Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/3461
Title: Structural behaviour of lapped cold-formed steel Z sections
Authors: Ho, Ho-cheung
Keywords: Hong Kong Polytechnic University -- Dissertations
Steel, Structural
Steel I-beams
Steel, Structural -- Specifications
Issue Date: 2005
Publisher: The Hong Kong Polytechnic University
Abstract: 1. Background Cold-formed steel sections are lightweight building materials with high strength to self-weight ratios, and they are suitable for building construction owing to their versatility in applications, and ease of fabrication and installation. They are coldformed into various shapes from steel strips by roll forming. The thickness of the steel sections is typically 1.2 to 3.0 mm thick, and steel sections with yield strengths at 280, 350 and 450 N/mm² are commonly available. In single storey industrial buildings, and low to medium rise offices and warehouses, cold formed steel sections are widely used as secondary structural members such as purlins and side rails to support roof and wall cladding. Since the 1990s, the application of cold formed steel sections in buildings was further extended into primary structural members, and low-rise domestic houses are built with cold formed steel sections as beams and columns to form primary structural frames. 1.1 Modern Purlin Systems In modern purlin systems, four different types of systems may be found with different degrees of continuity: - the single span system, - the double span system, - the continuous system with sleeves, and - the continuous system with lapped sections. Among all, the lapped purlin system is the most commonly used system due to simple and effective connection configurations of purlin-rafter connections. In general, building product manufacturers have developed various proprietary purlin systems with standardized connection configurations for cold formed steel sections with various shapes. It should be noted that the lapped moment connections are widely used in many countries due to high structural efficiency and ease of erection, and hence, the quantities of steel tonnages associated with this form of construction are huge. Conventionally, engineers and researchers have their primary concern on the strengths of the lapped sections, and over-simplified their stiffnesses and associated structural behaviour. Therefore, it is highly desirable to examine the structural behaviour of lapped Z sections, which may affect significantly the overall load carrying capacities of lapped purlin systems. 1.2 Scope of work This thesis presents a research project on the structural behaviour of cold formed steel lapped Z sections, and the project is composed of the following parts of investigation: - experimental investigation, - analysis and design of lapped Z sections, - numerical investigation, and - design development for multi-span lapped Z purlins. 2. Experimental Investigation In order to examine the structural performance of the lapped Z sections, a total of 38 laterally restrained one point load tests were carried out on lapped Z sections with different connection configurations. Both the strength and the deformation characteristics of these connections were examined in detail. A comprehensive comparison was also carried out for lapped Z sections with different connection configurations: number of bolts, bolt pitches and arrangements, lapped lengths, span lengths and section sizes. Among all tests, section failure at the ends of lap under combined bending and shear in the connected Z sections was always found to be critical. Moreover, lapped Z sections with different lap lengths have different moment resistances and effective flexural rigidities. It is found that the moment resistances of the lapped Z sections range from 79% to 162% of the moment capacities of connected sections, while the effective flexural rigidities of the lapped Z sections range from 10% to 163% of the flexural rigidities of connected sections. Consequently, it is shown that the degree of structural continuity in lapped Z sections connections depend on various parameters, and hence, the widely adopted assumption of full strength and stiffness connections in lapped Z sections is not always correct. Moreover, a total of 14 laterally unrestrained one point load tests were also carried out to examine the effect of lateral torsional buckling on lapped Z sections. It is found that the moment resistances of the unrestrained lapped Z sections depend on the lap lengths as the presence of overlaps reduces the un-restrained (effective) length of the lapped Z sections. Comparison between the moment resistances of the restrained and the unrestrained sections were also made, and the effective lengths of lapped Z sections can be determined accordingly. 3. Analysis and design of lapped Z sections Based on the findings of the experimental investigation, an analysis and design method for lapped Z sections is established after the following parts of investigation: 3.1 Force distribution within lapped connections Based on statics, the bolt forces within the lapped moment connections are determined after considering equilibrium, and hence, all internal forces within the connections are readily obtained. Once the co-existing moments and shear forces along the entire length of the Z sections are evaluated, the critical sections are checked against combined bending and shear using codified design rules. 3.2 Resistances against section failure under combined bending and shear Based on test observations, shear buckling of the section webs at the ends of lap of lapped Z sections is found to be fairly localized, and the length of a typical shear buckling mode shape ranges from 0.8 D to 1.25 D, where D is the section depth. Thus, it is proposed to revise the design rule for the assessment of shear capacities of cold-formed steel Z sections near the critical cross section, and this leads to a more economical design for critical cross-sections at the ends of lap under combined bending and shear. 3.3 Deformation characteristics of lapped Z sections Based on the test results of typical lap shear tests on bolted fastenings between cold formed steel strips with various steel thicknesses, steel grades and bolt sizes, a normalized bearing deformation curve was established. It was then adopted to predict the vertical deformations of 26 lapped Z sections under one point loads; deformations due to both global bending and shear actions were also allowed for. Good comparison between the measured and the predicted deformation characteristics was obtained, and the predicted effective flexural rigidities are found to vary from 80% to 110% of those measured values for lapped Z sections with practical lap lengths. Hence, it is possible to predict both the initial and the final effective flexural rigidities for lapped Z sections with practical bolt arrangements. In order to allow for moment redistribution in multi-span lapped purlin system, an empirical formula is also proposed to describe the unloading part of the deformation characteristics of the lapped Z sections. It should be noted that the unloading part of the curve depends not only on the section sizes, but also the lap lengths, and the moment resistances of the lapped Z sections.
