Lower Chord Research Articles

Formulas for Fundamental Natural Frequency of Plane Periodic Truss

This study considers a plane statically determinate truss with double lattice structure and without a lower chord. Well-known versions of this design are Fink and Bollman trusses. Two methods are used to derive the analytical relationship of the lower limit of the fundamental frequency with the number of panels in the periodic structure. It is assumed that mass of the truss is concentrated at its joints (nodes). The nodes vibrate vertically, and the number of degrees of freedom coincides with the number of nodes. The stiffness analysis of the truss is performed using the Maxwell - Mohr method. The forces in the elastic elements and the reactions of the roller and pin supports are calculated by the method of joints depending on the size of the truss and its order of periodicity. The system of linear equations is solved using the inverse matrix method. The Dunkerley method of partial frequencies is used to calculate the lower limit of the fundamental frequency. For a series of solutions obtained for trusses with different number of panels, the common term in the sequence of solution formulas is found by induction using Maple software. The solution coefficients have polynomial form in the number of panels of order not higher than the fifth. The solution is compared with an approximate version of the Dunkerley method, in which the sum of the terms corresponding to partial frequencies is calculated using the mean value theorem. The closeness of the frequency obtained by the two analytical methods to the numerical frequency spectrum solution is shown by particular examples. An approximate version of the Dunkerley method has a simpler form and an accuracy comparable to the original Dunkerley method.

Performance of reinforced concrete non-prismatic beams having multiple openings configurations

Abstract This experimental study demonstrates the gable-reinforced concrete beams’ behavior with several number of openings (six and eight) and posts’ inclination, aimed to find the strength reduction in this type of beam. The major results found are: for the openings extending over similar beam length it is better to increase the number of posts (openings), i.e., increasing opening number led to decrease in opening area, which allows us to transmit stresses and act as lever arms between the upper and the lower chords. Also, findings revealed that the inclined posts have larger loading at the mid-point relative to vertical ones. For gables with vertical posts having six and eight openings, the ultimate strength reduction was 31.5 and 25.6%, whereas it was 29 and 17.3% for those with inclined posts, respectively.

Application of Sensitivity Analysis to Progressive Collapse Resistance of Planar Truss Structures

The conventional sensitivity analysis method unanimously takes all remaining elements except the damaged ones as statistical objects, and element importance is evaluated by the mean value of the sensitive indices of statistical objects. However, from the perspective of resisting progressive collapse, the method is not sufficiently targeted, and the evaluation results have some mistakes. The shortcomings of the traditional sensitivity analysis method in element importance evaluation were analyzed and compared through finite element investigations of two types of planar trusses. Based on the anti-progressive collapse mechanism of the planar truss, the sensitivity analysis method with lower chords as statistical objects was proposed to evaluate the importance of planar truss structural elements. This method is conceptually straightforward, and the assessment results are beyond-compare regarding accuracy via comparison against the results of other evaluation methods. Furthermore, based on identifying important elements, the structure’s bearing capacity can be improved by targeted anti-progressive collapse design.

Seismic response of the long-span steel truss arch bridge with the thrust under multidimensional excitation

PurposeUnder different ground motion excitation modes, the spatial coupling effect of seismic response for the arch bridge with thrust, seismic weak parts and the internal force components of the control section of main arch ribs are analyzed.Design/methodology/approachTaking a 490 m deck type railway steel truss arch bridge as the background, the dynamic calculation model of the whole bridge was established by SAP2000 software. The seismic response analyses under one-, two- and three-dimension (1D, 2D and 3D) uniform ground motion excitations were carried out.FindingsFor the steel truss arch bridge composed of multiple arch ribs, any single direction ground motion excitation will cause large axial force in the chord of arch rib. The axial force caused by transverse and vertical ground motion excitation in the chord of arch crown area is 1.4–3.6 times of the corresponding axial force under longitudinal seismic excitation. The in-plane bending moment caused by the lower chord at the vault is 4.2–5.5 times of the corresponding bending moment under the longitudinal seismic excitation. For the bottom chord of arch rib, the arch foot is the weak part of earthquake resistance, but for the upper chord of arch rib, the arch foot, arch crown and the intersection of column and upper chord can all be the potential earthquake-resistant weak parts. The normal stress of the bottom chord of the arch rib under multidimensional excitation is mainly caused by the axial force, but the normal stress of the upper chord of the arch rib is caused by the axial force, in-plane and out of plane bending moment.Originality/valueThe research provides specific suggestions for ground motion excitation mode and also provides reference information for the earthquake-resistant weak part and seismic design of long-span deck type railway steel truss arch bridges.

