Presently, the industry accepted method for the determination of the governing buckling strength for cold-formed purlins supporting a standing seam metal roof system is the 1996 AISI Specification for the Design of Cold-Formed Steel Structural Members, which contains provisions for local and lateral buckling. Previous research has determined that the AISI provisions for local buckling strength predictions of cold-formed purlins are highly unconservative and that the AISI provisions for lateral buckling strength predictions of cold-formed purlins are overly conservative. Therefore, a more accurate "hand" method is needed to predict the buckling strengths of cold-formed purlins supporting standing seam roof systems. The primary objective of this study is to investigate the accuracy of the Hancock Method, which predicts distortional buckling strengths, as compared to the 1996 AISI Specification provisions for local and lateral buckling. This study used the experimental results of 62 third point laterally braced tests and 12 laterally unbraced tests. All tests were simple span, cold-formed Z-section supported standing seam roof systems. The local, lateral, and distortional buckling strengths were predicted for each test using the aforementioned methods. These results were compared to the experimentally obtained data and then to each other to determine the most accurate strength prediction method. Based on the results of this study, the Hancock Method for the prediction of distortional buckling strength was the most accurate method for third point braced purlins supporting standing seam roof systems. In addition, a resistance factor was developed to account for the variation between the experimental and the Hancock Method's predicted strengths. / Master of Science

Presently, the industry accepted method for determining the positive moment strength of gravity loaded standing seam metal roof systems is the "Base Test Method". The Base Test Method provides a means for determining the positive moment strength of a multiple span, multiple purlin line standing seam roof system using the results from a set of six single span, simply supported, two-purlin line experimental tests. A set of six base tests must be conducted for each combination of purlin profile, deck panel profile, clip type, and intermediate bracing configuration. The primary objective of this study is to investigate the possibility of eliminating some of the roof system parameters specifically, clip type, purlin flange width, and roof panel thickness. This study used the results from nine series of tests. Each series consists of 11 to 14 gravity loaded base tests. The first three series were used to examine the effects of clip type on the strength of standing seam roof system. The final six series was used to examine the effects of flange width and roof panel thickness. All nine series were constructed using Z-purlin sections with flanges facing the same direction (like orientation). Based on the results of this study, clip type, purlin flange width, and roof panel thickness all have an effect on the strength of standing seam roof systems. Although none of the roof components can be completely eliminated from the required test matrix, by using trend relationships an acceptable test protocol was developed that results in a significant reduction in the number of required base tests. / Master of Science

One of the major challenges of engineering is finding the proper balance between economical and safe. Currently engineers at Nucor Corporation have ignored the additional lateral bracing provided by standing seam roofing systems to joists because of the lack of methods available to quantify the amount of bracing provided. Based on the results of testing performed herein, this bracing is significant, potentially resulting in excessively conservative designs and unnecessary costs. This project performed 26 tests with Vulcraft joists in a pressure box to investigate the effects of how many variables influence the lateral bracing provided to joists from standing seam roofing systems, including the variables joist length, panel gauge, clip height, thermal block presence, insulation thickness, and top chord size. Two methods were developed to account for this additional bracing: finite element computer modeling and an application of the Rayleigh-Ritz method called the Column-on-Elastic-Foundation Method. Variables influencing the pressure at failure, namely chord size and deck gauge, were those with the greatest effect on additional lateral bracing provided from standing seam roof systems. It was determined that higher roof stiffness values and higher failure pressures yield shorter effective lengths.

Prediction of the clip reactions of a standing seam roof in a metal building under dynamic loading is of great interest because currently static uplift tests are the standard for determining the design load capacity. The use of a static test to replicate a dynamic loading leads to a great amount of debate because clearly a standing seam roof visually behaves very different under the two different types of loads. This leads to the question of whether a static test accurately replicates the magnitude of loads that the roof clips would feel under a dynamic wind load. This study uses a magnetic suspension uplift loading for the simulation of wind tunnel data in comparison with the ASTM E-1592 ?Standard Test Method for Structural Performance of Sheet Metal Roof and Siding Systems by Uniform Static Air Pressure Difference? test to determine clip reactions. An approximate finite element model is also utilized to verify the validity of the experimentally acquired clip reactions to form another comparison.

Z-sections are widely used as secondary members in metal building roof systems. Lateral restraints are required to maintain the stability of a Z-section roof system and provide resistance to the lateral forces generated by the slope of the roof and the effects due to the rotation of the principal axes of the Z-section relative to the plane of the roof sheathing. The behavior of Z-sections in roof systems is complex as they act in conjunction with the roof sheathing as a system and as a light gage cold formed member, is subject to local cross section deformations. The goal of this research program was to provide a means of predicting lateral restraint forces in Z-section supported roof systems. The research program began with laboratory tests to measure lateral restraint forces in single and multiple span sloped roof systems. A description of the test apparatus and procedure as well as the results of the 40 tests performed is provided in Appendix II. To better understand the need for lateral restraints and to provide a means of testing different variables of the roof system, two types of finite element models were developed and are discussed in detail in appended Paper I. The first finite element model is simplified model that uses frame stiffness elements to represent the purlin and sheathing. This model has been used extensively by previous researchers and modifications were made to improve correlation with test results. The second model is more rigorous and uses shell finite elements to represent the Z-section and sheathing. The shell finite element model was used to develop a calculation procedure referred to as the Component Stiffness Method for predicting the lateral restraint forces in Z-section roof systems. The method uses flexural and torsional mechanics to describe the behavior of the Z-section subject to uniform gravity loads. The forces generated by the system of Z-sections are resisted by the "components" of the system: the lateral restraints, the sheathing and Z-section-to-rafter connection. The mechanics of purlin behavior providing the basis for this method are discussed in appended Paper II. The development of the method and the application of the method to supports restraints and interior restraints are provided in appended papers III, IV and V. / Ph. D.

