial Engineering University of Toronto Copyright by Anastasia Wickeler 2017

2 Prying of a Large Span Base Plate Undergoing a Moment Load Applied by a Round Pier Anastasia Wickeler Masters of Applied Science and Engineering Graduate Department of Mechanical & Industrial Engineering University of Toronto 2017 Abstract Large span base plates with a moment load applied, in any direction, to the centre of the plate by a round pier are commonly used in the design of anchors for façade access systems. There is no current method of predicting the behaviour of these large span plates under a moment load. Six anchor base plate configurations are physically tested. The deflection of the plate is analysed using digital image correlation (DIC) to track the change in location of points on the base plates under various applied loads. The shapes are plotted and used to determine at what point the plates transition from linear to nonlinear deformation. A method of predicting the moment resistance of the base plates for each test was proposed and a finite element model for the base plates was analysed and validated using the test data. ii

3 Table of Contents Chapter 1 Introduction Safety Anchor Design Thesis Objectives Thesis Organization... 4 Chapter 2 Background and Literature Survey Safety Anchor and Davit Base Plate Introduction Types of Base Plate Connections Modelling of Cylindrical Steel Structures to Concrete Foundations Modelling of Column Base Plates to Concrete Foundations Modelling of Beam to Column Bolted Connections Modelling Issues and Limitations Summary Chapter 3 Experimental Setup Introduction to the Experimental Setup Test Objectives Measuring Techniques and Equipment Deformation Measurements Strain Measurements Safety Anchor Configurations and Geometry Test Frame Summary of the Complete Experimental Setup with Equipment Chapter 4 Analysis of Experimental Testing: Anchor Plates Under Moment Load Experimental Testing Overview Test 01: Four bolts base plate connection; horizontal load parallel to the supporting HSS Test 01 Setup Test 01 Strain Gauge Data and Analysis Test 02: Four bolts base plate connection; horizontal load at a 45 angle relative to the supporting HSS iii

4 4.3.1 Test 02 Setup Test 02 DIC Data and Analysis Test 03: Four bolts base plate connection; horizontal load perpendicular to the supporting HSS Test 03 Setup Test 03 DIC Data and Analysis Test 04: Two bolts base plate connection; horizontal load parallel to the supporting HSS Test 04 Setup Test 04 DIC Data and Analysis Test 05: Two bolts base plate connection; horizontal load perpendicular to the supporting HSS Test 05 Setup Test 05 DIC Data and Analysis Test 06: Two bolts base plate connection; horizontal load perpendicular to the supporting HSS Test 06 Setup Test 06 DIC Data and Analysis Comparison of Different Anchor Geometry Results Material Properties of the Steel Base Plate Moment Resistance of the Base Plates Chapter 5 Finite Element Analysis Finite Element Model Model Parameters and Constraints Finite Element Analysis Stress and Deflection Results Analysis Test 01 FEA Results Test 02 FEA Results Test 03 FEA Results Test 04 FEA Results Test 05 FEA Results Test 06 FEA Results FEA Model Conclusions Chapter 6 Conclusions and Recommendations iv

5 6.1 Conclusions Recommendations References v

6 List of Tables Table 4-1: Test 01 Yield Loads at the Strain Gauges Table 4-2: Max. loads in the base plates before permanent deformation occurs Table 5-1: Material properties used in the FEA model vi

7 List of Figure Figure 1.1: Anchor system general setup... 3 Figure 2.1: Anchor with connection bolts embedded in concrete... 6 Figure 2.2: Anchor with connection bolts wrapped around an I beam section... 6 Figure 3.1: Moment Load on Safety Anchor Base Plate Figure 3.2: Example of checkerboard images required for camera calibration Figure 3.3: Glare on base plate due to strain gauges Figure 3.4: Typical anchor currently in production vs. test anchor Figure 3.5: The six anchor test geometries with load directions (all loads are parallel to the top plate on the anchor base plate) Figure 3.6: Test frame with HSS cross-section dimensions and moment resistances Figure 3.7: Full experimental test setup Figure 3.8: Top left: steel plate with scribed lines; bottom right: galvanized steel plate with scribed lines Figure 3.9: Steel plate with lines scribed after plate sprayed with blue tool dye paint Figure 4.1: Test 01 Anchor setup and direction of applied test load Figure 4.2: Test 01 Strain Gauge Locations Figure 4.3: Test 01 strain gauge 1 data Figure 4.4: Test 01 strain gauge 2 data Figure 4.5: Test 01 strain gauge 3 data Figure 4.6: Test 01 strain gauge 4 data Figure 4.7: Line along which deflection measurements were taken; test load pull the pier to the right in this image Figure 4.8: Test 01 Deformation under 15kN Load Figure 4.9: Test 01 Deflection at the back of the base plate under 15.5kN load; strain gauge 4 can be seen on the right of the image and strain gauge 3 on the left Figure 4.10: Test 02 Anchor setup and direction of applied test load vii

8 Figure 4.11: Test 02 line along which deformation was measured; test load applied parallel the red line, to the right of the image Figure 4.12: Test 02 Failure of the anchor base plate Figure 4.13: Test 02 plot of the change in shape of the base plate along a line on the side of the plate Figure 4.14: Test 03 Anchor setup and direction of applied test load Figure 4.15: Test 03 Maximum deformation in the base plate before the observable weld failure Figure 4.16: Test 03 Line on side of plate over which permanent deformation was measured; horizontal load pulled to the right Figure 4.17: Test 03 Line at back of plate over which permanent deformation was measured; horizontal load pulled to the right Figure 4.18: Test 03 Out of plane deflection at the side of the base plate Figure 4.19: Test 03 Out of plane deflection at the back of the base plate Figure 4.20: Test 04 Anchor setup and direction of applied test load Figure 4.21: Test 04 Deformation of anchor base plate at 14.0kN load Figure 4.22: Test 04 Line at which permanent deformation in the base plate was measured Figure 4.23: Test 04 Out of plane deflection along the side of the base plate Figure 4.24: Test 05 Anchor setup and direction of applied load Figure 4.25: Test 05 shape of base plate under 10.0kN load; load pulled to the left in this image Figure 4.26: Test 05 Line along which deformation in plate is measured; load pulled to the left in this image Figure 4.27: Test 05 Out of Plane Deflection in the base plate Figure 4.28: Test 06 Anchor setup and direction of applied load Figure 4.29: Test 06 Shape of deflection in the plate with a 10.0kN load; load pulling the anchor to the left in this image Figure 4.30: Test 06 Line on side of plate at which deflection was measured Figure 4.31: Test 06 Out of plane deflection at side of plate viii

9 Figure 4.32: Test 06 Shape of deflection in the plate with a 10.0kN load; load pulling the anchor to the right in this image Figure 4.33: Test 06 Line along the back of the base plate along which deflection was measured Figure 4.34: Test 06 Out of plane deflection at back of plate Figure 4.35: Tensile test dogbone dimensions; 1/4" plate thickness Figure 4.36: Failure of tensile test coupons Figure 4.37: Section properties for a rectangular plate, taken from the Handbook of Steel Construction [102] Figure 4.38: Test 01 base plate bending lines used for calculating Z Figure 4.39: Test 02 base plate bending lines used for calculating Z Figure 4.40: Test 03 base plate bending lines used for calculating Z Figure 4.41: Test 04 base plate bending lines used for calculating Z Figure 4.42: Test 05 base plate bending lines used for calculating Z Figure 4.43: Test 06 base plate bending lines used for calculating Z Figure 5.1: FEA mesh Figure 5.2: FEA constraints and load Figure 5.3: Test 01 FEA stress in anchor Figure 5.4: Test 01 FEA stress in base plate Figure 5.5: Test 01 FEA out of plate deformation of base plate Figure 5.6: Test 02 FEA stress in anchor Figure 5.7: Test 02 physical test image showing plate fracture Figure 5.8: Test 02 FEA stress in base plate Figure 5.9: Test 02 FEA out of plane deformation in base plate Figure 5.10: Test 03 FEA stress in anchor Figure 5.11: Test 03 physical test image showing plate fracture Figure 5.12: Test 03 FEA stress in base plate Figure 5.13: Test 03 FEA out of plane deformation in base plate Figure 5.14: Test 04 FEA stress in anchor Figure 5.15: Test 04 shape of plate under test load of 13.0kN Figure 5.16: Test 04 FEA stress in base plate ix

10 Figure 5.17: Test 04 FEA out of plane deformation in base plate Figure 5.18: Test 05 FEA stress in anchor Figure 5.19: Test 05 image showing crack initiation around weld at the back of the pier Figure 5.20: Test 05 FEA stress in base plate Figure 5.21: Test 05 FEA out of plane deformation in base plate Figure 5.22: Test 06 FEA stress in anchor Figure 5.23: Test 06 fracture in base plate during experimental testing Figure 5.24: Test 06 FEA stress in base plate Figure 5.25: Test 06 FEA out of plane deformation in base plate x

11 1 Chapter 1 Introduction As high-rise buildings become increasingly complex, creating systems to safely access the outside of buildings is becoming more challenging. Features such as cascading balconies, large terraces, and small roof footprints all combined to create difficulties in creating systems that can access areas on the façade of a building. Façade access is important for cleaning, repairing and retrofitting buildings as they age. The challenges posed by modern architecture with respect to larger balconies or complex building shapes usually results in the need for longer outreach arms on davit systems. The longer arms increase the moment loads on the base of a machine. These bases must be designed to withstand higher loads, but still be attached to typical roof structures. This thesis will focus on the behaviour of safety anchor base plates. These base plates are currently being designed based on accepted industry standards. The actual behaviour of the plates under the applied load are not well understood [1]. A deeper knowledge of anchor base plates would be useful in the design of new equipment for increasingly complex façade access systems. 1.1 Safety Anchor Design Safety anchors are used as points in façade access systems to which workers and equipment are tied when either working suspended off the edge of a structure or close to an area with a fall hazard. In theory, anchor points may undergo a dynamic load during a fall arrest situation. To account for this, safety anchors are design to withstand static loads that have a safety factor of at least 4:1 compared to the maximum expected static load [2]. In addition, safety anchors are tested on a yearly basis to ensure that they are still acceptable for use. Façade access systems are designed so that workers can safely access any area on the outside of a building. To meet this requirement, safety anchor points are designed so that

12 the loads on the suspension points can be applied in any direction. For this reason, anchor piers connecting the anchor point to which workers tie off on to the base plate are typically round. Sections with round cross-sections have the same section properties in all directions, making them ideal for structures that are required to withstand a load applied in any direction. Anchors for use on the exterior of buildings are typically made from structural steel. The structures are usually galvanized for weather protection. They are commonly fastened to the building structure by rods embedded in concrete, being bolted to the existing building structure or by bolts wrapped around steel structural sections used in the framing of buildings. 1.2 Thesis Objectives The purpose of this thesis was to analyse the behaviour of base plates under a moment load. The moment was applied to the centre of the base plate by a round pier welded to the centre of the plate. How the moment load would be distributed throughout the plate was unknown (See Figure 1.1 for anchor structure, support locations and applied force location). The objective of this thesis was to analyse how the anchor base plate behaved under the moment load and to determine a method of predicting the load at which the anchor base plate will transition from elastic to plastic deformation. Because the base plate experienced out of plate bending due to the moment load at the centre of the plate, some sections of the base plate were loaded in compression and other sections were in tension. How the loads are distributed was unknown. This thesis explored how the base plate deformed under the moment load. Out of plane deformations of the base plates were measured, a method analytically predicting the load at which the base plates start permanently deforming was proposed and finite element analysis (FEA) was performed to simulate the behaviour of the anchor system observed during the experimental testing. 2

