Stiffness prediction for bolted moment-connections between cold-formed steel members

The authors have recently described a cold-formed steel portal framing system in which simple bolted moment-connections, formed through brackets, were used for the eaves and apex joints. Such connections, however, cannot be considered as rigid because of localised in-plane elongation of the bolt-holes caused by bearing against the bolt-shanks. To therefore predict the initial stiffness of such connections, it is necessary to know the initial bolt-hole elongation stiffness k(b). In this paper, a finite element-solid idealisation of a bolted lap joint in shear will be described that can be used to determine k(b); the results obtained are validated against experimental data. A beam idealisation of a cold-formed steel bolted moment-connection is then described, in which spring elements are used to idealise the rotational flexibility of the bolt-groups resulting from bolt-hole elongation: Using the value of k(b) in the beam idealisation, the deflections predicted are shown to be similar to those measured experimentally in laboratory tests conducted on the apex joint of a cold-formed steel portal frame. (C) 2003 Elsevier Ltd. All rights reserved.

Finite element idealization of a cold-formed steel portal frame

A simple linear beam idealization of a cold-formed steel portal frame is presented in which beam elements are used to idealize the column and rafter members, and rotational spring elements are used to represent the rotational flexibility of the joints. In addition, the beam idealization takes into account the finite connection length of the joints. Deflections predicted using the beam idealization are shown to be comparable to deflections obtained from both a linear finite element shell idealization and full-scale laboratory tests. Using the beam idealization, deflections under rafter load are divided into three components: Deflection due to flexure of the column and rafter members, deflection due to bolt-hole elongation, and deflection due to in-plane bracket deformation. Of these deflection components, the deflection due to bolt-hole elongation is the most significant and cannot, therefore, be ignored. Using the beam idealization, engineers can analyze and design cold-formed steel portal frames, including making appropriate allowances for connection effects, without the need to resort to expensive finite element shell analysis.

Serviceability design of a cold-formed steel portal frame having semi-rigid joints

Details are given of a cold-formed steel portal framing system that uses simple bolted moment-connections for both the eaves and apex joints. However, such joints function as semi-rigid and, as a result, the design of the proposed system will be dominated by serviceability requirements. While serviceability is a mandatory design requirement, actual deflection limits for portal frames are not prescribed in many of the national standards. In this paper, a review of the design constraints that have an effect on deflection limits is discussed, and rational values appropriate for use with cold-formed steel portal frames are recommended. Adopting these deflection limits, it is shown through a design example how a cold-formed steel portal frame having semi-rigid eaves and apex joints can be a feasible alternative to rigid-jointed frames in appropriate circumstances.

Cold-formed steel sections with web openings subjected to web crippling under two-flange loading conditions - part I: Tests and finite element analysis

The results of 82 web crippling tests are presented, with 20 tests conducted on channel sections without web openings and 62 tests conducted on channel sections with web openings. The tests consider both end-two-flange and interior-two-flange loading conditions. In the case of the tests with web openings, the hole was located directly under the concentrated load. The concentrated load was applied through bearing plates; the effect of different bearing lengths is investigated. In addition, the cases of both flanges fastened and unfastened to the support is considered. A non-linear elasto-plastic finite element model is described, and the results compared against the laboratory test results; a good agreement was obtained in terms of both strength and failure modes.

Cold-formed steel sections with web openings subjected to web crippling under two-flange loading conditions - Part II: Parametric study and proposed design equations

A parametric study of cold-formed steel sections with web openings subjected to web crippling was undertaken using finite element analysis, to investigate the effects of web holes and cross-section sizes on the web crippling strengths of channel sections subjected to web crippling under both interior-two-flange (ITF) and end-two-flange (ETF) loading conditions. In both loading conditions, the hole was centred beneath the bearing plate. It was demonstrated that the main factors influencing the web crippling strength are the ratio of the hole depth to the flat depth of the web, and the ratio of the length of bearing plates to the flat depth of the web. In this paper, design recommendations in the form of web crippling strength reduction factors are proposed, that are conservative to both the experimental and finite element results.