The lateral force resisting system (LFRS) of a steel building consist of two parts, i.e., a vertical LFRS such as braced frames or shear walls, and a horizontal LFRS with diaphragms playing a crucial role. There are various types of floor and roof diaphragms in steel buildings, such as concrete-filled steel deck diaphragms for the floor system and bare steel deck diaphragms for the roof system of a typical steel braced frame building, and standing seam roof diaphragms for a typical metal building. Compared to vertical elements of a building's LFRS, our understanding of the horizontal elements, i.e., the diaphragms, is grossly lacking. The motivation for this work comes from the gaps identified in the research, including the lack of generally adopted acceptance criteria and modeling protocols for seismic performance-based design of bare steel deck and concrete-filled steel deck diaphragms through linear and nonlinear analysis, the need to better understand the complex behavior of concrete-filled steel deck diaphragms with irregular configurations such as reentrant corners and openings under lateral loading, the absence of appropriate Rs values for the alternative diaphragm seismic design approach in the current building code that considers diaphragm inelasticity, and the demand for understanding the in-plane behavior of a standing seam roof system and its use in lateral bracing of rafters in metal buildings. A series of computational and experimental studies were conducted to investigate the behavior of diaphragms in buildings systems, including: 1) development of acceptance criteria and modeling protocol for performance-based seismic design of bare and concrete-filled steel deck diaphragms using a database of existing cantilever diaphragm tests; 2) a computational study on the nonlinear behavior of diaphragms with irregular configurations under lateral loading using high-fidelity finite element models validated against experiment test results; 3) investigation of the seismic behavior and performance of steel buildings with buckling restrained braced frames that considers different diaphragm design approaches and diaphragm inelasticity using nonlinear three-dimensional (3D) computational models; and 4) an experimental study that investigated the in-plane behavior of full-scale standing seam roof assemblies and their use in lateral bracing of rafters in metal building systems. The results of these studies contribute to a better understanding of the behavior of diaphragms in steel buildings and lead to several recommendations for diaphragm design. Firstly, a series of m-factors (ductility measures) and nonlinear modeling parameters (multi-linear cyclic backbone curves) were determined for bare steel deck diaphragms and concrete-filled steel deck diaphragms. These new provisions are recommended for adoption in ASCE 41 / AISC 342, which allows the use of ductility in steel deck diaphragms for their design and retrofits. Secondly, results of the finite element analysis on concrete-filled steel deck diaphragms revealed a concentrated distribution of shear transfer through the shear connections on the collectors of the diaphragm near braced frames and a stress concentration in the composite slab near reentrant corners and openings. Thirdly, results of eigenvalue analyses with nonlinear 3D building models showed that the consideration of diaphragm flexibility led to an increase in first mode period between 13% and 48%. A comparison of results from pushover analyses and response history analyses indicated that even though the pushover analyses (based on a first mode load pattern) identified the BRBF as being weaker than the diaphragms and therefore dominating the inelastic pushover behavior, response history analyses demonstrated that the diaphragms can experience substantial inelasticity during a dynamic response. The response history results also suggest that there would be a significant difference in seismic behavior of buildings modeled as two-dimensional (2D) planar frames as compared to the 3D structures modeled herein. Furthermore, the observed final collapse mode involves an interaction between large BRBF story drifts combined with diaphragm deformations that are additive and exacerbate second order effects leading to collapse. The computed adjusted collapse margin ratios for all buildings satisfied the FEMA P695 criteria for acceptance. Therefore, it is concluded that the alternative diaphragm design procedure with the proposed Rs values (Rs = 2 for concrete-filled steel deck diaphragm and Rs = 2.5 for bare steel deck diaphragm) are reasonable for use in design of these types of structures. Lastly, the effects of different standing seam roof configurations (panel type, clip type, thermal insulation, and purlin spacing) on the in-plane stiffness and strength of the standing seam roof system were investigated through an experimental testing program, and a method was described to use these experimental results in the calculations of required bracing for metal building rafters. / Doctor of Philosophy / A diaphragm is a horizontal structural component (e.g. floors and roof) that transfers lateral forces induced by wind or earthquakes to the vertical portions (e.g. frames and walls) of the lateral force resisting system (LFRS) of the building. There are various types of floor and roof diaphragms in steel buildings, such as concrete-filled steel deck diaphragms for the floor system and bare steel deck diaphragms for the roof system of a typical steel braced frame building, and standing seam roof diaphragms for a typical metal building. Compared to vertical elements of a building's LFRS, our understanding of the horizontal elements, i.e., the diaphragms, is grossly lacking. To address the research gaps in understanding the behavior of diaphragms and utilizing them in building design, this work presents a series of computational and experimental studies. In the first study, past experimental test data were analyzed to develop acceptance criteria and modeling protocol for performance-based seismic design of steel deck diaphragms. In the second study, finite element analyses were conducted to understand the nonlinear behavior of concrete-filled steel deck diaphragms subjected to in-plane lateral loading. In the third study, nonlinear three-dimensional computational building models were developed to investigate the seismic behavior and performance of steel buildings with different diaphragm design approaches and diaphragm inelasticity. In the fourth study, experimental testing on full-scale standing seam roof assemblies was conducted to investigate their in-plane behavior and their use in lateral bracing of rafters in metal building systems. The results of these studies contribute to a better understanding of the behavior of diaphragms in steel buildings and lead to several recommendations for diaphragm design.