uhpfrc cladding panels in façade applications

University of Calgary

PRISM: University of Calgary's Digital Repository

Graduate Studies The Vault: Electronic Theses and Dissertations

2014-12-15

Ultra High Performance Fibre Reinforced Concrete

Spandrel Cladding Panels in Façade Applications

Pesta, David Thomas

Pesta, D. T. (2014). Ultra High Performance Fibre Reinforced Concrete Spandrel Cladding Panels

in Façade Applications (Unpublished master's thesis). University of Calgary, Calgary, AB.

doi:10.11575/PRISM/28543

http://hdl.handle.net/11023/1960

master thesis

University of Calgary graduate students retain copyright ownership and moral rights for their

thesis. You may use this material in any way that is permitted by the Copyright Act or through

licensing that has been assigned to the document. For uses that are not allowable under

copyright legislation or licensing, you are required to seek permission.

Downloaded from PRISM: https://prism.ucalgary.ca

UNIVERSITY OF CALGARY

Ultra High Performance Fibre Reinforced Concrete Spandrel Cladding Panels in Façade

Applications

by

David Thomas Pesta

A THESIS

SUBMITTED TO THE FACULTY OF GRADUATE STUDIES

IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE

DEGREE OF MASTER OF ENGINEERING

GRADUATE PROGRAM IN CIVIL ENGINEERING

CALGARY, ALBERTA

NOVEMBER, 2014

© David Thomas Pesta 2014

ii

Abstract

A novel spandrel cladding panel design using Ultra High Performance Fibre Reinforced

Concrete (UHPFRC) with Glass Fibre Reinforced Polymer (GFRP) reinforcing bars are load

tested and compared to analytical calculations and the results of an elastic finite element

analysis. Five panels are load tested, three subjected to static load testing, and two subjected to

fatigue load testing. The deflection of the panels under serviceability wind pressure load testing

agreed well with the calculated values, in most cases deflecting less than the design limit. The

failure strength of the panels was shown to be as much as four times higher than calculated.

Results of the fatigue testing concluded that the panels were unaffected by cyclic loading at the

simulated wind loading levels.

iii

Preface

While this thesis presents a complete examination of the research conducted, it is

important to note that the author was not involved in the development of the test programme or

in conducting the testing itself. All testing was conducted prior to the author’s involvement in the

project. However, this information was included for the purpose of discussion and to provide

context to the analysis performed. The testing of the cladding panels was performed prior to the

construction of the building on which the panels were to be used; however construction of the

building and installation of the cladding panels was completed prior to the finalization of this

analysis. The author contributed the analytical and finite element modelling calculations and

analyzed the testing results.

iv

Acknowledgements

The research was completed at the M.A. Ward Structural Laboratory at the Department

of Civil Engineering, Schulich School of Engineering, University of Calgary. Funding for the

static testing of the panels was provided by Lafarge North America Ltd while the funding for the

fatigue testing of the panels was provided by the Natural Sciences and Engineering Research

Council. Lafarge North America Ltd also produced and provided the panels required for testing.

Special recognition is given to Jeffrey Beaudry and Cariaga Ignacio of Lafarge North America

Ltd for their contribution to this project. Additionally, thanks are given to the technical staff at

the Structures Laboratory for their assistance with conducting the testing, including Donald

Anson, Mirsad Berbic, Daniel Larson, Daniel Tilleman, and Terry Quinn.

Recognition is also given to the structural project team at DIALOG (formerly Cohos

Evamy Integratedesign). Specifically, recognition is given to Gamal Ghoneim for development

of the panel design to be tested and Russ Parnell for his contribution towards the finite element

analysis. Additionally, the author expresses his gratitude towards Ralph Hildenbrandt for

providing the opportunity to pursue advanced research. The creativity of the design team at

DIALOG facilitated the development of this unique building component despite challenging

project restrictions.

Lastly, the author would like to acknowledge Dr. Raafat El-Hacha for providing this

research opportunity and for his academic and professional guidance. His passion for the use of

high performance, cutting edge materials and his depth of knowledge on the subject matter

greatly enhanced the project.

v

Dedication

With thanks to my family and friends

– and especially my wife –

for their support and encouragement.

vi

Table of Contents

Abstract ............................................................................................................................... ii Preface................................................................................................................................ iii Acknowledgements ............................................................................................................ iv Dedication ............................................................................................................................v Table of Contents ............................................................................................................... vi List of Tables ..................................................................................................................... ix List of Figures and Illustrations ...........................................................................................x List of Symbols, Abbreviations and Nomenclature ......................................................... xiv

CHAPTER ONE: INTRODUCTION AND BACKGROUND ...........................................1 1.1 Introduction ................................................................................................................1

1.2 Project Description ....................................................................................................1 1.2.1 Curtain Wall System ..........................................................................................2 1.2.2 Ductal® UHPFRC Spandrel Panels ...................................................................4

1.3 Research Plan .............................................................................................................5 1.3.1 Static Load Testing ............................................................................................5 1.3.2 Fatigue Load Testing .......................................................................................10

CHAPTER TWO: INITIAL ANALYSIS ..........................................................................11 2.1 Required Resistance Analysis by Statics .................................................................11 2.2 Section Resistance by Statics ...................................................................................14

2.2.1 Determination of Moment-Curvature Diagrams .............................................14 2.2.2 Determination of Anticipated Deflection ........................................................24

2.3 Finite Element Analysis ...........................................................................................29

2.3.1 Definition of Element Type .............................................................................30 2.3.2 Definition of Material Properties .....................................................................30 2.3.3 Creation of Model Geometry ...........................................................................31 2.3.4 Generation of Mesh .........................................................................................31 2.3.5 Definition of Boundary Conditions .................................................................33 2.3.6 Results of Finite Element Analysis .................................................................34

2.3.6.1 Short Panel .............................................................................................34 2.3.6.2 Long Panels ............................................................................................38

CHAPTER THREE: CONSTRUCTION OF TEST SPECIMENS ...................................42 3.1 Procedure .................................................................................................................42 3.2 Materials ..................................................................................................................45

3.2.1 Ductal® UHPFRC ............................................................................................45

3.2.2 Pultrall V-ROD® GFRP Reinforcing...............................................................47 3.2.3 UCAN Cast-In Zamac Insert ...........................................................................48

3.3 Panel Ribs ................................................................................................................50 3.4 Strain Gauges ...........................................................................................................52

3.4.1 Static Test Short Panel .....................................................................................52 3.4.2 Static Test Long Panels ...................................................................................54

vii

3.4.3 Fatigue Test Short Panels ................................................................................55

CHAPTER FOUR: TEST SETUP AND PROCEDURES ................................................56 4.1 Static Test Panels .....................................................................................................56

4.1.1 Test Frame Setup .............................................................................................56 4.1.1.1 Test No. 1 – Positive Pressure Supports ................................................57 4.1.1.2 Test No. 2 and No. 3 – Negative Pressure Supports ..............................58

4.1.2 Instrumentation ................................................................................................59 4.1.3 Applied Loading ..............................................................................................62 4.1.4 Data Collection ................................................................................................67

4.2 Fatigue Test Short Panels ........................................................................................68 4.2.1 Test Frame Setup .............................................................................................68

4.2.1.1 Load Application ...................................................................................68

4.2.1.1.1 Fatigue Test Method ...........................................................................68 4.2.1.2 Testing Supports ....................................................................................70

4.2.2 Procedure .........................................................................................................70 4.2.2.1 Cyclic Loading .......................................................................................70 4.2.2.2 Data Collection ......................................................................................72

CHAPTER FIVE: TEST RESULTS .................................................................................73 5.1 Static Test Short Panel .............................................................................................73

5.1.1 Displacement ...................................................................................................73 5.1.2 Strains ..............................................................................................................77 5.1.3 Visual Observation ..........................................................................................79

5.2 Static Test Long Panels ............................................................................................80 5.2.1 Long Panel #1 ..................................................................................................80

5.2.1.1 Displacement .........................................................................................80 5.2.1.2 Strains ....................................................................................................85 5.2.1.3 Visual Observations ...............................................................................88

5.2.2 Long Panel #2 ..................................................................................................88 5.2.2.1 Displacement .........................................................................................88 5.2.2.2 Strains ....................................................................................................92

5.2.2.3 Visual Observations ...............................................................................95 5.3 Fatigue Test Short Panels ........................................................................................95

5.3.1 Displacement ...................................................................................................95 5.3.1.1 Cyclic Loading .......................................................................................95 5.3.1.2 Failure Loading ....................................................................................101

5.3.2 Strains ............................................................................................................102

5.3.3 Visual Observation ........................................................................................104

CHAPTER SIX: COMPARISON OF RESULTS AND DESIGN VALIDATION ........105 6.1 Static Test Comparison and Validation .................................................................105 6.2 Fatigue Test Comparison and Validation ..............................................................108

6.3 Sources of Uncertainty ...........................................................................................109

CHAPTER SEVEN: CONCLUSION AND RECOMMENDATIONS ..........................110

viii

REFERENCES ................................................................................................................111

APPENDIX A: EMBEDDED ANCHOR PULLOUT CALCULATIONS .....................114

APPENDIX B: COPYRIGHT PERMISSIONS ..............................................................116 2.1 D’AMBROSIO architecture + urbanism ...............................................................116 2.2 DIALOG ................................................................................................................118 2.3 Hoffmann Architects, Inc. .....................................................................................120 2.4 Lafarge Precast ......................................................................................................122

ix

List of Tables

Table 2.1 - Calculated contribution to stiffness of rib surface texture .......................................... 12

Table 2.2 - Calculated maximum moment for various panel sections .......................................... 14

Table 2.3 - Summary of calculated results for panel members ..................................................... 28

Table 2.4 - Comparison of selected results from various mesh densities ..................................... 33

Table 2.5 - Unfactored top and bottom stresses in short panel elements ...................................... 37

Table 2.6 - Unfactored top and bottom stresses in long panel elements....................................... 41

Table 3.1 - Selected Properties of Ductal® UHPFRC [4] [15] ..................................................... 46

Table 3.2 Selected Properties of Pultrall V-ROD® GFRP 6mm Reinforcing Bars [17] ............ 48

Table 3.3 ........................... 49

Table 4.1 - Applied loading for Test No. 1 ................................................................................... 63

Table 4.2 - Applied loading for Test No. 2 ................................................................................... 64

Table 4.3 - Fatigue Test Loading Method .................................................................................... 71

Table 5.1 - Summary of Test Results for Static Test Short Panel ................................................ 77

Table 5.2 - Summary of Test Results for Static Test Long Panel #1............................................ 85

Table 5.3 - Summary of Test Results for Static Test Long Panel #2............................................ 92

Table 6.1 - Comparison of predicted and measured panel deflections ....................................... 106

Table 6.2 - Comparison of calculated and measured cracking and failure pressure ................... 107

2 - S

2 - S Selected Properties for UCAN Cast-In Zamac PZI 24 Inserts [18] .

x

List of Figures and Illustrations

Figure 1.1 - Example of the UHPFRC cladding panels .................................................................. 1

Figure 1.2 - Completed 800 Yates building – the white cladding panels are the focus of this analysis. ................................................................................................................................... 2

Figure 1.3 - Typical curtain wall framing arrangement and components [1] ................................. 3

Figure 1.4 - Construction details of prototype short cladding panels ............................................. 8

Figure 1.5 - Construction details of prototype long cladding panels ............................................ 10

Figure 2.1 - Measurements to determine infill aspect ratio for short panel (left) and long panel (right) ........................................................................................................................... 11

Figure 2.2 - Labels used to identify panel members for short (left) and long (right) panels ........ 13

Figure 2.3 - Summary of analytical moment resistance calculations ........................................... 16

Figure 2.4 - Alpha and Beta factor variation with strain .............................................................. 20

Figure 2.5 - Calculated moment-curvature diagrams for various panel members ........................ 23

Figure 2.6 - Calculated deflection under load of elements ........................................................... 26

Figure 2.7 - Enlarged calculated deflection under load of elements ............................................. 26

Figure 2.8 - Comparison of mesh options for short panels ........................................................... 32

Figure 2.9 - Comparison of mesh options for long panels ............................................................ 32

Figure 2.10 - Applied boundary conditions to short (left) and long (right) finite element models ................................................................................................................................... 34

Figure 2.11 - Stresses in the panel due to self-weight .................................................................. 35

Figure 2.12 - Undeformed and deformed geometry (left) and predicted lateral deflections (right) due to negative pressure ............................................................................................. 36

Figure 2.13 - Moments in the short (left) and narrow (right) members for negative pressure ..... 36

Figure 2.14 - Maximum principal stress (tension) for positive pressure (left) and negative pressure (right) ...................................................................................................................... 37

Figure 2.15 - Stresses in the panel due to self-weight .................................................................. 38

xi

Figure 2.16 - Undeformed and deformed geometry (left) and predicted lateral deflections (right) due to negative pressure ............................................................................................. 39

Figure 2.17 - Moments in the long members for negative pressure ............................................. 39

Figure 2.18 - Maximum principal stress (tension) ........................................................................ 40

Figure 3.1 - Back form panel prepared with GFRP reinforcing bars and cast-in inserts .............. 42

Figure 3.2 - Preparing the forms for casting, front form with ribs on ground, back form upright ................................................................................................................................... 43

Figure 3.3 - Pouring the Ductal® concrete into the forms............................................................. 43

Figure 3.4 - Completed short panel (back side) ............................................................................ 44

Figure 3.5 - Completed long panel (back side) ............................................................................. 44

Figure 3.6 - Completed short panel (front side) ............................................................................ 45

Figure 3.7 - Idealized Ductal® UHPFRC Stress-Strain for compression (left), and tension (right) with the ULS relationship in red and the SLS in green ............................................. 47

Figure 3.8 - Failure mode of UCAN Cast-In Zamac Inserts in Ductal® concrete ........................ 49

Figure 3.9 - Surface formwork and casting (top), and completed textured surface (bottom) ....... 51

Figure 3.10 - Surface strain gauges applied to short panels ......................................................... 53

Figure 3.11 - Surface strain gauges applied to long panels .......................................................... 54

Figure 3.12 - Surface strain gauges applied to short fatigue panels ............................................. 55

Figure 4.1 - Use of an air mattress to provide uniform pressure .................................................. 57

Figure 4.2 - Schematic of Test No. 1 test setup ............................................................................ 58

Figure 4.3 - Positive pressure support condition .......................................................................... 58

Figure 4.4 - Schematic of Test No. 2 and No. 3 test setup ........................................................... 59

Figure 4.5 - Negative pressure support condition ......................................................................... 59

Figure 4.6 - Location of deflection transducers ............................................................................ 61

Figure 4.7 - Loading applied to short panel in Tests No. 1 and No. 2 .......................................... 65

Figure 4.8 - Loading applied to long panels in Tests No. 1 and No. 2 ......................................... 65

xii

Figure 4.9 - Loading applied to short panel in sustained loading following Tests No. 1 and No.2 ....................................................................................................................................... 66

Figure 4.10 - Loading applied to long panels in sustained loading following Tests No. 1 and No. 2 ...................................................................................................................................... 67

Figure 4.11 - Holes required in fatigue test panel to allow installation of test frame and top portion of the test frame ........................................................................................................ 69

Figure 4.12 - Assembled test frame .............................................................................................. 69

Figure 4.13 - Fatigue testing support condition ............................................................................ 70

Figure 4.14 - Applied fatigue loading levels ................................................................................ 72

Figure 5.1 - Short Panel: Central deflection under load through various load cycles .................. 73

Figure 5.2 - Short Panel: Central deflection under sustained loading after Test No. 1 & 2 ......... 74

Figure 5.3 - Short Panel: Central deflection with time under sustained load Test No. 1 & 2 ...... 74

Figure 5.4 - Comparison of deflections at various points of the short panel ................................ 75