ДВУТАВРОВАЯ БАЛКА С ПОЯСАМИ ИЗ ЗГСП И ГОФРИРОВАННОЙ СТЕНКОЙ

The idea of corrugating the wall of a steel beam in order to increase its local stability and reduce steel consumption by reducing the wall thickness was proposed in Russia quite a long time ago - back in the first half of the last century. This idea turned out to be quite productive. Its implementation took place in aircraft construction, in shipbuilding, and not only in the field of building structures. Over the past nearly a century, a large number of design solutions for beams with a corrugated wall have been developed in domestic and foreign metal building. These solutions differed in: the shape and orientation of the corrugations along the wall; the shape of the section of the belts; peculiarities of the adjoining of the wall along the length of the beam, the presence of technological holes in the wall, etc. Various aspects of the actual operation of beams with corrugated walls and the stress-strain state of the corrugated walls themselves (including taking into account the elastic-plastic stage of work) were studied in relation to various options for the design solutions noted above. This article presents the results of numerical simulation of the operation and analysis of the bearing capacity according to the criteria of several near-edge states of two new variants of structural solutions for beams with a corrugated wall, for which utility model patents have been obtained. In addition, a comparative analysis of the effectiveness of known structural solutions of beams with new solutions proposed by the author was carried out. The article shows that in a number of cases, beams of new design solutions, in terms of the totality of performance indicators for the studied limit states, are more efficient than traditional solutions. The novelty of the design solutions, the priority of which belongs to the authors, lies, in the first case, in the use in the beam of chords made of ZGSP with a rectangular section, the larger side of the contour of which is oriented from the plane of the corrugated wall. In the second case, the constructive solution described above is supplemented with a prestressed tightening located in the cavity of the lower chord SHG.

Old Iron and Steel Bridges. Historical and technical notes Static and strength of lattice truss girders. Part 4 (Conclusion)

A model was composed only of linear finite elements to simulate 5 consecutive spans (64m+3x66m+64m) of the D. Luiz bridge deck. It integrates the two main girders of the deck, the two horizontal bracings that exist between their upper and lower chords and the transverse vertical bracings located on the same planes of the girders’ verticals. It is already known (see previous parts of this article) that the diagonals of the trusses are single angles, the verticals are double angles and the chords are T-sections, formed by plates and angles, as it happens in many of the lattice truss girders built at that time (second half of the XIX century, first decades of the XX century).

Assessment on the Progressive Collapse Resistance of a Long-Span Curved Spatial Grid Structure with Main Trusses

The progressive collapse resistance of the terminal building of Zhongchuan Airport in Lanzhou, China was studied, which is a long-span curved spatial grid structure with main trusses. Firstly, the finite element model was built using MSC. Marc software adopting the fiber model based on material. Secondly, an improved method of zoned concept judgment and sensitivity analysis was proposed to determine the key components. Thirdly, the initial failure components were removed individually based on the alternate load path method (AP method). The responses of remaining structure were calculated using nonlinear dynamic analysis method. Lastly, the influences brought by the cross-sectional sizes of grid members were investigated through conducting parametric analysis. According to the results, the proposed selection method can avoid omitting the key components. The structural responses are significant when removing the concrete filled steel tubular (CFST) column SC14 directly supporting the front middle part of the roof, with a maximum vertical displacement of 10 m at cantilever end, which should be focused on for this kind of large-span spatial structure. In addition, the tensile strength and cross-sectional area of the upper and lower chords should be increased by 20% to enhance the progressive collapse resistance of the structure, and the changes of axial compression ratios of the columns supporting the roof have little effects.

