Probabilistic analysis of a space truss is presented in the paper. Reliability of such a structure is sensitive to geometrical and material imperfections. The objective of this paper is to present a variant of the point estimate method (PEM) to determine mean values and standard deviations of limit loads of engineering structures. The main advantage presented by this method is the small number of sample calculations required to obtain estimators of investigated parameters. Thus the method is straightforward, requiring only preliminaries of probability theory. This approach is illustrated by limit state analysis of a space truss, considering geometric and material imperfections. The calculations were performed for different random models, so the influence of random parameters on the limit load of the truss can be determined. A realistic snow load was imposed.

The paper describes a bridge over the Vistula River with two spans of 180 English feet (54.86 metres) in length, constructed in the middle of the 17th century in the city of Torun on the territory of the Polish-Lithuanian Commonwealth. A study on numismatic and iconographic sources as well as city plans and written sources is carried out in the article. The study shows that the Torun Bridge superstructure was made of wood and was based on a cantilever truss (Gerber carrier) solution which had never been applied in Europe before. The two large spans of Torun Bridge were in service between 1632 and 1657. Accord- ing to the author’s research on well-known bridge structures from Europe from the middle of the 17th century, the span of the Torun bridge appears to have been the larger than the other.

The paper demonstrates the potential of wavelet transform in a discrete form for structural damage localization. The efficiency of the method is tested through a series of numerical examples, where the real flat truss girder is simulated by a parameterized finite element model. The welded joints are introduced into the girder and classic code loads are applied. The static vertical deflections and rotation angles of steel truss structure are taken into consideration, structural response signals are computed at discrete points uniformly distributed along the upper or lower chord. Signal decomposition is performed according to the Mallat pyramid algorithm. The performed analyses proved that the application of DWT to decompose structural response signals is very effective in determining the location of the defect. Evident disturbances of the transformed signals, including high peaks, are expected as an indicator of the defect existence in the structure. The authors succeeded for the first time in the detection of breaking the weld in the truss node as well as proved that the defect can be located in the diagonals.

The work concerns the influence of the method of numerical modelling of the connections of the roof truss and vaults with the walls of historic masonry objects structures on the local stress distribution in the walls. At the outset, the need to search for rational modelling was justified due to the large size of the calculation models and the erroneous results obtained with oversimplification of the model. Four methods of modelling the connections between the walls and roof truss and vaults were analysed. The first method was to describe the elements of walls and foundations as solid elements, the ribs of the vaults and the roof truss as beam elements, and the vaulting webs as shell elements. The remaining methods 2–4 describe the walls as shell elements. In places where the walls join with the roof truss and vaults, fictitious/fictional elements in the form of rigid horizontally-oriented shells were used in model No. 2. In model No. 3, fictitious rigid horizontally-oriented shell elements in addition to local rigid vertically-oriented shells were used, while in model No. 4, only fictitious rigid vertically-oriented shell elements with stepwise decreasing protrusions were introduced. The best solution in terms of local stress distribution turned out to be the description of connections with fictitious shell elements in the case of model No. 4. This approach slightly increases the number of unknowns, and makes the results of stresses in the connection areas realistic in relation to full modelling with solid finite elements.

In 1875 a steel railway bridge was built in northern Warsaw. It had seven spans of 66.22 m and two spans of 15.24 m. In 1908 the second railway bridge was built downstream of the older one. The spacing of supports and spans were the same as in the older bridge. During World War I, both bridges were blown up and then rebuilt, first temporarily and then permanently. Again both were blown up in 1944. In 1945, a temporary crossing was built. In 1947 a permanent bridge was rebuilt, partially replacing rivets with welding. On the pillars of the older bridge, the Gdański Bridge was built (not in this study). In 1963 welded connections were strengthened, in 1980 the structure of the northern track was replaced. In 2016, the northern track was renovated. The replacement of the structure of the southern track is ongoing since 2018.

This paper analyzes the effect of additional masses for lattice structures on the nature of changes in the natural frequencies of the structure. An attempt to mathematically describe this nature and the scale of the effect with a known thickness of the icing layer was also made. The discussion concerns a structure with a sacred purpose – the Gate of the Third Millennium, located in the Lednickie Fields, in the Kiszkowo Municipality, Gniezno Poviat. The icing of structural bars (frost, rime) is treated as a source of additional masses, although the origin of non-structural mass is of secondary importance for the analysis in question. The analysis was carried out by Finite Element Method (FEM) modeling of the structure, assuming a single-parameter variation of its mass (that is, the additional mass of all elements of the test object varies proportionally to a single parameter, which is the outer surface of the element on which the ice layer is deposited). By solving the vibration eigenproblem for successive models, representing different intensities of icing of the object, the values of successive frequencies and descriptions of the corresponding eigenmodes were determined. The results obtained allow us to formulate a postulate that the possibility of a change in the mass of the analyzed object resulting from icing or other causes should be taken into account in strength analyses, wherein the dynamic properties of the structure play an important role, such as in assessing the susceptibility of the structure to dynamic loads.