4. Numerical investigations 4.1 Lapped Z sections In order to examine the structural behaviour of lapped Z sections over the entire deformation ranges, a numerical investigation using finite element method was also performed. Highly efficient four nodded shell elements were adopted to simulate the cold-formed steel Z sections while spring elements were adopted in modelling the bolted connections. Moreover, material non-linearity was incorporated in order to allow yielding in the sections under combined bending and shear, and the measured stress-strain curves obtained from coupon tests were adopted together with the Von- Mises yield criteria in the material modelling of the cold-formed steel sections. Geometrical non-linearity was also adopted to allow for large deformation under both local buckling and distortional buckling, and numerical integration was carried out at the centre of the shell elements with five integration points through the thickness. Initial geometric imperfection in the lapped Z sections was obtained as the first eigenmode of the lapped Z sections modified by of a suitable scale factor; the eigenmode was calculated with an elastic linear buckling analysis. The maximum magnitude of the initial imperfection was set to be 0.25 times the section thickness. It was shown that the section failure at the critical cross-sections at the ends of lap under combined bending and shear was modelled satisfactorily. Moreover, the predicted deformation characteristics of the test specimens followed closely to those measured from tests over the entire range of deformation. 4.2 Multi-span lapped purlin systems The same finite element models are adopted to investigate the structural behaviour of multi-span lapped purlin systems with different lap lengths under gravity loads. It should be noted that after extensive data analysis, the moment resistances of the Z sections along their member lengths during the entire deformation ranges are obtained. Thus, it is possible to reveal the exact mechanism of moment redistribution in the multi-span lapped purlin systems from the critical cross-sections at the ends of lap to those at mid-span. 5. Design development for multi-span lapped Z purlins 5.1 Analysis and design procedure Based on the results of various tasks of investigation, a complete analysis and design procedure is formulated for multi-span lapped purlin systems under both gravity loads and wind uplift. The effect of lapped Z sections is fully incorporated in determining the distribution of internal forces of purlin members, and hence the co-existing moment and shear force at the ends of lap in purlin members are readily obtained. Various design coefficients for moments and shear forces in purlin members of practical material and geometrical configurations with different lap lengths are also provided. Moreover, based on the proposed deformation characteristics of lapped Z sections, a non-linear analysis on the multi-span lapped purlin systems are performed to evaluate their ultimate load carrying capacities. Various failure modes are identified in purlin members with different lap lengths, span lengths, and section sizes. 5.2 Load span tables A number of load span tables are generated for multi-span lapped Z sections with practical material and geometrical configurations as well as connection arrangements. They are compared with those derived from testing and also with those derived from the conventional design method. Comparison on the load carrying capacities derived from the proposed design method to those obtained from testing shows good agreement over a range of section sizes and system span lengths while they show an improvement of 10% to 25% over those derived from the conventional design method. Consequently, the proposed design method is demonstrated to be effective and rational in assessing the load carrying capacities of purlin systems using cold formed steel lapped Z sections. 6. Originality of the research study Throughout my study, I have applied my technical knowledge to investigate the structural performance of cold-formed steel Z sections during the design development of multi-span cold-formed steel purlin systems. The following tasks are performed in my independent manner: -Data analyses on one point load tests and four point load tests on lapped Z sections with bolted connections, as well as complementary lap shear tests between cold-formed steel strips. -Establishment of the proposed design and analysis method to determined internal force distributions within lapped connections; this enables the important check of section failure under combined bending and shear at the ends of lap. - Formulation of the proposed analysis method to evaluate the effective flexural rigidities of lapped connections based on measured load-deflection curves. -Formulation of the normalized bearing-extension curve of bolted fastenings based on lap shear tests; this enables general design of bolted connections between cold-formed steel sections - Establishment of the proposed analysis method to determine analytically deformation characteristics of lapped connections at both the initial and the failure stages; this provides an important design and analysis tool to predict the structural behaviour of cold-formed steel Z sections with lapped moment connections without testing. - Finite element modeling of multi-span lapped purlin systems with different degrees of continuity over lapped connections as well as different amount of moment redistribution from internal supports to mid-span region. -Establishment of the proposed design and analysis method to determine internal force distribution in multi-span lapped purlin members with a wide range of lap length to section depth ratios and lap length to system length ratios. -The Formulation of a rational design of multi-span lapped purlin systems under both gravity load and wind uplift. 7. Values and Significances The research work carries a great impact to the conventional design concept on connections between cold formed steel sections that not only the strengths of the connections are important, but also the stiffnesses of the connections are important as well in practical design and construction of indeterminate structures. Moreover, a clear understanding on the structural behaviour of cold-formed steel lapped Z sections with bolted moment connections is presented, and the proposed analysis and design method provides important understandings on the effects of effective flexural rigidities of lapped Z sections in multi-span lapped purlin systems during the entire deformation ranges. Furthermore, a rational and rigorous analysis and design method is proposed for practical design of multi-span lapped Z purlin systems as a supplement to current codes of practice and design recommendations. This will greatly facilitate the practical design process of efficient lapped purlin systems with improved load carrying capacities. Moreover, any product development of lapped purlin systems with different material and geometrical configurations as well as bolt arrangements will also be speeded up, with less reliance on full scale testing.
Description: 1 v. (various pagings) : ill. ; 30 cm.
PolyU Library Call No.: [THS] LG51 .H577P CSE 2005 Ho
URI: http://hdl.handle.net/10397/3461
Rights: All rights reserved.
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