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TRANSCRIPT
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
ii
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.
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Table of Contents
Chapter 1 Introduction ........................................................................................................... 1
1.1 Safety Anchor Design ................................................................................................................. 1
1.2 Thesis Objectives ......................................................................................................................... 2
1.3 Thesis Organization .................................................................................................................... 4
Chapter 2 Background and Literature Survey................................................................ 5
2.1 Safety Anchor and Davit Base Plate Introduction ............................................................ 5
2.2 Types of Base Plate Connections ............................................................................................ 7
2.2.1 Modelling of Cylindrical Steel Structures to Concrete Foundations .............................. 8
2.2.2 Modelling of Column Base Plates to Concrete Foundations ........................................... 10
2.2.3 Modelling of Beam to Column Bolted Connections ............................................................ 11
2.3 Modelling Issues and Limitations ....................................................................................... 13
2.4 Summary ...................................................................................................................................... 14
Chapter 3 Experimental Setup .......................................................................................... 16
3.1 Introduction to the Experimental Setup .......................................................................... 16
3.2 Test Objectives .......................................................................................................................... 16
3.3 Measuring Techniques and Equipment ............................................................................ 17
3.3.1 Deformation Measurements ........................................................................................................ 17
3.3.2 Strain Measurements...................................................................................................................... 20
3.4 Safety Anchor Configurations and Geometry ................................................................. 22
3.5 Test Frame .................................................................................................................................. 24
3.6 Summary of the Complete Experimental Setup with Equipment ............................ 27
Chapter 4 Analysis of Experimental Testing: Anchor Plates Under Moment Load
...................................................................................................................................................... 30
4.1 Experimental Testing Overview .......................................................................................... 30
4.2 Test 01: Four bolts base plate connection; horizontal load parallel to the
supporting HSS ................................................................................................................................. 30
4.2.1 Test 01 Setup ..................................................................................................................................... 30
4.2.2 Test 01 Strain Gauge Data and Analysis ................................................................................. 31
4.3 Test 02: Four bolts base plate connection; horizontal load at a 45° angle relative
to the supporting HSS ..................................................................................................................... 38
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4.3.1 Test 02 Setup ..................................................................................................................................... 38
4.3.2 Test 02 DIC Data and Analysis .................................................................................................... 39
4.4 Test 03: Four bolts base plate connection; horizontal load perpendicular to the
supporting HSS ................................................................................................................................. 43
4.4.1 Test 03 Setup ..................................................................................................................................... 43
4.4.2 Test 03 DIC Data and Analysis .................................................................................................... 43
4.5 Test 04: Two bolts base plate connection; horizontal load parallel to the
supporting HSS ................................................................................................................................. 47
4.5.1 Test 04 Setup ..................................................................................................................................... 47
4.5.2 Test 04 DIC Data and Analysis .................................................................................................... 48
4.6 Test 05: Two bolts base plate connection; horizontal load perpendicular to the
supporting HSS ................................................................................................................................. 50
4.6.1 Test 05 Setup ..................................................................................................................................... 50
4.6.2 Test 05 DIC Data and Analysis .................................................................................................... 51
4.7 Test 06: Two bolts base plate connection; horizontal load perpendicular to the
supporting HSS ................................................................................................................................. 53
4.7.1 Test 06 Setup ..................................................................................................................................... 53
4.7.2 Test 06 DIC Data and Analysis .................................................................................................... 54
4.8 Comparison of Different Anchor Geometry Results ..................................................... 58
4.9 Material Properties of the Steel Base Plate ..................................................................... 60
4.10 Moment Resistance of the Base Plates ........................................................................... 62
Chapter 5 Finite Element Analysis ................................................................................... 69
5.1 Finite Element Model .............................................................................................................. 69
5.2 Model Parameters and Constraints ................................................................................... 71
5.3 Finite Element Analysis Stress and Deflection Results Analysis ............................. 72
5.3.1 Test 01 FEA Results......................................................................................................................... 73