Effect of offset web holes on web crippling strength of cold-formed steel channel sections under end-two-flange loading condition

A combination of experiments and non-linear finite element analyses are used to investigate the effect of offset web holes on the web crippling strength of cold-formed steel channel sections under the end-two-flange (ETF) loading condition; the cases of both flanges fastened and unfastened to the support are considered. The web holes are located at the mid-depth of the sections, with a horizontal clear distance of the web holes to the near edge of the bearing plate. Finite element analysis results are compared against the laboratory test results; good agreement was obtained in terms of both strength and failure modes. A parametric study was then undertaken to investigate both the effect of the position of holes in the web and the cross-section sizes on the web crippling strength of the channel sections. It was demonstrated that the main factors influencing the web crippling strength are the ratio of the hole depth to the depth of the web, and the ratio of the distance from the edge of the bearing to the flat depth of the web. Design recommendations in the form of web crippling strength reduction factors are proposed in this study.

Effect of serviceability limits on optimal design of steel portal frames

The design of hot-rolled steel portal frames can be sensitive to serviceability deflection limits. In such cases, in order to reduce frame deflections, practitioners increase the size of the eaves haunch and / or the sizes of the steel sections used for the column and rafter members of the frame. This paper investigates the effect of such deflection limits using a real-coded niching genetic algorithm (RC-NGA) that optimizes frame weight, taking into account both ultimate as well as serviceability limit states. The results show that the proposed GA is efficient and reliable. Two different sets of serviceability deflection limits are then considered: deflection limits recommended by the Steel Construction Institute (SCI), which is based on control of differential deflections, and other deflection limits based on suggestions by industry. Parametric studies are carried out on frames with spans ranging between 15 m to 50 m and column heights between 5 m to 10 m. It is demonstrated that for a 50 m span frame, use of the SCI recommended deflection limits can lead to frame weights that are around twice as heavy as compared to designs without these limits.

Cold-formed steel portal frames in fire: Full-scale testing and finite element analysis

A full-scale, non-uniform natural fire test on a cold-formed steel portal frame building is described. The results of the test are used to validate a non-linear, elasto-plastic, finite element shell idealisation, for the purposes of later forming the basis of a performance-based design approach for cold-formed steel portal frames at elevated temperatures.

Chloride induced corrosion of steel in alkali activated slag concretes

Alkali activated slag (AAS) is an alternative cementitious material. Sodium silicate solution is usually used to activate ground granulated blast furnace slag to produce AAS. As a consequence, the pore solution chemistry of AAS differs from that of Portland cement (PC). Although AAS offers many advantages over PC, such as higher strength, superior resistance to acid and sulphate environments and lower embodied carbon due to 100% PC replacement, there is a need to assess its performance against chloride induced corrosion duo to its different pore solution chemistry. For PC systems, resistivity measurement, as a type of nondestructive test, is usually used to evaluate its chloride diffusivity and the corrosion rate of the embedded steel. However, due to the different pore solution chemistry present in the different AAS systems, the application of this test in AAS concretes would be questionable as the resistivity of concrete is highly dependent on its conductivity of the pore solution. Therefore, a study was carried out using twelve AAS concretes mixes, the results of which are reported in this paper. The AAS mixes were designed with alkali concentration of 4%, 6% and 8% (Na₂O% of the mass of slag) and modulus (Ms) of sodium silicate solution of 0.75, 1.00, 1.50 and 2.00. A PC concrete with the same binder content as the AAS concretes was also studied as a reference. The chloride diffusion coefficient was determined using a non-steady state chloride diffusion test (NT BUILD 443). The resistivity of the concretes before the diffusion test was also measured. Macrocell corrosion current (corrosion rate) for steel rods embedded in the concretes was measured whilst subjecting the concretes to a cyclic chloride ponding regime (1 day ponded with salt solution and 6 days drying). The results showed that the AAS concretes had lower chloride diffusivity with associated higher resistivity than the PC concrete. The measured corrosion rate was also lower for the AAS concretes. However, unlike the PC, in which a higher resistivity yields a lower diffusivity and corrosion rate, there was no relationship apparent between the resistivity and either the diffusivity or the corrosion rate of steel for the AAS concretes. This is assigned to the variation of the pore solution composition of the AAS concretes. This also means that resistivity measurements cannot be depended on for assessing the chloride induced corrosion resistance of AAS concretes.

Post-tensioning of glulam timber with steel tendons

This paper describes a series of four-point bending tests that were conducted, under service loads and to failure, on unreinforced, reinforced and post-tensioned glulam timber beams, where the reinforcing tendon used was 12 mm diameter toughened steel bar. The research was designed to evaluate the benefits offered by including an active reinforcement in contrast to the passive reinforcement typically used within timber strengthening works, in addition to establishing the effect that bonding the reinforcing tendon has on the materials performance.