Figure 5.5 - Short Panel: Central deflection of panel through Test No. 3 (to failure) .................. 76

Figure 5.6 - Strain of elements in short panel under Test No. 1 (positive) loading ...................... 78

Figure 5.7 - Strain of elements in short panel under Test No. 2 (negative) loading ..................... 79

Figure 5.8 - Cracking in the short panel prior to failure ............................................................... 80

Figure 5.9 - Permanent deformation following loading to failure ................................................ 80

Figure 5.10 - Long Panel 1: Central deflection under load through various loading cycles ........ 81

Figure 5.11 - Long Panel 1: Central deflection under sustained loading for Tests No. 1 & 2 ..... 82

Figure 5.12 - Long Panel 1: Central deflection under sustained load for Tests No. 1 & 2........... 82

Figure 5.13 - Comparison of deflections at various points of Long Panel 1 ................................ 83

Figure 5.14 - Long Panel 1: Central deflection of panel through Test No. 3 (to failure) ............. 84

Figure 5.15 - Strain of elements in Long Panel 1 under Test No. 1 (positive) loading ................ 86

Figure 5.16 - Strain of elements in Long Panel 1 under Test No. 2 (negative) loading ............... 87

Figure 5.17 - Strain in the GFRP reinforcing bars for Long Panel 1 ............................................ 87

xiii

Figure 5.18 - Final failure of Panel #1 .......................................................................................... 88



Figure 5.21 - Long Panel 2: Central deflection under sustained load for Tests No. 1 & 2........... 90

Figure 5.22 - Long Panel 2: Central deflection of panel through Test No. 3 (to failure) ............. 91

Figure 5.23 - Strain of elements in Long Panel 2 under Test No. 1 (positive) loading ................ 93

Figure 5.24 - Strain of elements in Long Panel 2 under Test No. 2 (negative) loading ............... 94

Figure 5.25 - Strain in the GFRP reinforcing bars for Long Panel 2 ............................................ 94

Figure 5.26 - Final failure of Panel #2 .......................................................................................... 95

Figure 5.27 - Select load-deflection charts for load level A fatigue testing ................................. 98

Figure 5.28 - Select load-deflection charts for load level B fatigue testing ................................. 99

Figure 5.29 - Select load-deflection charts for load level C & D fatigue testing ....................... 100

Figure 5.30 - Peak deflection and deflection range progression through fatigue testing ........... 101

Figure 5.31 - Test to failure of panels following fatigue testing ................................................ 102

Figure 5.32 - Strain measurements at the cast-in insert in failure loading following fatigue testing .................................................................................................................................. 103

Figure 5.33 - Failure of cast-in inserts following fatigue loading .............................................. 104

xiv

List of Symbols, Abbreviations and Nomenclature

Symbol Definition CSA Canadian Standards Association GFRP Glass Fibre Reinforced Polymer LEED Leadership in Energy and Environmental Design LDS Linear Displacement Sensor LPS Laser Position Sensor NBCC National Building Code of Canada SLS Serviceability Limit State UHPFRC Ultra High Performance Fibre Reinforced

Concrete ULS Ultimate Limit State

1

Chapter One: Introduction and Background

1.1 Introduction

The purpose of the study was to confirm the design of spandrel panels for use in the

curtain wall system of a mid-rise building subject to wind loading. This project used Ultra High

Performance Fibre Reinforced Concrete (UHPFRC) as an alternative to stone or concrete. Initial

design was done by analytical calculations and finite element modelling, with prototypes of the

selected design then subjected to load testing. Both static load tests and fatigue load tests were

conducted to ensure satisfactory performance of the panels throughout the design life. An

example of one of the panels can be seen in Figure 1.1.

Photo by: Lafarge Precast

Figure 1.1 - Example of the UHPFRC cladding panels

1.2 Project Description

The building on which the spandrel panels are to be used – 800 Yates – is a Class AA

commercial development, shown in Figure 1.2, located in Victoria, British Columbia, Canada. It

is a seven storey, 20,000 square meter concrete construction building achieving LEED Gold

2

Certification. The building integrates a curvilinear building shape and the appearance of a

random cladding panel arrangement, both being aspects of particular importance to the cladding

panel system discussed. A result of the irregular pattern of the cladding was the requirement for a

selection of cladding panel sizes to complete the curtain wall system.


Figure 1.2 - Completed 800 Yates building – the white cladding panels are the focus of this

analysis.

1.2.1 Curtain Wall System

A curtain wall system is a means of cladding a building with the benefit of the cladding

support being predominantly separate from the primary structure of the building. This allows the

primary construction to proceed independently of the cladding, easing construction scheduling.

The curtain wall system will typically support its own self-weight plus any horizontal loads

applied to the façade such as wind loading and the induced seismic loading from the motion of

the primary structure during a seismic event. The system consists of mullions spanning vertically

between floors, which may be divided by horizontal transoms if required. These mullions

3

provide support for the infill panels, which can consist of stone veneer, metal sheets, glazing, or

louvers, among others.

Curtain walls have been in use for nearly 100 years, but their use increased significantly

in the 1930s with advances in the use of sheet metal, in the 1950s with the advent of float glass,

and again in the 1970s with the use of aluminum mullions [1] [2]. Relevant to this research, the

curtain wall system provides a backing frame to which the spandrel panels are attached. The

mullions provide a continuous support along the edges for positive (into the building) wind

pressure, while negative (suction) pressure is resisted by bolts through the mullions. A typical

curtain wall system is shown in Figure 1.3.

Graphic by: Hoffmann Architects, Inc.

Figure 1.3 - Typical curtain wall framing arrangement and components [1]

4

1.2.2 Ductal® UHPFRC Spandrel Panels

Through collaboration with the designer, owner, and engineers, it was determined that

Ductal®, an UHPFRC material, would be the ideal material for use as the spandrel panels in the

cladding system. The primary factors dictating the use of Ductal® concrete was the potential for

thin sections, and the appearance of a natural stone product. The ability to achieve thin sections

is important to reduce the seismic loading on the structure, since Victoria, British Columbia is a

high seismicity zone. It is possible to achieve these sections due to the high tensile strength and

high stiffness of the Ductal® material. This allowed some cladding sections to be as thin as

17 mm. A typical stone system can vary from 9.5 mm to 50 mm in thickness and the stone panel

is limited to maximum panel dimensions of 300 mm to 400 mm [3], whereas the Ductal®

concrete panels in this project are 1300 mm in height and vary from 750 mm up to 2150 mm in

length, with the majority of the panels being 1300 mm in length. Regular precast concrete

cladding can be of similar overall dimensions as offered by the Ductal® concrete; however they

are typically 100 mm thick or greater. These dimensions are possible for Ductal® concrete due to

its high strength, in this case 100 MPa in compression and 4 MPa in tension [4]. The use of

organic fibre reinforcing was preferred over steel fibres to reduce the potential for rust stains

appearing on the surface of the cladding panels.

The appearance of natural stone offered by the Ductal® product is of particular

importance to the architects of the building. The fluidity of the Ductal® concrete also allowed for

rib details to be cast into the panels providing texture to the finish surface and also allowed a

number of the panels to be cast in curves to adhere to the building profile. Ductal® concrete also

performs wells as a rain screen, a primary role of the curtain wall system, due to its low porosity

and permeability.

5

Due to the uncertainty of the performance of Ductal® concrete in shear for the thin

members, the lack of proven design codes or standards for UHPFRC and because there was

limited data on the effects of size on tensile and flexural behaviour, full scale testing was

performed for both static loading and fatigue loading. Similarly, there is limited understanding

on behaviour of GFRP reinforcing in thin sections. The full scale testing was compared to

analytical design calculations and an elastic finite element analysis of the panels in order to

determine the acceptability for their use on the building.

1.3 Research Plan

To validate the real-world feasibility of the cladding panels, strength, strain, and fatigue

of the panels was determined through analytical calculations, finite element analysis, and full

scale testing. The scope of the testing included one full scale short panel (1300 mm in height by

1287 mm in length) for static load testing, two full scale long panels (1300 mm in height by

1757 mm in length) for static load testing, and an additional two short panels for fatigue load

testing. The testing included deformation measurements of the panels, strain measurements of

the panels at various points both on the top and bottom surfaces of the panels and strain

measurement on the embedded GFRP reinforcing bars. Analysis of the short panel static load

testing was previously discussed in [5], however additional detail and analysis is provided in this

report.

1.3.1 Static Load Testing

Curtain wall panels were subjected to transient wind loading resulting in both positive

and negative pressures. The intent of the static load testing is to determine the panel’s ability to

withstand the design loads established through the National Building Code of Canada (NBCC)

2005, and checked against the 2006 British Columbia Building Code. Given the textured ribbed

6

surface of the panels, there is the potential for increased localized wind pressures due to vortices

forming adjacent to the panels. This effect could not be adequately determined without wind

tunnel testing, however, because of the scale of the ribs compared to the size of the panels (5 mm

ribs compared to a minimum of 750 mm smallest panel dimension) it was assumed to average to

a neutral pressure. The resulting net unfactored positive and negative wind pressure loads,

including internal pressure effects and the effects at the corner or end zone of the building were

1.54 kPa and 1.91 kPa, respectively. The loading imparts both bending stresses and shear stresses

on the panels as the forces are transferred back to the supporting curtain wall framing. Various

load cycles were implemented on one of the short panel sizes and two of the long panel sizes.

The selected load cycles are intended to simulate positive and negative pressure on the panel at

Serviceability Limit States (SLS) and Ultimate Limit States (ULS) load levels, sustained loading

(for 24 hours), and ultimately taking the panels through to failure. Further discussion of the

applied static loading is provided in Section 4.1.3.

In order to better understand the suitability of the design, one short panel and two long

panels were fabricated for the purpose of being subjected to uniform pressures. All of the

prototype panels were 1300 mm in height, with the short panel being 1287 mm and the long

panel being 1757 mm in length. All panels had thickenings around the perimeter of the panel as

required to properly seal the joints between panels. In addition, the long panels had a thickening

in the centre of the panel to assist with load carrying capabilities. Refer to Figure 1.4 for

additional construction details of the short cladding panels and Figure 1.5 for the long cladding

panels. The cast-in inserts for support are labelled on the details as ‘a’ through ‘f’. An additional

line of cast-in inserts is located on the top and bottom of the panels, which are used to interface

with the adjacent wall system.

7

a) Plan view of short panel

8

b) Sections through short panel

Figure 1.4 - Construction details of prototype short cladding panels

a) Plan view of long panel

9

b) Vertical sections through long panel

10

c) Horizontal sections through long panel

Figure 1.5 - Construction details of prototype long cladding panels

1.3.2 Fatigue Load Testing

Due to the transient nature of wind loading, the cladding panels are subject to a large

number of loading cycles throughout the life cycle. The fatigue load testing was implemented to

determine the long-term feasibility of using the cladding panels made from UHPFRC with GFRP

reinforcing bars. Since wind is a cyclic loading condition, it is necessary to determine if the

design is susceptible to brittle failure under repetitive loading.

For this test, two short panels were tested, both loaded through 20,402 cycles including

alternating positive and negative pressures. Loading began with cycles at 40%, followed by 50%,

65%, and 120% load, and culminating in a failure test of the panel. Each panel is 1287 mm in

length and 1300 mm in height with thickenings around the perimeter of the panel, identical to the

short panel used for the static load testing shown in Section 1.3.1. The loading that was applied

and the corresponding number of cycles is discussed further in Section 4.2.2.1.

11

Chapter Two: Initial Analysis

2.1 Required Resistance Analysis by Statics

The initial design of the panels was achieved through analytical calculations. In order to

simplify the calculations, a one-way slab and beam system was assumed for the long panels,

while the short panels were calculated as a two-way slab and beam system. This differentiation

was required due to the aspect ratios of the infill sections following the requirements of

CAN/CSA A23.3-04 Design of Concrete Structures [6], which states that an aspect ratio of

greater than two is calculated as a one-way system. As shown in Figure 2.1 and Equation 2-1, the

aspect ratio of the infill section for the short panel is 1.19, while for the long panel, accounting

for the intermediate thickened section, the aspect ratio is 4.39.

Figure 2.1 - Measurements to determine infill aspect ratio for short panel (left) and long

panel (right)

12

r =lc

wc

Equation 2-1

Long Panels: r =

1.537 m

0.350 m= 4.39

Short Panels: r =

1.067 m

0.900 m= 1.19

Where,

r = Aspect ratio of infill section

lc = Clear span length (longer direction) (m)

wc = Clear span width (shorter direction) (m)

With these assumptions and further analysis by statics, it is possible to calculate the

required strength for elements within the panel in order to resist the wind pressure forces. The

additional cross-sectional area provided by the rib surface texture was also ignored for simplicity

of calculation and to be conservative due to the uncertainty in the effectiveness of these features,

despite the large impact it was calculated to have on the panels. This is shown in Table 2.1 for

the infill sections of the panel in the direction of the rib texture, with a 70% stiffness increase for

the short panels and a 59% increase for the long panels.

Table 2.1 - Calculated contribution to stiffness of rib surface texture

Calculated Moment of Inertia (per meter width)

15 mm thick Infill (mm4) 17 mm thick Infill (mm4)

Ignoring contribution of ribs 281,250 409,417

Including contribution of ribs 477,846 652,205

13

Figure 2.2 - Labels used to identify panel members for short (left) and long (right) panels

The labels used throughout this analysis for each of the elements of the panels are shown

in Figure 2.2. The long span edge member is the top, bottom, and middle thickened portion for

the long spandrel panels, with dimensions of width of 200 mm, thickness of 34 mm, and span

length of 1637.3 mm. The short span edge member is similarly the top and bottom thickened

portion for the short spandrel panel, with dimensions of a width of 200 mm, thickness of 30 mm,

and span length of 1167.3 mm. The narrow edge member is the thickened portion on the left and

right sides of the spandrel panel with dimensions of 110 mm wide and 30 mm thick, and is the

same for both the short and long spandrel panels with a 1000 mm span for the short panel and a

500 mm span for the long panel. The infill sections are 15 mm and 17 mm thick for the short and

long spandrel panels, respectively, and are calculated for a per-metre width of panel for the

purpose of comparison. For all of the members, any contribution from the interface of the infill

panel with the thickened members to create a ‘T’ or ‘L’ section was ignored since loading is

possible in both positive and negative directions, and these portions would be of little benefit

during negative bending.

14

The design moments of the infill sections and the thickened members for the given wind

pressure for factored and service loading under positive and negative wind pressures is shown in

Table 2.2. Based on the NBCC, the ultimate load factor used in the Ultimate Limit State (ULS) is

1.4 and the service load factor for the Service Limit State (SLS) is 0.75 [6].

Table 2.2 - Calculated maximum moment for various panel sections

Positive Wind Load (1.54 kPa) Negative Wind Load (1.91 kPa)

Member SLS ULS SLS ULS

Long Edge 0.145 kN·m 0.271 kN·m 0.180 kN·m 0.336 kN·m

Long Middle 0.213 kN·m 0.397 kN·m 0.264 kN·m 0.493 kN·m

Short Edge 0.085 kN·m 0.159 kN·m 0.106 kN·m 0.197 kN·m

Narrow Edge 0.060 kN·m 0.111 kN·m 0.074 kN·m 0.138 kN·m

Short Infill (max) 0.018 kN·m/m 0.033 kN·m/m 0.020 kN·m/m 0.041 kN·m/m

Long Infill (max) 0.047 kN·m/m 0.087 kN·m/m 0.058 kN·m/m 0.108 kN·m/m

2.2 Section Resistance by Statics

2.2.1 Determination of Moment-Curvature Diagrams

A moment-curvature diagram was developed for the various elements of the panels in

order to determine the state of stress of the elements under various loading conditions and as a

method to determine the strength of the members. This analysis used the idealized stress-strain

charts for the Ductal® concrete and the Pultrall V-ROD® GFRP reinforcing bars, as discussed in

Section 3.2. The engineering assumptions of ‘plane sections remain plane’ and ‘small

15

deformations’ was used for this analysis, which is sufficient for typical loading values, but

becomes less accurate as the calculations approach failure states.

