Roof Truss Research Articles

Design optimisation for cold-formed steel residential roof truss using genetic algorithm

PurposeThis paper aims to present the design optimisation using genetic algorithm (GA) to achieve the highest strength to weight (S/W) ratio, for cold-formed steel residential roof truss.Design/methodology/approachThe GA developed in this research simultaneously optimises roof pitch, truss configurations, joint coordinates and applied loading of typical dual-pitched symmetrical residential roof truss. The residential roof truss was considered with incremental uniform distributed loading, in both gravitational and uplift directions. The structural analyses of trusses were executed in this GA using finite element toolbox. The ultimate strength and serviceability of trusses were checked through the design formulation implemented in GA, according to the Australian standard, AS/NZS 4600 Cold-formed Steel Structures.FindingsAn optimum double-Fink roof truss which possess highest S/W ratio using GA was determined, with optimum roof pitch of 15°. The optimised roof truss is suitable for industrial application with its higher S/W ratio and cost-effectiveness. The combined methodology of multi-level optimisation and simultaneous optimisation developed in this research could determine optimum roof truss with consistent S/W ratio, although with huge GA search space.Research limitations/implicationsThe sizing of roof truss member is not optimised in this paper. Only single type of cold-formed steel section is used throughout the whole optimisation. The design of truss connection is not considered in this paper. The corresponding connection costs are not included in the proposed optimisation.Practical implicationsThe optimum roof truss presented in this paper is suitable for industrial application with higher S/W ratio and lower cost, in either gravitational or uplift loading configurations.Originality/valueThis research demonstrates the approaches in combining multi-level optimisation and simultaneous optimisation to handle large number of variables and hence executed an efficient design optimisation. The GA designed in this research determines the optimum residential roof truss with highest S/W ratio, instead of lightest truss weight in previous studies.

Experimental study on the effect of heel plate thickness on the structural integrity of cold-formed steel roof trusses

Applications of Cold-Formed Steel (CFS) are widely used in buildings, bridge and etc. Many researchers initiate the study of CFS to be used as a roof truss system. There is a need to enhance the configurations of CFS roof trusses due to the uncertainty on structural stability and failures in terms of materials and rigidity of joints. The objectives of this research are to determine the effect of heel plate thickness related to the ultimate strength of the roof truss system. Three different thicknesses of heel plate specimens were fabricated and subjected to concentrated loads applied until the specimens failed. The highest ultimate capacity for the experiment was 27 kN. The results showed that the increment of the thickness of the heel plate had slightly increased the ultimate load and the maximum deflection at bottom chord. The top chords could not sustain the loading was the main factor contributed to the structural failure.

Flexural Strength Behaviour of Bolted Built-Up Cold-Formed Steel Beam with Outstand and Extended Stiffener

Cold-formed steel (CFS) is a popular structural and non-structural material that is utilised as roof truss, wall panel and storage racks. But nowadays, CFS is selected and proposed as column and beam in building construction. CFS with open-section and very thin thickness is prone to deform and buckle in large condition. Therefore, the problem must be solved by proposing a new section that is matched up or formed of two or more open-sections to be one new section, shape and cross-section area. There are two types of channel-section and a connection is used to produce a bolted built-up CFS beam in the study. The first type is jointed with bolt and nut on stiffener or lipped, which is known as outstand stiffener, and another type is connected by locating the bolt and nut on web element and recognised as extended stiffeners. The objective of the study is to determine the flexural strength and load-deformation behaviour of both types of bolted built-up CFS section. Then, the experimental result is verified with the Standard of Practice, American Iron and Steel Institute and BS EN 1993-1-3, Design of steel structures (2006). As a result, bolted built-up CFS beam with extended stiffener and a span of bolt with constant value of 22.5 mm is expressed as a good result of flexural strength. In addition, the flexural strength of both beams is dependent only on spacing or bolt location.