13 Figure 1.1: Anchor system general setup Six different configurations of test anchors were experimentally tested. The test setup was designed such that the force applied at the top of the anchor point would, as much as possible, be entirely transferred to the base plate as a moment load. The anchor pier and supporting structure were designed to be capable of supporting higher loads than the base plate so that the base plate was the first component of the structure to permanently deform. The results of the experimental testing were used to propose a method of analytically calculating the moment resistance of the base plate. There were no methods for analytically calculating the maximum load an anchor base plate can withstand. Anchor base plates typically have large spans to accommodate installation on typical roof structures. Redesigning the configuration of the plate to meet the geometrical limits of previously studied base plates was not possible. A finite element model for the base plate was created and compared to the test results for validation. The model was built to include all necessary components that affected the behaviour of the anchor base plates. Like with the experimental testing, the finite element model was designed such that the moment load was concentrated in the base plate. 3

14 1.3 Thesis Organization This thesis is divided into four sections. Chapter 2 starts with a background and literature survey discussing various studies regarding the analysis of structural base plates and connection plates. Studies were researched that involved both experimental testing components and finite element modelling. Chapter 3 provides an in-depth explanation for the design of the experimental test setup for the anchor base plates being studied in this thesis. A test frame to support the six different anchor configurations was designed and various measurement methods were explored. This chapter also included details regarding how deformation in the base plates was measured. This is especially important for interpreting the results of the experimental testing. The next section, Chapter 4, analyses the data acquired during the experimental testing. The test was performed as described in the previous section: Chapter 3. Through the observations in this section, an analytical method of predicting the moment resistance in the plate was proposed. Chapter 5 discussed the finite element model of the anchor structure. The model made in this section was designed to represent the anchor structures tested using the setup described in Chapter 3. The finite element analysis results in Chapter 5 are also compared with the results of the analysis in Chapter 4 regarding the experimental testing of the anchor base plates. This thesis ends with a conclusion for the thesis as a whole and future recommendation. 4

15 5 Chapter 2 Background and Literature Survey 2.1 Safety Anchor and Davit Base Plate Introduction Safety anchors and davits are products commonly used in façade access systems for building structures. The loading requirements for safety anchors and davits are given based on building design codes. The products themselves are designed using a variety of sources; for example, calculations for the strength of anchor bolts in concrete are performed based on Canadian Standards Association codes (CSA-A32.2 Design of Concrete Structures; Annex D: Anchorage [3]), the strengths and load resistances of steel components are determined using the Handbook of Steel Construction, etc. Most components of safety anchor and davit bases can be modelled analytically or easily tested. The one component, however, that is difficult to model is the base plate used to connect safety anchor and davit bases to the building structure. Base plates for safety anchor and davit bases consist of a square steel plate with a round steel pier welded in the centre and four connection bolts in the four corners of the plate. The bolts in the corners of the plate can be fastened to building structures using multiple methods; they can be embedded in concrete (Figure 2.1), bolted to an existing structure or the bolts can be wrapped around a beam section (Figure 2.2). The difficulty in modelling the base plate is predicting how the plate will react when a moment load is applied (in any direction) by the round pier welded to the centre of the plate.

16 Figure 2.1: Anchor with connection bolts embedded in concrete Figure 2.2: Anchor with connection bolts wrapped around an I beam section Current analytical methods for predicting base plate reactions under given loads assume that the sections of plate extending beyond the pier welded to the base plate acts as a cantilever and the pressure distribution under the base plates is linear, which results in conservative base plate designs[1, 4-7]. This is due to the lack of understanding of how loads and stresses are distributed throughout the base plate and due to the assumptions used to simplify calculations. 6

17 Finite element analysis (FEA) has also been used as a means of predicting the behaviour of base plate connections [8-12]. Given the many factors that affect the reactions of bolted base plates and connection plates under given loads, FEA models are made and applied to very specific applications. Base plate behaviour predictions obtained from these models are specific to base plate connection geometry and loading conditions, therefore the results cannot be extrapolated and applied to different base plate connections. The accuracy of finite element (FE) models is confirmed through physical testing of the base plate connection. Typically, strain and deflection measured during physical testing is compared to the strain and deflection obtained using FEA [5]. One of the advantages of correctly representing a model in FEA is that FEA can provide engineering data that is difficult or impossible to measure during physical testing, such as internal stresses in the connection plate. Results obtained using FEA have varying degrees of accuracy due to assumptions made, model accuracy, software limitation etc. 2.2 Types of Base Plate Connections Although there is no previously performed research specific to the design of safety anchor and davit base plates, there are other, more commonly used, base plate designs that have been studied. Previously examined base plates include base plate connections for signposts [13], column base plate connections to concrete foundations [14-18], and beam to column bolted connections. A variety of approaches have been used to model these connection plates. Studies have analysed base plates through experimental testing [19-24], creating configuration specific calculations for given loading conditions and base geometries [25], and used computer simulation models to attempt to predict base behaviour achieved through physical tests [26-33]. Understanding the successes and failures of previously modelled base plate connections will help guide the process of creating an accurate FEA model for the design of safety anchor and davit base plates. Regarding the creation of FE models to represent base plates, there are some common features of importance for all the previously studied base plate designs. In the interest of 7

18 making the FEA efficient, only half of any base plate connection that has a symmetrical geometry is made and analysed. Mesh sizes are reduced in areas that have large changes in internal stresses over relatively small areas. These locations include, but are not limited to, locations where sections are welded to base plates, the segment of bolts that go through the base plate and around boltholes. Given all the assumptions and variables required in the representation of base plates using FEA, it is important to thoroughly understand the capabilities and limitations of FE programs and to have a clear scope and definition of the design being modelled Modelling of Cylindrical Steel Structures to Concrete Foundations Round hollow structural steel sections welded to square base plates that are bolted to a concrete foundation are used for several applications. These include traffic sign support structures, industrial chimneys, wind towers, and cranes. Typical column base plate to concrete foundation applications are studied for columns with I and H cross-sections. The use of hollow round steel sections, rather than conventionally used sections, welded to the base plate affects how the loads are transmitted through the base plate. Analytical calculations for the design of steel base plates in columns have been modified and adapted to represent the connection between cylindrical steel structures and concrete foundations [34, 35]. Traffic sign support structure base plates are square, with four bolt connections in the four corners of the plate and a round hollow section welded to the centre of the base plate. These base plates undergo compression loads, moment loads, and torsion loads. The base plates were originally designed using physical testing. Production companies have stock configurations of traffic sign base plates and the geometrical configuration of the plates are kept constant. In order to produce traffic sign base plates with varying geometries, Owens et al. created standard procedures to analytically model traffic sign base plates [13]. These procedures operate under the assumption that the mast is sufficiently strong to transfer all 8

19 loads to the base plate, and the plate has adequate strength for transferring shear and torsion forces to the bolts. The calculations determine the forces on the four bolts in the corners of the plate, however separate calculations/analysis must be done to check that the bolts have adequate strength to withstand any applied loads. To calculate the forces in the bolts, there is an assumed pressure line location. When a moment load is applied to the base plate, there is a resulting compression load applied to part of the base plate, and an uplift on the remaining section of the base plate. The line through the plate that marks the transition between the compressive and tensile load is the pressure line. For this analysis, the pressure line is assumed to be perpendicular to the direction of the moment load and tangent to the round mast. Due to the extensive computational effort required to perform the analytical calculations, a spreadsheet was created to iteratively solve different base plate designs within a specific scope. Base plate geometry and loading conditions are inputted into the program and the minimum plate thickness is then determined. Hoang et al. (2015) adapted analytical base plate procedures to analyse the connection between cylindrical steel structures and concrete foundations typically used for industrial chimneys, wind towers, and cranes [34]. These structures have mast diameters between 2m and 6m. This analysis utilized the component method to analyse the base plate in the elastic region of use. The following components were analysed in this application: compression and bending in the round structural wall, flexion and shear in the base plate, torsion and bending in the bolts, bending in the repartition plate, and compression in the concrete foundation. Both above mentioned analytical methods of analysing the connection between cylindrical steel structures and concrete foundations employ only analytical means of modelling. They are geometry specific and the analysis cannot accurately be adapted to represent the reaction of safety anchor and davit bases under moment loads. 9

20 2.2.2 Modelling of Column Base Plates to Concrete Foundations Base plates connecting columns to concrete foundations are an important part of steel structures in buildings [36-42]. Columns typically support large compressive axial loads, which result in large compressive loads on the concrete foundation. There are instances, however, when moment loads are also applied to column bases. Column base plates undergoing moment and axial loads, versus only axial loads, behave differently with respect to internal stress distribution and deformation. Literature that specifically examines the effects of a moment load on column base plates will be the focus of this section. There are many different configurations of connections between column base plates and concrete foundations. Geometrical differences include column sections (such as hollow square section, hollow rectangular sections and W sections (I beams)), plate size (plate length, width and thickness), and anchor bolt configuration, diameter and embedment depth. Differences in physical geometries and loading conditions of column base plates have a large influence on their behaviour. A variety of FE programs have been used to model different configurations of column base plates, including commercially available programs such as ABAQUS [43-47] and ANSYS [48-50], and proprietary programs written by various academic institutions for their own use, such as FEABOC [51, 52] and SUT_DAM [53]. The success with which column base plates are modelled is dependent on the complexity of the models and any assumptions made to simplify the analysis. Early FE models were very basic due to computer limitations. Krishnamurthy et al. (1989, 1990), using the FEA program FEABOC written by Krishnamurthy, modelled column base plates under a moment load using 2D and 3D analysis [51, 52]. In the original simplified model, only the section of the anchor bolt (modelled with a square cross-section) passing though the base plate was included in the FE model. The assumptions that the influence of the bolt head and the section of the anchor bolt embedded in the concrete are negligible yielded inaccurate results when compared to the behaviour of the column base plate during physical testing. The model was later refined to include the previously omitted sections of 10