Three fundamental equations were used in determining the moment resistance of the

sections: the strain compatibility equation, balance of forces, and balance of moments as shown

in Equation 2-2, Equation 2-3, and Equation 2-4; in order to achieve static equilibrium.

Strain: εx = εc (x − c

c) Equation 2-2

Balance of Forces: ∑ F = 0 Equation 2-3

Balance of Moments: ∑ M = 0 Equation 2-4

Where,

εx = Calculated strain at depth x

εc = Strain at the compression surface of the member

x = Location of desired strain, from compressive surface (m)

c = Depth of neutral axis, measured from compressive surface (m)

F = Forces normal to the plane (N)

M = Moments about any point (N·m)

These equations, in combination with the stated assumptions, allow the strain through the

depth of the member to be calculated. The procedure involves assuming a concrete compressive

strain (εc), then using an optimization procedure to calculate the required depth of the neutral

axis in order to satisfy the balance of forces equation and calculate resulting moment resistance

to satisfy the balance of moments. Figure 2.3 depicts an illustrative example of how the

component forces were calculated.

16

Figure 2.3 - Summary of analytical moment resistance calculations

Where in Figure 2.3,

CDuctal = Compression force in the Ductal® concrete (N)

TDuctal = Tension force in the Ductal® concrete (N)

TGFRP = Tension force in the GFRP reinforcing (N)

c = Material resistance factor for precast concrete = 0.70 [8]

GFRP = Material resistance factor for GFRP = 0.75 [9]

f′c = Compression strength of Ductal® concrete = 100 MPa [4]

f′t = Tension strength of Ductal® concrete = 4 MPa [4]

αc(εc) = Ductal® concrete compression stress ratio, a function of the

Ductal® concrete compression strain

αt(εt) = Ductal® concrete tension stress ratio, a function of the Ductal®

εt

εc

c

h

βc(εc)c

βt(εt)(h − c)

CDuctal = cαc(εc)f′ccb φ

TGFRP = GFRP εGFRP EGFRP φ

TDuctal = cαt(εt)f′t(h − c)b φ

φ

φ

a) Strain distribution b) Resultant internal section forces

17

concrete tension strain

βc(εc) = Location of equivalent compression force ratio, a function of

maximum Ductal® concrete compression strain

βt(εb) = Location of equivalent tension force ration, a function of

maximum Ductal® concrete tension strain

εt = Strain at the tension surface of the member


εGFRP = Strain in the GFRP

c = Depth of neutral axis, measured from top (m)

b = Width of the compression surface (m)

h = Overall depth of the member (m)

The recommendations of [7], as discussed in this section and in more detail in Section

3.2.1, were used to provide the stress-strain relationship of the UHPFRC in both tension and

compression. These recommendations provide different idealizations for SLS conditions and

ULS conditions. The moment-curvature diagrams for each case were developed in order to

compare to the respective load cases. At this point, a distinction between GFRP reinforced panels

and unreinforced panels was introduced in order to examine the benefit of the reinforcing.

The tension contribution of the Ductal® concrete is significant and as such cannot be

ignored as is common in normal concrete design. The factors α(ε) and β(ε), for both the Ductal®

concrete compression and tension contributions, are used to create equivalent Ductal® concrete

compression and tension forces based on the maximum compression and tension strain,

respectively [8]. The α(ε) function is defined as the integral of the stress-strain relationship to

18

the given maximum strain, normalized with respect to the peak stress, as shown in Equation 2-5

for the compression case.

αc =1

f′c∫ fc(ε)dε

εc

0

Equation 2-5

Where,

αc = Ductal® concrete compression stress ratio, a function of



f′c = Compression strength of Ductal® concrete = 100 MPa [4]

fc(ε) = Compressive strength of Ductal® concrete as a function of strain

(MPa)

ε = Strain in the concrete

The function β(ε) is defined as the ratio of the centroid of the stress-strain relationship to

the given strain relative to the depth of the neutral axis, and thus the location of application of the

equivalent force, as calculated in Equation 2-6.

βc = 1 −1

αcf′c∫ εfc(ε)dε

εc

0

Equation 2-6

Where,

αc = Ductal® concrete compression stress ratio, defined in Equation 2-5


βc = Location of equivalent compression force ratio, a function of


f′c = Compression strength of Ductal® concrete (MPa)

19

fc(ε) = Compressive strength of Ductal® concrete as a function of strain

(MPa)

ε = Strain in the concrete

The variation of α(ε) and β(ε) with respect to the concrete strain for both the tension and

compression factors is shown in Figure 2.4. Note that in the compression case, the SLS

relationship follows the ULS relationship, with the only difference being the SLS case limits the

strain to approximately 0.00217, while the ULS case continues to a strain of 0.003 as per the

previously discussed recommendations. Also note that the α for the tension strain in the SLS

case is simply a proportion of the ULS. This is due to exclusion of the partial safety factor for the

SLS case. As the two tension strain cases therefore have the same shape, the β values for each

case are identical.

a) Variation of 𝛂𝐜 and 𝛃𝐜 with UHPFRC compression strain

0

0.1

0.2

0.3

0.4

0.5

0 0.0005 0.001 0.0015 0.002 0.0025 0.003

αc

and

βc R

atio

s

Concrete Compression Strain (εc)

ULS Alpha_Compression ULS Beta_Compression

SLS Alpha_Compression SLS Beta_Compression

ULS and SLS βc

ULS and SLS αc

0.00

217

20

b) Variation of 𝛂𝐭 and 𝛃𝐭 with UHPFRC tension strain

Figure 2.4 - Alpha and Beta factor variation with strain

Once the strains throughout the section depth are known, it is possible to calculate the

curvature through Equation 2-7.

κ =(εc + εt)

h Equation 2-7

Where,

κ = Curvature (m-1)

εt = Strain at the tension surface of the member


h = Overall depth of the member (m)

In order to complete the large number of calculations required to create a moment-

curvature diagram using this process, the equations were input into a Microsoft Excel

0

0.2

0.4

0.6

0.8

1

0 0.025 0.05 0.075 0.1 0.125 0.15

αt an

d β

t R

atio

s

Concrete Tension Strain (εt)

ULS Alpha_tension ULS Beta_tension

SLS Alpha_tension SLS Beta_tension

ULS and SLS βt

ULS and SLS αt

21

spreadsheet. Through a combination of the Solver Add-In and a custom written Macro, the

procedure was largely automated for the given inputs. The resultant moment-curvature diagrams

for each member type are thus shown in Figure 2.5. This incremental analysis allows the

determination of the cracking moment by locating the first step within the spreadsheet at which

the tension stress exceeds the tension strength of the Ductal® concrete. The moment-curvature

diagrams also display the calculated loading as determined in Section 2.1 in order to discuss the

expected condition of the panels under load. Also note that since the GFRP reinforcing is located

at mid-depth of the member, no distinction is required between positive and negative bending.

For each member, both the nominal and factored resistances are calculated. The factored

resistance accounts for potential variability in the material properties and is used for comparison

to the ULS load cases. The nominal resistance is calculated setting the material resistance factors

to one and is analyzed as the expected real-world performance of the member and is compared to

the SLS load cases.

22

a) Moment-curvature diagram for the long (edge and middle) members

b) Moment-curvature diagram for the short members

0

100

200

300

400

500

600

0 0.5 1 1.5 2 2.5 3 3.5

Mo

men

t (N

·m)

Curvature (m-1) Long: Unreinforced - Nominal Long: GFRP Reinforced - NominalLong: Unreinforced - Factored Long: GFRP Reinforced - Factored

1

2

3 4 5 6 7 8

Load Line Labels 1 - Long Middle: Negative ULS 5 - Long Middle: Negative SLS 2 - Long Middle: Positive ULS 6 - Long Middle: Positive SLS 3 - Long Edge: Negative ULS 7 - Long Edge: Negative SLS 4 - Long Edge: Positive ULS 8 - Long Edge: Positive SLS

0

50

100

150

200

250

300

350

400

0 0.5 1 1.5 2 2.5 3 3.5

Mo

men

t (N

·m)

Curvature (m-1)

Short: Unreinforced - Nominal Short: GFRP - NominalShort: Unreinforced - Factored Short: GFRP Reinforced - Factored

1

2

3 4

Load Line Labels 1 - Short: Negative ULS 2 - Short: Positive ULS 3 - Short: Negative SLS 4 - Short: Positive SLS

23

c) Moment-curvature diagram for the narrow members

d) Moment-curvature diagram for the infill members

Figure 2.5 - Calculated moment-curvature diagrams for various panel members

0

50

100

150

200

250

0 0.5 1 1.5 2 2.5 3 3.5

Mo

men

t (N

·m)

Curvature (m-1)

Narrow: Unreinforced - Nominal Narrow: GFRP Reinforced - NominalNarrow: Unreinforced - Factored Narrow: GFRP Reinforced - Factored

1

2

3 4

Load Line Labels 1 - Narrow: Negative ULS 2 - Narrow: Positive ULS 3 - Narrow: Negative SLS 4 - Narrow: Positive SLS

0

100

200

300

400

0 1 2 3 4 5 6 7 8

Mo

men

t (N

·m/m

)

Curvature (m-1) Long Infill - Nominal Short Infill - NominalLong Infill - Factored Short Infill - Factored

Load Line Labels 1 - Short Infill: Negative ULS 5 - Long Infill: Negative SLS 2 - Short Infill: Positive ULS 6 - Long Infill: Positive SLS 3 - Short Infill: Negative ULS 7 - Long Infill: Negative SLS 4 - Short Infill: Positive ULS 8 - Long Infill: Positive SLS

1 2 3 4 5/6 7/8

24

From the figures, it is evident that under service loading conditions, the majority of the

members appear to remain in the linear-elastic phase, a key goal of the design as requested by the

project architect. It is also apparent that the GFRP reinforcing bars are necessary in order to

resist the factored loads, with the Long Middle loading exceeding the calculated ULS strength of

the long member even with the GFRP reinforcing bars. It was decided, however, to go ahead

with experimental tests of the design due to the expected compound effect of the simplifying

assumptions and the general conservativeness of the design procedure followed. Due to the

novelty of the spandrel panels being designed and the uncertainty of their performance, the

additional moment resistance as a result of the GFRP reinforcing bars was determined to be an

asset. Additionally, the GFRP reinforcing bars resulted in significantly stiffer performance at

higher loading levels and after cracking of the panels.

2.2.2 Determination of Anticipated Deflection

Using the developed moment-curvature diagrams, it is possible to determine the effective

moment of inertia at each loading level, as per Equation 2-8.

Ie =Ma

Ecκ Equation 2-8

Where,

Ie = Effective moment of inertia (m4)

Ma = Applied moment (N·m)

Ec = Modulus of Elasticity of Ductal® concrete (MPa)

κ = Curvature, defined in Equation 2-7 (m-1)

Combining this calculated moment of inertia with the Moment-Area method, it is possible to

determine the deflection of the member accounting for the variable stiffness along the length of

25

the member due to cracking [9]. First, the moment along the length of the member is determined

and combined with the corresponding moment of inertia at incremental points. Then, the

moment-area method can be applied in a numerical fashion as outlined in [13], producing the

rotation and deflection along the length of the member based on the end conditions. The member

was assumed to be loaded as a simple beam in this case subjected to a uniform load for the long

panels, due to the one-way assumption for the infill panel, and a triangular load for the short

panels, due to the two-way assumption. Thus, the initial displacement at each end is zero. It is

more difficult, however, to determine the initial rotation since the stiffness of the beam varies

along its length under loading. Once again, the Solver Add-In in Microsoft Excel was used to

find the initial rotation that would result in a balanced final rotation, as required due to the

symmetry of the beam and the loading. This calculation was repeated for a steadily increasing

load in order to create a load-deflection curve for each member to compare to the load testing.

For this procedure, only the SLS moment-curvature diagram was transformed as this would

provide the basis of the deflection design limits. These charts are shown in Figure 2.6 for each of

the members, with an enlargement of the applicable region of primary concern shown in Figure

2.7.

26

Figure 2.6 - Calculated deflection under load of elements

Figure 2.7 - Enlarged calculated deflection under load of elements

0

1

2

3

4

5

0 20 40 60 80 100

Win

d P

ress

ure

(p

osi

tive

or

neg

ativ

e) (

kPa)

Calculated Member Midspan Deflection (mm)

Long Edge: GFRP Nominal

Long Middle: GFRP Nominal

Short: GFRP Nominal

Narrow: GFRP Nominal

Positive SLS

Negative SLS

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

0 2 4 6 8

Win

d P

ress

ure

(p

osi

tive

or

neg

ativ

e) (

kPa)

Calculated Member Midspan Deflection (mm)

Long Edge: GFRP Nominal

Long Middle: GFRP Nominal

Short: GFRP Nominal

Narrow: GFRP Nominal

Positive SLS

Negative SLS

Area enlarged in Figure 2.7

27

Through Figure 2.7, it can be seen that the anticipated deflection for the various elements

under serviceability loading is:

Long Edge Member: 2.82 mm under negative and 2.11 mm under positive pressure;

Long Middle Member: 7.30 mm under negative and 3.82 mm under positive pressure;

Short Member: 1.07 mm under negative and 0.86 mm under positive pressure;

Narrow Member: 1.07 mm under negative and 0.80 mm under positive pressure.

Unfortunately, the long middle member exceeds the recommended maximum lateral deflection

of span/600 – 2.93 mm in this case – for curtain wall applications that can be considered similar

to masonry construction with brick veneer [11]. With these calculations, the deflection for this

member is approximately span/240. Similar to the strength of this member, the design was

advanced to prototype testing anticipating that the design assumptions would prove to be

conservative.

The deflection values under serviceability, deflection at cracking, and ultimate failure

load for each of the elements is summarized in Table 2.3. Cracking was defined in this analysis

as the point at which the tension strain ceased linearity, at 80 με. Refer to Section 3.2.1 for

further discussion of the material properties.

28

Table 2.3 - Summary of calculated results for panel members M

embe

r

Loa

d C

ase

Loa

d

Mom

ent

Def

lect

ion

(kPa) (N·m) (mm)

Lon

g E

dge Positive SLS 1.156 145.21 2.11

Negative SLS 1.433 180.00 2.82

Cracking 1.01 126.92 1.80

Failure 3.16 396.85 -

Lon

g M

iddl

e Positive SLS 1.156 212.97 3.82

Negative SLS 1.433 264.01 7.30

Cracking 0.68 126.92 1.78

Failure 2.15 393.85 -

Shor

t

Positive SLS 1.156 82.28 0.86

Negative SLS 1.433 105.71 1.07

Cracking 1.34 98.81 1.00

Failure 4.39 323.57 -

Nar

row

Positive SLS 1.156 59.63 0.80

Negative SLS 1.433 73.92 1.07

Cracking 1.05 54.35 0.73

Failure 4.29 221.46 -

Extending these calculations, it is possible to determine the expected failure load of each

of the panels based on the lowest failure mode of each of the members within the panel. Thus,

the long panel is expected to fail at a load of 2.15 kPa, failing at the middle thickened member

(long middle). The short panel is expected to fail at a load of 4.29 kPa.

29

2.3 Finite Element Analysis

After the design of the spandrel panels through analytical calculations was complete, a

finite element analysis of the panels was undertaken in order to determine if any unanticipated

effects occurred within the panels and to compare finite element analysis deflections to those

achieved through analytical calculations. Based on the results of the analytical calculations, it

was assumed that the spandrel cladding panels would be in an uncracked state for SLS loading

levels and as such the GFRP reinforcing bars would have little effect on the performance of the

panel. This is demonstrated in Equation 2-9, which shows that the contribution of the GFRP

reinforcing bar under uncracked flexure is 0.01% of the contribution of the concrete section as

shown for the long member.