Bending tests for the structural safety assessment of space truss members

This article compares two nondestructive static methods used for the axial load assessment in prismatic beam-columns of space trusses. Examples include the struts and ties or the tension chords and diagonal braces of steel pipe racks or roof trusses. The first method requires knowledge of the beam-column’s flexural rigidity under investigation, whereas the second requires knowledge of the corresponding Euler buckling load. In both procedures, short-term flexural displacements must be measured at the given cross sections along the beam-column under examination and subjected to an additional transverse load. The proposed methods were verified by numerical and laboratory tests on beams of a small-scale space truss prototype made from aluminum alloy and rigid connections. In general, if the higher second-order effects are induced during testing and the corresponding total displacements are accurately measured, it would be easy to obtain tensile and compressive force estimations.

Mass Customisable Roofing Solutions for the New Build and Retrofit Markets in the UK

Major house builders and contractors in the UK are seeking alternative solutions to form the structural frame of pitched roofs for various reasons; speed, health and safety, quality ease of use. They are exploring the use of offsite systems, which arguably provide all of the above benefits. However, these systems are typically considerably more expensive, often difficult to scale-up and limited in their design scope compared to traditional roof truss solutions. The strategic aim of the research reported on in this paper was therefore to develop a mass customisable roofing solution to allow the UKäó»s largest roof truss manufacturer to enter into the off-site construction sector without reinventing their business architecture. The research considered both the new build and retrofit market. The first roof solution for the new build market is a äóÖsliding roofäó», a roof truss installation method which includes a pre-prepared system created under factory conditions. The system is delivered to the construction site where it is lifted onto one end of the structure. After the system is in placed it is opened the length of the roof. The second system investigated, to be used for the retrofit market, is a self-supporting and thermally insulated roof panel, designed and developed for a multitude of pitched roofs. Working with the industry partner the suitability of the roof systems as effective off-site solutions has been trialled. The full process was monitored from a design, manufacture and construction perspective with a critical appraisal undertaken for evaluation purposes. These finding are reported.

Effectiveness and Shape Design of CFRP Structural Sections in Roof Trusses

Roof trusses have always been constructed using traditional materials such as timber and steel which have been used in industrial, agricultural and residential structures. This study aims at obtaining further effectiveness which can be attained when Carbon Fibre Reinforced Plastic (CFRP) is used as the structural section materials of a roof truss. A CFRP truss section is compared with the same 350W (AISC 2005) steel truss section subjected to same loading conditions Results indicate that the steel truss withstand deflections more than the CFRP truss in both linear and non linear analysis. The CFRP truss was 77% lighter that the steel truss. It was also concluded that the shape of sections used in steel can be adopted for CFRP structures.

Numerical analysis of truss systems with stiffened flattened end-bars

Abstract Circular hollow sections are usually used in long-span roof truss systems. One of the typology for connecting elements in such structures involves the flattening of bar ends. This article presents the numerical analysis of a plane truss composed of circular hollow sections, in which diagonal bars have flattened ends. In this sense, a new flattening typology called stiffened flattening is proposed, characterized by a non-flat geometry, with the creation of stiffeners in the lateral edges of the diagonal flattened ends. The diagonal connecting system with the chord members uses connecting plates. The plates are welded to the chords and the diagonals are connected to latter through a single bolt. The numerical analysis using finite elements method was developed in two stages through ANSYS software with the Parametric Design Language (APDL), in which parameters such as geometry, materials, element types, boundary conditions and loads are specified. A non-linear analysis was performed using shell elements on the chords, diagonals, plates and welds, and contact elements between the diagonals with stiffened flattened ends and the connecting plates. Initially, a numerical study of the connecting node and the stiffened flattened end was performed, and the results directed the modeling of the plane truss. The numerical results were calibrated with the experimental truss results in full scale. The numerical result of the plane truss was also compared to a theoretical study, considering the axial load eccentricity applied in the diagonal with stiffened flattened ends. The study was based on the consideration of combined effects of axial force and bending moment provided by the Brazilian standard ABNT NBR 8800:2008. The final results indicate that the numerical model proposed is efficient and has good correlation with the experimental and theoretical results.