5.3.2 Test 02 FEA Results......................................................................................................................... 75
5.3.3 Test 03 FEA Results......................................................................................................................... 78
5.3.4 Test 04 FEA Results......................................................................................................................... 81
5.3.5 Test 05 FEA Results......................................................................................................................... 85
5.3.6 Test 06 FEA Results......................................................................................................................... 87
5.4 FEA Model Conclusions ........................................................................................................... 90
Chapter 6 Conclusions and Recommendations ........................................................... 93
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6.1 Conclusions ................................................................................................................................. 93
6.2 Recommendations ................................................................................................................... 94
References ................................................................................................................................ 96
vi
List of Tables
Table 4-1: Test 01 Yield Loads at the Strain Gauges .............................................................. 35
Table 4-2: Max. loads in the base plates before permanent deformation occurs ....... 59
Table 5-1: Material properties used in the FEA model ......................................................... 71
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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 ........................................................ 17
Figure 3.2: Example of checkerboard images required for camera calibration .......... 19
Figure 3.3: Glare on base plate due to strain gauges.............................................................. 22
Figure 3.4: Typical anchor currently in production vs. test anchor ................................. 24
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
Figure 3.6: Test frame with HSS cross-section dimensions and moment resistances
..................................................................................................................................................................... 26
Figure 3.7: Full experimental test setup ..................................................................................... 28
Figure 3.8: Top left: steel plate with scribed lines; bottom right: galvanized steel
plate with scribed lines ...................................................................................................................... 29
Figure 3.9: Steel plate with lines scribed after plate sprayed with blue tool dye paint
..................................................................................................................................................................... 29
Figure 4.1: Test 01 Anchor setup and direction of applied test load ............................... 31
Figure 4.2: Test 01 Strain Gauge Locations ............................................................................... 32
Figure 4.3: Test 01 strain gauge 1 data ....................................................................................... 33
Figure 4.4: Test 01 strain gauge 2 data ....................................................................................... 33
Figure 4.5: Test 01 strain gauge 3 data ....................................................................................... 34
Figure 4.6: Test 01 strain gauge 4 data ....................................................................................... 34
Figure 4.7: Line along which deflection measurements were taken; test load pull the
pier to the right in this image .......................................................................................................... 36
Figure 4.8: Test 01 Deformation under 15kN Load ................................................................ 36
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 .............. 37
Figure 4.10: Test 02 Anchor setup and direction of applied test load ............................ 39
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Figure 4.11: Test 02 line along which deformation was measured; test load applied
parallel the red line, to the right of the image .......................................................................... 41
Figure 4.12: Test 02 Failure of the anchor base plate ........................................................... 41
Figure 4.13: Test 02 plot of the change in shape of the base plate along a line on the
side of the plate ..................................................................................................................................... 42
Figure 4.14: Test 03 Anchor setup and direction of applied test load ............................ 43
Figure 4.15: Test 03 Maximum deformation in the base plate before the observable
weld failure............................................................................................................................................. 44
Figure 4.16: Test 03 Line on side of plate over which permanent deformation was
measured; horizontal load pulled to the right .......................................................................... 44
Figure 4.17: Test 03 Line at back of plate over which permanent deformation was
measured; horizontal load pulled to the right .......................................................................... 45
Figure 4.18: Test 03 Out of plane deflection at the side of the base plate ..................... 46
Figure 4.19: Test 03 Out of plane deflection at the back of the base plate .................... 47
Figure 4.20: Test 04 Anchor setup and direction of applied test load ............................ 48
Figure 4.21: Test 04 Deformation of anchor base plate at 14.0kN load ......................... 49
Figure 4.22: Test 04 Line at which permanent deformation in the base plate was
measured ................................................................................................................................................. 49
Figure 4.23: Test 04 Out of plane deflection along the side of the base plate .............. 50
Figure 4.24: Test 05 Anchor setup and direction of applied load ..................................... 51
Figure 4.25: Test 05 shape of base plate under 10.0kN load; load pulled to the left in
this image ................................................................................................................................................ 52
Figure 4.26: Test 05 Line along which deformation in plate is measured; load pulled
to the left in this image ...................................................................................................................... 52
Figure 4.27: Test 05 Out of Plane Deflection in the base plate .......................................... 53
Figure 4.28: Test 06 Anchor setup and direction of applied load ..................................... 54