Ie =1

12bh3 + (n − 1)

π

4r4

Ie = 450 000 mm4 + 43 mm4

Equation 2-9

Where,

Ie = Effective moment of inertia (m4)

b = Element width (m)

h = Element depth (m)

n = EGFRPEc

= Ratio of modulus of elasticity = 1.54

r = Radius of GFRP reinforcing bar (m)

Thus, for simplicity of modelling, the GFRP reinforcing bars were not modelled and a purely

linear-elastic analysis was used. This eliminates the ability of the model to calculate the

Contribution of concrete shape

Contribution of GFRP reinforcing bars

30

anticipated failure load for the panels, and reduces the accuracy of the model beyond the

cracking load. This was considered to be acceptable since the goal of the finite element analysis

was to verify the distribution of stresses and to show there are no unusual stress patterns. The

structural analysis program S-FRAME Analysis by S-FRAME Software Inc. was chosen to

conduct the finite element analysis of these panels. This software was chosen for the ability to

quickly and accurately create models for design iterations during the initial design process.

2.3.1 Definition of Element Type

There are three types of plate mesh elements available in S-FRAME: triangular, mixed-

mesh, and quadrilateral. Each of the plates is based on a modified version of the Mindlin-

Reissner plate theory [15], which allows for shear deformation within the plate thickness,

providing higher accuracy compared to alternative plate theories such as the Kirchhoff-Love

plate theory [13]. Both the triangular and quadrilateral elements are first-order numerical

elements, meaning the strain varies linearly between the nodes. While both the triangular and

quadrilateral elements exist in the Mindlin-Reissner plate theory and in S-FRAME, it is generally

expected that the quadrilateral elements will provide the most accurate results since they are not

restricted to constant strain as is the case with first-order triangular elements. Given the regular

geometry of the cladding panels, it was possible to model the entire panel without the use of

triangular elements.

2.3.2 Definition of Material Properties

The material properties for the Ductal® concrete input into the finite element model

match those discussed further in Section 3.2.1. Since a linear-elastic model is being developed,

the properties beyond cracking of the Ductal® concrete and of the GFRP reinforcing bars are not

required.

31

2.3.3 Creation of Model Geometry

The geometry of the model was created to accurately represent the geometry of the

design cladding panels. The plate sections were given thicknesses corresponding to their location

within the member and panels were offset from each other to align the centroid of the element at

the correct location (to maintain a flush outside face). As with the analytical calculations, the

additional thickness and hence stiffness from the textured rib surface was ignored for simplicity,

and is expected to result in a conservative analysis.

2.3.4 Generation of Mesh

Meshing was predominantly established through the automesh feature of the software

which was subsequently visually examined for acceptability. Within the program, the user

adjustable parameters are the type of mesh, the seed density, and the quadrilateral density. Each

of these parameters was manually adjusted until an arrangement that appeared suitable was

supplied.

The suitability of the model meshing was verified by increasing the seed density and

ensuring the deformation and stress achieve convergence. The various mesh densities for the

short panels can be seen in Figure 2.8, and for the long panels in Figure 2.9. A comparison of the

results from the three mesh densities is shown in Table 2.4. Since the model is purely linear-

elastic, it is only necessary to evaluate one load case for each mesh, with all other load cases

simply being proportional to the first.

32

a) initial mesh

b) double mesh

c) quadruple mesh

Figure 2.8 - Comparison of mesh options for short panels

a) initial mesh

b) double mesh

a) quadruple mesh

Figure 2.9 - Comparison of mesh options for long panels

33

Table 2.4 - Comparison of selected results from various mesh densities

Property

Initi

al M

esh

Dou

ble

Mes

h

% C

hang

e vs

Initi

al

Qua

drup

le

Mes

h

% C

hang

e vs

Initi

al

% C

hang

e vs

Dou

ble

Shor

t Pan

el

Posi

tive

Pres

sure

(1

.54

kPa)

Relative Mesh Density 1 2 - 4 - -

Central Deflection (mm) -1.871 -1.878 0.38% -1.886 0.80% 0.42%

Max Tension Stress (MPa) 4.336 4.374 0.88% 4.391 1.28% 0.40%

Max Comp. Stress (MPa) -3.249 -3.266 0.53% -3.270 0.65% 0.13%

Lon

g Pa

nel

Posi

tive

Pres

sure

(1

.54

kPa)

Relative Mesh Density 1 2 - 4 - -

Central Deflection (mm) -3.227 -3.241 0.44% -3.243 0.49% 0.4%

Max Tension Stress (MPa) 6.439 6.482 0.66% 6.489 0.77% 0.11%

Max Comp. Stress (MPa) -4.565 -5.000 9.44% -5.331 16.78% 6.71%

Thus, from comparing the results of the various mesh densities it was determined that the

‘Double Mesh’ provides the optimal mix of computation efficiency and result accuracy for both

the short and long panels.

2.3.5 Definition of Boundary Conditions

The boundary conditions for the panel are defined as recommended in [14] and shown in

Figure 2.10. This arrangement provides restraint against the wind pressure at all supports,

however the vertical load is only restrained at the bottom two supports and the in-plane

horizontal is only supported at the left two supports. The intent of this arrangement of supports is

to limit the effects that panel membrane forces may have on the behaviours of the panel. The

real-world connections of the cladding system were designed to mimic this behaviour.

34

Figure 2.10 - Applied boundary conditions to short (left) and long (right) finite element

models

2.3.6 Results of Finite Element Analysis

For both the long and short panel finite element results, only select results are presented

here, predominantly from the negative load case, as this is the case that applies the greatest

pressure to the panels. Given the linear-elastic nature of the analysis performed, unfactored

results are presented, since determining the response at the serviceability and ultimate limit states

is simply a matter of proportion.

2.3.6.1 Short Panel

The stresses in the panel as a result of the self-weight of the panel in the upright position

are shown in Figure 2.11. From this analysis, it is shown that the self-weight in this axis is a

minor contribution to the total stress (0.023 MPa compared to the 4.47 MPa expected from

bending, or approximately 0.5% of the maximum stress) and as such it is not detrimental to

further analysis to ignore this contribution. The expected deflection under load can be scaled

35

from that shown in Figure 2.12. As such, the expected deflection under serviceability condition

is 1.75 mm for negative pressure and 1.41 mm for positive pressure (these are the output from

the model multiplied by the SLS factor of 0.75 [7]). The moments in the perimeter members of

the panel is shown in Figure 2.13 for the purpose of comparison to the analytical calculations

performed in Section 2.2. Finally, the overall unfactored maximum tension principal stresses for

positive and negative pressure is shown in Figure 2.14 in order to determine if any portions of

the panel are demonstrating unexpected behaviour. A summary of the maximum and minimum

stresses experienced within short panel is given in Table 2.5.

Figure 2.11 - Stresses in the panel due to self-weight

36

Figure 2.12 - Undeformed and deformed geometry (left) and predicted lateral deflections

(right) due to negative pressure

Figure 2.13 - Moments in the short (left) and narrow (right) members for negative pressure

37

Figure 2.14 - Maximum principal stress (tension) for positive pressure (left) and negative

pressure (right)

Table 2.5 - Unfactored top and bottom stresses in short panel elements

Positive Pressure (1.54 kPa) Negative Pressure (1.91 kPa)

Top Stress (MPa) Bottom Stress (MPa) Top Stress (MPa) Bottom Stress (MPa)

Short -2.000 3.136 2.476 -3.889

Narrow -3.172 1.842 3.934 -2.285

Infill x -2.611 4.320 3.238 -5.358

Infill y -3.266 1.791 4.015 -2.221

Applying the ULS factor of 1.4 [7] to the above values, it is apparent that the stress in the

infill panel itself exceeds 4 MPa in tension (1.4 x 4.320 MPa = 6.048 MPa). Thus, at this point it

is expected that the loading has exceeded the linear-elastic nature of the finite element model and

the exclusion of GFRP reinforcing in the model becomes significant.

38

2.3.6.2 Long Panels

Similar to the analysis from the short panels, the stresses due to the self-weight of the

panel in the upright position is shown in Figure 2.15. Once again, the stresses from the self-

weight are minimal in comparison to the stresses in the panel due to bending (0.041 MPa

compared to 6.48 MPa, or 0.6%) and can presumably be ignored during further analysis. The

deformation of the panel under unfactored negative pressure is shown in Figure 2.16. Scaling this

to the serviceability load level (multiplying the finite element analysis results by the 0.75 SLS

factor), the expected deformation becomes 3.02 mm, and likewise for positive pressure, the

expected serviceability deformation is 2.43 mm. Figure 2.17 displays the moments in the long

members of the panel for comparison to the analytical calculations. Finally, the maximum

unfactored tension principal stresses are shown in Figure 2.18, with a summary of the stresses in

the members given in Table 2.6.

Figure 2.15 - Stresses in the panel due to self-weight

39

Figure 2.16 - Undeformed and deformed geometry (left) and predicted lateral deflections

(right) due to negative pressure

Figure 2.17 - Moments in the long members for negative pressure

40

a) positive pressure

b) negative pressure

Figure 2.18 - Maximum principal stress (tension)

41

Table 2.6 - Unfactored top and bottom stresses in long panel elements

Positive Pressure (1.54 kPa) Negative Pressure (1.91 kPa)

Top Stress (MPa) Bottom Stress (MPa) Top Stress (MPa) Bottom Stress (MPa)

Long -4.582 6.227 5.683 -7.724

Middle -4.461 6.450 5.533 -8.000

Infill y -4.551 1.291 5.644 -1.601

Similar to the short panels, the finite element model for the long panel shows that many

of the members exceed the cracking limit of the Ductal® concrete material, and as such the

limitations of the model – the linear-elastic assumption and the exclusion of the GFRP

reinforcing bars – were exceeded. In order to suitably verify the performance of the panels, it

was deemed necessary to perform load testing on the panels.

42

Chapter Three: Construction of Test Specimens

3.1 Procedure

All of the test panels were constructed by Lafarge North America at their precast concrete

facility in Calgary, Alberta. The forms were constructed in two pieces – a front form containing

the rib texture mold and a rear form that set the rebar and cast-in anchors, and shaped the

thickened portions of the panel. The panels were cast in a horizontal position allowing the use of

a bucket crane to pour the Ductal® concrete. Figure 3.1, Figure 3.2, and Figure 3.3 show the

panel construction process and Figure 3.4, Figure 3.5, and Figure 3.6 show the completed panels.


Figure 3.1 - Back form panel prepared with GFRP reinforcing bars and cast-in inserts

43

Photo by: D’AMBROSIO architecture + urbanism

Figure 3.2 - Preparing the forms for casting, front form with ribs on ground, back form

upright

Photo by: D’AMBROSIO architecture + urbanism

Figure 3.3 - Pouring the Ductal® concrete into the forms

44


Figure 3.4 - Completed short panel (back side)


Figure 3.5 - Completed long panel (back side)

45


Figure 3.6 - Completed short panel (front side)

3.2 Materials

3.2.1 Ductal® UHPFRC

The Ductal® UHPFRC mix D-AN1300FW used in these panels and its material properties were

provided by the Lafarge Precast Group responsible for fabricating the panels. A special mix of

the UHPFRC utilizing a white aggregate was required in order to suite the architect and owner’s

design for a light coloured cladding panel. This aggregate was imported from France specifically

for use in this project. Relevant material properties provided by the concrete supplier for the

purpose of design are shown in Table 3.1.

46

Table 3.1 - Selected Properties of Ductal® UHPFRC [4] [15]

Property Value

Elastic Modulus (E) 30 GPa

Compressive Strength (f′c) 100 MPa

Tensile Strength (f′t) 4 MPa

Fibre Length 12 mm

Fatigue Endurance Limit 90% of f′t

The recommendations from [7] were used to determine the idealized stress-strain

relationship for the Ductal® UHPFRC. Recommendations relevant to this analysis include:

A maximum ULS UHPFRC strain of 𝜀𝑢 = 0.003;

A ULS tensile reduction factor of 1.3, and;

Definition of the ULS and SLS stress-strain relationship.

The above mentioned tensile reduction factor is to account for the variability in material

properties and the uncertainty of proper fibre distribution and orientation, particularly when the

Ductal® concrete was flowed into place as was done in this project when filling the forms. This

approach may be excessively conservative since the supplier provided tensile strength is more

akin to a design strength and not a mean strength acquired through testing of the material. This is

similar to ordering a 30 MPa mix of regular concrete with the actual values typically being far

beyond, in order to satisfy the CAN/CSA A23.1-09/A23.2-09 requirements for satisfactory

material performance certainty [16]. However, more suitable testing data was not available at the

time of analysis, thus it was necessary to continue with the values provided by the manufacturer.

47

The idealized stress-strain relationship for the material in tension and compression can be seen in

Figure 3.7 [4] [10]. Due to the previously mentioned reduction factors, the specified compressive

and tensile strengths are reduced from those provided in Table 3.1.

Figure 3.7 - Idealized Ductal® UHPFRC Stress-Strain for compression (left), and tension

(right) with the ULS relationship in red and the SLS in green

3.2.2 Pultrall V-ROD® GFRP Reinforcing

Glass Fibre Reinforced Polymer (GFRP) reinforcing bars were used in each of the ribs of

the panels to provide greater ductility in the panels beyond the tension failure of the Ductal®

concrete. The GFRP reinforcing bars are important to the strength and ductility of the panels

beyond the cracking of the Ductal® concrete in tension as demonstrated in the analytical

calculations, and as such allow a greater utilization of the compression capacity of the Ductal®

concrete. As previously discussed, the contribution of the GFRP reinforcing bars was ignored in

the finite element model. The Pultrall V-ROD® GFRP is composed of glass fibres and vinyl ester

resin, with a textured coating to enhance the bond with the concrete. This material performs in a

0

10

20

30

40

50

60

70

0 0.001 0.002 0.003

Co

mp

ress

ion

Str

ess

(MP

a)

Compression Strain (m/m)

0

0.5

1

1.5

2

2.5

3

3.5

0 0.05 0.1 0.15

Ten

sio

n S

tres

s (M

Pa)

Tension Strain (m/m)

48

pure linear-elastic manner to failure. The relevant properties of the GFRP rods used for analysis

are shown in Table 3.2.

Table 3.2 - Selected Properties of Pultrall V-ROD® GFRP 6mm Reinforcing Bars [17]

Property Value

Nominal Diameter 6.350 mm

Cross Section Area 31.7 mm2

Weight 77.4 g/m

Tensile Modulus of Elasticity (E) 46.1 GPa

Nominal Ultimate Tensile Strength (Fu) 874 MPa

Guaranteed Design Tensile Strength (ffu) 784 MPa

Ultimate Strain in Tension (εfu) 1.90 %

Poisson’s Ratio (μ) 0.25

3.2.3 UCAN Cast-In Zamac Insert

In order to attach the wall cladding panels to the curtain wall system, the UCAN Cast-In

Zamac Inserts were chosen due to the high strength and shallow embedment depth. The inserts

are produced from the Zamac 5 alloy (a high strength zinc, aluminum, copper, and magnesium

allow) for corrosion resistance. Table 3.3 lists relevant properties of the selected anchors.

49

Table 3.3

Property Value

Insert Length 25.4 mm (1 in)

Base Width 22.2 mm (7/8 in)

Thread Size 3/8 - 16

Ultimate Tension Load – 17.24 MPa (2500 psi) concrete 8.23 kN (1850 lbs)

Ultimate Tension Load – 34.28 MPa (5000 psi) concrete 11.57 kN (2600 lbs)

Given the unique nature of Ductal® concrete compared to normal concrete, an analysis of the

cast-in inserts was completed based on the recommendations in CAN/CSA A23.3-04 [6], as

shown in Appendices A:, with a calculated anchor strength of 7.32 kN. Three pull-out tests of the

anchors were also performed, achieving pull-out strengths of 7.5 kN, 8.3 kN, and 8.6 kN,

averaging to 8.1 kN. Figure 3.8 shows the failure mode of two of the pull-out tests.