Innovation of Iron Reinforcing Column of Partical From Frame of Light Steel

Almost half of houses in Indonesia are using lightweight steel roof truss today. The phenomenon in the field is that lightweight steel roof truss can blend with mortar mixture. Thus this phenomenon is captured for later applied dynamically, creatively, and innovatively with new idioms such as reinforcement for columns. This research aims to investigate the comparison of the way of making and the price of the materials between the column material made of the light steel and the column material made of the iron reinforcement which is the most efficient. Type of research is qualitative with a comparative causal approach. This research is divided into several stages, namely; Literature study, column creation, and validation. This study concluds that the manufacture of column material from reinforcement is more efficient, than the lightweight steel column material. The reinforcement column material is more efficient because of the more effective way of making and the price of the working materials more economical than the lightweight steel column material. Lightweight steel columns can be used for public housing on condition made by experienced craftsmen to make the process faster, and the dimensions of lightweight steel can be scaled down to make it more economical.

An efficient global reliability sensitivity analysis algorithm based on classification of model output and subset simulation

The global reliability sensitivity analysis measures the effect of each model input variable on the failure probability, which is very useful for reliability-based optimization design. The aim of this paper is to propose an alternative method to estimate the global reliability sensitivity indices by one group of model input–output samples. Firstly, Bayes formula is used to convert the original expression of global reliability sensitivity index into an equivalent form where only the unconditional failure probability and the failure-conditional probability density function (PDF) of each model input variable are required. All global reliability sensitivity indices can be simultaneously estimated by this new equivalent form, and the computational cost of the process is independent of the dimensionality of model input variables. Secondly, to improve the efficiency of sampling which aims at calculating the unconditional failure probability and estimating the failure-conditional PDF of every model input simultaneously, subset simulation method is extended to achieve these two aims. In the proposed procedure, subset simulation is used to estimate the unconditional failure probability, and Metropolis-Hastings algorithm is employed to convert the samples in failure domain from the current PDF in subset simulation to the PDF corresponding to the original PDF of model inputs for estimating the failure-conditional PDF of each model input variable. Thirdly, Edgeworth expansion is employed to approximate the failure-conditional PDF of each model input variable. Finally, the global reliability sensitivity index can be easily computed as byproducts using the unconditional failure probability and the failure-conditional PDF of each model input in failure probability analysis, and this process does not need any extra model evaluations after the unconditional failure probability analysis is completed by subset simulation. A headless rivet model, a roof truss structure and a composite cantilever beam structure are analyzed, and the results demonstrate the effectiveness of the proposed method in global reliability sensitivity analysis.

Structural response of existing spatial truss roof construction based on Cosserat rod theory

Paper presents the application of the Cosserat rod theory and newly developed associated finite elements code as the tools that support in the expert-designing engineering practice. Mechanical principles of the 3D spatially curved rods, dynamics (statics) laws, principle of virtual work are discussed. Corresponding FEM approach with interpolation and accumulation techniques of state variables are shown that enable the formulation of the C^{0} Lagrangian rod elements with 6-degrees of freedom per node. Two test examples are shown proving the correctness and suitability of the proposed formulation. Next, the developed FEM code is applied to assess the structural response of the spatial truss roof of the “Olivia” Sports Arena Gdansk, Poland. The numerical results are compared with load test results. It is shown that the proposed FEM approach yields correct results.

The effect of inclination of scarf joints with four pins

ABSTRACTDuring the renovation of roof trusses and roof structures, damaged wood must be replaced with new wood. To keep the original material adjustment slab joints can be used. Unfortunately, this type of joint has not been observed from the structural perspective. The shape of the joint, the inclination of its faces, the type and the number of connectors still represent an unknown area. A simplified analytical model is briefly derived in the article and the effect of the face inclination is solved. The results obtained from experiments are compared with the results from the model.

