K.F. Chung

Mechanical properties of structural bamboo for bamboo scaffoldings

Abstract This paper presents an investigation on the mechanical properties of two bamboo species, namely Bambusa Pervariabilis (or Kao Jue) and Phyllostachys Pubescens (or Mao Jue), which are commonly used in access scaffoldings in the South East Asia, in particular, in Hong Kong and the Southern China. A pilot study was carried out to examine the variation of compressive strength against various physical properties along the length of bamboo culms for both bamboo species. Moreover, systematic test series with a large number of compression and bending tests were executed to establish characteristic values of both the strengths and the Youngs moduli of each bamboo species for limit state structural design. It is shown that both Kao Jue and Mao Jue are good constructional materials with excellent mechanical properties against compression and bending. With a suitable choice of partial safety factors, structural engineers are able to design bamboo structures at a known level of confidence against failure. Structural engineers are thus encouraged to take the advantage offered by bamboo to build light and strong structures to achieve enhanced economy and buildability. The effective use of structural bamboo as a substitute to structural timber will mitigate the pressures on the ever-shrinking natural forests in developing countries, and thus, facilitate the conservation of the global environment.

Investigation on Vierendeel mechanism in steel beams with circular web openings

Abstract In the current design method for steel I beams with circular web openings, the load carrying capacities of the beams is assumed to be limited by the formation of plastic hinges at the top tee-sections at the low moment side of the web opening. Moreover, a linear interaction formula is used to assess the moment capacity of the tee-sections above and below the web openings under co-existing axial and shear forces. The method is regarded as conservative since the formation of plastic hinges in the top tee-sections at the low moment side of the web openings does not always cause failure. The beams are capable of carrying additional load until four plastic hinges at critical locations of the perforated sections are developed to form a Vierendeel mechanism. Moreover, the reduction in the moment capacities of the tee-sections under coexisting axial and shear forces is less severe than that anticipated by the linear interaction formula. The paper presents an investigation of the Vierendeel mechanism in steel beams with circular web openings based on analytical and numerical studies. The current design method is examined in detail with plastic hinges formed at the low moment side (LMS) and the high moment side (HMS) of the web openings separately. A finite element model is then established with both material and geometrical non-linearity so that load redistribution across the web openings may be incorporated. Moreover, the moment capacities of the tee-sections above and below the web openings may be properly evaluated in the presence of co-existing axial and shear forces in the finite element model. The load carrying capacities of typical universal steel beams with circular web openings are also presented and discussed. An empirical shear moment interaction curve at the perforated sections is also suggested for practical design of steel beams with circular web openings against the Vierendeel mechanism. It is found that shear yielding in steel beams with circular web openings is very important as it promotes the plastic hinge formation at the high moment side of the web opening. Such effect is less significant in steel beams with rectangular web openings where the bending moment is often dominant.

Finite element modeling of bolted connections between cold-formed steel strips and hot rolled steel plates under static shear loading

Abstract A finite element model with three-dimensional solid elements is established to investigate the structural performance of bolted connections between cold-formed steel strips and hot rolled steel plates under shear. Non-linear material, geometrical and contact analysis is carried out to predict the load–extension curves of typical bolted connections with cold-formed steel strips of high yield strength and low ductility. The failure mode of interest in the present investigation is the bearing failure of cold-formed steel strip around bolt holes; a full description of the finite element model is presented. Based on test data, a stress–strain curve for the cold-formed steel strip is proposed which allows the cold-formed steel strip to yield and degrade in strength at large strain. The load–extension curves of four sets of test specimens were successfully predicted up to an extension of 3 mm. The predicted bearing resistance and the extensional stiffness of the bolted connections compare well with test data. It is found that stress–strain curves, contact stiffness and frictional coefficient between element interfaces, and clamping force developed in bolt shanks are important parameters for accurate prediction of the load–extension curves of bolted connections.

Experimental investigation on bolted moment connections among cold formed steel members

Abstract The paper presents an experimental investigation on the structural performance of cold formed steel members with bolted moment connections. Two lipped C sections back-to-back with interconnections are used as beam and column members. A number of connection configurations with gusset plates of both hot rolled steel and cold formed steel are proposed to form bolted moment connections to accommodate members in practical orientations. Only the webs of lipped C sections are connected with bolts; the section flanges are not connected for ease of construction. The structural performance of all the tests are presented in detail. Four modes of failure were identified among the tests: • BFcsw—bearing failure in section web around bolt hole • LTBgp—lateral torsional buckling of gusset plate • FFcs—flexural failure of connected member, and • CBcol—combined compression and bending failure of column member. It is shown that bearing failure is a ductile mode with large deformation capacity, and other failure modes may creep in to cause sudden collapse. While lateral torsional buckling of gusset plates causes pre-mature failure of the connections at low applied load, flexural failure is more desirable as over 80% of the moment capacity of the connected members may be safely mobilised at the connections. In the absence of effective torsional restraint at the column ends, the column members may fail in combined compression and bending. Among sixteen component and system tests, the moment resistance of bolted moment connections with four bolts per member was found to lie between 42% and 84% of the moment capacities of the connected members. Thus, it was demonstrated that moment connections among cold formed steel members are structurally feasible and economical through rational design.