21 the anchor bolt. The improved FE model could qualitatively predict the reaction of the column base plate under an applied load [51, 52]. As the capabilities of FE programs improve, FE models are capable of modelling column base plates more accurately and with fewer restrictions due to software limitations. Despite these advancements, it is still required that assumptions be made when the column base plate FE model is created. For example, some FE column base plate models assume that the anchor rods undergo only tensile loads [4], other models constrain the vertical displacement of the anchor bolts at the end furthest from the base plate, then allow the rest of the bolt to react accordingly [53]. Seemingly small changes in assumptions and restraints can greatly influence FE results. With careful analysis and a thorough understanding of the behaviour of column base plates under a given load, it is possible to create an accurate FE model defining the behaviour and stress distribution in a base plate. Unfortunately, due to the large number of variables (including differences in geometry and loading conditions), results for a given column base plate configuration cannot be extrapolated and used to predict the behaviour of different column base plate models. General, quantitative, trends in column base plate behaviour under moment loading can be observed when geometric variables are changed. As plate thickness and bolt diameter are increased, the overall stiffness of the column base plate increases; this affects the internal stress distribution in the base plate [4, 35, 51-54] Modelling of Beam to Column Bolted Connections Beam to column bolted connections are common in steel structures. These connections usually involve a beam welded to a connection plate. The plate has a series of bolt holes used to bolt the connection plate to the column, which has matching holes for the bolts. Typically beam to column bolted connections are subject to a shear load through the connection bolts. Some connections also experience a bending load on the beam, which results in a moment load on the base plate [55-61]. The effects of this bending load will 11

22 cause the connection plate to behave differently compared to a connection plate only subject to a shear load. There are multiple FE models that have been made to examine the stress distribution and deflection in connection plates undergoing a moment load. Finite element models of beam to column bolted connections have been analysed using many different software packages, such as ANSYS [5, 62] and ABAQUS [6, 63]. With careful consideration of all the factors involved due to loading conditions and geometries, these software packages can be used to accurately model the behaviour of beam to column bolted connections. Again, the geometry of the connection has a large effect on base plate behaviour such that results cannot be extrapolated beyond a given scope of study for a beam to column bolted connection analysis. There are many possible parameters to consider in the design of beam to column bolted connections, such as whether the end plate extends beyond the beam, beam and column sections used, bolt grade and diameter, bolt spacing, bolt pretension load, load applied to beam, connection plate thickness, steel yield strength, co-efficient of friction etc. There are also assumptions made in the FE models to be able to run the FEA. A common assumption, which may affect the accuracy of FE models, is that there is no deflection in the column to which the base plate is attached [3]. Different parameters have varying degrees of influence on the overall behaviour of beam to column bolted connection behaviour under applied load. Overall, the two most influential variables are plate thickness and bolt diameter [5, 62]. Plate thickness is important because it affects the rigidity of the connection. This connection is semi-rigid and changes in rigidity affect the stress and pressure distribution throughout the connection plate. This in turn affects how the load is distributed to the bolts [5, 62]. Relatively thicker plates are more rigid, have smaller deflections, and tend to load the bolts mainly in tension. Plates that are thinner have greater deformations and apply prying loads to the connection bolts. When a bending load is applied to the connection plate, part of the plate pulls away from the column to which it is bolted, and a section of the connection plate pushes against the column. The line dividing these sections of the plate is called the yield line. The location of the yield line is directly related to how the 12

23 connection plate distributes the bending load to the bolts and to the deflection of the connection plate. The location of the yield line cannot be accurately determined through analytical means; FEA determines the location of the yield line through iterative calculations [64, 65]. Depending on the thickness of the connection plate, as well as the diameter and strength of the connection bolts, beam to column bolted connections tend to fail either due to bolt failure or connection plate failure at the yield line [5, 62]. Bolted connections between beams and columns can have another load at bolt connections apart from shear and bending forces applied by the beam, such as; bolt pretension forces. When the bolts are pre-tensioned, an initial tension load is added to the bolts and it affects the deflection of the connection plate. The compression load added by the washer to the plate around bolt holes makes it more difficult for the connection plate to slide against the steel column due to the increase in friction forces [5, 64-66]. When bolt pretension is considered as part of a FE model, the loading on the connection is done in two steps. First, the analysis is run with only the bolt tension load. Second, the bending and shear loads are added to the beam and the simulation is run again. 2.3 Modelling Issues and Limitations All of the above-mentioned connection plates are analysed for specific base plate applications and the results cannot be extrapolated to predict the behaviour of safety anchor and davit base plates. The specific loading conditions and base plate geometries of previously analysed moment connection in base plates have limited scopes which do not include the requirements for safety anchor and davit base plate designs. The geometry and loading of the cylindrical steel structures to concrete foundations are the most similar to that of safety anchor and davit bases. This is due to the fact that the loads can be applied in any direction and the mast welded to the base plate is round. The types of loading on the connection vary depending on the application, and the geometry is only similar with respect to the section used. Safety anchor and davit base plates are unique in 13

24 that the length of the base plate is relatively long compared to the diameter of the round pier. The large space between the pier and bolt locations in the plate will affect the way the load is distributed through the base plate. Furthermore, the analysis of cylindrical steel structures to concrete foundations is solely based on analytical calculations which, given all the assumptions required to solve the calculations, tend to yield conservative base plate designs. The utilization of FEA to model safety anchor and davit base plates has the potential to give more accurate results. With respect to column to concrete connections and beam to column connections, the structural steel beam sections used are all hollow square sections, hollow rectangular sections or I beam sections. There was no analysis of the influence of circular hollow steel structural section on the behaviour of connection base plates. The reason that these sections, and not circular sections, are used in beams and columns is that the moment or bending loads acting on these structures are applied in one, predictable direction. These sections are chosen to be strong in the direction required given the applied loads. Circular sections are used for safety anchor and davit bases because the given load can be applied in any direction. Round sections ensure that the strength of the section is the same in every direction. The square base plate with the connection bolts in the four corners, however, does not have the same load resistance in every direction. The orientation of the moment load applied to the base plate will affect how the internal loads are distributed throughout the plate and how the base plate will deform. An accurate FE model can help determine the effects of different load directions on the safety anchor and davit base plates. 2.4 Summary Overall there are many FE models that successfully predict the behaviour of base plates in different scenarios. Therefore, it should be possible to create a FE model for the analysis of safety anchor and davit base plates. The results of FEA will have to be compared to physical testing of safety anchor and davit base plates, as there is no accurate analytical 14

25 model for the prediction of the reactions of safety anchor and davit base plates under a moment load. 15

26 16 Chapter 3 Experimental Setup 3.1 Introduction to the Experimental Setup The test setup for the experimental section of this thesis played an important role in determining the accuracy of the physical testing and the measurements that could be taken for both the analytical section of the thesis (Chapter 4) and for verifying the FEA model created in a subsequent section of this thesis (Chapter 5). This chapter explained how the test was designed to meet the objective of this thesis: analysing the deflection in the anchor base plates when a moment load was applied to the centre of the plate by a round anchor pier. It also explored different possible measuring methods that could have been used to track the change in shape of the base plate. The designed experimental test setup and selected measurement methods described in this section were used in Chapter 4 in the discussion of the loads under which the anchor base plates transitioned from elastic to plastic deformation. 3.2 Test Objectives The goal of the experimental testing was to analyse the behaviour of safety anchor base plates under typical loading conditions as required by CSA Z271 [2]. The carbon steel base plate had a moment load applied through a round pier welded to the plate s centre. The plate sat on top of a rectangular steel hollow structural section (HSS) and was held in place by threaded rods (two or four rods depending on the design) in the corners of the plate. The threaded rods wrapped around the HSS and bolted through a steel angle section under the HSS (See Figure 3.1 for anchor setup and moment load location for one of the test configurations). The base plate was expected to experience out of plane bending and deflection between the round steel pier and the bolts. The results of the testing were used

27 to determine an analytical method of predicting when the base plates start to undergo plastic deformation. Figure 3.1: Moment Load on Safety Anchor Base Plate 3.3 Measuring Techniques and Equipment Deformation Measurements In this experiment, the out of plane deflection of a 10 x 10 plate, 3/8 thick, was be measured. Loads were applied incrementally to the anchor. After each load was applied, the load was removed and measurements of the plate shape were taken before the next load increment was applied. This process was repeated after each load increment until the system started to plastically deform. The data was used to determine when the plate started permanently deforming. Due to the moment load applied to the centre of the plate through the round pier, the deflection of the plate was varied throughout the length and width of the plate. Given the unique configuration and loading of the base plate, it was not possible 17

28 to accurately predict the behaviour of the plate under the moment load; including the areas of maximum and minimum deflection, stress and strain. Therefore, when the deflection in the plate was measured, it was required that the change in location of points over the entire top surface of the plate be tracked to properly examine the overall change in shape of the base plates. There are multiple measuring techniques used to determine changes in position during tests. The simplest of measurement methods would be to use a ruler for measuring a straight distance. More accurate tools for length measurements include callipers and point lasers; these however also could only measure the distance in a straight line. These measurement techniques would not have been practical for tracking the change in shape of the base plates. Every point on the plate would have had to have been manually measured at each load increment. In addition, there would need to be a reference set up to which the point locations could be measured to track changes in position. The test frame underneath the anchor base plate and the round pier extending above the anchor base plate further hampered setting up a reference. When a load was applied to the pier, the pier may also have deformed and interfered with any reference geometry that was set up for measuring purposes. There exist laser scanners that can scan and record the shape of surfaces. However, these systems and their related software (required for interpreting data) were costly. Since these systems were outside the budget for this project, a different and more cost-effective measurement method was found. Digital image correlation (DIC) is another measuring method that could be used to track the 3D movement of points [67-73]. It required the use of two or more cameras taking synchronized images, and then using the images to find the 3D world coordinates of points seen by both images [74, 75]. The process of translating 2D image coordinates from multiple cameras into 3D world coordinates is known as triangulation [76-79]. DIC is more frequently used in experimental mechanics due to its ability to measure displacement both in-plane and out-of-plane [80-85]. This displacement data can be used to graph the change in shape of structures due to applied loads. 18

29 To accurately use DIC, the cameras had to be properly calibrated [86-88]. There were multiple valid techniques and programs that could have been used for camera calibration [89-97]. For this experiment, the Camera Calibration Toolbox for MATLAB, written by Jean-Yves Bouget [98-101], was used to calibrate the cameras. This MATLAB code could be used to calibrate a pair of cameras. This experiment used four cameras positioned around the base plate to capture images. The reason for this setup was that it allowed every point on the base plate to be captured by at least two cameras simultaneously, providing the ability for every point location on the plate to be determined. The cameras had to be calibrated in pairs and the data collected from different pairs of cameras was combined to determine the overall behaviour of the entire plate. The calibration was performed by taking a series of synchronized images of a checkerboard pattern that can be seen by the camera pairs (See Figure 3.2 for example of the checkerboard images taken by one camera). These images were uploaded into the program and, through a series of functions, the calibration parameters, including focal length, principal point, skew coefficient, distortions, rotations, and translations, were calculated. These parameters, along with the pixel coordinates of a point from the left and right cameras, were then inputted into the triangulation code to calculate the 3D world coordinates from the point from the point of view of the left and right cameras. Figure 3.2: Example of checkerboard images required for camera calibration 19

