Search Results (11)

The end conditions of columns constitute an important design parameter as they change their stiffness. The degree of restraint of the column modifies its fundamental frequency and mode of vibration. The rotational stiffness at its ends may transform from zero (hinged) to infinite (clamped). For intermediate values, the rotational movement is partially restricted, and it is classified as semi-rigid. In this work, the seismic response for a linearly variable section column and with gradual change in the rotational fixity is studied. A parametric solution is developed using the Rayleigh method, derived for cases of non-prismatic columns, and considering the axially distributed force along the column height. The obtained generalized stiffness and mass are used to perform approximate seismic evaluation at low effort and examine the influence of the changes to the structure. The analysis indicated that with a spring coefficient of 5 EI/l, the displacement drops by 50%, meaning that this range can produce significant influence on the structural response. The relationship between the top load and the column self-weight equal to 0.3 defines the limit for the hinged–hinged boundary condition to exist. As research recommendations, analysis of columns with variable cross-sections and different shapes, different distributed loadings, applying the rotational spring for both ends and over the shape functions, and analysis of buildings by an equivalent system are suggested. Experimental activity is indicated as a possibility for future investigations. Full article

Hydraulic asphalt concrete is virtually impervious. Hydraulic fracturing due to the generation of pore water pressure can be generally excluded for asphalt facings and asphalt cores in embankment dams. However, when some cracks and/or large voids exist in the asphalt core in dams, hydraulic fracturing could take place during reservoir impounding. Cracks and/or large voids may be caused by either earthquake shaking, large differential settlements during construction and operation, or poor construction quality. Therefore, asphalt specimens with either cracks of different depths or large air porosity were prepared, and a model test apparatus was developed to investigate the possibility of hydraulic fracturing. Model tests were conducted on cylindrical asphalt concrete specimens of 100 mm in diameter and 180 mm in height. The top boundary of the specimens was either prevented (restrained) from moving in the vertical direction or free to move (unrestrained). The model test results for asphalt concrete with cracks under unrestraint conditions were numerically back-analysed. The model test results indicated that the cracks in the asphalt concrete under the restraint conditions could experience an “open–close” progress with increasing water pressure. That suggested that if the asphalt concrete were long, low water pressure would trigger a fracturing through the cracks. Under the unrestraint conditions, low water pressure could cause the asphalt specimens with either cracks or large air porosity to fail. The extensional strains at failure were reduced, and the reductions depended on the magnitude of the crack depth or air porosity. Suggestions are given for designing the asphalt core dams to reduce the possibility of the occurrence of cracks and/or dilations in the core, especially for dams in unfavourable geological and topographical conditions. A specialty contractor is preferable to do the asphalt core job to rule out the possibility of a weak bond between the layers and an air porosity larger than 3.0% in the core. Full article

Additive manufacturing with the DED-arc process offers limited freedom in terms of the geometric shape of work pieces. The process and fabrication systems restrict the part geometry producible, which must be taken into account during design already. For this reason, a design process was investigated in which geometry generation is based on a self-organizing system. The aim of using a self-organizing system is the possibility to directly control the geometry-defining points. Next to load cases, the design method considers geometric boundary conditions from the production process when generating the geometry. In order to identify these geometrical constraints from production experimentally, a concept of Case Study Demonstrators was applied. This was used to investigate how path planning and production can be carried out for specific geometrical features and to identify restraints of the process and the manufacturing system, e.g., smallest producible wall thickness and overhangs. Subsequently, the obtained restraints were considered as boundary conditions for the design process and were included in the modification of an example geometry. By applying the presented design method, it was possible to maintain a minimum wall thickness throughout the structure while generating a topologically optimized geometry. In contrast to compliance with the minimum wall thickness, no satisfactory behavioral rule could be found for limiting the overhang. Full article

This paper formulates a modified differential quadrature finite element method (DQFEM) by a combination of the standard DQFEM and the virtual boundary spring technique, which makes it easy to implement arbitrary elastic restraints by assigning reasonable values to the boundary spring stiffnesses. This new formulated method can offer a unified solution for flexural vibrations of composite laminates subjected to general elastic boundary combinations including all the classical cases. The influences of the number of Gauss–Lobatto nodes and the boundary spring stiffnesses on the convergence characteristics of natural frequencies are investigated, and some conclusions are drawn in terms of the minimum number of unilateral nodes required to generate convergent solutions and the optimal values of the boundary spring stiffnesses to simulate classical boundaries. Numerical examples are performed for composite laminates under various classical boundary conditions. Excellent accuracy, numerical stability, and reliability of the present method are demonstrated by comparisons with available exact and numerical solutions in open literatures. Additionally, for elastically constrained composite laminates, which are beyond the scope of most existing approaches, numerous new results obtained by the present method may serve as reference values for other research. Full article