Damage Identification in Warren Truss Bridges by Two Different Time–Frequency Algorithms

Recently, a number of authors have been focusing on drive-by monitoring methods, exploiting sensors mounted on the vehicle rather than on the bridge to be monitored, with clear advantages in terms of cost and flexibility. This work aims at further exploring the feasibility and effectiveness of novel tools for indirect health monitoring of railway structures, by introducing a higher level of accuracy in damage modelling, achieve more close-to-reality results. A numerical study is carried out by means of a FE 3D model of a short span Warren truss bridge, simulating the dynamic interaction of the bridge/track/train structure. Two kinds of defects are simulated, the first one affecting the connection between the lower chord and the side diagonal member, the second one involving the joint between the cross-girder and the lower chord. Accelerations gathered from the train bogie in different working conditions and for different intensities of the damage level are analyzed through two time-frequency algorithms, namely Continuous Wavelet and Huang-Hilbert transforms, to evaluate their robustness to disturbing factors. Compared to previous studies, a complete 3D model of the rail vehicle, together with a 3D structural scheme of the bridge in place of the 2D equivalent scheme widely adopted in the literature, allow a more detailed and realistic representation of the effects of the bridge damage on the vehicle dynamics. Good numerical results are obtained from both the two algorithms in the case of the time-invariant track profile, whereas the Continuous Wavelet Transform is found to be more robust when a deterioration of track irregularity is simulated.

Performance of quadrilateral perforated prestressed concrete rafters

This study focuses on the behavior of simply supported perforated prestressed concrete rafters (PPCRs) under single midspan monotonic static loading. The experimental program consisted of testing seven specimens; one solid (control) rafter, and six perforated with quadrilateral openings. The main investigated variables are the number and height of the openings. The test findings indicate that, in comparison to the solid rafter, the presence of quadrilateral openings in the PPCRs led to reducing the load capacity by (4.3-36%) and increase the midspan deflection at ultimate by (14.8-33%). Also, increasing the number of concrete posts between openings resulted in increasing the failure load and decreasing the deflection at all stages of performance of the prestressed concrete rafter. On the other hand, decreasing the depth of the upper and lower chords by 25% for PPCRs with the same number of openings led to a reduction in the failure load by (36, 29.5, and 24.5%) for rafters with 6, 8, and 10 openings, respectively.

Collapse of the spatial double-layer cylinder shell by experimental study

Large span spatial steel structures, such as gymnasiums, exhibition halls, airport terminals, or railway hubs, have developed rapidly over the last four decades. However, the mechanical properties of these structures under complex loads, particularly their seismic performance under severe earthquakes, are not sufficiently understood. During the 2013 M7.0 Lushan earthquake in China, some of the large span spatial structures suffered damage of varying degrees, which necessitates a review of previous seismic designs and theories. This paper investigates the characteristics and rules of the seismic damage of large span spatial structure during the Lushan earthquake and discusses the possible causes of such damage. A shaking table test was conducted with a down-scaled model of a double-layer cylindrical shell structure to obtain the dynamic response of a structure by reasonably arranging the acceleration, velocity and displacement measuring points. The failure pattern and progressive collapse process of the structure under a severe earthquake were investigated. The buckling of members increased with the increment of ground motion, although this effect was not considered in the present code for seismic design for double-layer shell spatial structures. The seismic damage in the test was mainly represented by overall buckling of the upper chord, web member and lower chord, which is the direct reason for the structural collapse during a severe earthquake. The test results indicated that the change in surface curvature of the structure resulting from deformation during a severe earthquake transformed gravitational potential energy into kinetic energy and caused chord members to impact and fracture, thereby inducing progressive collapse of the structure. The findings of this paper provide a basis for the seismic theory and design of large span spatial steel structures. The buckling effect of double-layer cylindrical shell structures, the dynamic amplification effect of the support structures, and the transformation of gravitational potential energy to kinetic energy in particular would be of interest to researchers and designers.

Structural form and experimental research of truss arch bridge with multi-point elastic constraints

With the increase of the arch bridge span, the mechanical properties of arch bridges will decrease rapidly. In order to solve this problem, triangular net is set between the arch rib and girder to form a kind of truss arch bridge in which arch rib acts as top chord, girder acts as lower chord, triangular net acts as web member, and hangers provide elastic restrains at several points. The triangle stability of the truss can improve linear stiffness of arch rib and girder, which will thus improve the mechanical properties of arch bridges. A test bridge with a span of 50 m was built to prove the superiority of the truss arch bridge with multi-point elastic constraints (MTAB). Structural stresses and displacements were obtained through dead load experiments, and the mechanical properties of the structure were calculated through the finite element (FE) software. It is turned out that, compared with the conventional through arch bridge (CTAB), the mechanical performance of the MTAB is greatly improved. The test values of structural stresses and displacements match calculation values well. Moreover, with the same steel consumption, the more layers of the triangular net, the better the mechanical properties of the structure.