30 Once the cameras were calibrated, the distance between pairs of points on the checkerboards was measured using DIC and compared to the distance measured between these same two points using a calliper. The squares on the grid used for calibrating the cameras had dimensions of 29.0 mm by 29.0 mm. Using DIC, the average length between two grid corner points was 29.0 mm, and the standard deviation of this measurement was 0.1 mm. These measurements were taken between the same two points on 152 images, taken from eight different stereo calibrated camera pairs. The average length measured between the grid point corners, and the accompanying standard deviation, showed that using DIC for measuring deformation in the base plates would provide results accurate enough to analyse the deformation in the base plates. The 3D world coordinates determined by the Camera Calibration Toolbox for MATLAB were given from the point of view of the left and right cameras. To extract meaningful data from these coordinates, a MATLAB code specific to this project was written to translate and rotate the coordinates. The points on the plate were always measured along a line; this line became the new x-axis. The new y-axis run perpendicular to the x-axis, on the same plane as the top surface of the plate. The new z-axis is the out of plane direction perpendicular to the plate, with up always in the positive direction. The measurements taken along a line of the plate were plotted to show how the shape and location of the base plate points changed as the test progressed Strain Measurements Measuring strain (on the order of 10-6 ) the anchor base plate was another method that could be used to determine at what load the base plate transitions from plastic to elastic deformation. Given the accuracy of the DIC measuring technique, it was not possible to measure the deformation in the plate with enough precision to accurately calculate the strain in the plate. A precision of approximately mm or more would have been required to calculate strain based on deformation measurements. 20

31 Strain gauges adhered to the top surface of the plate could be used to measure the strain during the experimental testing. Strain gauges were used in the first experimental test. It was not possible to calculate the force, and therefore the stress, in the locations of the strain gauge. Therefore, a plot of strain vs. test load at the top of the anchor was used to find the transition point between linear and non-linear strain reading (elastic vs. plastic deformation). There were two disadvantages with the use of strain gauges during testing. The first was that there was no method for precisely predicting which locations on the anchor base plates would start to yield first. Four strain gauges were used during the first test. They were located in areas of anticipated higher deflections. Two of the strain gauges showed linear to non-linear strain data at approximately the same load, the other two strain gauges showed plastic deformation occurring at distinctly different loads. The problem with using the strain gauges was that the data may lead to inaccurate conclusions if the strain gauges were not placed in the correct locations to capture maximum strain areas on the anchor base plates. The second disadvantage was that the use of the strain gauges interfered with the images captured for DIC. The surface preparation requirements for adhering the strain gauges caused some damage to the grid drawn on the anchor base plates (the grid was used for tracking the change in location of points on the anchor base plates using DIC). The strain gauges and adhesive also created areas of glare on the anchor base plates (Figure 3.3). These negative effects led to the decision that only DIC be used during testing. DIC was chosen over the use of strain gauges because the deformation measurements were determined after the testing was complete. Therefore, the test images could be used to determine the locations of maximum deformation and the measurements at those locations could be used to determine when the anchor base plate starts plastically deforming. 21

32 Figure 3.3: Glare on base plate due to strain gauges 3.4 Safety Anchor Configurations and Geometry There are many possible anchor designs that can be used to meet building code requirements. The design of an anchor point is influenced by the building on which it is being installed. Anchors can be embedded into concrete or fastened to the steel structure of the building. Other engineering teams decide the strength and depth of concrete on a building and the structural steel sections used in the framing. Designers of safety anchor points must create anchors that accommodate the designed building structure and comply with required codes, such as CSA Z271. This code states that the anchorage point must be able to withstand a load of 11.1kN applied in any direction without permanent deformation and a load of 22.2kN without fracture of pullout [2]. It was outside the scope of this project to analyze every possible anchor base plate design. The base plate analysis tested two different, and commonly used, anchor designs. The typical anchor design off which this analysis was based consisted of a 10 x 10 x 5/8 base plate with a 4 diameter, ¼ thick, round HSS pier welded to the center and an anchorage point (onto which the load would be applied) welded to the top of the anchor 22

33 pier. The differences in the two designs used for experimentation was that one design was fastened to the building structure by bolts in the four corners of the base plate and the other base plate was secured by two bolts in opposite corners of the base plate. The focus of this test was to analyze the behaviour of the safety anchor base plates with a moment load applied to the center of the base plates by the round HSS pier. To transfer the entire load to the plate, the rest of the test system was designed to withstand loads larger than the expected test loads. The thickness of the 4 diameter pier was increased from ¼ to 5/16, which is the largest readily available thickness for the outside diameter of HSS. This thicker section increased the moment resistance of the pier from 15.0kN to 18.2kN. The anchor point onto which the test load was applied was also modified to withstand larger loads without deforming. A typical anchor point can have loads applied in any direction. The anchors used in this test had one predetermined load direction. A ¾ steel rod with a length of 30 mm between support points was the hook up point for the load in the test. According to beam diagram calculations for a beam fixed at both ends concentrated load at center (Beam Diagram and Formula 16 in the Handbook of Steel Construction [102],this anchor point should be able to withstand a force of 370kN applied at the rod s center. The final deviation from the typical safety anchor design was the base plate thickness. The anchor base plate thickness was reduced from 5/8 thick to 3/8 thick. The thinner plate was used so that lower loads would be required to obtain larger deformations in the anchor base plates. See Figure 3.4 for an image of a typical anchor design used and the test anchor design. 23

34 Figure 3.4: Typical anchor currently in production vs. test anchor 3.5 Test Frame Safety anchors are typically installed on roofs and balconies of high-rise buildings. They can be embedded in concrete or fastened to the steel structure of the building. This experiment was designed to represent a safety anchor that had been fastened to a steel structure. The safety anchor bases were bolted around rectangular hollow structural steel sections (HSS). A test frame was designed to support the bolted anchor base and hook up location for the applied horizontal force on the anchor point. One single test frame was built to accommodate testing of both anchor geometries. Typical anchors can be loaded in any direction; therefore, three tests per anchor geometry were performed to examine the effects of different applied moment directions to the deformation in the anchor base plates. All the loads were applied horizontally (parallel to the top surface of the anchor base plate) to maximize the moment on the plate. The three load directions were: horizontal force parallel 24

35 to the supporting HSS, horizontal force perpendicular to the supporting HSS and horizontal force on a 45 angle relative to the supporting HSS. Two anchor geometries and three load directions resulted in a total of 6 tests. Top views of the six test anchor geometries and loading directions can be seen in Figure 3.5. Figure 3.5: The six anchor test geometries with load directions (all loads are parallel to the top plate on the anchor base plate) 25

36 The horizontal load on the anchor point was applied by a tirfor or a chain pull. The tirfor, or chain pull, was supported on the other end by an anchor point on a trolley located at the centre of the test frame on a vertical square HSS. The trolley on the centre HSS could be moved down as testing proceeds and the anchor pier starts deflecting; this was done to keep the applied load horizontal. The strength of the pier on the anchor base plate had already been increased within the limits of commercially available sections with the required outside diameter. The test frame dimensions did not have the same restrictions as the pier, therefore they were designed to withstand moment loads much larger than expected test loads. According to the moment resistances of the HSS sections in the test frame, the test frame was able to withstand a moment of 87.3kNm before plastically deforming. See Figure 3.6 for the moment resistances of the main frame sections. The maximum moment load that the anchor design could withstand given the pier moment resistance is a moment of 18.2kN, therefore the test frame was designed to withstand a load 4.8 times greater than the maximum test load the pier can withstand before deforming. This was determined based on the moment resistances of the HSS sections used in the test frame, beam deflection calculations and weld calculations. All relevant data and equations used were found in the Handbook of Steel Construction [102]. Figure 3.6: Test frame with HSS cross-section dimensions and moment resistances 26

37 As mentioned above, the test anchors were fastened to the test frame by either two or four bolts wrapped around the HSS of the test frame. A325 threaded steel rods were bolted through the anchor base plates on the top side of the HSS and went through steel angles (angle dimensions of 3 x3 x1/2, two angles for the four bolt bases and one angle for the two bolt bases) on the underside of the HSS. The holes in the angles were the same size and distance apart as the bolt holes in the anchor base plates being tested. One nut was used on either end of the threaded rod and hand tightened to hold the test anchors in place. No washers were used. Washers were omitted because they covered more of the base plate, which interfered with the camera images of the base plate and, in turn, would limit the locations at which the deformation can be measured. 3.6 Summary of the Complete Experimental Setup with Equipment The completed, assembled, setup of the experimental testing can be seen in Figure 3.7. Between the anchor point in the test anchor and the hook up point in the centre of the test frame were a dynamometer and a tirfor or manual chain pulley hoist. The dynamometer showed the magnitude of the load being applied to the anchor point, and the tirfor or manual chain pulley hoist provided the power/mechanical advantage that enabled the load to be applied to the system. The maximum load on the dynamometer was 50kN, and the load increments on the dynamometer scale were 0.5kN. The tirfor used in Test 01 had a twoton (imperial tons; 2 ton = 4000 lbs = 17.76kN) capacity and the manual chain pulley hoist had a maximum capacity of five metric tons (49.05kN). 27

38 Figure 3.7: Full experimental test setup The four cameras used for DIC are mounted on their own frame. The camera frame was kept independent from the test frame so that the locations of the cameras were not disturbed when the load was applied to the test anchors. If the placement of the cameras was compromised, then the calibration of the cameras would be affected and any measurements taken with DIC would be inaccurate. The cameras used for this testing were FLIR Systems; model number CM3-U3-31S4M- CS. The cameras were connected to a laptop via USB cables and they were wired for synchronized image capturing. The Flycap software was used to capture the images and the synchronized triggering of the cameras was controlled through a C+ program. The lenses used were from Edmond Optics. There were two different lens models used: 12mm C series lenses and 12mm UC series lenses. Both lens types were similar and no difference in performance was observed in the data collected through DIC. The cameras used were monochrome and had a resolution of 2048x1536 pixels. The high resolution and contrast in the monochrome images were essential for accurate DIC data. Some sample pictures taken of steel plates before testing showed glare in some of the images. It was also difficult to see the scribed grid on the plate. To aid with the visibility of the etched lines and to lessen the glare on the plate, blue tool dye paint was sprayed onto the plates before the grid was drawn. Tool dye paint was sprayed onto the metal plate in a 28

39 very thin layer, had a matte finish and provided a better contrast in the images. See (Figure 3.8) and (Figure 3.9) for images (taken from the same camera) of a scribed plate without and with blue tool dye paint, respectively. Figure 3.8: Top left: steel plate with scribed lines; bottom right: galvanized steel plate with scribed lines Figure 3.9: Steel plate with lines scribed after plate sprayed with blue tool dye paint 29

40 30 Chapter 4 Analysis of Experimental Testing: Anchor Plates Under Moment Load 4.1 Experimental Testing Overview This section analysed the deformation of the six base plate configurations when a moment load was applied to the centre of the plate. The testing was done using the test setup and methods described in Chapter 3. The measured results for each test configuration were discussed separately. Analysis for each test discussed the measured deflection of the anchor base plate (or measured strain gauge data in test 01) and the load at which the anchor base plates start plastically deforming. Finally, an analytical method of predicting the point at which permanent deformation occurred was proposed. The discussed results were also used in the next section, Chapter 5, to verify the proposed finite element model. 4.2 Test 01: Four bolts base plate connection; horizontal load parallel to the supporting HSS Test 01 Setup As discussed in the previous chapter, the test anchor in this experiment was fastened to the test frame by four bolts, in the four corners of the anchor base plate, wrapped around the supporting HSS. The load on this anchor was parallel to the top face of the anchor base plate, and parallel to the length of the supporting HSS. (See Figure 4.1 for Test 01 anchor and direction of applied load).