Figure 3.8 - Failure mode of UCAN Cast-In Zamac Inserts in Ductal® concrete

- SSelected Properties for UCAN Cast-In Zamac PZI 24 Inserts [18]

50

3.3 Panel Ribs

All of the cladding panels incorporated a textured surface in the form of ribs cast into the

outside surface of the panels. The ribs were formed by allowing the architect to hand carve ribs

in a clay panel, which was used to create a negative form from which the panels could be cast.

The ribs are a maximum of 5 mm thick. The fluidity of the Ductal® concrete ensured the forms

were completely filled and a desirable surface finish was achieved. The rib casting process and

complete texture is shown in Figure 3.9.

51

Figure 3.9 - Surface formwork and casting (top), and completed

textured surface (bottom)

Photo by: D’AMBROSIO architecture + urbanism (top) and Lafarge Precast (bottom)

52

3.4 Strain Gauges

The cladding panels were instrumented with strain gauges both on the exterior surfaces of

the panels and on the GFRP reinforcing bars cast within. The strain gauges were placed to allow

the determination of the cracking load and – once converted to stress using the relationship

discussed in Section 3.2.1 – for the purpose of comparison to the analytical calculations and the

finite element model.

3.4.1 Static Test Short Panel

The locations of the surface strain gauges applied to the short cladding panels are shown

in Figure 3.10.

53

Figure 3.10 - Surface strain gauges applied to short panels

54

3.4.2 Static Test Long Panels

The locations of the surface strain gauges applied to the long cladding panels are shown

in Figure 3.11.

Figure 3.11 - Surface strain gauges applied to long panels

55

3.4.3 Fatigue Test Short Panels

The locations of the surface strain gauges applied to the short cladding panels subjected

to fatigue loading are shown in Figure 3.12.

Figure 3.12 - Surface strain gauges applied to short fatigue panels

56

Chapter Four: Test Setup and Procedures

4.1 Static Test Panels

4.1.1 Test Frame Setup

The full-scale static testing was performed with the panels in a horizontal position.

Ideally, the panels would have been tested in a vertical position to include the in-plane self-

weight effects in the test; however difficulties in accurately applying the required pressure made

this impractical. As a result of using a horizontal test setup, the applied pressures (as indicated in

Section 4.1.3) were adjusted to account for the loading by the self-weight of the panel applied in

this condition. It is important to note, however, that the deflection and strain measurements were

zeroed with the panels supporting their self-weight, introducing a measurement offset bias in the

testing.

The test frame was designed to replicate the supports that would be present in the real

world condition, reproducing the mullions to act as primary supports. The positive and negative

pressures were applied in independent tests in order to facilitate the testing setup. In order to

ensure the pressure was uniformly applied to the panel, an inflatable mattress was placed

between the load piston and the panel to distribute the loading. This also allowed the load to

continue to be distributed as a uniform pressure even with the substantial deformations that were

observed in the later stages of the testing. An example of this setup is shown in Figure 4.1. Once

the capability of the air mattress to uniformly transfer load to the panels was exceeded in the

loading to failure, the mattress was replaced with point loads at the quarter points of the panel to

induce stresses similar to uniform pressure.

The load was applied in the downward direction for both tests; however the orientation of

the panel was adjusted in order to test the appropriate pressure direction. For the positive load

57

test, the panel was tested with the ribs directed upwards (external face upwards), whereas for the

negative pressure case the panel was flipped, with the ribs directed downward (external face

downwards).

Figure 4.1 - Use of an air mattress to provide uniform pressure

4.1.1.1 Test No. 1 – Positive Pressure Supports

Test No. 1 applied positive pressure to the panels with the panels supported on ball

bearings at each of the cast-in anchors. In this configuration, the panel was oriented with the

textured surface (outside face) of the panel facing upwards. A schematic of the test setup is

shown in Figure 4.2. The use of ball bearings at the support ensured that a true pin connected

was provided. A close up of the supports provided is shown in Figure 4.3.

58

Figure 4.2 - Schematic of Test No. 1 test setup

Figure 4.3 - Positive pressure support condition

4.1.1.2 Test No. 2 and No. 3 – Negative Pressure Supports

Test No. 2 and No. 3 applied negative pressure to the panels with the panels supported

from rods threaded into each of the cast-in anchors and suspended from the test frame. For this

test, the panel was reversed, with the textured ribs oriented downwards, as shown in the

schematic test setup in Figure 4.4. Suspending the panels was selected as the support method in

order to prevent any membrane forces from developing within the panel. This support is shown

in Figure 4.5.

59

Figure 4.4 - Schematic of Test No. 2 and No. 3 test setup

Figure 4.5 - Negative pressure support condition

4.1.2 Instrumentation

In addition to the strain gauges discussed in section 3.4.2, strain gauges were also applied

to the support rods in the negative pressure test. The intent of these strain gauges was to be able

to remove the elongation of the support rods from the deflection of the overall panel and to

confirm the uniformity of the applied load by allowing the calculation of the support reactions. In

60

practice, however, these strain gauges did not perform as expected and produced unintelligible

data. It is believed that this was a result of the difficulty in adhering the strain gauges to the

threaded rod, and from the bending induce in the rods by the inflatable mattress pressing against

them. Fortunately, the expected elongation of the rod under the maximum loading achieved in

the testing is marginal compared to the deformation of the panel itself and can thus be ignored, as

shown in the calculation in Equation 4-1.

.

∆=NL

EA=

(5 kN)(197.2 mm)

(200 GPa)(50.0 mm2)= 0.10 mm

Equation 4-1

Where,

Δ = Change in length, displacement (mm)

N = Applied Load (kN)

L = Total length of member (mm)

E = Young’s Modulus (GPa)

A = Cross-sectional area of member (mm2)

Additional instrumentation installed included Linear Displacement Sensors (LDS) and

Laser Position Sensors (LPS) used to measure the displacement of the panels under load. For the

static testing of the long panels, these were placed as indicated in Figure 4.6. Both the LDS and

the LPS had small metal plates bonded to the surface of the test panels in order to provide a

smooth measurement surface in order to eliminate any variability presented by the rough Ductal®

concrete finish on the panel backs or the ribs on the panel fronts.

61

a) Short panel static (left) and fatigue (right) transducer locations

b) Long panel transducer locations

Figure 4.6 - Location of deflection transducers

62

4.1.3 Applied Loading

Loading of the panels in Test No. 1 and No. 2 was applied in steps and in cycles to simulate the

variability of wind loading as shown in Table 4.1 for Test No. 1 (positive pressure) and in Table

4.2 for Test No. 2 (negative pressure). This pattern of loading is shown in Figure 4.7 for the short

panel and Figure 4.8 for the long panel, with the ‘Applied Load’ as measured from the load cell

in the testing apparatus, converted to the ‘Applied Pressure’ based on the area of the panel being

tested. Since the panels were tested in the horizontal position, the self-weight of the panels was

removed from applied loading (applied in the downward direction) in order to more accurately

simulate the desired pressure. Note that in each load step the load is reinstated to the intended

loading every 30 seconds to account for any load losses incurred in the system, either through

dynamic effects or losses from the air mattress.

63

Table 4.1 - Applied loading for Test No. 1 L

oad

Step

% o

f non

- Fa

ctor

ed

Loa

d

Posi

tive

Pres

sure

–

Shor

t Pan

el

(kPa

)

Posi

tive

Loa

d –

Shor

t Pan

el

(kN

)

Posi

tive

Pres

sure

–

Lon

g Pa

nel

(kPa

)

Posi

tive

Loa

d –

Lon

g Pa

nel

(kN

)

Rem

arks

Cycle 1

0 0 0 0 0 0

1 20 0.240 0.402 0.222 0.557 3 x 30 seconds

2 40 0.480 0.803 0.443 1.062 3 x 30 seconds

3 60 0.720 1.205 0.665 1.569 3 x 30 seconds

4 80 0.960 1.607 0.886 2.074 3 x 30 seconds

5 90 1.080 1.807 0.997 2.328 3 x 30 seconds

6 100 1.200 2.008 1.108 2.581 3 x 30 seconds

Cycle 2 – repeat loadings from Cycle 1

7 100 1.200 2.008 1.108 2.581 Sustained 24

hours

64

Table 4.2 - Applied loading for Test No. 2 L

oad

Step

% o

f non

- Fa

ctor

ed

Loa

d

Neg

ativ

e Pr

essu

re –

Sh

ort P

anel

(k

Pa)

Posi

tive

Loa

d –

Shor

t Pan

el

(kN

)

Neg

ativ

e Pr

essu

re –

L

ong

Pane

l (k

Pa)

Posi

tive

Loa

d –

Lon

g Pa

nel

(kN

)

Rem

arks

Cycle 1

0 0 0 0 0 0

1 20 0.314 0.525 0.296 0.726 3 x 30 seconds

2 40 0.628 1.051 0.592 1.402 3 x 30 seconds

3 60 0.942 1.576 0.887 2.076 3 x 30 seconds

4 80 1.256 2.102 1.182 2.750 3 x 30 seconds

5 90 1.413 2.365 1.330 3.088 3 x 30 seconds

6 100 1.570 2.627 1.478 3.426 3 x 30 seconds

Cycle 2 – repeat loadings from Cycle 1

7 100 1.570 2.627 1.478 3.426 Sustained 24

hours

65

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

0

0.3

0.6

0.9

1.2

1.5

1.8

2.1

2.4

2.7

3

0:00:00 0:05:00 0:10:00 0:15:00 0:20:00 0:25:00

Ap

pli

ed

Pre

ss

ure

(k

Pa

)

Ap

pli

ed

Lo

ad

(k

N)

Time (h:mm:ss)

Load Application: Short Panel 1-Test No. 1&2: Cycle#1&2

Panel 1 - Test No. 2


Adjusted for Panel Self-Weight

Figure 4.7 - Loading applied to short panel in Tests No. 1 and No. 2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

0

0.5

1

1.5

2

2.5

3

3.5

4

0:00:00 0:06:00 0:12:00 0:18:00 0:24:00 0:30:00 0:36:00

Ap

pli

ed

Pre

ssu

re (kP

a)

Ap

pli

ed

Lo

ad

(k

N)

Time (h:mm:ss)

Load Application: Long Panels 2&3-Test No. 1&2: Cycle#1&2

Panel 2 - Test No. 1 Panel 2 - Test No. 2Panel 3 - Test No. 1 Panel 3 - Test No. 2

Adjusted for Panel Self-weight

Figure 4.8 - Loading applied to long panels in Tests No. 1 and No. 2

66

Following each of Test No. 1 and Test No. 2, a sustained load was applied to the panels

for a period of 18 or 24 hours (depending on test facility availability). The intent of the sustained

loading was to establish whether the panels displayed any time-dependent effects. These loading

cases are shown in Figure 4.9 for the short panel Figure 4.10 for the long panels, again as

measured from the load cell during testing. The cause of the variability in applied loading in Test

No. 1 is uncertain.

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

0

0.3

0.6

0.9

1.2

1.5

1.8

2.1

2.4

2.7

3

0:00:00 6:00:00 12:00:00 18:00:00 0:00:00

Ap

pli

ed

Pre

ssu

re (kP

a)

Ap

pli

ed

Lo

ad

(kN

)

Time (h:mm:ss)

Load Application: Short Panel 1-Test No. 1&2 Sustained Loading



Adjusted for Panel Self-Weight

Figure 4.9 - Loading applied to short panel in sustained loading following Tests No. 1 and

No.2

67

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

0

0.5

1

1.5

2

2.5

3

3.5

4

0:00:00 4:00:00 8:00:00 12:00:00 16:00:00 20:00:00 0:00:00

Ap

pli

ed

Pre

ss

ure

(k

Pa

)

Ap

pli

ed

Lo

ad

(k

N)

Time (h:mm:ss)

Load Application: Long Panels 2&3-Test No. 1&2 Sustained Loading

Panel 2 - Test No. 1 Panel 2 - Test No. 2Panel 3 - Test No. 1 Panel 3 - Test No. 2

Adjusted for Panel Self-weight

Figure 4.10 - Loading applied to long panels in sustained loading following Tests No. 1 and

No. 2

Finally, after the previous testing was complete, each of the panels was loaded through to

failure in Test No. 3.

4.1.4 Data Collection

Data through the variable loading of Tests No. 1 and No. 2 was recorded at a rate of two

readings per second (2 Hz), while the sustained loading was recorded at one reading per minute

(1/60 Hz) to reduce file size. Test No. 3 to failure was once again increased to two readings per

second to achieve the desired resolution in the measurements. The deflection measurements

(both the LPS and the LDS) were recorded to a resolution of 0.01 mm and the strain

measurements were recorded to a resolution of 1 με.

68

4.2 Fatigue Test Short Panels

4.2.1 Test Frame Setup

In the fatigue tests, loading was to be applied in both the positive and negative directions,

and as such it was necessary to develop both panel supports and load application that could

achieve such a condition.

4.2.1.1 Load Application

A four-point bending arrangement was determined to be a reliable method to achieve

load application analogous to uniform loading without significant sacrifices in panel behaviour.

The use of concentrated loading points as opposed to the air cushion used in the static tests also

ensured that the dynamic effect from compression of the air volume was eliminated. It was

anticipated that the fatigue failure would occur surrounding the cast-in insert supports, and as

such the focus was primarily on achieving adequate representation of the loading at these points.

4.2.1.1.1 Fatigue Test Method

This test applied both positive and negative loading, and as such, a test frame was

developed that was applied on either side of the panel and was clamped in place using bolts

passing through the panel itself. This allowed the load actuator to both pull and push on the panel

as required. The location of the required holes in the panel for the through bolts and the top

portion of the test frame is shown in Figure 4.11. The assembled test frame is shown in Figure

4.12. In order to accommodate the large deflections incurred during the later stages of the testing

– and hence the rotation at the load points – polystyrene blocks were placed beneath the load

points prior to commencing the tests to more evenly distribute the pressure.

69

Figure 4.11 - Holes required in fatigue test panel to allow installation of test frame and top

portion of the test frame

Figure 4.12 - Assembled test frame

70

4.2.1.2 Testing Supports

In order to resist both the positive and negative panel pressures applied during the fatigue

tests, the panel supports married the two methods used during the static testing. This method

involved using the threaded rods to hold the panels against a structural steel backing member.

Bearing plates were placed between the panel and the backing member to ensure the panels were

only supported at the correct points. This support configuration is shown in Figure 4.13.

Figure 4.13 - Fatigue testing support condition

4.2.2 Procedure

4.2.2.1 Cyclic Loading

Cyclic loading was applied to each of the fatigue test panels according the load schedule

shown in Table 4.3 and depicted in Figure 4.14. The loading was gradually increased starting

Threaded rod supports

Bearing plates

71

with a large number of cycles at a low load, progressively increasing to a single cycle at a high

load. This was done in order to represent the of load levels that the panel is expected to

encounter on the building, with lower strength winds occurring more frequently.