Calculation of the improved steel beams of buildings and structures of the mining and metallurgical complex

Load-bearing elements of buildings and structures of the mining and metallurgical complex in recent decades need to develop new more effective design solutions due to the intensification of technological processes, an increase in temperature loads and aggressiveness of the environment. The main direction of increasing the efficiency of such elements is their design from economically alloyed steel, which allows to increase the resource of structures and prevent accidents with a significant increase in temperature. Due to the fact that alloyed steels have higher mechanical characteristics at elevated temperatures, the question arises of creating lightweight beam structures from such steels, reducing their material consumption while maintaining the stability and fatigue strength of beams, the most promising is the use of welded beams with a perforated wall and composite beams.
 The creation of the most effective cross-sectional shape of metal beams with a perforated wall and welded beams, as well as crane beams in transverse bending, considering strength, local stability, flat bending stability and fatigue strength is considered. It is shown that an effective shape of beams with a perforated wall is a box-shaped structure made of perforated channels. A calculation was carried out to select a rational design made of an assortment of hot-rolled channel profiles. It is shown that due to the use of the proposed sectional shape, significant savings in the weight of the structure can be achieved. Considering the three-dimensional stress-strain state, the fatigue strength of welded metal crane girders operating in severe conditions is estimated. The efficiency of using a hot-rolled I-beam as the upper chord of such welded beams is shown. The necessity of using a hot-rolled I-beam and to ensure the fatigue strength of the lower chord is demonstrated.
 The use of the previously proposed combined method for calculating the structures of industrial buildings and structures and the use of economically alloyed steels allows us to create new designs of critical elements that reduce their material consumption and increase their resource. Further research can be carried out for real object designs in order to reduce their cost and increase reliability during operation in the conditions of mining and metallurgical production.

Parametric Analysis of the Dome of the Sports Palace of Mexico City

The Sports Palace of Mexico City was built in 1968 and became a turning point in the design and construction of laminar shells, leading the transition from reinforced concrete to metallic grid structures. Felix Candela observed that the use of concrete in designing laminar structures was limited to achieve great spans for sport spaces; he thus changed his first proposal for using a concrete laminar shell to a metallic structure. However, in the first architectural conception of the metallic structure, a lighter cable structure was proposed respecting the built geometry, with the intent of using high-strength wires in the upper and lower chords of the arches. In this paper, three different proposals are modeled. The first uses a 3D modelled concrete shell for understanding the geometry. The others use the final geometry and are analyzed using advanced NURBS (Non-uniform rational Bspline) modeling techniques with Rhinoceros and a parametric design with Grasshopper, where the parameters and results obtained in previous tests are compared with the results obtained in the simulations. Paneling plugins, forces simulation add-ons, finite elements analysis and environmental design simulation tools in Grasshopper are used to compare the results under normal design conditions.

Study on Mechanical behavior and equivalent calculation of GFRP- stainless Steel Composite Truss Bridge

GFRP is a kind of carbon fiber composite reinforced material, which has attracted wide attention in the engineering field because of its light weight, high strength, corrosion resistance and so on.The solid plate and shell finite element model of full GFRP truss bridge is established by ABAQUS, and its mechanical characteristics are analyzed. The study shows that the stress of each element is less than the material strength, but the mid-span deflection of the truss bridge exceeds the allowable value of the specification, so three kinds of stainless steel plate layout schemes are considered, and the structural gravity, mid-span deflection change and element stress are compared and analyzed. Finally, it is concluded that the upper and lower stainless steel plate has a great contribution to enhance the vertical stiffness of the GFRP truss bridge. The stainless steel plate largely replaces the upper chord under pressure and the lower chord is pulled. On this basis, the stainless steel plate beam filled between oblique bars is equivalent to the upper and lower chords by using the idea of average equivalence and the principle of equal mass. The finite element software analysis shows that the equivalent error is very small.