41 Figure 4.1: Test 01 Anchor setup and direction of applied test load Test 01 Strain Gauge Data and Analysis As discussed in Chapter 3: Experimental Setup, section 3.2.2, the first test performed was documented using both strain gauges and camera images. Unlike the following tests, in this test the horizontal load applied to the anchor point was increased in increments and the load was never removed. The reasoning for this was that the cycles of applying and removing the load repeatedly may have interfered with the strain gauges. Therefore, the strain gauge data, and not the DIC data, was used for determining the transition point from linear to non-linear deformation. The strain gauge locations can be seen in Figure

42 Figure 4.2: Test 01 Strain Gauge Locations The strain gauges in this test measured the microstrain (strain x10-6 ) in four different areas of the plate. Since there was no way of determining the stress in these four locations throughout the test, the strain measurements were plotted against the applied horizontal load at the top of the anchor pier. From these graphs, the load at which the base plate transitions from linear to nonlinear deformation was then determined. The load vs. strain graphs for strain gauges 1, 2, 3 and 4 can be seen in Figure 4.3, Figure 4.4, Figure 4.5, and Figure 4.6 respectively. There was an attempt made to measure the strains in the locations of the strain gauges using DIC. Unfortunately, the DIC was not precise enough to accurately measure strain. The measured strains varied greatly (and not linearly at any point during the testing) such that it was decided that the analysis based on the DIC measurements will focus on deformation rather than strain. 32

43 Horizontal Force on Anchor Point (kn) Horizontal Force on Anchor Point (kn) 15 Test 01: Strain Gauge 1 Data Measured test strain Strain x10e-3 (in compression) Figure 4.3: Test 01 strain gauge 1 data Test 01: Strain Gauge 2 Data Measured test strain 0.2% offset strain line Series Strain x10e-3 (in tension) Figure 4.4: Test 01 strain gauge 2 data 33

44 Horizontal Load on Anchor Point (kn) Horizontal Load on Anchor Point (kn) 15 Test 01: Strain Gauge 3 Data Measured test strain 0.2% offset strain line Strain x10e-3 (in tension) Figure 4.5: Test 01 strain gauge 3 data 15 Test 04: Strain Gauge 4 Data Measured test strain 0.2% offset strain line Strain x10e-3 (in compression) Figure 4.6: Test 01 strain gauge 4 data 34

45 On the load vs strain graphs, an offset line with the slope of the linear region of the graph was drawn at strain 2e10-6. From where this line intersects with the measured strain data, the test load at which plastic deformation begins was determined. The loads at which the plates start to nonlinearly deform at each strain gauge are summarized in Table 4-1. Table 4-1: Test 01 Yield Loads at the Strain Gauges Strain Gauge # Yield Load (kn) Table 4-1 shows that the locations of strain gauges 1 and 2 on the plate started plastically deforming under the same load of 4.2kN. The measured strain at gauge 1 was negative, therefore this section of the plate is being compressed. Strain gauge 2 gave positive strain readings, meaning that section on the plate was being deformed through a tension load. At strain gauges 3 and 4 the steel plate started yielding at higher loads than the other two strain gauges, 8.4kN and 5.7kN respectively. Strain gauge 3, like strain gauge 2, gave positive strain readings and was also therefore in tension. Strain gauge 4, like strain gauge 1, had negative strain gauge reading, meaning this section of the plate was also being compressed along the length of the strain gauge. The two strain gauges that reached yield strain first during testing were both on the font half of the plate (the side over which the load was being applied). This is interesting to note because at the end of the test, the largest deformation was visible at the back end of the plate. Deformation measurements were taken along the line on the anchor image shown in Figure 4.7 using DIC. The plot of the out of plane deformation along this line at a 15.0kN load compared to zero load can be seen on Figure

46 Figure 4.7: Line along which deflection measurements were taken; test load pull the pier to the right in this image Figure 4.8: Test 01 Deformation under 15kN Load There are multiple possible reasons why the strain gauges closest to the areas of maximum deflection started yielding at a higher load. Linear strain gauges were used in this experiment, meaning only unidirectional strain was measured. However, it can be seen in the test images that the base plate experienced multidirectional deformation and would therefore have strain in the plate acting in multiple directions. A rosette style strain gauge could have been used to measure the plane strain in the plate. However, this would not have been able to measure the strain in the plane orthogonal to the plate surface, which would likely be important given the observed out of plane deformation. A rosette strain gauge would also be larger than a liner strain gauge. The larger gauge would obscure more of the area that was being photographed for the purposes of DIC measurements. Finally, a rosette strain gauge 36

47 would not solve the issue of attempting to predict where the strain gauges must be located to measure the largest strains in the plate. The fact that two of the linear strain gauges used measured compressions strains and the other two linear strain gauges measured tension strains shows that the distribution of the load and strains in the base plate changes abruptly over the surface of the plate. Figure 4.9: Test 01 Deflection at the back of the base plate under 15.5kN load; strain gauge 4 can be seen on the right of the image and strain gauge 3 on the left Strain gauge 3, shown in Figure 4.9, was positioned between the pier and the anchoring bolt. This strain gauge exhibited linear strain deformation up to a load of 8.4kN on the anchor pier. This was the last section of the plate to start permanently deforming. Strain gauge 4, also shown in Figure 4.9, started to record nonlinear strain readings after a load of 5.7kN of the top of the anchor pier. What was interesting about strain gauge 4 was that the strain in this area was negative, therefore the plate was being compressed in this area along the direction of the linear strain gauge. If this strain gauge were in the same area, but oriented at 90 relative to its current position, it may have been able to capture the strain around the section of the plate at the back 37

48 of the base that was bending and the strain reading would likely have been positive rather than negative. Given the variation in strain measurements at the four plate locations, it was possible that plastic deformation may have started at an even lower applied load at different locations on the plate. For the purposes of further analysis, it was assumed that plastic deformation in the plate started when a horizontal load of 4.2kN was applied to hook up point on the top of the anchor pier. 4.3 Test 02: Four bolts base plate connection; horizontal load at a 45 angle relative to the supporting HSS Test 02 Setup This test anchor was fastened to the test frame by four threaded rods in the four corners of the anchor base plate. The width of the supporting HSS was 6 and the pier of the anchor was centred on the supporting HSS. The test load was horizontal (parallel to the top surface of the base plate) and oriented at a 45 angle relative to the supporting HSS. See Figure 4.10 for an image of the anchor and test load direction. 38

49 Figure 4.10: Test 02 Anchor setup and direction of applied test load Test 02 DIC Data and Analysis As previously discussed, this test and the subsequent tests in this analysis were analysed using only the data from DIC. Images were taken of the base plate at a staring load of 0.5kN. This was used as the baseline for comparing any subsequent deformation during testing. When the horizontal force was applied, the load was held constant while the cameras were capturing images of the base plate. After each new load increment was applied, the force was removed and images were captured at the starting base load of 0.5kN. This was repeated until plastic deformation occurred in the plate; at that point it was deemed unnecessary to track the plastic deformation in the plate once the steel started to yield. To determine whether the anchor was plastically deforming, a laser was set up to track the movement of the anchor pier. The laser was attached to the camera frame, directly opposite to the side of the pier on which the horizontal force was being 39

50 applied. In each test, the laser measured a point on the centre of the pier a couple of inches away from the top of the pier. The distance measured by the laser was taken at each load increment and at each point in the test when the load was released. If there was no significant increase between the lengths measured by the laser when the test load was released, data was collected for the loaded and unloaded anchor plate at each test increment. Slight changes in the pier location (on the order of 2-3mm) between tests were not considered permanent deformation. These changes in pier location could be attributed to the anchor shifting or the steel settling around the weld location. It was decided that although constantly applying and releasing the load on the anchor was time consuming, it would be better to have collected more data than necessary to be cautious, rather than assume plastic deformation had occurred at a given point only to determine later through the image analysis that no permanent deformation had yet begun. To track the changes in the shape of the plate, a line along which to track the change in displacement of points on the plate was chosen. This line can be seen in Figure This section of plate was chosen because it was the longest continuous line on the plate that intersected the bend line at which the largest deformation occurs before failure. See Figure 4.12 for an image of the test anchor after failure; this anchor base plate cracked around the weld at a load of 28kN. The anchor plate ultimately failed around the back edge of the weld between the pier and the anchor plate. Before the ultimate failure occurred, the plate bent between the pier and the back bolt. Measurements along the red line in Figure 4.11 were able to capture this bending. 40

51 Figure 4.11: Test 02 line along which deformation was measured; test load applied parallel the red line, to the right of the image Figure 4.12: Test 02 Failure of the anchor base plate The location of the grid points located on the line in Figure 4.11 were determined in MATLAB, using the Camera Calibration Toolbox for MATLAB written by Jean-Yves Bouget [98-101]. The change in the out of plane location of the plate along the line in Figure 4.11 was plotted in Figure The location of the points plotted were determined using the images taken after each load increment was released. The graph therefore shows the permanent change in location of the point along the plotted line. 41

52 Figure 4.13: Test 02 plot of the change in shape of the base plate along a line on the side of the plate In Figure 4.13 the change in shape after various loads are applied, then released, can be seen. The bold line shows the initial location of all the point at the minimum baseline load of 0.5 kn. The line showing the location of points after the 7.5 kn load was applied then released is similar in shape to the initial line, it is just rotated slightly around the centre in the clockwise direction. The shape of the next line, measured after the release of the 7.75 kn load, had a different shape compared to the previous two lines. The points between -15mm and 70mm along the plate have a peak and the points past 70 mm start to dip down relative to the rest of the points. This trend became more pronounced after the release of the 8.75 kn, 9.25 kn and 10.0 kn loads respectively. Given the change in shape of the plate between the application 7.5 kn and 7.75 kn loads, it was determined that the plate permanently deforms between these two loads. 42

53 4.4 Test 03: Four bolts base plate connection; horizontal load perpendicular to the supporting HSS Test 03 Setup In this test, the anchor base plate was secured to the HSS of the test frame by four bolts, in the four corners of the base plate, wrapping around the HSS. The horizontal test load on this anchor was applied in a direction perpendicular to the length of the supporting HSS. See Figure 4.14 for anchor setup and load direction. Figure 4.14: Test 03 Anchor setup and direction of applied test load Test 03 DIC Data and Analysis In this anchor configuration, the deformation was tracked along two separate lines. In Figure 4.15 the deformation of the base plate can be seen. This image was captured at a test load of 24.0 kn. This was the last captured image before cracking was observed around the weld at a load of 36.0kN. There is large observable deformation 43

54 at the side and back edges of the plate. The deformation at both these locations was measured and used to determine at what load the base plate transitions from linear to nonlinear deformation. This first line on which the permanent deformation at various loads was examined was along the entire length of plate, from back to front, 2 ½" away from the side edge of the plate (See Figure 4.16). The second line was at the back of the plate between the two back bolts, 2 away from the edge of the plate (See Figure 4.17) Figure 4.15: Test 03 Maximum deformation in the base plate before the observable weld failure Figure 4.16: Test 03 Line on side of plate over which permanent deformation was measured; horizontal load pulled to the right 44