Structural behaviour of bolted moment connections in cold-formed steel beam-column sub-frames

Abstract This paper presents an experimental investigation on bolted moment connections between cold-formed steel sections. A total of 20 column base connection tests and beam-column sub-frame tests with different connection configurations were carried out to assess the strength and stiffness of bolted moment connections between cold-formed steel sections. Among the tests, four different modes of failure were identified: • Mode BFcsw: Bearing failure in section web around bolt hole • Mode LTBgp: Lateral torsional buckling of gusset plate • Mode FFgp: Flexural failure of gusset plate • Mode FFcs: Flexural failure of connected cold-formed steel section For those connections failed in Mode BFcsw, the moment resistances of the connections were typically found to be below 50 % of the moment capacities of the connected sections. For those connections failed in Modes LTBgp and FFgp, the moment resistances of the connections were found to be about 60% and 75% of the moment capacities of the connected sections. Among all, the moment resistances of those connections failed in Mode FFcs were the highest with a minimum of 85% of the moment capacities of the connected sections. Consequently, it is demonstrated that through rational design and construction, effective moment connections between cold-formed steel sections may be readily achieved. Engineers are encouraged to build light-weight low to medium rise moment frames with cold-formed steel sections.

Finite element investigation on the structural behaviour of cold-formed steel bolted connections

Abstract A finite element model with three-dimensional solid elements was established to investigate the bearing failure of cold-formed steel bolted connections under shear. It was demonstrated (Chung and Ip. Engineering Structures 2000;22:1271–1284) that the predicted load–extension curves of bolted connections in lap shear tests followed closely to the measured load–extension curves provided that measured steel strengths and geometrical dimensions were used in the analysis. Furthermore, it was shown (Chung and Ip. Proceedings of the Second European Conference on Steel Structures, Praha, May 1999, p. 503–506) that stress–strain curves, contact stiffnesses and frictional coefficients between element interfaces, and clamping forces developed in bolt shanks were important parameters for accurate prediction of the deformation characteristics of bolted connections. This paper presents an extension of the finite element investigation onto the structural behaviour of cold-formed steel bolted connections, and three distinctive failure modes (Ip and Chung. Proceeding of the Second International Conference on Advances in Steel Structures, Hong Kong, December 1999) as observed in lap shear tests are successfully modelled: bearing failure; shear-out failure; and net-section failure. Furthermore, a parametric study on bolted connections with different configurations is performed to provide bearing resistances for practical design, and the results of the finite element modelling are also compared with four codified design rules. It is found that the design rules are not applicable for bolted connections with high strength steels due to reduced ductility. Consequently, a semi-empirical design formula for bearing resistance of bolted connections is proposed after calibrating against finite element results. The proposed design rule relates the bearing resistances with the design yield and tensile strengths of steel strips through a strength coefficient. It is demonstrated that the design rule is applicable for bolted connections of both low strength and high strength steels with different ductility limits.

Steel beams with large web openings of various shapes and sizes: finite element investigation

Abstract Vierendeel mechanism is always critical in steel beams with single large web openings, where global shear force is transferred across the opening length, and the Vierendeel moment is resisted by the local moment resistances of the tee-sections above and below the web openings. At present, most of the current design methods recommend empirical interaction formulae on the moment resistances of the tee-sections to allow for the presence of local axial and shear forces. They ignore the true ultimate behaviour of the tee-sections under co-existing axial and shear forces and bending moment, and also the load redistribution within the perforated sections after yielding. A comprehensive finite element investigation on steel beams with web openings of various shapes and sizes is reported in this paper, and the primary structural characteristics of those steel beams are examined in detail. It is found that all steel beams with large web openings of various shapes behave similarly under a wide range of applied moments and shear forces. The failure modes are common in all beams, and the yield patterns of those perforated sections at failure are also similar to each other. Comparison on the global moment–shear interaction curves of those steel beams shows that they are similar to each other in shape, and thus, it is possible to derive empirical moment–shear interaction curves to assess the load capacities of all steel beams with web openings of various shapes and sizes. Furthermore, it is shown that for all web openings of various shapes and sizes considered in the present investigation, the most important parameter in assessing the structural behaviour of perforated sections is the length of the tee-sections above and below the web opening which controls the magnitude of local Vierendeel moments acting on the tee-sections. Based on the results of an extensive parametric study using finite element method, a simple empirical design method applicable for perforated sections with web openings of various shapes and sizes is developed. Details of the design method are fully presented in a complementary paper.