Analysis on Flexural Capacity of Square Steel Tube Truss Concrete Beams with Grouted Chords

In this research paper, simulations on five specimens of square steel tube truss concrete beams with grouted chords were conducted by finite element analysis (FEA) software ABAQUS. Comparison of failure modes, vertical load‐deflection curves, and steel tube strain variation with tests was done. The rationality and validity of the FEA models were also verified. On this basis, parameter analysis was carried out, and the influence of concrete strength, steel ratio of upper and lower chords, and spacing of steel tube truss joints on the vertical load‐deflection curves were obtained. From the results of tests and parameter analysis, design formulae of flexural bearing capacity for composite beams were proposed based on the assumption that steel tubes are equivalent to ordinary longitudinal steel bars. Accordingly, the results indicated that the steel tubes of the upper chords in the composite beams cannot get yield for full sections due to the structural requirements; the steel tube of the lower chords will be the first to reach fully yielding and the upper concrete crushed subsequently, showing a failure mode analogous to that of the under‐reinforced concrete beam; the steel ratio of lower chords is the primary factor affecting the flexural capacity of the normal section among the parameters; the calculation from the proposed design formulae for the flexural capacity of normal section is in agreement with the tests and simulations. This research could provide reference for the design of this kind of composite beam.

Structural analysis of a large aluminum alloy truss double-arch bridge

In recent years, aluminum alloy bridges have been constructed in China, but a lack of aluminum alloy design and construction standards limits their further development. Traditional concrete and steel design theory cannot be completely adopted for aluminum alloy in large bearing structures. To introduce the structural design of a two-span continuous aluminum alloy truss arch bridge, this paper describes the material type, section design, component connections and bridge bearings in detail. Deflection and stress under live load are analyzed by means of a finite-element model to prove that the allowable deformation can be much greater than L/800 due to low stress in the members. Additional flexural stress subject to large eccentricity cannot be neglected, and the allowable joint eccentricity is proposed as 5% of the section height of the upper or lower chord, or about 15.0 mm. As a result of large ratio of live load to dead load, aluminum alloy footbridges reveal a rapid drop in frequency and pedestrian comfort when pedestrian mass is considered in the vibration analysis. Aluminum alloy footbridges are more sensitive to pedestrian mass than steel footbridges, and the comfort evaluation considering pedestrian mass is very necessary in design. Elastic buckling results reveal that steel and aluminum alloy footbridges have similar buckling modes, while aluminum alloy footbridges have lower buckling eigenvalue and ultimate bearing capacity. Furthermore, nonlinear buckling analysis of bridges is used to identify vulnerable members and improve structural stability by strengthening the local members. As a result, four rows of additional diagonal members near the middle pier were installed, and the elastic and nonlinear buckling bearing capacities reached 2.67 and 2.89 times the design pedestrian load, respectively. The additional diagonal web members were proved to play a significant role in increasing structural stability and evenly distributing the pedestrian load.

A new approach to the design of suspension roof systems

Over the last century, the suspension roofs design has progressed until the advent of the shells theory in the first half of the 20th century, due to a rapid pace in technological advancement. A paradigm shift emerged with the new trend in structural design towards a new design process that cooperatively integrated economy, efficiency, and elegance. Different approaches in computation, design and reliability assessment of roof structures are discussed in this work to identify the key conditions that have significantly contributed to modern suspension roof design principles. A new algorithm to assess the reliability of suspension roofs at the design stage is proposed and a novel method for computational design and reliability evaluation of suspension roofs is presented in this paper. The proposed method provides solutions for the following problems: obtaining rational geometric parameters of a structure; finding appropriate rigidity characteristics of basic supporting elements; determining the elements failure trajectory for typical roof diagram with the following evaluation of stress - strain state of a structure; calculating numerical safety indices of a structure (determining the lower and upper safety limits). The method enables to find the zones, where failure will be initiated. It offers an opportunity to create additional strength and reliability of structures, located in dangerous places, such as bearing joints of the connecting trusses to external contour and internal contour, the braces to the lower chord of the trusses, intermediate joints of upper and lower chords of supporting trusses etc., at the stage of design and construction. Large-span roofs have increased liability level, since their failure can lead to severe economic and social consequences. In this case, the design of these unique structures should be based on complex approach for selecting the rational structural concept related to the structure’s function, architectural concept, manufacturing methods, construction, etc. Reliability requirements, adaptability to manufacture, economic efficiency, ecological and social factors should be also fulfilled. Young engineers should be inspired by the great structural forms of the past and be encouraged to study more works from our generation to spark improved designs in the future. Based on the above, we can recommend to young researchers the universal algorithm, based on: - preliminary computation; - analysis of survivability; - design according to the limit states requirements; - design based on the numerical reliability indicators. It will allow improvement of computation methods quality and more accurate analysis of roof structures. Using this approach also leads to increasing of reliability and durability of such types of structures and minimizes mistakes in designin and computation.