55 Figure 4.17: Test 03 Line at back of plate over which permanent deformation was measured; horizontal load pulled to the right Figure 4.18 plots the gradual change in shape of the base plate after various test loads were released. Again, the bold line was the shape of the measured line with the application of the baseline load of 0.5 kn. After the 6.5 kn was removed, it was observed that the anchor had rotated around a point approximately 180 mm away from the back of the plate. The general shape of the plate between the 0.5 kn and 6.5 kn loads remained the same. After the removal of the 7.0 kn load, a slight curve in the back section of the plate was observed. Following the application and removal of the subsequent loads of 7.5 kn and 8.0 kn, the curve in the back of the plate became more pronounced. Therefore, according to this plot, permanent deformation begins between the applied loads of 6.5 kn and 7.0 kn. 45

56 Figure 4.18: Test 03 Out of plane deflection at the side of the base plate The change in shape of the plate between the two back bolts is shown in Figure In most of the graphs plotted from the DIC data, many of the lines depicting the shape of the plate after the test load increments were released overlap, creating messy and confusing plots. Many of the unnecessary lines were removed so that only the data relevant to the transition from linear to nonlinear deformation was shown. In this analysis, the plotted points after various loads did not often overlap, therefore more points where kept on the graph. The points depicting the change in shape of the back of the base plate (along the line drawn on the back of the plate in Figure 4.17) move up slightly between load increments starting at a load of 4.0 kn up until 6.5 kn. This shows that there was a slight shift in the location of the plate; the overall shape of the plate remained the same. This means that there was no bending in the plate and it was not plastically deforming. Starting after the load of 7.0 kn, the centre of the line on the plate can be seen to have curved upwards. This means that starting at the

57 kn load the back section of the plate started to plastically deform. This curve becomes more pronounced as the load increments were slowly increased. Figure 4.19: Test 03 Out of plane deflection at the back of the base plate The data collected from the line on the side of the plate and the line on the back of the plate both agree that plastic deformation began between the loads of 6.5 kn and 7.0 kn. 4.5 Test 04: Two bolts base plate connection; horizontal load parallel to the supporting HSS Test 04 Setup In this test, the anchor was secured to the supporting HSS by two bolts, in opposite corners of the base plate, wrapped around the HSS and bolted to a supporting angle on the bottom of the HSS. The HSS was 8 wide and the pier of the anchor was centred on the supporting section. The horizontal load was applied in a direction parallel to the supporting HSS (see Figure 4.20). 47

58 Figure 4.20: Test 04 Anchor setup and direction of applied test load Test 04 DIC Data and Analysis Figure 4.21 shows how the anchor base plate was deformed under an applied horizontal load of 14.0kN on the anchor hook up point. In this figure, there is visible a bend line on the front section of the plate at the edge of the weld between the anchor pier and base plate. To capture the bending at this line, the DIC measurements were taken along the line depicted in Figure

59 Figure 4.21: Test 04 Deformation of anchor base plate at 14.0kN load Figure 4.22: Test 04 Line at which permanent deformation in the base plate was measured The plot showing the change in shape of the plate along the line in Figure 4.22 after various loads were removed can be seen in Figure In this plot, the bold line represents the initial shape and position on the plate under the 0.5 kn initial load. The next line in the graph above the bold line shows the shape and location of the line on the plate after the 5.0 kn load had been removed. This line shows that the plate shifted slightly, but given that the shape of the line remains the same, the plate was still undergoing elastic deformation. The line showing the shape of the plate after the 5.25 kn load was removed started to show more of a curve in the shape of the plate. Therefore, it was at this load that the plate started plastically deforming. This curve 49

60 became more pronounced after the application of the 5.75 kn load, as shown on the graph. In this test, the base plate started permanently deforming between the loads of 5.0 kn and 5.25 kn. Figure 4.23: Test 04 Out of plane deflection along the side of the base plate 4.6 Test 05: Two bolts base plate connection; horizontal load perpendicular to the supporting HSS Test 05 Setup In this test, the anchor was fastened to the supporting HSS by two anchor bolts wrapped around the support structure and fastened to an angle under the HSS. The supporting HSS was 8 wide and the centre of the anchor was centred on the supporting HSS. The horizontal load was applied at a direction perpendicular to the length of the supporting HSS (See Figure 4.24). 50

61 Figure 4.24: Test 05 Anchor setup and direction of applied load Test 05 DIC Data and Analysis The shape to which this anchor base plate deformed can be seen in Figure The previous anchor test 04 (Figure 4.20) had a similar setup; the difference in the two tests was that the load direction was rotated by 90 relative to the supporting HSS in the two tests. In the previous test the front of the base plate was bent at a line perpendicular to the load direction and tangent to the weld. In this test, there was also a clear bending line in the plate. It was also perpendicular to the applied load direction and tangent to the weld. The differences in the deflection in this test compared to the previous test was that the bend line was at the back of the pier instead of the front, and that the plate was bending in the opposite direction. To 51

62 capture the change in shape of the plate, the deformation measurements were in relatively the same location as the previous test, as can be seen in Figure Figure 4.25: Test 05 shape of base plate under 10.0kN load; load pulled to the left in this image Figure 4.26: Test 05 Line along which deformation in plate is measured; load pulled to the left in this image The measurements of the point locations along the line in Figure 4.26 are shown in Figure The bold line was the initial shape of the plate along the line under the baseline load of 0.5 kn. After the load of 5.25 kn was applied and released, the base 52

63 plate shifted by rotating in the counter clockwise direction. The overall shape of the line remained similar to that of the initial plate shape, which means the plate had shifted slightly, but no plastic deformation had occurred in the plate. After the 5.5 kn load was applied and released the shape of the plate changed slightly. The back section of the line in the plate started to curve upwards. This shows that after the 5.5 kn was applied, the plate started to permanently deform. Figure 4.27: Test 05 Out of Plane Deflection in the base plate 4.7 Test 06: Two bolts base plate connection; horizontal load perpendicular to the supporting HSS Test 06 Setup For this test, the anchor was fastened to the supporting HSS by two bolts, in two opposite corners of the plate, wrapped around the 8 wide HSS and bolted through an 53

64 angle. The horizontal load was applied at an angle of 45 relative to the supporting HSS. Figure 4.28: Test 06 Anchor setup and direction of applied load Test 06 DIC Data and Analysis The deflection in the base plate for this test can be seen in Figure 4.29 and Figure 4.32; note that the applied horizontal load was being pulled in opposite directions in these two pictures. Both images were taken with an applied load of 10.0 kn. Once the load was increased to 10.5 kn, the base plate started to fracture along the weld line in the section of the weld closest to the back bolt. Since the deflection within the plate was not symmetric about any axis, the deflection along two lines was analysed. One line was on the side of the plate, as shown in Figure 4.30, and the other line was at the back of the plate as shown in Figure

65 Figure 4.29: Test 06 Shape of deflection in the plate with a 10.0kN load; load pulling the anchor to the left in this image The nut on the threaded rod at the back of the plate blocks part of the grid on the plate from the view of the cameras. For this reason, the line of points being measured using DIC did not run the entire length of the plate. This was true for both sets of measurements taken for this anchor configuration. Both lines of points intersected the areas of bending shown in Figure 4.29 and Figure 4.32 thus only measuring the location of points along partial lines of the plate should not have affected the quality of the results. Figure 4.30: Test 06 Line on side of plate at which deflection was measured 55

66 The plot of point locations measured at the side of the plate drawn along the line in Figure 4.30 can be seen in Figure The bold line showed the original shape of the line being analysed. The line showing the shape after the application and release of the 5.25 kn load was similar in shape to the original line. The line showing the out of plane deflection after the release of the 5.5 kn load started to show the plate curving upwards at the back of the plate. The curves seen on the graph showing the out of plane deflection after the 6.25 kn, 6.75 kn and 7.75 kn loads showed that the amount of deflection continued to increase as the load increases. This means that the anchor base plate started permanently deforming between the application of the 5.25 kn and 5.5 kn loads. Figure 4.31: Test 06 Out of plane deflection at side of plate 56

67 Figure 4.32: Test 06 Shape of deflection in the plate with a 10.0kN load; load pulling the anchor to the right in this image Figure 4.33: Test 06 Line along the back of the base plate along which deflection was measured Figure 4.32 shows how the back of the base plate deformed under loading. The unbolted back corner lifted and the back section of the base plate closest to the nut started to bend. This was reflected in the points measured along the line drawn in Figure The graph in Figure 4.34 shows the progression of the out of plane deformation after various loads. The bold line shows the location of the points along the line at the baseline load of 0.5 kn. The next line was plotted after the release of the 5.25 kn; it was slightly raised, but the shape remained similar. The plot of the line 57

68 after the 5.5 kn load was released started to change shape and curved slightly on the right of the graph; this was the side of the line of points being measured that is closer to the bolt at the back of the plate. As higher loads were applied and released, the curve on the right side of the graph became more pronounced and the section of plate on the left side of the graph rose upwards as was anticipated from Figure The data plotted in this graph showed that plastic deformation occurred between the application of the 5.25 kn and 5.5 kn loads. This agreed with the deflection of the line plotted in Figure Figure 4.34: Test 06 Out of plane deflection at back of plate 4.8 Comparison of Different Anchor Geometry Results Table 4-2 shows the maximum recorded loads on the anchor measured before the onset of plastic deformation. Test 01 determined this from the strain gauge that was the first to start showing nonlinear behaviour (in this test both strain gauges 1 and 2 have the same, lower load). Test 02 through Test 06 determined this based on the deformation of the plate measured though DIC. The loads in the table were the highest recorded loads before the plate started to permanently deform. However, given the load increments applied to the top of the anchors, the anchor may have resisted 58

69 slightly higher loads then those recorded before permanently deforming. The maximum moment loads in the table were determined by multiplying the horizontal test for by the vertical distance between the load hook up point and the base plate (0.675 m). Test Max. Horizontal Load (kn) Moment Load in Centre of Plate (kn m) Test Test Test Test Test Test Table 4-2: Max. loads in the base plates before permanent deformation occurs 59

70 It is interesting to note, in Table 4-1, that the three different test load directions on the two-bolt anchor experience similar yield loads whereas the four bolts anchors all yield at different loads. It can be argued that because the yield load for the first test was determined using strain gauges, and the second and third test were analysed using DIC it was difficult to compare the yield loads between those tests. However, given the difference in yield loads between the second and third test, the effected of load direction affected the yield load limit in the four-bolt anchor configuration more than the two bolts anchor system. 4.9 Material Properties of the Steel Base Plate Since the anchor base plate was the part of the system that was being analysed, it was important to find the material properties of the steel used to make the base plate. The grade of steel used for the plate was 300W. There are standards that dictate the minimum strength of the steel; however, it would have been inaccurate to assume that the plate was made to the minimum strength specified by the standard. Three coupon samples of the base plate were tensile tested to determine the yield strength and ultimate strength of the steel (See Figure 4.35 for coupon dimensions). The yield strength was especially important for predicting the moment resistance of the base plate. When performing the FEA analysis, young s modulus was also required. This was determined using the stress-strain graph results from the tensile test. 60