Table 4.3 - Fatigue Test Loading Method

Pressure Level Cycles %Load Rate in Hz Time (s) Notes

1.65 kPa Positive

Presure Test

A 8000 40 0.667 11,994 At unloading,

load should be

zero or maximum

10% of load in

each step and hold

single cycle load

for 60 seconds

B 2000 50 0.667 2,999

C 200 65 0.667 300

D 1 120 0.667 1

1.95 kPa Negative

Pressure Test

A 8000 40 0.667 11,994

B 2000 50 0.667 2,999

C 200 65 0.667 300

D 1 120 0.667 1

Time subtotal Positive Pressure Test 10,201 Cycles 15,294 Sec

4.25 Hr

Time subtotal Negative Pressure Test 10,201 Cycles 15.294 Sec

4.25 Hr

Total 20,402 Cycles

72

-1.2

-0.8

-0.4

0

0.4

0.8

1.2

-2-1.5

-1-0.5

00.5

11.5

2

0 0.05 0.1 0.15 0.2 0.25 0.3

Ap

pli

ed

Lo

ad (

kPa)

Ap

pli

ed

Lo

ad (

kN)

Time (min)

Applied Load: Fatigue Levels A, B & C

Fatigue Level A Fatigue Level B Fatigue Level C

-2.4

-1.8

-1.2

-0.6

0

0.6

1.2

1.8

2.4

-4

-3

-2

-1

0

1

2

3

4

0 5 10 15

Ap

pli

ed

Lo

ad (

kPa)

Ap

pli

ed

Lo

ad (

kN)

Time (min)

Applied Load: Fatigue Level D

Fatigue Level D

Figure 4.14 - Applied fatigue loading levels

4.2.2.2 Data Collection

Data for the fatigue load testing was collected at 100 Hz in order to achieve the desired

level of resolution. This equates to 150 readings per full cycle (through positive and negative

loadings) with the applied loading rate of 0.667 Hz. The sheer volume of data this provided

necessitated separation into smaller files at 30 minute intervals. As a result, a small amount of

data was lost during the transition to the new file. Once again, the deflection measurements (both

the LPS and the LDS) were recorded to a resolution of 0.01 mm and the strain measurements

were recorded to a resolution of 1 με.

73

Chapter Five: Test Results

5.1 Static Test Short Panel

5.1.1 Displacement

Examining the central deflection of the short panel under the load testing, it is seen that

this panel appears to respond in a largely linear-elastic manner, as demonstrated by the straight

line relationship shown in Figure 5.1 and Figure 5.2. It is interesting to note that under sustained

loading, there appears to be a slight creep deformation, however this effect rebounds with the

removal of load. This is further examined in Figure 5.3, which indicates large variability in the

deflection from the sustained loading following Test No. 1, which may be an anomaly due to the

test environment (such as leaving the overhead door in the test facility open for extended

periods).

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

0 0.01 0.02 0.03 0.04 0.05

0

0.3

0.6

0.9

1.2

1.5

1.8

2.1

2.4

2.7

3

0 0.2 0.4 0.6 0.8 1 1.2 1.4

Pre

ssu

re (kP

a)

Central Deflection (in.)

Ap

pli

ed

Lo

ad

(k

N)

Central Deflection (mm)

Panel 1-Test No.1: Cycle#1




Test No. 2: Cycle #1


Test No.1: Cycle #1


Figure 5.1 - Short Panel: Central deflection under load through various load cycles

74

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

0 0.01 0.02 0.03 0.04 0.05

0

0.3

0.6

0.9

1.2

1.5

1.8

2.1

2.4

2.7

3

0 0.2 0.4 0.6 0.8 1 1.2 1.4

Pre

ssu

re (kP

a)


Ap

pli

ed

Lo

ad

(kN

)


Sustained Load for 24hrs after

Test No.1 then Unloading to Zero



Figure 5.2 - Short Panel: Central deflection under sustained loading after Test No. 1 & 2

0

0.01

0.02

0.03

0.04

0.05

0

0.2

0.4

0.6

0.8

1

1.2

1.4

0.00 0.25 0.50 0.75 1.00

Cen

tral D

efl

ecti

on

(in

.)

Ce

ntr

al D

efl

ec

tio

n (m

m)

Time (day)

Sustained Load for 24hrs after Test No.2


Figure 5.3 - Short Panel: Central deflection with time under sustained load Test No. 1 & 2

75

A comparison among various points of the panel under the Test No. 1 load is also shown

in Figure 5.4. The purpose of this comparison is to determine any effect the rib texture has on the

stiffness of the panel, since these ribs would primarily only have effects in the direction of their

axis since this is the only arrangement in which they are continuous. It appears as though the ribs

did provide a notable stiffness increase in the one direction, limiting the effectiveness of the two-

way slab assumption from the analytical calculations, as can be seen from the ‘DefE’ and

‘DefW’ deflection readings, which are located at the top and bottom short members, being higher

than the ‘DefN’ and ‘DefS’ deflection readings located at the side narrow members, despite the

short members being stiffer than the narrow members.

0

0.2

0.4

0.6

0.8

1

1.2

0 0.01 0.02 0.03 0.04

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

2.2

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Pre

ss

ure

(k

Pa

)

Deflection (in.)

Ap

pli

ed

Lo

ad

(k

N)

Deflection (mm)

DefCen

DefN

DefE

DefS

DefW

Panel 1 - Test No. 1 Cycle #1

Figure 5.4 - Comparison of deflections at various points of the short panel

The test of the panel to failure (Test No. 3) is shown in Figure 5.5. In this figure, it

appears a linear elastic relationship can be observed up to a loading of approximately 8 kN,

76

corresponding to nearly 4.8 kPa of applied pressure. Accounting for the self-weight of the panel,

this translates to approximately 5.2 kPa of loading at a deflection of 4.10 mm. During testing, the

central deflection transducer was dislodged and as such the ultimate failure of the panel was

interpolated from various other transducers still in operation.

0

2

4

6

8

10

12

0 0.5 1 1.5 2 2.5 3 3.5 4

0

2

4

6

8

10

12

14

16

18

20

0 10 20 30 40 50 60 70 80 90 100

Pre

ss

ure

(k

Pa

)


Ap

pli

ed

Lo

ad

(k

N)


Test No.3 : Test to Failure

Deflection transducer stopped reading

Maximum deflection interpolated from other transducer

TEST NO.3

Figure 5.5 - Short Panel: Central deflection of panel through Test No. 3 (to failure)

A summary of the relevant test results for the static testing on the short panel is shown in

Table 5.1.

77

Table 5.1 - Summary of Test Results for Static Test Short Panel

Test # Criteria Load (kN) Pressure (kPa) Central Deflection (mm)

Test

No.

1

Cycle #1 1.96 1.171 0.84

Cycle #2 2.00 1.195 0.84

After 24hrs sustained 1.99 1.189 0.83

Residual after unloading 0 0 0

Test

No.

2

Cycle #1 2.64 1.578 1.23

Cycle #2 2.63 1.572 1.24


Residual after unloading 0 0 0.05

Test

No.

3

At max load from Test 1 2.01 1.201 0.96


At estimated failure 3.25 1.948 1.54

At end of linear-elastic 8.01 4.788 4.10

At load value of: 16.90 10.101 50.81

At failure (ultimate) 19.45 11.625 ≈102

5.1.2 Strains

Observation of the strain data for the Test No. 1 and Test No. 2 load cycles indicate that

the short panels remained entirely within the elastic region of the Ductal® concrete material, as

depicted by the generally linear relationship shown in Figure 5.6 and Figure 5.7. It is also of note

in these figures that there is a distinct difference between the variations of the strain with applied

78

load on the side with the infill panel as compared to the side without the infill panel. Thus, it can

be deduced that the ‘L’ section produced from the connection between the thickened perimeter

member and the infill portion results in a relevant contribution to the performance of the panel as

a whole. Finally, the maximum tension stress at any of the measurement locatins is 1.95 MPa

under load Test No. 1, and 1.2 MPa under load Test No. 2. The strain data for the failure testing

is not presented, as many of the strain gauges quickly failed and began producing erroneous

results. The difference between SG-11 and SG-15 located on opposite edges of the panel, which

were expected to be similar, is potentially due to localized variability in material strength or

panel construction and corroborates the differences in deflections observed in Figure 5.4 at the

corresponding points.

0

0.2

0.4

0.6

0.8

1

1.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

-60 -40 -20 0 20 40 60 80

Ap

pli

ed

Pre

ssu

re (k

Pa)

Ap

pli

ed

Lo

ad (

kN)

Strain (μm/m)

SG-5

SG-15

SG-1

SG-11

SG-7

SG-17

SG-9

SG-19

Figure 5.6 - Strain of elements in short panel under Test No. 1 (positive) loading

79

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

2.2

2.4

2.6

2.8

3

-120 -100 -80 -60 -40 -20 0 20 40 60

Ap

pli

ed

Pre

ssu

re (k

Pa)

Ap

pli

ed

Lo

ad (

kN)

Strain (μm/m)

SG-5

SG-15

SG-1

SG-11

SG-7

SG-17

SG-9

SG-19

Figure 5.7 - Strain of elements in short panel under Test No. 2 (negative) loading

5.1.3 Visual Observation

The ultimate failure of the short panel was through excessive deformation. A number of

large cracks developed within the panel, an example of which is shown in Figure 5.8, which

resulted in reduced panel stiffness. In this image, both a large crack and an assortment of smaller

cracks that formed in the panel are visible. The subsequent permanent deformation in the panel is

shown in Figure 5.9.

80

Figure 5.8 - Cracking in the short panel prior to failure

Figure 5.9 - Permanent deformation following loading to failure

5.2 Static Test Long Panels

5.2.1 Long Panel #1

5.2.1.1 Displacement

The central deflection under Test No. 1 and Test No. 2, as shown in Figure 5.10,

indicates that an amount of initial permanent deformation is observed in the panels prior to cycle

2. It is possible that this initial deformation is a result of ‘setting-in’ of the test apparatus, since in

81

both tests, the second cycle of testing resulted in the panels rebounding to nearly the initial

deformation. However, it is more likely that this permanent deformation is a characteristic of the

panel, since under the sustained loading condition performed after Test No. 1 and No. 2, Figure

5.11 also indicates some creep as a result of the loading. This effect is also shown in Figure 5.12,

which shows the deflection as a function of time under the sustained load. This figure clearly

demonstrates that the panel central deflection progressively increases with no further increase in

load, and having a resultant deformation of approximately 2.0 mm after test number 1 and 2.4

mm after Test No. 2. It is not apparent if this permanent deformation is a realistic expectation in

real world use, since the variability and reversibility of the wind load means these deflections

could cancel each other out. Further testing would be required to determine if any cumulative

permanent deflections would be experienced.

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

0 0.05 0.1 0.15 0.2 0.25

0

0.5

1

1.5

2

2.5

3

3.5

4

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6

Pre

ss

ure

(k

Pa

)


Ap

pli

ed

Lo

ad

(k

N)








Test No.1: Cycle #1


Long Panel #1 - Test No. 1: Cycles #1 and #2Long Panel #1 - Test No. 1: Cycles #1 and #2

Figure 5.10 - Long Panel 1: Central deflection under load through various loading cycles

82

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

0 0.05 0.1 0.15 0.2 0.25 0.3

0

0.5

1

1.5

2

2.5

3

3.5

4

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5

Pre

ss

ure

(k

Pa

)


Ap

pli

ed

Lo

ad

(k

N)






Figure 5.11 - Long Panel 1: Central deflection under sustained loading for Tests No. 1 & 2

0

0.05

0.1

0.15

0.2

0.25

0.3

0

1

2

3

4

5

6

7

8

0.00 0.25 0.50 0.75 1.00

Ce

ntr

al D

efl

ec

tio

n (in

.)

Ce

ntr

al D

efl

ec

tio

n (m

m)

Time (day)



Figure 5.12 - Long Panel 1: Central deflection under sustained load for Tests No. 1 & 2

83

As was done with the short panel, the deflections measured at various points on the panel

under loading were compared to ascertain the shape of the deflection and the similarity to the

assumed one way loading in the analytical calculations. This comparison is made in Figure 5.13.

The deflection curves for ‘Def-L-Cen’, ‘Def-L-E’, and ‘Def-W’ are the deflections for the long

middle, and long edge at the top and bottom of the panel, respectively. The deflection curves for

‘Def-S’ and ‘Def-N’ are at the quarter points of the long middle member. Due to the close

similarity of the deflections across the width of the panel (Def-W, Def-L-E, and Def-L-Cen), it is

observed that the panel behaved as a single unit spanning between the supports.

0 0.05 0.1 0.15 0.2

0

0.2

0.4

0.6

0.8

1

1.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

2.2

2.4

2.6

2.8

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

Deflection (in.)

Pre

ssu

re (k

Pa)

Ap

pli

ed

Lo

ad

(k

N)

Deflection (mm)

Def-S

Def-W

Def-N

Def-L-E

Def-L-Cen

Long Panel 1 - Test No. 1 Cycle #1

Figure 5.13 - Comparison of deflections at various points of Long Panel 1

Test No. 3, shown in Figure 5.14, shows the central deflection of the panel through to

failure under negative pressure. In this test, elastic behaviour of the panel is shown under applied

loading approaching 2.5 kPa, at which point cracking of the panel notably reduces the panel

84

stiffness, indicated by the reduced slope of the graph. Ultimately, this panel failed at an applied

load of approximately 8.4 kPa, which equals approximately 8.8 kPa including the self-weight of

the panel, at a deflection of approximately 146 mm.

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6 7 8

0

2

4

6

8

10

12

14

16

18

20

0 25 50 75 100 125 150 175 200

Pre

ss

ure

(k

Pa

)


Ap

pli

ed

Lo

ad

(k

N)




Deflection extrapolated from other transducer

TEST NO.3

Cracking of panel

Figure 5.14 - Long Panel 1: Central deflection of panel through Test No. 3 (to failure)

A summary of the deflection values through the testing is shown in Table 5.2.

TEST NO.3

85

Table 5.2 - Summary of Test Results for Static Test Long Panel #1


Test

No.

1

Cycle #1 2.47 1.08 4.21

Cycle #2 2.53 1.11 4.54



Test

No.

2

Cycle #1 3.38 1.48 5.16

Cycle #2 3.34 1.46 5.58



Test

No.

3




At estimated failure 7.54 3.30 235


5.2.1.2 Strains

Unfortunately, the strain data record proved to be less reliable and intelligible than

anticipated. A selection of the available information is provided here, however further analysis

was limited. In Figure 5.15 and Figure 5.16, the strain data corroborates the permanent

deformations measured by the deflection data in both Test No. 1 and Test No. 2. However, it is

noted that some of the gauges displayed linear-elastic behaviour. Figure 5.17 shows that the

86

GFRP reinforcing bars did aid in the strength of the panels, with the stress in the reinforcing

reaching an average of 9.0 MPa in Test No. 1 and 16.5 MPa in Test No. 2. In the following

figures, results that were incomprehensible were omitted from the graphing, though included in

the legend for consistency.

0

0.2

0.4

0.6

0.8

1

1.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

2.2

2.4

2.6

2.8

3

-400 -300 -200 -100 0 100 200 300 400 500 600A

pp

lie

d P

ress

ure

(kPa

)

Ap

pli

ed

Lo

ad (

kN)

Strain (μm/m)

SG-5

SG-15

SG-1

SG-11

SG-3

SG-13

Figure 5.15 - Strain of elements in Long Panel 1 under Test No. 1 (positive) loading

87

0

0.25

0.5

0.75

1

1.25

1.5

1.75

0

0.5

1

1.5

2

2.5

3

3.5

4

-1500 -1250 -1000 -750 -500 -250 0 250 500

Ap

pli

ed

Pre

ssu

re (k

Pa)

Ap

pli

ed

Lo

ad (

kN)

Strain (μm/m)

SG-5

SG-15

SG-1

SG-11

SG-3

SG-13

Figure 5.16 - Strain of elements in Long Panel 1 under Test No. 2 (negative) loading

0

0.2

0.4

0.6

0.8

1

1.2

0

0.5

1

1.5

2

2.5

3

3.5

0 50 100 150 200 250 300 350

Ap

pli

ed

Pre

ssu

re (k

N)

Ap

pli

ed

Lo

ad (

kN)

Strain (μm/m)

SG-44

SG-45

SG-44

SG-45

Test No. 1

Test No. 2

Figure 5.17 - Strain in the GFRP reinforcing bars for Long Panel 1

88

5.2.1.3 Visual Observations

As expected for this panel, the ultimate failure occurred as a crack propagating across the

short direction of the panel, located predominantly within the decorative ribs, as these act to

reduce the effective section of the panel. The final failure crack is shown in Figure 5.18.