The laboratory investigations established that the flexural strength and stiffness increased for both the reinforced and post-tensioned timbers compared to the unreinforced beams. The flexural strength of the reinforced timber increased by 29.4%, while the stiffness increased by 28.1%. Timber that was post-tensioned with an unbonded steel tendon showed a flexural strength increase of 17.6% and an increase in stiffness of 8.1%. Post-tensioned beams with a bonded steel tendon showed increases in flexural strength and stiffness of 40.1% and 30% respectively.

Topographical optimisation of single-storey non-domestic steel framed buildings using photovoltaic panels for net-zero carbon impact

A methodology is presented that combines a multi-objective evolutionary algorithm and artificial neural networks to optimise single-storey steel commercial buildings for net-zero carbon impact. Both symmetric and asymmetric geometries are considered in conjunction with regulated, unregulated and embodied carbon. Offsetting is achieved through photovoltaic (PV) panels integrated into the roof. Asymmetric geometries can increase the south facing surface area and consequently allow for improved PV energy production. An exemplar carbon and energy breakdown of a retail unit located in Belfast UK with a south facing PV roof is considered. It was found in most cases that regulated energy offsetting can be achieved with symmetric geometries. However, asymmetric geometries were necessary to account for the unregulated and embodied carbon. For buildings where the volume is large due to high eaves, carbon offsetting became increasingly more difficult, and not possible in certain cases. The use of asymmetric geometries was found to allow for lower embodied energy structures with similar carbon performance to symmetrical structures.

An efficient genetic algorithm for the design optimization of cold-formed steel portal frame buildings

The design optimization of a cold-formed steel portal frame building is considered in this paper. The proposed genetic algorithm (GA) optimizer considers both topology (i.e., frame spacing and pitch) and cross-sectional sizes of the main structural members as the decision variables. Previous GAs in the literature were characterized by poor convergence, including slow progress, that usually results in excessive computation times and/or frequent failure to achieve an optimal or near-optimal solution. This is the main issue addressed in this paper. In an effort to improve the performance of the conventional GA, a niching strategy is presented that is shown to be an effective means of enhancing the dissimilarity of the solutions in each generation of the GA. Thus, population diversity is maintained and premature convergence is reduced significantly. Through benchmark examples, it is shown that the efficient GA proposed generates optimal solutions more consistently. A parametric study was carried out, and the results included. They show significant variation in the optimal topology in terms of pitch and frame spacing for a range of typical column heights. They also show that the optimized design achieved large savings based on the cost of the main structural elements; the inclusion of knee braces at the eaves yield further savings in cost, that are significant.

Advanced design optimization of cold-formed steel portal frame buildings

The design optimization of cold-formed steel portal frame buildings is considered in this paper. The objective function is based on the cost of the members for the main frame and secondary members (i.e., purlins, girts, and cladding for walls and roofs) per unit area on the plan of the building. A real-coded niching genetic algorithm is used to minimize the cost of the frame and secondary members that are designed on the basis of ultimate limit state. It iis shown that the proposed algorithm shows effective and robust capacity in generating the optimal solution, owing to the population's diversity being maintained by applying the niching method. In the optimal design, the cost of purlins and side rails are shown to account for 25% of the total cost; the main frame members account for 27% of the total cost, claddings for the walls and roofs accounted for 27% of the total cost.

Compressive behavior of steel fiber reinforced recycled aggregate concrete after exposure to elevated temperatures

For sustainability considerations, the use of recycled aggregate in concrete has attracted many interests in the research community. One of the main concerns for using such concrete in buildings is its spalling in fire. This may be alleviated by adding steel fibers to form steel fiber reinforced recycled aggregate concrete (SFRAC). This paper presents an experimental investigation into the compressive properties of SFRAC cylinders after exposure to elevated temperatures, including the compressive strength, Young's modulus (stiffness), stress-strain curve and energy absorption capacity (toughness). The effects of two parameters, namely steel fiber volume content (0%, 0.5%, 1%, 1.5%) and temperature (room temperature, 200 °C, 400 °C and 600 °C) on the compressive mechanical properties of concrete were investigated. The test results show that both compressive strength and stiffness of the concrete are significantly reduced after exposure to high temperatures. The addition of steel fibers is helpful in preventing spalling, and significantly improves the ductility and the cracking behavior of recycled aggregate concrete (RAC) after exposure to high temperatures, which is favorable for the application of RAC in building construction.