71 Figure 4.35: Tensile test coupon dimensions; 1/4" plate thickness The tensile tests were performed by Engineering Material Research. The dimensions of the tensile samples are shown in Figure The plate thickness was originally 3.8 (9.53mm). To accommodate the machines used for testing, the plate sample was thinned down to ¼ (6.35mm). The average yield stress and ultimate strength was 372MPa and 543MPa respectively. The fractured test coupons can be seen in Figure Figure 4.36: Failure of tensile test coupons 61

72 4.10 Moment Resistance of the Base Plates The anchor base plate was designed to be the weakest part of the system. The other sections of the anchor and test frame were designed to be stronger, rigid and to transfer the moment load to the anchor base plate. For this reason, it was assumed that the entire horizontal force applied during test was transferred, as a moment load, to the base plate. There is no current way of calculating the moment resistance of the plate under the moment loading conditions. By observing the areas at which the plate bent, a method of calculating the moment resistance for each specific anchor plate was proposed. The moment resistance of a section was calculated by multiplying a section s elastic section modulus (Z) by the yield strength of the material (Fy). The elastic section modulus for a rectangular plate is shown in Figure Since the base plate analysed in this testing did not undergo pure bending, calculating Z=b*d 2 /4 will not give a section modulus that would result in a correct moment resistance. If Z were calculated along the 10 length of the plate, Z=254 mm*9.53 mm 2 /4= 5757 mm 3, then multiplied by the yield strength, Mr=5757 mm 3 *372 MPa= 2.14 knm, then the calculated moment resistance of the plate would be 2.14kNm. Table 4-2 shows that the lowest moment that any of the anchor configurations started plastically deforming was 2.84 knm. This was higher than the moment resistance calculated along the length of the plate. 62

73 Figure 4.37: Section properties for a rectangular plate, taken from the Handbook of Steel Construction [102] A new method of calculating the moment resistance for each test configuration was proposed. A section modulus for each plate configuration was found based on the locations of bending in the plate. The lengths of the bend location were combined and used as the variable b in the equation Z=b*d 2 /4, used for calculating the elastic section modulus, as shown in Figure In Figure 4.38 through to Figure 4.43, the grid lines drawn on the base plates are ½ apart; the same spacing as the grids scribed onto the anchor base plates for the experimental testing. Figure 4.38: Test 01 base plate bending lines used for calculating Z 63

74 Figure 4.38 shows the approximate lines at which the base plate bent during testing. The four straight lines were approximately 2 ½ long each, and the two-curved section combined were approximated at 1/3 the circumference of the outside weld circle. Under these assumptions, Z was calculated as 10.3x10 3 mm 3 and the moment resistance was 4.39 knm. The maximum moment on the plate before the onset of plastic deformation was 2.8 knm according to the strain gauge analysis. This calculated moment resistance was higher than the maximum moment in the base plate before plastic deformation. However, this anchor configuration yielded at a relatively low load compared to the other five tests, especially the two other tests that tested four-bolt anchor base plates. When compared to the yield strengths of the other two four-bolt anchor base tests, 4.39 knm moment resistance in the base plate was reasonable. Figure 4.39: Test 02 base plate bending lines used for calculating Z The bending lines on the test 02 anchor base plate were drawn on Figure The straight line had a length of 233 mm, the two smaller quarter circles had radii of 55 mm and the larger quarter circle at the back of the base plate had a radius of 116 mm. The radius of 55 mm around the bolt holes was assumed because the arc of the circle, assuming the centre of the circle was at the corner of the base plate closest to the bolt hole, touched the outside of the bolt hole furthest from the corner of the plate to which 64

75 the hole was closest. The radius of 116 at the back of the base plate had similar reasoning. In this case, with the centre of the arc positioned at the back corner of the base plate, the outer edge of the arc touched the edge of the weld around the pier. Using these lengths to determine Z, a moment resistance of 4.98kNm was calculated. The tests measured using DIC determined between which horizontal loads on the top of the anchor pier the plate starts to permanently deform. Test 02 started plastically deforming between the loads of 7.5kN*0.675m=5.05kNm and 7.75kN*0.675m=5.23kNm. The calculated moment resistance of 4.98kNm was lower, but very close, to the moment calculated while the plate was still elastically deforming This showed that the calculated moment resistance in the plate was reasonable and slightly conservative. Figure 4.40: Test 03 base plate bending lines used for calculating Z Figure 4.40 shows the lines along which test 03 bends. The four short straight lines on the right side of the plate were approximated as 2 ½ long each, and the two round sections combined were assumed to be 1/3 the circumference of the outside weld line. This gave a moment resistance of 4.39 knm. This was the same as the moment in the plate at the last recorded load before permanent deformation: 6.5kN*0.675m=4.39kNm. 65

76 Figure 4.41: Test 04 base plate bending lines used for calculating Z Test 04 shown in Figure 4.41 had a bending line at the front of the anchor pier that was 233 mm long and two quarter circles with radii of 55mm each around the bolts. Using these lengths, the moment resistance of the base plate was calculated to be 3.43 knm. This fell between the moment given by the load before the onset of plastic deformation (5.0kN*0.675m=3.38kNm) and the load at which plastic deformation was first observed (5.25kN*0.675m=3.54kN). Figure 4.42: Test 05 base plate bending lines used for calculating Z Figure 4.42 shows the locations at which the base plate in test 05 bent. The line at the front of the plate was 233 mm long, the radius of the larger quarter circle at the back 66

77 of the plate was 116mm. These lengths combined resulted in a moment resistance of 3.51 knm. This calculated moment resistance for the plate was slightly lower than the moment in the plate at the last measured horizontal load before the base plate started to permanently deform: 5.25kN*0.675m=3.54kNm. Figure 4.43: Test 06 base plate bending lines used for calculating Z In test 06 the base plate bent along the two lines shown in Figure The vertical line on the right side of the plate was 254 mm long and the quarter circle at the bottom left corner of the plate had a radius of 116 mm. These lengths combined resulted in a calculated moment resistance in the plate of 3.69 knm. This fell in between the moment in the plate at the last recorded load experiencing elastic deformation at 5.25kN*0.675m=3.54kNm and the load at which the base plate started plastically deforming at 5.5kN*0.675m=3.71kNm. The moment resistances calculated according to the bend lines observed during testing resulted in moment resistances that were either slightly lower than the last recorded moment loads before the base plate started plastically deforming or they were in between the moment loads that marked the transition from elastic to plastic deformation. The only exception was the moment resistance predicted for the first test anchor. The reason for the discrepancy between the accuracy of this prediction compared to the other five anchor configurations was that this base plate yielded at 67

78 a lower load according to the strain gauge data; the other five tests used DIC data for determining the onset of plastic deformation. Unfortunately, this DIC data is not available for the first test. Overall, the moment calculations for the six specific test configurations predicted moment resistances more accurately that the typical moment resistance calculation in Figure 4.37 for a rectangular section. 68

79 Chapter 5 Finite Element Analysis Finite element analysis (FEA) is an important and powerful tool used to predict the behaviour of structures under given loads. For this analysis, the FEA software ANSYS was used for the computer modelling and simulations. This chapter discusses how a FEA model was created to predict the stress and deformation of the anchor base plates tested in Chapter 4. The data collected during the experimental testing was used to validate the accuracy of the FEA. 5.1 Finite Element Model The focus throughout this thesis project was analysing the behaviour of anchor base plates. This still held true for the computer modelling. The six test configurations that were experimentally tested were the same base plate configurations that were simulated in ANSYS. However, when building the computer model, it was not necessary to includes all the test components that were required for the physical testing. The more components that were included in an FEA, the longer the run time for the simulation and the greater the computational cost. In this model, all the necessary components that will affect the anchor base plates were included and the rest of the parts used in the experimental testing were omitted. A short piece of HSS, a few inches longer that the base plate, acted as a base for the modelled anchor. The test frame was designed to withstand much higher loads than the base plate, therefore it was assumed that the support HSS did not move during testing. By adding a fixed constraint to the HSS section, this fixed support was modelled without needing to model the entire frame. The same HSS section dimensions were used as the section dimension of the supporting HSS on the test frame. 69

80 The rods and nuts holding the corners of the base plate were also partially included in the model. This simulation was run at the maximum loads each anchor withstood before plastically deforming. This leads to the assumption that, if the anchor bolts do deform, the deformation will be negligible. To increase the efficiency of the model, only a short section of the bolts was modelled. The pier was kept in this model, but anchor point at the top of the pier to which the horizontal force was applied was removed. In the model, the load was applied to the top face of the round HSS pier. The pier was lengthened so that the top of the section was the same distance away from the top surface of the plate as the centre of the anchor point was during physical testing. This was done so that the moment load on the centre of the base plate resulting from the applied load on the top of the anchor pier was the same in the FEA model as it was during the experimental testing. Failure in the test anchors during experimental testing occurred typically around the weld between the pier and the anchor plate. This suggests that the weld is an important part of the anchor design. Therefore, the full ½ weld between the pier and plate was included in the ANSYS model. The material properties for the base plate were inputted to be the strength values determined in the tensile testing of the base plate metal. Grade 300W steel was used for the plate. This grade must have a minimal yield strength of 300MPa; from the tensile testing, the base plate was determined to have a yield strength of 372MPa, which is much higher than expected. Since the base plate was the focus of the analysis it was important to have accurate materials properties, rather than use assumed minimum values for the grade of steel used. To control the maximum allowable stress in the base plate, the 300W plate material was set to behave under bilinear isotropic hardening conditions. The HSS pier and rectangular support sections were designed to withstand much higher loads than the steel base plate. For this reason, the materials properties for the round HSS pier and the rectangular HSS support were assumed to be the minimal values for these section according to the Handbook of Steel Construction [102]. See Table 5-1 for the steel material properties used in the FEA model. If the maximum stresses were concentrated in the base plate, the exact material properties for the other sections were not required. These sections were 70

81 strong enough that they should transfer all the loads to the base plate. If they fulfilled this purpose, their exact properties were not going to affect the stress in the base plate. Section Yield Strength (MPa) Ultimate Strength (MPa) Young s Modulus (MPa) Base plate Pier HSS Rectangular HSS Table 5-1: Material properties used in the FEA model 5.2 Model Parameters and Constraints Since the experimental testing was performed with incremental loads being held on the anchor, the static structural analysis model in ANSYS was used for the setup. The top face of the rectangular supporting HSS was set as a fixed support. This was done because in the experimental testing the test frame was designed to be able to withstand loads significantly higher than the maximum loads applied to the anchor during testing. The nut and rod were also assumed to not deform before the onset of plastic deformation in the plate. For this reason, the nuts and rods in the model were set as rigid bodies; this means that they were not permitted to change shape during the computer analysis. The stresses in rigid bodies were not computed and the bodies were not meshed; this allowed the model to be solved quicker during analysis. In ANSYS, rigid bodies were not permitted to have their surfaces constrained with a fixed support. Therefore, a remote displacement constraint was applied to the bolts and all the coordinate directions and rotation angle displacements were set to zero. This essentially meant that the nuts and bolts were fixed in place. The force on the system was applied to the top surface of the anchor pier. The magnitude of the applied force was set to the maximum load applied before plastic deformation of each test configuration and the direction of the load was set to be the same 71