Figure 5.18 - Final failure of Panel #1

5.2.2 Long Panel #2

5.2.2.1 Displacement

Long Panel #2 behaved similarly to Long Panel #1, with the notable exception of the

panel deforming considerably less despite the loading conditions being similar. Additionally,

under Test No. 1 Cycle 1 and the sustained loading that followed, there was marginal permanent

deformation observed for the positive pressure testing in both the cyclic loading and the

89

sustained loading, contrary to the observations for Long Panel #1. These results are shown in

Figure 5.19 for the loading cycles and Figure 5.20 and Figure 5.21 for the sustained loading. For

comparison, Long Panel #1 deformed a maximum of approximately 7.0 mm in the sustained

loading following Test No. 2, while Long Panel #2 deformed approximately 2.4 mm, nearly 65%

less. It is unclear what caused this difference in the panel behaviour, as there was no observable

or intentional variance between the panels. It is notable in the sustained loading case following

Test No. 1 that some creep deformation was observed, however the panel rebounded upon

unloading.

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

0 0.02 0.04 0.06 0.08 0.1 0.12

0

0.5

1

1.5

2

2.5

3

3.5

4

0 0.5 1 1.5 2 2.5 3

Pre

ss

ure

(k

Pa

)


Ap

pli

ed

Lo

ad

(k

N)








Test No.1: Cycle #1


Long Panel #1 - Test No. 1: Cycles #1 and #2Long Panel #2 - Test No. 1: Cycles #1 and #2


90

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

0 0.02 0.04 0.06 0.08 0.1 0.12

0

0.5

1

1.5

2

2.5

3

3.5

4

0 0.5 1 1.5 2 2.5 3

Pre

ss

ure

(k

Pa

)


Ap

pli

ed

Lo

ad

(k

N)







0

0.02

0.04

0.06

0.08

0.1

0.12

0

0.5

1

1.5

2

2.5

3

0.00 0.25 0.50 0.75 1.00

Cen

tral D

efl

ecti

on

(in

.)

Ce

ntr

al D

efl

ec

tio

n (m

m)

Time (day)



Figure 5.21 - Long Panel 2: Central deflection under sustained load for Tests No. 1 & 2

Test No. 2

91

The differences observed in the loading cycles between Panel #1 and Panel #2 also

extended to the test to failure under negative pressure, with the central deflection for Panel #2

through to failure shown in Figure 5.22. Panel #2 withheld substantially higher pressures while

also deforming less than Panel #1, reaching approximately 14.1 kPa (14.5 kPa including the

panel self-weight) with 118 mm of central deflection. For comparison, at the failure load of

Panel #1 (8.8 kPa at 146 mm deflection), Panel #2 exhibited 87 mm of deflection, a 40%

reduction. Unfortunately, these test panels are no longer available for observation, thus no further

examination is possible to determine the discrepancy.

0

2

4

6

8

10

12

14

0 1 2 3 4 5 6 7 8

0

5

10

15

20

25

30

35

0 25 50 75 100 125 150 175 200

Pre

ss

ure

(k

Pa

)


Ap

pli

ed

Lo

ad

(k

N)




Deflection extrapolated from other transducer

TEST NO.3

Cracking of panel

Figure 5.22 - Long Panel 2: Central deflection of panel through Test No. 3 (to failure)

92

Table 5.3 - Summary of Test Results for Static Test Long Panel #2


Test

No.

1

Cycle #1 2.54 1.11 1.75

Cycle #2 2.54 1.11 1.66


Residual after unloading 0 0 0

Test

No.

2

Cycle #1 3.34 1.46 2.56

Cycle #2 3.36 1.47 2.70



Test

No.

3




At estimated failure 7.54 3.30 16.93


5.2.2.2 Strains

Thankfully, the strain data for this panel appears to be more reliable than that obtained in

Panel 1. Figure 5.23 of the panel under positive loading shows that the behaviour was very

nearly linear-elastic, which generally agrees with the deflection data. A maximum tension stress

of approximately 3.69 MPa was achieved in this case. In the negative pressure test shown in

Figure 5.24, the strain data indicates a significant amount of compression occurred. It is unclear

93

if these measurements are accurate, although the deflection data for this case does seem to

indicate a permanent deformation, which corresponds with the strain data. Finally, Figure 5.25

shows the strain in the GFRP reinforcing bars through the loading. In this panel, two of the

reinforcing bars experience very little strain in test number 1. This is likely due to the uncracked

condition of the panel and the placement of the reinforcing at mid-depth of the panel. The third

reinforcing bar in this test experienced a stress of approximately 4.4 MPa. In the second test, the

reinforcing bars were utilized to a greater extent, with the stress ranging from 2.2 MPa to 7.7

MPa across the three primary GFRP reinforcing bars.

0

0.2

0.4

0.6

0.8

1

1.2

0

0.5

1

1.5

2

2.5

3

-100 -50 0 50 100 150

Ap

pli

ed

Pre

ssu

re (k

Pa)

Ap

pli

ed

Lo

ad (

kN)

Strain (μm/m)

SG-5

SG-15

SG-1

SG-11

SG-3

SG-13

Figure 5.23 - Strain of elements in Long Panel 2 under Test No. 1 (positive) loading

94

0

0.25

0.5

0.75

1

1.25

1.5

1.75

0

0.5

1

1.5

2

2.5

3

3.5

4

-450 -400 -350 -300 -250 -200 -150 -100 -50 0 50 100

Ap

pli

ed

Pre

ssu

re (k

Pa)

Ap

pli

ed

Lo

ad (

kN)

Strain (μm/m)

SG-5

SG-15

SG-1

SG-11

SG-3

SG-13

Figure 5.24 - Strain of elements in Long Panel 2 under Test No. 2 (negative) loading

0

0.25

0.5

0.75

1

1.25

1.5

1.75

0

0.5

1

1.5

2

2.5

3

3.5

4

-50 -25 0 25 50 75 100 125 150

Ap

pli

ed

Pre

ssu

re (k

Pa)

Ap

pli

ed

Lo

ad (

kN)

Strain (μm/m)

SG-43

SG-44

SG-45

SG-43

SG-44

SG-45

Test No. 2

Test No. 1

Figure 5.25 - Strain in the GFRP reinforcing bars for Long Panel 2

95

5.2.2.3 Visual Observations

Once again, the failure of this panel was a crack through the panel at nearly midspan, as

shown in Figure 5.26.

Figure 5.26 - Final failure of Panel #2

5.3 Fatigue Test Short Panels

5.3.1 Displacement

5.3.1.1 Cyclic Loading

In order to assess the performance of the panels under fatigue loading, the load-deflection

curves were plotted at selected cycles throughout the loading. Cycle selection followed a

logarithmic pattern in each loading level to evaluate any changes that occur as cycles continue.

These graphs can be seen in Figure 5.27 for loading level A, Figure 5.28 for loading level B, and

Figure 5.29 for loading levels C and D. Both of the tested panels were plotted on the same graphs

for ease of comparison. In these figures, due to the test setup, a positive deflection and a positive

load represent negative wind pressure.

96

In both of these cases, the central deflection measurements from the LDS were too

inaccurate to gather useful information during the fatigue testing. It appears an issue with

instrument precision was the root cause. As such, the central deflection was interpolated from the

deflections measured at the outside edges which used laser transducers with a greater precision.

For the low load levels that are encountered in the fatigue testing, the deflection of the panel

overall was assumed to take the shape of a parabaloid, as would be expected for a thin plate

under uniform loading [19]. A ratio between the deflection at the edge and the centre of the panel

was developed based on the dimensions of the panel, and is shown in Equation 5-1.

Equation of a parabaloid: z = b(x2 + y2)

zc = zl

(xc2 + yc

2)

(xl2 + yl

2)= 2.3626zl Equation 5-1

Where,

zc = Interpolated deflection at the panel centre (m)

zl = Measure deflection, average of two points (m)

xi, yi = Coordinates of zc and zl (m)

Through evaluation of Figure 5.27 through Figure 5.29, it is apparent that the panels

respond in a largely elastic manner through all the applied loading levels, as demonstrated by the

straight line created through the loading and unloading cycles. The slight deviation from true

elastic behaviour (creating the deviation between the loading and unloading) is likely a result of

dynamic behaviour in the panel created by the loading rate. It is noted that the centre of the load-

deflection graph appears to gradually shift towards a permanent deflection in the negative wind

pressure direction. However, further analysis of the peak deflections of each cycle and the

maximum range of deflection, as shown in Figure 5.30, indicates there is no cumulative

97

permanent deflection or any increase in the range of deflection. It is unclear where this drift in

values originated, but it may be attributed to a variation in the instrumentation as testing

proceeded. Thus, it appears the fatigue loading has little detrimental effect on the performance of

the panels.

98

Figure 5.27 - Select load-deflection charts for load level A fatigue testing

-1.2

-0.8

-0.4

0

0.4

0.8

1.2

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

-0.6 -0.3 0 0.3 0.6

Ap

plie

d P

ress

ure

(kP

a)

Ap

plie

d L

oad

(kN

)

Deflection (mm)

Load Level A: Cycles 1-5

Panel 1

Panel 2

-1.2

-0.8

-0.4

0

0.4

0.8

1.2

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

-0.6 -0.3 0 0.3 0.6

Ap

plie

d P

ress

ure

(kP

a)

Ap

plie

d L

oad

(kN

)

Deflection (mm)


Panel 1Panel 2

-1.2

-0.8

-0.4

0

0.4

0.8

1.2

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

-0.6 -0.3 0 0.3 0.6

Ap

plie

d P

ress

ure

(kP

a)

Ap

plie

d L

oad

(kN

)

Deflection (mm)


Panel 1Panel 2

-1.2

-0.8

-0.4

0

0.4

0.8

1.2

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

-0.6 -0.3 0 0.3 0.6

Ap

plie

d P

ress

ure

(kP

a)

Ap

plie

d L

oad

(kN

)

Deflection (mm)


Panel 1Panel 2

-1.2

-0.8

-0.4

0

0.4

0.8

1.2

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

-0.6 -0.3 0 0.3 0.6

Ap

plie

d P

ress

ure

(kP

a)

Ap

plie

d L

oad

(kN

)

Deflection (mm)


Panel 1Panel 2

-1.2

-0.8

-0.4

0

0.4

0.8

1.2

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

-0.6 -0.3 0 0.3 0.6

Ap

plie

d P

ress

ure

(kP

a)

Ap

plie

d L

oad

(kN

)

Deflection (mm)


Panel 1Panel 2

99

Figure 5.28 - Select load-deflection charts for load level B fatigue testing

-1.2

-0.8

-0.4

0

0.4

0.8

1.2

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

-0.6 -0.3 0 0.3 0.6

Ap

plie

d P

ress

ure

(kP

a)

Ap

plie

d L

oad

(kN

)

Deflection (mm)

Load Level B: Cycles 1-5

Panel 1Panel 2

-1.2

-0.8

-0.4

0

0.4

0.8

1.2

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

-0.6 -0.3 0 0.3 0.6

Ap

plie

d P

ress

ure

(kP

a)

Ap

plie

d L

oad

(kN

)

Deflection (mm)


Panel 1

Panel 2

-1.2

-0.8

-0.4

0

0.4

0.8

1.2

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

-0.6 -0.3 0 0.3 0.6

Ap

plie

d P

ress

ure

(kP

a)

Ap

plie

d L

oad

(kN

)

Deflection (mm)


Panel 1Panel 2

-1.2

-0.8

-0.4

0

0.4

0.8

1.2

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

-0.6 -0.3 0 0.3 0.6

Ap

plie

d P

ress

ure

(kP

a)

Ap

plie

d L

oad

(kN

)

Deflection (mm)


Panel 1Panel 2

-1.2

-0.8

-0.4

0

0.4

0.8

1.2

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

-0.6 -0.3 0 0.3 0.6

Ap

plie

d P

ress

ure

(kP

a)

Ap

plie

d L

oad

(kN

)

Deflection (mm)


Panel 1Panel 2

100

Figure 5.29 - Select load-deflection charts for load level C & D fatigue testing

-1.2

-0.8

-0.4

0

0.4

0.8

1.2

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

-0.6 -0.3 0 0.3 0.6

Ap

plie

d P

ress

ure

(kP

a)

Ap

plie

d L

oad

(kN

)

Deflection (mm)

Load Level C: Cycles 1-5

Panel 1Panel 2

-1.2

-0.8

-0.4

0

0.4

0.8

1.2

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

-0.6 -0.3 0 0.3 0.6

Ap

plie

d P

ress

ure

(kP

a)

Ap

plie

d L

oad

(kN

)

Deflection (mm)


Panel 1Panel 2

-1.2

-0.8

-0.4

0

0.4

0.8

1.2

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

-0.6 -0.3 0 0.3 0.6

Ap

plie

d P

ress

ure

(kP

a)

Ap

plie

d L

oad

(kN

)

Deflection (mm)


Panel 1Panel 2

-2.4

-1.6

-0.8

0

0.8

1.6

2.4

-4

-3

-2

-1

0

1

2

3

4

-1.5 -1 -0.5 0 0.5 1 1.5

Ap

plie

d P

ress

ure

(kP

a)

Ap

plie

d L

oad

(kN

)

Deflection (mm)

Load Level D: Cycle 1

Panel 1

101

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

0 25 50 75 100 125 150 175 200 225 250 275

Ce

ntr

al D

efl

ect

ion

(mm

)

Time (min)

Envelope of Deflections through Loading Levels A, B & C

Panel 1 - Positive Panel 1 - Negative Panel 2 - Positive Panel 2 - Negative

Load Level A - 8000 Cycles Load Level B - 2000 CyclesLoad Level C - 200 Cycles

0

0.2

0.4

0.6

0.8

1

1.2

De

fle

ctio

n R

ange

(mm

) Panel 1 - Range Panel 2 - Range

Figure 5.30 - Peak deflection and deflection range progression through fatigue testing

5.3.1.2 Failure Loading

The performance of the fatigue tested panels when loaded to failure is shown in Figure

5.31. Of note here is the similar performance that is achieved in comparison to the static load

testing performed on the unfatigued panel; however the failure mode is different. The unfatigued

panel failed through flexure, and thus cracking within the span, while both the fatigued panels

failed at the cast-in inserts, as shown in Section 5.3.3. The failure appears to occur as either

concrete breakout, or shear failure of the headed end of the insert and subsequent pull-out. This

difference is likely one of two possibilities: either the fatigue loading had a significant effect on

the ability of the cast-in inserts to maintain load, or the different support condition imposed by

102

the fatigue testing apparatus resulted in a deleterious stress distribution at the supports. It is

believed that the test supports had the most significant impact, since the fatigue setup supports

appear to resist rotation more than the supports in the static testing, and as such adding a pry out

component to the cast-in anchor forces, however the strain gauges were not adequately arranged

to validate this theory.

0

2

4

6

8

10

12

14

-25

-20

-15

-10

-5

0

0 5 10 15 20 25 30 35 40 45 50A

pp

lie

d P

ress

ure

(kP

a)

Ap

pli

ed

Lo

ad (

kN)


Static Test to Failure Following Fatigue Testing

Panel 2 Panel 1

Figure 5.31 - Test to failure of panels following fatigue testing

5.3.2 Strains

The strain data from the cyclic loading corroborated the conclusions obtained through the

deflection data. It appears the panels remained in the linear-elastic range of their performance for

all of the load levels. The strain data was also useful in determining the capacity of the cast-in

Panel 1 Panel 2

Cracking of Panels

103

inserts. Referring to Figure 5.32, which shows the strain gauges located immediately adjacent to

the four cast-in inserts as show in Section 3.4.3, the first crack at two of the cast-in inserts that

eventually failed occurred at 3.29 kPa and 4.75 kPa applied pressure. This corresponds to

1.38 kN and 1.99 kN applied load on the cast-in inserts. The strain gauges exceeded their

capacity shortly after the first cracks were recorded, however comparing the maximum load

applied to the panel prior to failure, it is estimated that the cast-in inserts reached a maximum

capacity of approximately 5.7 kN, compared to the calculated resistance of 7.23 kN and the load

test average of 8.1 kN.