Steel beams with large web openings of various shapes and sizes: an empirical design method using a generalised moment-shear interaction curve

Vierendeel mechanism is always critical in steel beams with single large web openings. While the depth of web openings controls both the shear and the flexural failures of the perforated sections, it is the length of the web openings that governs the ‘Vierendeel’ mechanism which in turn depends on the local shear and moment capacities of the tee sections above and below the web opening. A comprehensive finite element investigation on steel beams with web openings of various shapes and sizes was reported in a complementary paper, and the primary structural characteristics of those steel beams were presented in detail. Comparison on the global moment-shear interaction curves of those steel beams shows that they are similar to each other in shape, and thus, it is possible to develop a generalised moment-shear interaction curve to assess the load capacities of all steel beams with web openings of various shapes and sizes. As the global shear forces cause both shear failure and ‘Vierendeel’ mechanism in perforated sections, the effect of local ‘Vierendeel’ moments acting onto the tee-sections above and below the web openings may be incorporated through a reduction to the global shear capacities of the perforated sections. A global coupled shear capacity is thus established and its values for web openings of various shapes and sizes are obtained directly from the finite element investigation. Details of the design method are fully presented in this paper. Moreover, an indicative parameter, the ‘Vierendeel’ parameter, is established to assess the performance of ‘Vierendeel’ mechanism in perforated sections. Through comparison among the moment and the shear utilisation ratios, m and v, and the ‘Vierendeel’ parameter, vi , the critical modes of failure in perforated sections under different moment-shear ratios may be readily assessed.

Column buckling of structural bamboo

Abstract Bamboo scaffolding is widely used in construction in the South East Asia, in particular, the Southern China and Hong Kong for many decades. However, bamboo scaffolds are generally erected by scaffolding practitioners based on their intuition and experiences without any structural design. In general, column buckling is considered to be one of the critical modes of failure in bamboo scaffolds, often leading to their overall collapse. This paper presents a research and development project for structural bamboo where the column buckling behaviour of two structural bamboo species, namely Bambusa pervariabilis (or Kao Jue) and Phyllostachys pubescens (or Mao Jue) were investigated. A total of 72 column buckling tests with bamboo culms of typical dimensions and properties were executed to study the column buckling behaviour of structural bamboo. Furthermore, a limit state design method against column buckling of structural bamboo based on modified slenderness was established and carefully calibrated against test data. It is shown that for Kao Jue, the average model factors of the proposed design method are 1.63 and 1.86 for natural and wet conditions, respectively. Similarly, the average model factors of the proposed design method for Mao Jue are 1.48 and 1.67 for natural and wet conditions, respectively. Consequently, the proposed design method is shown to be adequate. With the availability of design data on the dimensions and the mechanical properties of structural bamboo together with the proposed column buckling design rule, structural engineers are encouraged to take the advantage offered by bamboo to build light and strong bamboo structures to achieve enhanced economy and buildability.

Simplified design of composite beams with large web openings to Eurocode 4

Abstract The design of composite beams with large rectangular or circular openings is an important structural and practical problem which is caused by the need to pass service ducts through the structural zone of floor systems. Careful sizing and positioning of these openings in the beam webs can minimise their adverse effects on the shear and the bending resistances of composite beams. A design method [1] [Lawson, RM. Design for openings in the webs of composite beams. The Steel Construction Institute/CIRIA joint publication SCI-P068, 1987.] for composite beams with large web openings was first formulated in accordance with BS5950 and calibrated against full-scale tests in 1992 [2] [Lawson RM, Chung KF, Price AM. Tests on composite beams with large web openings to justify existing design methods. Struct Eng 1992:70(1).]. With the release of the draft Eurocode 4 in 1994 [3] [ENV 1994-1-1: Eurocode 4: design of composite steel and concrete structures. BSI, 1994.], this paper re-presents the design method in the format of application rules to Eurocode 4 for detailed design of composite beams with large web openings. Moreover, the designer needs advice at the scheme design stage, and this paper also presents general information on sizing of openings as a function of the utilisation of the shear and the bending resistances of composite beams. Furthermore, the effect of these openings on deflections is estimated by a simple factor which is dependent on the size and the location of the openings. Typical design tables for composite beams with large rectangular openings are presented. Design rules for other forms of construction such as circular openings and notched beams are also presented with general detailing rules to assist designers.