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 ............................................................................................... 55
Figure 4.30: Test 06 Line on side of plate at which deflection was measured ............ 55
Figure 4.31: Test 06 Out of plane deflection at side of plate ............................................... 56
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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 ............................................................................................ 57
Figure 4.33: Test 06 Line along the back of the base plate along which deflection was
measured ................................................................................................................................................. 57
Figure 4.34: Test 06 Out of plane deflection at back of plate ............................................. 58
Figure 4.35: Tensile test dogbone dimensions; 1/4" plate thickness ............................. 61
Figure 4.36: Failure of tensile test coupons............................................................................... 61
Figure 4.37: Section properties for a rectangular plate, taken from the Handbook of
Steel Construction [102] ................................................................................................................... 63
Figure 4.38: Test 01 base plate bending lines used for calculating Z .............................. 63
Figure 4.39: Test 02 base plate bending lines used for calculating Z .............................. 64
Figure 4.40: Test 03 base plate bending lines used for calculating Z .............................. 65
Figure 4.41: Test 04 base plate bending lines used for calculating Z .............................. 66
Figure 4.42: Test 05 base plate bending lines used for calculating Z .............................. 66
Figure 4.43: Test 06 base plate bending lines used for calculating Z .............................. 67
Figure 5.1: FEA mesh .......................................................................................................................... 72
Figure 5.2: FEA constraints and load ........................................................................................... 72
Figure 5.3: Test 01 FEA stress in anchor .................................................................................... 73
Figure 5.4: Test 01 FEA stress in base plate .............................................................................. 74
Figure 5.5: Test 01 FEA out of plate deformation of base plate......................................... 75
Figure 5.6: Test 02 FEA stress in anchor .................................................................................... 76
Figure 5.7: Test 02 physical test image showing plate fracture ........................................ 76
Figure 5.8: Test 02 FEA stress in base plate .............................................................................. 77
Figure 5.9: Test 02 FEA out of plane deformation in base plate........................................ 78
Figure 5.10: Test 03 FEA stress in anchor .................................................................................. 79
Figure 5.11: Test 03 physical test image showing plate fracture ...................................... 79
Figure 5.12: Test 03 FEA stress in base plate ........................................................................... 80
Figure 5.13: Test 03 FEA out of plane deformation in base plate ..................................... 80
Figure 5.14: Test 04 FEA stress in anchor .................................................................................. 82
Figure 5.15: Test 04 shape of plate under test load of 13.0kN ........................................... 82
Figure 5.16: Test 04 FEA stress in base plate ........................................................................... 83
x
Figure 5.17: Test 04 FEA out of plane deformation in base plate ..................................... 84
Figure 5.18: Test 05 FEA stress in anchor .................................................................................. 85
Figure 5.19: Test 05 image showing crack initiation around weld at the back of the
pier............................................................................................................................................................. 86
Figure 5.20: Test 05 FEA stress in base plate ........................................................................... 86
Figure 5.21: Test 05 FEA out of plane deformation in base plate ..................................... 87
Figure 5.22: Test 06 FEA stress in anchor .................................................................................. 88
Figure 5.23: Test 06 fracture in base plate during experimental testing ....................... 88
Figure 5.24: Test 06 FEA stress in base plate ........................................................................... 89
Figure 5.25: Test 06 FEA out of plane deformation in base plate ..................................... 90
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
2
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.
3
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.
4
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.
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.
6
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.
7
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
8
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.
2.2.1 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
9
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.
10
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
11
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].
2.2.3 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
12
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
13
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
14
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
15
model for the prediction of the reactions of safety anchor and davit base plates under a
moment load.
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
17
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
3.3.1 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
18
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.
19
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
20
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.
3.3.2 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 0.00001 mm or more would have been
required to calculate strain based on deformation measurements.
21
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.
22
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
23
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.
24
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
25
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)
26
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
27
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 two-
ton (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).
28
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
29
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
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
4.2.1 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).
31
Figure 4.1: Test 01 Anchor setup and direction of applied test load
4.2.2 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 4.2.
32
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.