An efficient reliability analysis method combining adaptive Kriging and modified importance sampling for small failure probability

A vital challenge problem of structural reliability analysis is how to estimate the small failure probability with a minimum number of model evaluations. The Adaptive Kriging combined with Importance Sampling method (AK-IS) which is developed from the adaptive Kriging combined with Monte Carlo simulation (AK-MCS) is a viable method to deal with this challenge. The aim of this paper is to reduce the number of model evaluations of the existing AK-IS algorithm. Firstly, we use a contributive weight function to divide the candidate samples of model input variables generated in AK-IS. The candidate samples are used to select the best next sample to update the Kriging model in AK-IS. Secondly, select the best next sample only in the important area obtained according to the contributive weight value to failure probability to update the Kriging model until the stopping condition is satisfied. Thirdly, use the Kriging model constructed in the important area to predict the other area and update the important area by adding the point with the maximum contributive weight value in the area except the important area ceaselessly until the probability of the accurate identification on the limit state function’s signs (positive limit state value or negative limit state value) of all the importance sampling points satisfies a criterion. Finally, the updated Kriging model is used to estimate the failure probability especially for the small failure probability. The proposed method uses a thought from local to global in order to reduce the computational cost of AK-IS and simultaneously guarantees the accuracy of estimation. A non-linear oscillator system, a roof truss structure and a planar ten-bar structure are analyzed by the proposed method. The results demonstrate the efficiency and accuracy of the proposed method in structural reliability analysis especially for small failure probability.

Framing Failures in Wood-Frame Hip Roofs under Extreme Wind Loads

Wood-frame residential roof failures are among the most common and expensive types of wind damage. Hip roofs are commonly understood to be more resilient during extreme wind in relation to gable roofs. However, inspection of damage survey data from recent tornadoes has revealed a previously unstudied failure mode in which hip roofs suffer partial failure of the framing structure. In the current study, evidence of partial framing failures and statistics of their occurrence are explored and discussed, while the common roof design and construction practice is reviewed. Two-dimensional finite element models are developed to estimate the element-level load effects on hip roof trusses and stick-frame components. The likelihood of failure in each member is defined based on relative demand-to-capacity ratios. Trussed and stick-frame structures are compared to assess the relative performance of the two types of construction. The present analyses verify the common understanding that toe-nailed roof-to-wall connections are likely to be the most vulnerable elements in the structure of a wood-frame hip roof. However, the results also indicate that certain framing members and connections display significant vulnerability under the same wind uplift, and the possibility of framing failure is not to be discounted. Furthermore, in the case where the roof-to-wall connection uses hurricane straps, certain framing members and joints become the likely points of failure initiation. The analysis results and damage survey observations are used to expand the understanding of wood-frame residential roof failures, as they relate to the Enhanced Fujita Scale, and provide assessment of potential gaps in residential design codes.

Vaults, roof truss and walls interaction issue in monumental masonry structures

The paper discusses the subject of interaction between a roof truss, vaults and load-bearing walls in a masonry monumental structure. The static structural analysis of the Assumption of the Blessed Virgin Mary Basilica in Bialystok, as an example of Polish neogothic architecture from the turn of the 19th and 20th centuries has been carried out. The building consists of a three-aisled masonry walls system, which in cooperation with cross-ribbed vaults and a timber roof truss determine the spatial rigidity of the structure. Lack of concrete ring-beams and horizontal oriented ceiling slabs cause global stiffness reduction to the horizontal loads. In the past, it could have been one of the main reason for the appearance of cracks in the structure. The basic aspect having a real influence on building global behaviour is interaction of load-bearing structural parts. This structure was subjected to the static analysis with an investigation about the influence of interaction between the roof truss, vaults and walls. The values of horizontal displacements of walls were compared as a result of wind pressure acting on the structure. Numerical calculations were carried out using finite element method.

Experimental Study on the Effect of Heel Plate Length on the Structural Integrity of Cold-formed Steel Roof Trusses

Applications of Cold-Formed Steel (CFS) are widely used in buildings, machinery and etc. Many researchers began the research of CFS as a roof truss system. It is required to increase the knowledge of the configurations of CFS roof trusses due to the uncertainty of the structural failures regarding the materials and rigidity of joints. The objective of this research is to investigate the effect of heel plate length to the ultimate load capacity of CFS roof truss system. Three different lengths of heel plate specimens were fabricated and subjected to concentrated loads until failure. The highest ultimate capacity for the experiment was 30 kN. The results showed that the increment of the length of the heel plate had slightly increased the ultimate capacity and strain. The increment of the length of the heel plate had increased the deflection of the bottom chords but decreased the deflection of the top chords. Local buckling of top chords adjacent to the heel plate was the primary failure mode for all the heel plate specimens.