82 as that in the experimental testing (as summarized in Table 4-2). The mesh in the model can be seen in Figure 5.1 and the force and constraints can be seen in Figure 5.2. Figure 5.1: FEA mesh Figure 5.2: FEA constraints and load 5.3 Finite Element Analysis Stress and Deflection Results Analysis The FEA results focused mainly on the stress and deformation calculated in the base plate. For all six anchor geometries that were modelled, the location of maximum stress in the system was always in the base plate. This result was anticipated because all the other components were overdesigned for the expected test load. In addition, the anchor base plate was made thinner than typically used for anchor base plates so that the locations at which the plate bends could be easily seen and studied with smaller test loads required within the system. 72

83 Since the experimental testing focused mainly on measuring the deflection in the base plate, the FEA results for deflection were compared to the measured deflection within the plate at the areas of maximum deformation. The areas of maximum stress were compared to the areas in the plate that fractured when the system failed Test 01 FEA Results As seen in Figure 5.3, the largest stress concentrations were concentrated in the base plate and the weld connecting the pier to the base plate. The welded area between the pier and plate experienced the highest moment loading. This moment load was then dispersed throughout the plate. Figure 5.3: Test 01 FEA stress in anchor Figure 5.4 shows the stress distribution in just the base plate. The 300W grade plate had a yield strength of 372 MPa. The maximum stress calculated by the FEA model was 362 MPa in the plate. This high stress occurred only in a small section of the plate close to the two back bolt holes. Interestingly, the section of the base plate where the strain gauges 73

84 showed yielding in the plate at the lowest test loads was the section of the plate that has the lowest stress values according to FEA. This discrepancy suggested that either the model or the experimental testing did not accurately capture the behaviour of the base plate under the moment load. Figure 5.4: Test 01 FEA stress in base plate Figure 5.5 shows the out of plane directional deformation in the anchor base plate. The fact that both the stresses in Figure 5.4 and the deformation in Figure 5.5 had a concentrated area of stress and deformation, respectively, centred around the edge of the weld at the back of the pier agrees well with the information learned during the experimental testing. It was at this location that the plate failed and started to fracture (well after the onset of plastic deformation). 74

85 Figure 5.5: Test 01 FEA out of plate deformation of base plate The maximum out of plane deformation shown in Figure 5.5 was 0.44 mm. The change in position of this area measured using DIC was 0.31 mm. The point at which deformation was measured was on the centreline of the plate, 2 away from the back edge of the plate, between the loads of 2.22 kn and 4.44 kn. In this simulation, the maximum deformation was predicted to be slightly larger than the measured deformation Test 02 FEA Results In this simulation, the maximum stress was predicted to be 545 MPa, which is close to the ultimate stress of 543 MPa, and is shown in Figure 5.6 by the areas in red. The red area around the weld was in the location of the plate that fractured when the system failed (Figure 5.7). The other red location, by the back bolt, was obscured from view by the bolt during physical testing. This made the location difficult to observe during testing. Looking at the deformation of the plate and back bolt in Figure 5.7 taken after the plate fractured, 75

86 it can be reasonably assumed that there was a high stress concentration surrounding the back bolt location on the base plate. Figure 5.6: Test 02 FEA stress in anchor Figure 5.7: Test 02 physical test image showing plate fracture 76

87 Figure 5.8: Test 02 FEA stress in base plate The location of maximum stress and deformation shown in Figure 5.8 and Figure 5.9, respectively, corresponded with the location of fracture around the weld where this anchor geometry failed. The stresses along the line (shown in Figure 4.11) where the deflection measurements were taken to determine at what load the plate transitioned from linear to non-linear behaviour all fell in an area of the base plate that demonstrated stresses within the yield strength of the material (according to FEA and the test material properties of the base plate). This demonstrated that the distribution of the stresses in the plate determined with the finite element model agreed with the experimental test results. Due to the weld (around which the grid drawn on the plate used for DIC was slightly obscured) and the nut on the threaded rod, DIC measurement that tracked the deformation of the plate could not be taken at the areas that showed the maximum stress. If strain gauges were used during experimental testing rather than DIC, the strain gauges could not be used close enough to the weld in the heat affected zone of the base plate and the nut still obscured the area around the bolt hole so that a strain gauge could not have been attached to the base plate in that location either. 77

88 Figure 5.9: Test 02 FEA out of plane deformation in base plate The maximum out of plane deformation predicted by FEA and shown in Figure 5.9 was 0.75 mm. The deformation measured by DIC at a point 3 to the left and 3 up from the bottom right of the plate shown in Figure 5.9 gave a deformation of 2.46 mm between the loads of 0.5 kn and 7.5 kn. The larger deformation measured from the experimental testing could have been due to the plate possibly rotating rigidly around the supporting HSS. Also, the FEA model did not consider the fact that there was a heat affected zone around the weld that may have affect the deformation, stress levels and distributions, in the plate Test 03 FEA Results Figure 5.10 shows that a maximum stress of 553 MPA in this anchor geometry occurred at the back of the plate around the edge of the weld and around the back two bolt holes. The maximum stress location around the weld occurred in the area of the base plate that fractured when the anchor plate failed, and the two bolt locations at the time of failure experienced large deflections (See Figure 5.11). From the shape of the deformed plate, it 78

89 could be concluded that the plate was being pulled in tension between the area of high stress around the weld and the bolt locations. Figure 5.10: Test 03 FEA stress in anchor Figure 5.11: Test 03 physical test image showing plate fracture 79

90 Figure 5.12: Test 03 FEA stress in base plate The areas of maximum stress shown in Figure 5.12 on the base plate occurred in areas of the plate that could not be monitored during the physical testing using either DIC or strain gauges. The stresses calculated by FEA in the plate along the areas of the plate that were analysed and used to determine the load at which the plate started plastically deforming in the experimental test results remained under the yield strength of 372MPa. Figure 5.13: Test 03 FEA out of plane deformation in base plate 80

91 The predicted maximum out of plate deflection of the plate determined by FEA was 0.69 mm (see Figure 5.13). This was much smaller than the deflection of 5.85 mm measure in the centre of the plate, 2 away from the back of the plate, using DIC. The larger deflection measured in the experimental testing could again be due to shifting of the entire anchor and the effect of the heat affected zone around the weld that was not accounted for in the finite element model Test 04 FEA Results The FEA stress results for this anchor, seen in Figure 5.14, showed that the area of maximum stress occurred at the front of the plate and around the bolt holes. During the experimental testing, a bend line was observed along the front edge of the weld where the base plate was being compressed and the threaded rods were bent as the moment on the pier caused the plate to deform and pull the rods in towards the centre of the plate (see Figure 5.15). These experimental test observations suggested that the areas of maximum stress in the base plate, given as 445 MPa, occurred in the areas of max stress shown in Figure

92 Figure 5.14: Test 04 FEA stress in anchor Figure 5.15: Test 04 shape of plate under test load of 13.0kN 82

93 Figure 5.16: Test 04 FEA stress in base plate The areas of maximum stress on the plate shown in Figure 5.16 were not analysed with the use of DIC. It was not possible to collect image data at these locations because of the interference on the grid pattern by either the nuts or the weld. The line along which deflection was analysed ran parallel to the supporting HSS and as close to the weld as possible (see Figure 4.22). Along this line over which DIC measurements were taken to observe the point at which plastic deformation began, the stresses in the plate were less than the yield stress of 372 MPa. This showed that, in the area measured by the test, both the FEA model and the experimental testing agreed that there was no plastic deformation. 83

94 Figure 5.17: Test 04 FEA out of plane deformation in base plate The back corner in this plate experienced the largest deflection. This was shown both in the experimental testing (Figure 5.15) and in the FEA result (Figure 5.17). In FEA, under a load of 5.0 kn, the predicted deformation was 4.13 mm. From the experimental test data at this load, the deformation was measured to be mm. This value was measured at ½ down and ½ to the left from the top right corner of the plate. Using DIC it was difficult to accurately select a point on the edge, and especially on the corner edge of the plate. The plate does not form a perfect right angle between the top and side surfaces of the plate; therefore, the perception of the edge location may change between different cameras that captured the image of the base plate at different angles. The discrepancy between the FEA and experimentally measured deformation may be due to shifting of the plate during testing; the bottom surface of the base plate and the top surface of the supporting HSS may not both have been perfectly flat. Welding the pier onto the base plate may have slightly deformed the base plate. The 3/8 thick base plate was only slightly larger that the ½ weld size. The edges of the plate were observed to angle upwards slightly after the pier was welded to the plate compared to the shape of the plate before welding. The discrepancy between deformation in the test compared to the discrepancies in tests 1, 2 and 3 may have 84

95 been larger because there were fewer bolts holding the base in place. This geometry relied more on the strength of the anchor base plate and less on the fasteners Test 05 FEA Results In this anchor base configuration, there was a bolt holding down the back corner of the plate. The areas of maximum stress were in the back of the plate between the weld and the plate, in the area closest to the bolts, and around the bolt hole (see Figure 5.18). This anchor configuration showed a large tension on the back of the plate. This agreed with the way in which the base plate deformed during testing (see Figure 5.19). Figure 5.18: Test 05 FEA stress in anchor 85

96 Figure 5.19: Test 05 image showing crack initiation around weld at the back of the pier Figure 5.20: Test 05 FEA stress in base plate The maximum stress on the plate given by the FEA was 530 MPa. This was larger than the yield strength (372MPa) of the plate, but below the ultimate strength of 543 MPa. In Figure 5.20 the areas in red show where the stress exceeded 372 MPa. Again, these areas of high stress occurred in places of the plate that were difficult to analyse during the experimental testing. The line on the plate along which the deformation was tracked using DIC runs along the plate perpendicular to the supporting HSS on the outside of the pier (see Figure 86

97 4.26). Along this area of the plate, the stress remained below the 372MPa limit. Therefore, this FEA model did not contradict the measured experimental data. Figure 5.21: Test 05 FEA out of plane deformation in base plate The area of maximum deformation in the FEA model shown in Figure 5.21 agreed with the bend location observed in the experimental testing in Figure The maximum deformation according to FEA was 0.77 mm and according to the DIC data the deformation was 2.18 mm. The DIC measurement was taken between the loads of 0.5 kn and 5.25 kn and was taken 4 to the left and 2 up from the bottom right corner of the plate shown in Figure Test 06 FEA Results The final anchor configuration tested had the least symmetric geometry, and therefore demonstrated an unsymmetrical stress distribution (see Figure 5.22). There were areas of high stress around both bolt holes; with more stress around the back bolt hole than the front. There were also two locations of high stress around the weld. The larger 87

98 concentration occurred at the section of weld closest to the back bolt. Between this section of stress and the area around the back bolt hole the plate was being pulled in tension. The other area of high stress around the weld was shown at the front of the anchor where the pier was applying a compressive load on the base plate. These regions of high stress agreed with the deformation and fracture observed in the base plate during physical testing (see Figure 5.23). Figure 5.22: Test 06 FEA stress in anchor Figure 5.23: Test 06 fracture in base plate during experimental testing 88