33
Figure 4.3: Test 01 strain gauge 1 data
Figure 4.4: Test 01 strain gauge 2 data
0
5
10
15
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35Hori
zonta
l F
orc
e on A
nch
or
Poin
t (k
N)
Strain x10e-3 (in compression)
Test 01: Strain Gauge 1 Data
Measured test
strain
0
5
10
15
0 0.5 1 1.5 2 2.5 3 3.5
Hori
zonta
l F
orc
e on A
nch
or
Poin
t (k
N)
Strain x10e-3 (in tension)
Test 01: Strain Gauge 2 Data
Measured test strain
0.2% offset strain line
Series3
34
Figure 4.5: Test 01 strain gauge 3 data
Figure 4.6: Test 01 strain gauge 4 data
0
5
10
15
0 0.5 1 1.5 2 2.5 3
Hori
zonta
l L
oad
on A
nch
or
Poin
t
(kN
)
Strain x10e-3 (in tension)
Test 01: Strain Gauge 3 Data
Measured test
strain0.2% offset
strain line
0
5
10
15
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8Hori
zonta
l L
oad
on A
nch
or
Poin
t (k
N)
Strain x10e-3 (in compression)
Test 04: Strain Gauge 4 Data
Measured test
strain0.2% offset
strain line
35
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)
1 4.2
2 4.2
3 8.4
4 5.7
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 4.8.
36
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
37
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
38
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
4.3.1 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.
39
Figure 4.10: Test 02 Anchor setup and direction of applied test load
4.3.2 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
40
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 4.11.
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.
41
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 4.13. 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.
42
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.
43
4.4 Test 03: Four bolts base plate connection; horizontal load
perpendicular to the supporting HSS
4.4.1 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
4.4.2 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
44
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
45
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.
46
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 4.19.
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 7.0
47
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
4.5.1 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).
48
Figure 4.20: Test 04 Anchor setup and direction of applied test load
4.5.2 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 4.22.
49
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 4.23. 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
50
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
4.6.1 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).
51
Figure 4.24: Test 05 Anchor setup and direction of applied load
4.6.2 Test 05 DIC Data and Analysis
The shape to which this anchor base plate deformed can be seen in Figure 4.25. 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
52
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 4.26.
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 4.27. 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
53
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
4.7.1 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
54
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
4.7.2 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 4.33.
55
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
56
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 4.31. 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
57
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 4.33. 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
58
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 4.32. 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 4.31.
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
59
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 01
4.2 2.84
Test 02
7.5 5.06
Test 03
6.5 4.39
Test 04
5.0 3.38
Test 05
5.25 3.54
Test 06
5.25 3.54
Table 4-2: Max. loads in the base plates before permanent deformation occurs
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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.
61
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 4.35. 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
4.36.
Figure 4.36: Failure of tensile test coupons
62
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 4.37. Since the base plate analysed
in this testing did not undergo pure bending, calculating Z=b*d2/4 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 mm2/4= 5757 mm3, then
multiplied by the yield strength, Mr=5757 mm3*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.
63
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*d2/4, used for calculating the elastic section
modulus, as shown in Figure 4.37. 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
64
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 10.3x103mm3 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 4.39. 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
65
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.
66
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
67
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 4.43. 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
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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.
69
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.
70
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
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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 372 543 190 000
Pier HSS 317 450 200 000
Rectangular HSS 350 450 200 000
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
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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.
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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.
5.3.1 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
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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).
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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.
5.3.2 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,
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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
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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.
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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.
5.3.3 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
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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
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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
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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.
5.3.4 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 5.14.
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Figure 5.14: Test 04 FEA stress in anchor
Figure 5.15: Test 04 shape of plate under test load of 13.0kN
83
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.
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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 10.96 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
85
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.
5.3.5 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
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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
87
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 5.19. 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 5.21.
5.3.6 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
88
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
89
Figure 5.24: Test 06 FEA stress in base plate
The maximum stress in the plate determined by the FEA in Figure 5.24 was 481 MPa.
These locations occurred in areas that could not be analysed with DIC or strain gauges.
The DIC results measured the change in shape of two lines on this plate. One line was 2”
away from the bottom edge of the plate and the other was 2” away from the right edge of
the plate shown in Figure 5.24. The lines on the plate can be seen in Figure 4.30 and
Figure 4.33. These areas of the plate showed stresses below the yield stress of the plate.