Effect of filling steel tube chords by concrete on the structural behaviour of composite truss girders

In this study, three specimens of Warren truss girders composite with concrete deck slab were tested experimentally under a central monotonic load to study the effect of the existence of concrete inside the chords. The load capacity, deflection, slip between the concrete slab and steel tube, and failure modes were reported. Both chords were filled with concrete to the first specimen, only the lower chord was filled with concrete and the upper chord remained hollow to the second specimen and both chords were kept hollow in the third specimen. The result indicated that the existence of concrete inside the chords has a significant effect on the load capacity, failure pattern, and the slip. The steel tubes of the upper chord filled by concrete prevent surface plasticity failure of the upper chord under loading and increase the ultimate load by 6.68 %. Also, filling the lower chord with concrete prevents the surface plasticity failure in the supports zone and caused an increase in the ultimate load by 39.59 %. The slip at the end of the specimen of two chords filled with concrete is less by 71% than the end slip of specimen of hollow top chord and higher by 46.8 % than the specimen of two hollow chords.

In-plane failure mechanism and stability bearing capacity design of planar plate-tube-connected circular steel arches

ABSTRACT: This study investigates the failure mechanisms and strength of plate-tube-connected circular steel arches. The upper and lower chord of the arch are joined by a series of uniformly distributed steel plates in a radial direction. The chord of the arch mainly bears bending moment, shear force and axial force. The connecting plates mainly resist bending moment, so its failure mechanisms and strength design are different from the traditional truss arch with diagonal tubes and web-opening arches. In this paper, the finite element (FE) software ABAQUS is used to study the in-plane failure mechanism and stability bearing capacity of planar plate-tube-connected circular steel arches, which is subjected to full-span uniform radial load (FSURL), full-span uniform vertical load (FSUVL) and half-span uniform vertical load (HSUVL). The elastic buckling load formula of two-hinged plate-tube-connected circular steel arches is proposed under FSURL.. Also, the limited condition of avoiding local buckling is also proposed under FSURL. The stability bearing capacity design formula of the arch under FSURL is proposed. Studies have shown that under FSURL, the arch will be subjected to global elastoplastic failure, and the upper chord will exhibit a full-section yield at the scope of 1/4 L span and the lower chord will exhibit a full-section yield at the scope of 3/4 L span. Under F(H)SUVL, the global failure mode may occur. The global failure stability bearing capacity design formulas of the arch under FSUVL and HSUVL are also proposed. The FE results are in good agreement with these formulas. Finally, the design suggestions of plate-tube-connected circular steel arches are proposed.

Experimental dynamic characterization of a new composite glubam-steel truss structure

The main characteristics of an original bamboo-steel composite truss structure are presented in this work. Specifically, the considered system is a spatial truss structure whose upper chord and diagonal bars are made by glubam elements whereas its lower chord is made by steel members with a hollow cross-section. This novel structural system has been conceived to build roofs and low/mid-span bridges (for example, footbridges), in such a way to ensure easy and rapid construction, efficient use of the constituent materials, low manufacturing costs and good environmental sustainability. A prototype spatial truss beam for laboratory tests is initially described by providing details about geometry, connections and materials properties. The results obtained from dynamic experimental tests are then discussed. In particular, the dynamic response under ambient vibrations and the free-decay response of this truss structure have been recorded and analyzed in order to estimate its modal properties. Design values of the viscous damping ratio for glubam truss structures with steel bolted connections are finally recommended. The numerical assessment of the human-induced vibration serviceability conditions for footbridges built by means of this structural system is finally performed.