0

1

2

3

4

5

6

7

8

9

10

11

-20

-18

-16

-14

-12

-10

-8

-6

-4

-2

0

-200 -100 0 100 200 300 400 500

Ap

pli

ed

Pre

ssu

re (k

Pa)

Ap

pli

ed

Lo

ad (

kN)

Strain (μm/m)

SG-41

SG-42

SG-43

SG-44

Figure 5.32 - Strain measurements at the cast-in insert in failure loading following fatigue

testing

104

5.3.3 Visual Observation

The mode of failure of the fatigue panels is notable because both the panels failed at the

cast-in inserts rather than in flexure. Figure 5.33 shows two of the failed inserts.

a) Concrete breakout

b) Pull-out of cast-in insert

Figure 5.33 - Failure of cast-in inserts following fatigue loading

105

Chapter Six: Comparison of Results and Design Validation

6.1 Static Test Comparison and Validation

The primary criteria for acceptability of the wall panels is the deflection under

serviceability load conditions. A comparison of the deflection values obtained through the

analytical calculations, the finite element model, and the static testing is shown in Table 6.1. It is

noted that the analytical calculations predicted the highest deflections, most likely due to the

number of simplifying assumptions made, including ignoring the contribution of the surface ribs

to the panel strength, analyzing the panels as a one-way and two-way slab and beam system, and

ignoring the contribution of the ‘T’ and ‘L’ sections to the member strength. For the short panel,

the actual deflection at the SLS load level was significantly less, nearly half as much, as that

calculated in the finite element model. This could be due to the additional stiffness offered by the

textured rib surface, which was not accounted for in the modelling, but was shown to have a

significant impact as demonstrated in Section 5.1.1. The short panel static testing displayed

deflections significantly below the established deflection limit for both the positive and negative

pressures.

For the long panels tested, the average deflection of the panels agreed well with the

analytical calculations, but was higher than the finite element analysis calculations. However,

there was a substantial disparity in the performance of the two panels, for which there appears to

be little explanation. Here, Long Panel 1 deflects less under load than both the analytical

calculations and the finite element analysis predict and is within the acceptable deflection limit,

while Long Panel 2 had measured deflections greater than expectations and limitations. Given

that the performance of the Long Panel 2 continues the trend of deflecting less than the predicted

deflection, similar to the Short Panel, it is theorized that Long Panel 1 is an anomaly and may not

106

be representative of the typical panel behaviour. However, since only two Long Panels were

tested, this could not be confirmed. When the average of the two Long Panels is considered, the

maximum of 4.00 mm under negative SLS pressure results in a deflection of span/400, which is

deemed to be acceptable given the established limit is based on masonry construction, and these

Ductal® concrete panels exhibit much greater ductility than would be expected with masonry.

Based on the Short Panel and the Long Panel 2, the spandrel panels as designed satisfy the

deflection design requirements.

Table 6.1 - Comparison of predicted and measured panel deflections

Analysis Method

SLS Positive Pressure Deflection

(mm)

SLS Negative Pressure Deflection

(mm) Short Panel Long Panel Short

Panel Long Panel

Established Limit: L/600 1.95 2.73 1.95 2.73

Analytical Calculations 2.03 3.02 2.53 3.96

Finite Element Analysis 1.41 2.43 1.75 3.02

Static Load Testing Note 1 0.84

Panel 1 Panel 2

1.24

Panel 1 Panel 2

4.38 1.71 5.37 2.63

3.05 (average) 4.00 (average)

Note 1: The measured deflection from the static load testing does not account for the deflection caused in the panel under self-weight in the horizontal position, as noted in Section 4.1.1.

In addition to the deflection requirement, it was also desirable for the panels to exhibit

sufficient strength to not crack under service loads, for aesthetic reasons. The loads at which

cracking occurred – both for the analytical calculations and as a result of the static testing – are

shown in Table 6.2 together with the calculated and measured failure loads. Since the finite

107

element analysis was conducted as an elastic model only, it could not be used to calculate

cracking loads. While the analytical calculations predicted cracking at loads below the service

loads, the measured loads at which cracking occurred in the panels was above the service loads

in all cases. In fact, the short panel cracked at a loading higher than the ultimate load condition,

and as such would not be expected to crack at all through the life cycle of the panel. In general,

the cracking loads predicted through analytical calculations were approximately three to four

times less than the static test loads.

The measured failure loads of the panels during the static testing were also notably higher

than the load predicted through analytical calculations. This can likely be attributed to the

simplifications made in the analytical calculations and the material reduction factors applied to

the Ductal® concrete and GFRP reinforcing bars.

Given the fact that these panels were able to resist forces much higher than the ultimate

limit states design loads and that none of the tested panels exhibited cracking under serviceability

load conditions, it is determined that the panels are acceptable for the intended use as spandrel

cladding panels. All of the panels demonstrated large deflection prior to the failure of the panels,

thus a ductile failure mode was exhibited.

Table 6.2 - Comparison of calculated and measured cracking and failure pressure

Panel

Analytical Calculations Static Load Testing

Cracking Load

(kPa)

Failure Load

(kPa)

Cracking Load

(kPa)

Failure Load

(kPa)

Short Panel #1 1.05 3.97 5.19 12.03

Long Panel #2 0.68 2.15

2.02 8.80

Long Panel #3 2.16 14.75

108

6.2 Fatigue Test Comparison and Validation

Despite the analytical calculations and the finite element analysis indicating that the stress

levels in the short panels exceed the fatigue endurance limit of ninety percent of the tensile

strength (2.52 MPa), the testing of the short panels under fatigue loading demonstrated that the

panel responds in the linear-elastic range through the fatigue loading levels. This is further

demonstrated in the failure testing of these panels, which indicates cracking of the panels

occurred at negative pressures of 11.2 kPa and 9.1 kPa and in the static test short panel at 5.19

kPa, greater than either the negative serviceability or ultimate wind pressures of 1.43 kPa and

2.67 kPa, respectively.

Interestingly, the fatigue panels both failed through a different mechanism than the static

load panels. Both the fatigue panels failed by pull-out or breakout of the cast-in anchors which

would be considered a brittle failure mode, while the static load tests failed through bending, a

ductile failure mode. The fatigue test panels did present substantial deflection prior to failure, on

the order of 37 mm and 47 mm, thus presumably any potential failure would be apparent. The

fatigue test panels resisted a similar load as the short static test panels when loaded to failure (an

average of 13.71 kPa compared to 11.63 kPa, respectively), and thus it is reasonable to establish

that the fatigue loading did not have a detrimental effect on the panel design. It is concluded that

the short fatigue panels do not appear to be susceptible to fatigue loading and are therefore

suitable for use as spandrel cladding panels in the project.

It is noted, however, that the long panels utilize a greater proportion of the Ductal®

concrete strength, as demonstrated by cracking occurring at a lower applied load of 2.02 kPa and

2.16 kPa in the two panels tested under static loading. Both of these cracking loads are lower

than the ultimate limit states load levels and as such it is conceivable that the long panels may

109

experience some load cycling beyond the tensile limit. Further testing similar to the fatigue

testing performed on the short panels would be required to ascertain the fatigue performance of

the long panels.

6.3 Sources of Uncertainty

As with all experimental procedures, an amount of uncertainty is present in the results. In

this case, some of the primary sources of uncertainty include:

Variation in the material properties, since testing of the individual materials was

not conducted;

Variation in the dimensions of the constructed panels due to dimensional tolerance

required in construction;

Variations due to the test setup, including testing in the horizontal position, losses

from the air mattress, and validity of assumed support conditions, and;

Precision, accuracy, and calibration of the test equipment.

Additionally, given the small number of panels tested – one short and two long panels under

static testing, and two short panels under fatigue testing – it is not possible to reject a statistical

aberration.

110

Chapter Seven: Conclusion and Recommendations

The Ultra-High Performance Fibre Reinforced Concrete (UHPFRC) spandrel cladding

panels with Glass Fibre Reinforced Polymer (GFRP) reinforcing bars as designed and tested are

sufficient to withstand the positive and negative wind pressures for the intended application in

Victoria, British Columbia. The prototype panels subjected to load testing proved to exceed

expectations from both the analytical calculations and the finite element analysis. Better realism

in the finite element analysis could have been achieved by developing a model that included the

tension and compression properties of the Ductal® concrete by inputting the stress-strain

relationship of the material, as opposed to the linear-elastic model that was used. Additionally,

while the analytical calculation method undertaken proved to provide a reasonable

approximation for the deflections, it was shown to estimate a failure load approximately three

times lower than the failure load establish through testing. It was also concluded that the textured

rib surface did have a beneficial impact on the performance of the panel, contrary to the

assumptions made in the initial analysis.

Recommended further research for panels of this type should they be used in other

situations would be:

to test the panels in the upright condition to establish a better understanding of

real-world stresses;

to assess the effect of temperature fluctuations on the panels;

to perform compression and tension material tests on the chosen UHPFRC

material to obtain more relevant stress-strain relationships, and;

to conduct instrumentation and observation of the installed panels to evaluate the

long-term real-world performance.

111

References

[1] R. M. Sanders, "Curtain Walls: Not Just Another Pretty Façade," Hoffmann Architects'

JOURNAL, vol. 23, no. 1, pp. 1-8, 2006.

[2] David Yeomans, "The Pre-History of the Curtain Wall," Construction History, vol. 14, pp.

59-82, 1998.

[3] Michael J. Scheffler. (2010, Apr.) Building Envelope Design Guide - Thin Stone Wall

Systems. [Online]. Available: http://www.wbdg.org/design/env_wall_thin_stone.php

[January 5, 2014].

[4] Lafarge North America Inc., Ductal FO B3 Behaviour-10f2 Datasheet, 2011.

[5] G. Ghoneim, R. El-Hacha, G. Carson, and D. Zakariasen, "Precast Ultra High Performance

Fibre Reinforced Concrete Replace Stone and Granite on Building Façade," in Third fib

Congress and Exhibition, Washington, D.C., 2010.

[6] Canadian Standards Association, CAN/CSA A23.3-04 - Design of Concrete Structures.

Rexdale, ON, 2004.

[7] National Research Council Canada, 2005 National Building Code of Canada. Ottawa, ON,

2005.

[8] Canadian Prestressed Concrete Institute, CPCI Design Manual 4 - Precast and Prestressed

Concrete. Ottawa, ON, 2007.

[9] Canadian Standards Association, CSA S806-02 - Design and construction of Building

Structures with Fibre-Reinforced Polymers. Rexdale, ON, 2002.

http://www.wbdg.org/design/env_wall_thin_stone.php

112

[10] Service d'études techniques des routes et autoroutes/Association Française de Génie Civil,

Ultra High Performance Fibre-Reinforced Concretes - Interim Recommendations., 2002.

[11] R. El-Hacha, "Behaviour and Design of Reinforced Concrete Members", class notes for

ENCI 623, Department of Civil Engineering, University of Calgary, 2011.

[12] A. Ghali, A. N. Neville, and T. G. Brown, "Displacement of Elastic Structures by Special

Methods," in Structural Analysis, A Unified Classical and Matrix Approach, 5th ed. New

York, NY: Spon, 2003, ch. 10, pp. 280-312.

[13] Colin Caprani. (2011). "Structural Analysis III" [Online]. Available:

http://www.colincaprani.com/files/notes/SAIII/5%20-%20Moment-Area%20Method%20-

%20R2.pdf [February 12, 2014].

[14] American Concrete Institute, ACI 530-08 - Building Code Requirements & Specifications

for Masonry Structures. Farmington Hills, MI, 2008.

[15] M. Sauer, personal communication, Feb. 2014.

[16] K. Bathe and E. N. Dvorkin, "Short Communication, A Four-Node Plate Bending Element

Based on Mindlin/Reissner Plate Theory and a Mixed Interpolation," Int. J. for Numberical

Methods in Eng., vol. 21, pp. 367-383, 1985.

[17] Lafarge North America Inc. Mechanical Performances. [Online]. Available:

http://www.ductal-lafarge.com/wps/portal/ductal/6_5-Mechanical_performaces [January 13,

2014].

http://www.colincaprani.com/files/notes/SAIII/5%20-%20Moment-Area%20Method%20-%20R2.pdf

http://www.colincaprani.com/files/notes/SAIII/5%20-%20Moment-Area%20Method%20-%20R2.pdf

http://www.ductal-lafarge.com/wps/portal/ductal/6_5-Mechanical_performaces

113

[18] Canadian Standards Association, CAN/CSA A23.1/A23.2 - Concrete Materials and Methods

of Concrete Construction/Test Methods and Standard Practices for Concrete. Rexdale, ON,

2009.

[19] Pultrall Inc., V-ROD Std (50 GPa) Datasheet, May 2011.

[20] UCAN Fastening Products, "Technical Manual," Toronto, 2005. [Online]. Available:

http://www.ucanfast.com/pds/Tabulation/Tech_Manual.pdf [February 16, 2014].

[21] I. D. Cooley, Equilibrium of a Shallow Elliptic Paraboloid Shell Subjected to Uniform

Normal Pressure. Gainesville, FL: University of Florida, 1958.

http://www.ucanfast.com/pds/Tabulation/Tech_Manual.pdf

114

Appendices A: Embedded Anchor Pullout Calculations

The recommendations of CAN/CSA A23.3-04 regarding the resistance of cast-in inserts

require testing for concrete strengths greater than 55 MPa. However, the calculations were

completed here for comparison to the test results.

Ncbr =AN

ANoψed,Nψc,Nψcp,NNbr Equation A-1

Where,

Ncbr = Concrete breakout resistance of anchor (kN)

AN

ANo

= Ratio of area of single anchor versus area of group = 1 for single anchor

ψed,N = Edge effect factor = 1 (edge distance greater than 1.5hef)

ψc,N = Cracking factor = 1 (expect cracking)

ψcp,N = Installation factor = 1 (not post-installed)

Nbr = Breakout resistance of a single anchor, defined in Equation A-2

Nbr = kφc√f′chef1.5R Equation A-2

Where,

Nbr = Tension breakout resistance of anchor (kN)

k = Value for cast-in anchors = 10

φc = Material resistance factor for precast concrete = 0.70

f′c = Compressive strength of concrete, maximum of 70 MPa (MPa)

hef = Effective depth of embedment

R = Condition B (tension, cast-in) = 1.0

115

Combining these, the breakout resistance of the anchors is as shown below.

Ncbr =AN

ANoψed,Nψc,Nψcp,Nkφc√f′chef

1.5R

Ncbr = (1)(1)(1)(1)(10)(0.70)√(70 MPa)(25 mm)1.5(1)

Ncbr = 7.32 kN

The remainder of the failure cases outlined were found not to govern and are thus omitted.

116

Appendices B: Copyright Permissions 2.1 D’AMBROSIO architecture + urbanism

B.1

Contact Information

Redacted

Contact Information

Redacted

Contact Information

Redacted

117

Signature Redacted

Contact Information

Redacted

118

2.2 DIALOG

B.2

Contact Information

Redacted

Contact Information

Redacted

119

Signature Redacted

120

2.3 Hoffmann Architects, Inc.

B.3

Contact Information

Redacted

Contact Information

Redacted

121

Signature Redacted

122

2.4 Lafarge Precast

B.4

Contact Information

Redacted

Contact Information

Redacted

123

Signature Redacted

uhpfrc cladding panels in façade applications

Documents