The results of the FEA for the stresses in the plate matched the data collected during the
experimental testing of this anchor configuration.
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Figure 5.25: Test 06 FEA out of plane deformation in base plate
The maximum deformation shown the in FEA model of the plate occurred at the back
corner of the plate that was not bolted. The predicted out of plane deformation in Figure
5.25 was 3.18 mm and the measured deformation using DIC was 7.59 mm. The reasoning
for this discrepancy was the same as discussed in previous tests. It was interesting to note
that there was no deformation in the plate at the front of the pier. When the plate started to
permanently deform, a bend line was seen along the front of the plate, tangent to the front
tip of the weld area (see Figure 5.23). It was possible that the deformation in this area only
starts to occur once the plate had started yielding between the pier and the back bolt (also
a location of bending that can be seen in Figure 5.23). Once the back sections of the base
plate started to permanently deform, more of the load was dispersed to the front of the
plane, creating a second line of bending at the front of the plate.
5.4 FEA Model Conclusions
Overall, the finite element model results agreed reasonably well with the data
collected during experimental testing in Chapter 4. The highest stresses in the FEA
were in the base plate. This was as expected because the anchor pier and support HSS
91
were designed to withstand larger loads than the base plate. The maximum stress
concentrations around the pier in the weld occurred at areas that ultimately failed in
the experimental testing at higher loads. The stress around the bolt holes was
concentrated at bolts that deformed significantly by the end of the tests.
Some of the stresses predicted were higher than the yield stress of the plate. However,
these predicted areas of high stress were at or below the ultimate strength and were
in areas of the plate for which stress could not be measured. It was possible that these
stresses were present during physical testing. There were several reasons some of
the high stress areas could not have been analysed in the physical testing. The areas
around the bolts were obscured by the nut on the top of the rod. The nut prevented
DIC readings being taken for deflection around the bolt holes; the omission of
washers under the nut was done to prevent further obstruction on the plate around
the area of the threaded rods. The nut also prevented strain gauges from being
adhered to these areas to measure the strain around the bolt holes. The other area of
high stress was around the weld connecting the pier to the base plate. Strain gauges
cannot be used in this area of the plate because of the heat affected zone created by
the weld. The weld also obscured parts of the grid scribed in the blue tool dye paint.
The grid was used to select the point used for DIC analysis of the base plate. In the
areas where the grid was ruined by the welding, DIC reading could not be taken.
Most of the deformation results predicted by FEA were smaller that the measured
deformation using DIC at the same loads as those applied in the finite element model.
There were multiple reasons which, acting together, can explain this discrepancy. The
first was that the anchor may have shifted and settled once the load was applied to
the top of the anchor pier. The anchor plate and HSS support may not have been
completely flat, leading to the rotation of the anchor plate between the load
increments applied before plastic deformation. This was especially likely given the
lines plotted from the DIC results in the experimental testing analysis confirm this
phenomenon. In multiple tests, the line along which points were measured retained
its overall shape, but the location shifted (either up, down or rotated) before the onset
of permanent deformation. This shift may have explained the relatively large
92
displacement measured during testing versus the deformation predicted by FEA.
Another phenomenon that affected the physical testing was the fact that the plate
deformed slightly around the heat affected weld area during the welding process. The
addition of heat in the centre of the plate caused the edges of the plate to tilt upwards.
A relatively large weld (1/2”) was used on the 3/8” plate so that the weld, like the
pier and supporting HSS, was overdesigned for anticipated test loads. The fact that
the weld was overdesigned was further supported by the fact that the fracture in the
system often occurred through the base plate at the edge of the welded section.
Recommendations for the improving the model to better reflect measured test data
includes adding the heat affected zone around the weld as part of the model. This area
had a stress concentration in all the models and many of the base plates failed in this
area during experimental testing. Another suggestion would be to include more of the
components that were removed to simplify the model. These include the anchor hook
up point, a longer section of the supporting HSS, the full length of the threaded anchor
rods and the angles underneath the supporting HSS used to fasten the anchor to the
test frame. Adding these items to the model may result in FEA deflection predictions
closer to the measured deflection from the experimental testing.