The paper proposes a procedure for the conceptual design of reinforced concrete (RC) structures under a multiple load case (MLC), based on the truss-like topology optimization method. It is assumed that planar truss-like members are densely embedded in concrete to simulate RC structures. The densities and orientations of the reinforcing bars at nodes are regarded as optimization variables. The optimal reinforcement layout is obtained by solving the problem of minimizing the total volume of reinforcing bars with stress constraints. By solving a least squares problem, the optimized reinforcement layout under theMLCis obtained.According to the actual needs of the project, the zones to be reinforced are determined by reserving a certain percentage of elements. Lastly, a recommended reinforcement design is determined based on the densities and orientations of truss-like members. The reinforcement design tends to be more perfect by adding necessary structural reinforcements that meet specification requirements. No concrete cover is considered. Several examples are used to demonstrate the capability of the proposed method in finding the best reinforcement layout design.

An analysis of sandwich beams with truss core is an important issue in many fields of industry such as civil engineering, automotive, aerospace or maritime. The objective of the present study is a nonlinear static response of sandwich beams subjected to the three-point bending test configuration. The beams are composed of two parent components: upper and lower laminated face sheets (unidirectional tape) and a pyramidal truss core manufactured by means of 3D printing. A polyamide filament strengthened with chopped carbon fibres – CF-PA-12 is used for the core development. The both, experimental and numerical analyses are presented. A detailed numerical model of the sandwich beam was developed in Abaqus software. The numerical model considers modelling of the adhesive joint with an additional layer of material placed between the parent components of the beam. A continuum hybrid solid shell elements were used to model the adhesive layer. In addition, a special care was taken to use an appropriate material model for the CF-PA-12 filament. To do so, the uniaxial tensile tests were performed on 3D printed samples. Having acquired the test data, a hyperelastic material model was evaluated based on a curve fitting approach.

Steel frame wind bracing systems are usually made of hot rolled profiles connected to frame elements directly or through a gusset plate. The behaviour of angle bracing members is generally complex since controlled by tension or compression, bending and torsion. The common practice is to transform the problem of complex behaviour into the buckling strength of a truss member. This paper deals with an analytical formulation of the force-deformation characteristic of a single angle brace subjected to compression. A strut model takes into consideration the effect of brace end connections and softening effect of its force-deformation characteristic. Two different boundary conditions, typical for engineering practice, are dealt with. Experimental program of testing the behaviour of angle brace in portal sub-frame specimens is described. Results of experimental investigations are presented. They are used for the validation of developed model. Conclusions are formulated with reference to the application of validated brace model in the analysis of braced steel frameworks.

The study makes an attempt to model a complete vibrating guitar including its non-linear features, specifically the tension-compression of truss rod and tension of strings. The purpose of such a model is to examine the influence of design parameters on tone. Most experimental studies are flawed by uncertainties introduced by materials and assembly of an instrument. Since numerical modelling of instruments allows for deterministic control over design parameters, a detailed numerical model of folk guitar was analysed and an experimental study was performed in order to simulate the excitation and measurement of guitar vibration. The virtual guitar was set up like a real guitar in a series of geometrically non-linear analyses. Balancing of strings and truss rod tension resulted in a realistic initial state of deformation, which affected the subsequent spectral analyses carried out after dynamic simulations. Design parameters of the guitar were freely manipulated without introducing unwanted uncertainties typical for experimental studies. The study highlights the importance of acoustic medium in numerical models.

This paper proposes a method to optimize reinforcement layout of three-dimensional members under a state of complex stress and multiple load cases (MLCs). To simulate three-dimensional members, the spatial truss-like material model is adopted. Three families of truss-like members along orthotropic directions are embedded continuously in concrete. The optimal reinforcement layout design is obtained by optimizing the member densities and orientations. The optimal design of three-dimensional member is carried out by solving the problem of minimum volume of reinforcing bars with stress constraints. Firstly, the optimized reinforcement layout under each single load case (SLC) is obtained as per the fully stressed criterion. Second, on the basis of the previous results, an equivalent multi-case optimization is proposed by introducing the idea of stiffness envelope. Finally, according to the characteristics of the truss-like material, a closed and symmetrical surface is adopted to fit the maximum directional stiffness under all SLCs. It can be proved that the densities and orientations of truss-like members are the eigenvalues and eigenvectors of the surface coefficient matrix, respectively. Several three-dimensional members are used as examples to demonstrate the capability of the proposed method in finding the best reinforcement layout design of each reinforced concrete (RC) member and to verify its efficiency in application to real design problems.

The self-centering buckling-restrained brace (SC-BRB) may achieve self-restoration for structures and, to a certain degree, diminish the substantial seismic residual deformation following rare earthquakes when compared to the usage of the conventional buckling-restrained brace (BRB). It may be possible to reduce the abrupt change in stiffness at the location of the strengthened stories and make the outrigger better at dissipating energy by improving the design of the energy-dissipation outrigger. This study compares the seismic performances of two types of energy-dissipation outriggers with BRB and SC-BRB web member designs during rare earthquakes so that the changes can be measured. The results show that using the SC-BRB web member design reduces the maximum inter-story drift ratio by an average of 7.68% and increases the average plastic-energy dissipation of the outrigger truss by 8.75%. The evaluation results showthat the SC-BRB outrigger truss structure has better structural regularity and energy-dissipation performance. It has the ability to efficiently regulate the structural seismic response and lessen primary-structure damage.