Stability of roof trusses stiffened by trapezoidal sheeting and purlins

In the article linear buckling analysis of a set of steel trusses braced by purlins and trapezoidal sheeting are conducted. The buckling load factor due to the height of a corrugated sheeting profile is investigated in parametric studies. The minimal height of trapezoidal sheeting required for preventing the sheeting and chords of the trusses against the buckling is obtained. Two groups of models are considered: “axial” model as a simple one and “eccentric” model as a more complex one. In the second group of models, eccentricity between the top chord of the trusses and purlins is considered, by means of equivalent beam elements. The differences between models are indicated and the results are discussed.

Full and Partial Structures of Historical Roof Trusses in Assessment of Volume of Timber Used for Construction

Abstract Rafter framing is the basic roof frame that, through the trusses, transfers the load from the roofing to the main supports of the building. The construction material of these structures is usually wood. The development of roof framing construction for wider and wider covers has caused an increased demand for construction timber for their construction. This paper points to this economic aspect based on an example of a geometric pattern of a rafter framing based on repetitive construction of full and partial girders. For such an understanding of the use of simple trusses by carpentry masters who constructed roof framings in past centuries, it is pointed out in Ryszard Ganowicz’s works titled “Historical roof trusses of Polish churches” with section by Piotr Rapp’s “Historical development of roof structures in Polish churches”. This work is intended to provide an initial estimate of the percentage of wood saved in this solution. This assessment will be made on the basis of the inventory documentation of the roof framing of the church of the Michael the Archangel Church in Wierzbnik.

Axial load detection in compressed steel beams using FBG-DSM sensors

Nondestructive testing methods are required to assess the condition of civil structures and formulate their maintenance programs. Axial force identification is required for several structural members of truss bridges, pipe racks, and space roof trusses. An accurate evaluation of in situ axial forces supports the safety assessment of the entire truss. A considerable redistribution of internal forces may indicate structural damage. In this paper, a novel compressive force identification method for prismatic members implemented using static deflections is applied to steel beams. The procedure uses the Euler–Bernoulli beam model and estimates the compressive load by using the measured displacement along the beam\'s length. Knowledge of flexural rigidity of the member under investigation is required. In this study, the deflected shape of a compressed steel beam is subjected to an additional vertical load that was short-term measured in several laboratory tests by using fiber Bragg grating–differential settlement measurement (FBG–DSM) sensors at specific cross sections along the beam\'s length. The accuracy of midspan deflections offered by the FBG–DSM sensors provided excellent force estimations. Compressive load detection accuracy can be improved if substantial second-order effects are induced in the tests. In conclusion, the proposed method can be successfully applied to steel beams with low slenderness under real conditions.

EARLY FABRIC IN HISTORIC TOWNS: THE BEVERLEY PROJECT

This paper provides a summary of some of the key findings of a volunteer project undertaken by the Yorkshire Vernacular Buildings Study Group as part of Historic England’s early fabric programme, the purpose of which was to examine and highlight the types of early fabric that can survive in urban contexts. The group studied early buildings in Beverley, East Yorkshire, using a combination of building investigation and recording, and documentary research. Case studies are presented for a selection of timber-framed buildings for which dates ranging from 1330 to 1674 were obtained through a combination of dendrochronology and radiocarbon wiggle-matching. The carpentry of crown-post roof trusses of the two earliest buildings is compared with similar buildings of the mid-fifteenth century. Two multiphase buildings are examined and the early fabric and later changes identified. Finally, a late seventeenth-century building is considered as an example of a type at the end of the timber-framing tradition.

Construction of Large Scale Steel Truss Roof and S-Shaped Prestressed Concrete Roof─Building Construction Work “Industrial Sports Center in Tsu City”─

Construction of Large Scale Steel Truss Roof and S-Shaped Prestressed Concrete Roof─Building Construction Work “Industrial Sports Center in Tsu City”─