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Chapter 6 Conclusions and Recommendations
6.1 Conclusions
There were two different anchor models studied: one was fasted to the supporting HSS
with four threaded rods wrapped around the support structure and the other was fastened
to the HSS by two threaded rods wrapping around the HSS. Since the anchor must be able
to withstand a load applied in any direction, three different load directions were tested for
each anchor.
The test frame performed as was expected. No deformation was observed in the test frame.
As test loads increased, the angle of the pier changed as the plate started to bend. However,
the pier itself underwent no visible deformation. The threaded rods holding the anchor to
the supporting system did undergo visible deformation. This deformation was observed to
only have started after the plate started yielding and bending out of shape. Therefore, it was
concluded that since this deformation only began after the permanent deformation of the
base plate began, that the bending in the threaded rods did not affect the DIC results used
to determine when the base plate started plastically deforming.
The use of DIC for measuring the deformation of the plate was an effective method for
analyzing the deflection of the anchor base plates under a moment load. The greatest
advantage of this measurement method was that the location of points on the plate can be
measured after the test was finished. This allowed the areas of maximum deflection to be
observed before the measurements were taken. Using the MATLAB program for DIC
analysis provided a strong platform for processing and presenting the collected data.
Every component of the test setup functioned as expected. In the future, this setup could
continue to be used for further testing. This can include different anchor configurations
which could include variables such as plate thickness, base plate span, pier diameter, bolt
diameter and different materials. Through further analysis using this test setup, the variable
in the anchor design could be optimized for multiple applications.
94
The load at which the base plates started permanently deforming was spread over a wider
range for the four-bolt anchor, ranging from 4.2 kN to 7.5 kN. The two-bolt anchor plates
started plastically deforming in a range of 5.0 kN to 5.5 kN. The two-bolt fastening system
was generally weaker. This is to be expected as there were fewer bolts holding the anchor
base plate in place. The fact that the base plates started plastically deforming at similar
loads in all directions showed that the two-bolts anchor configuration was less sensitive to
the direction of the applied load.
Most of the anchors tested experienced fracture in the plate around the outside edge of the
weld. The one exception was test 03; this anchor had no bolt on the back half of the plate
and therefore no large tension load between the weld area and a bolt hole. For the other
five anchor configurations, a crack formed in the base plate at the edge of the weld in the
closest area to any bolts being pulled in tension. For the anchor bolts with two threaded
rods under tension loads, the cracks formed in two locations, then eventually joined in the
center. The area of the plate under the anchor pier was stiffened by the presence of the pier.
Around the pier, the ½” weld also provided additional strength. Therefore, the section of
plate at the outside of the weld became a weak spot in the structure and, consequently, the
area in the plate that fractures when the structure ultimately fails.
The FEA model proposed agreed with the data collected during the experimental analysis.
The maximum predicted stresses were shown to be in the areas of the plate that ultimately
failed. The deflection in the FEA model was smaller in general than the measurements
measured during the physical testing. This was likely due to the plate shifting and from the
base plate deforming after the pier was welded to the center.
6.2 Recommendations
The analysis of anchor base plates in this thesis provides a start to understanding the
behaviour of large span plates undergoing moment loads applied to the center of the
plate through round piers. To get a more comprehensive understanding of these base
plates, more configurations of plates should be tested. As base plate thicknesses are
95
increased the system becomes more rigid. It would be interesting to test thicker
plates to determine if the plate thickness affects which areas of the plate deform.
The tests performed gave an idea of where the base plates should deform. In future
tests, the grid can potentially be drawn with points closer together in areas that are
suspected to be of higher interest. This will provide more plot points, which can lead
to more accurate data.
Further work on the FEA model to include the effects of the head affected zone around
the weld area could help to obtain more accurate deformation predictions. Another
improvement to the model could be to include more of the components from the
experimental test setup that were excluded in the model.
The finite element model was shown to predict that the areas of high stress were seen
in areas for which deflection and strain could not be measured. If a method could be
found to measure the behaviour of the base plates in these areas, that would be
helpful in determining the validity of the finite element model. One possible solution
could be welding the pier to the plate before spraying the anchor base with the blue
tool dye paint and scribing the grid. It would be more difficult to draw the grid in this
case, but it may be possible to take DIC deformation closer to the welded area on the
plate.
96
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