The vibration serviceability assessment of slender and/or lightweight pedestrian systems with high sensitivity to walk-induced effects is rather challenging. In the same way, laminated glass (LG) is used in buildings for structural applications but still represents a not well known and vulnerable material. For pedestrian LG systems, the characterization of dynamic and mechanical parameters may require specific procedures which do not adapt from other constructional typologies. Among others, the mass of pedestrians is generally high compared with LG structural components. Size and restraints in LG may also lead to more pronounced vibration effects. For existing LG systems, moreover, knowledge of residual capacity may be rather difficult. In this paper, an original uncoupled experimental investigation is proposed to numerically address the accuracy and potential of low-cost laboratory body measures for vibration analysis of LG slabs to support (or even replace) field tests or more complex calculation approaches. A total of 40 experimental records are taken into account, in the form of body center of mass (CoM) acceleration time histories for an adult volunteer walking on a rigid concrete slab and equipped with a single high-precision, Wi-Fi triaxial sensor based on micro electromechanical systems (MEMS) technology. Body CoM records are elaborated and used as input for finite element (FE) nonlinear dynamic analysis in the time domain (WL1) of two LG slab configurations (GS1 and GS2) with identical geometry but different boundaries. A third reinforced concrete slab of literature (CS3) is also investigated for further assessment. Numerical parametric results from a total of 120 WL1-based nonlinear dynamic analyses are compared with FE numerical results based on a conventional deterministic approach (WL2) to describe walk-induced effects, as well as towards past field experiments (GS2). The accuracy and potential of the proposed procedure are discussed. Full article

Free vibration analyses of lattice sandwich beams with general elastic supports have rarely been discussed in this field’s literature. In this paper, a unified method is proposed to study the free vibration characteristics of lattice sandwich beams under various boundary conditions. The proposed method is to convert the three truss cores of lattice sandwich beams into an equivalent homogeneous layer and introduce two different types of constraint springs to simulate the general elastic support boundary at both ends of lattice sandwich beams. By changing the rigidity of the boundary restraint spring, various boundary conditions can be easily obtained without modifying the solving algorithm and solving process. In order to overcome all the discontinuities or jumps associated with the elastic boundary support conditions, the displacement function of lattice sandwich beams is usually obtained as an improved Fourier cosine series along with four sine terms. On this basis, the unknown series coefficients of the displacement function are treated as the generalized coordinates and solved using the Rayleigh–Ritz method. The correctness of the present method is verified through comparison with existing literature. The calculation results of the present method are highly accurate, indicating that the present method is suitable for analyzing the vibration characteristics of lattice sandwich beams with general elastic supports. In addition, the effects of beam length, panel thickness, core height, radius and truss inclination on the natural frequencies of lattice sandwich beams with arbitrary boundary conditions have been discussed in this paper. Full article

Structural glass beams and fins are largely used in buildings, in the form of primary load-bearing members and bracing systems for roof or facade panels. Several loading and boundary conditions can be efficiently solved by means of bonded composites that involve the use of laminated glass sections. Additionally, the so-obtained glass members are often characterized by high slenderness. To this aim, several literature studies were dedicated to the lateral–torsional buckling (LTB) behavior of laterally unrestrained (LU) glass elements, with the support of full-scale experiments, analytical models, or finite element (FE) numerical investigations. Standardized design recommendations for LU glass members in LTB are available for designers. However, several design issues still require “ad hoc” (and often expensive) calculation studies. In most of the cases, for example, the mechanical interaction between the structural components to verify involves various typologies of joints, including continuous sealant connections, mechanical point fixings, or hybrid solutions. As a result, an accurate estimation of the theoretical LTB critical moment for such a kind of laterally restrained (LR) element represents a first key issue toward the definition and calibration of generalized design recommendations. Careful consideration should be spent for the description of the intrinsic features of materials in use, as well as for a combination of geometrical and mechanical aspects (i.e., geometry, number, position of restraints, etc.). In this paper, the attention is focused on the calculation of the elastic critical buckling moment of LR glass beams in LTB. Existing analytical approaches of the literature (mostly developed for steel constructional members) are briefly recalled. An additional advantage for extended parametric calculations is then taken from finite element (FE) numerical analyses, which are performed via the LTBeam or the ABAQUS software codes. The actual role and the effect of discrete mechanical restraints are, thus, explored for selected configurations of practical interest. Finally, the reliability of simplified calculation approaches is assessed. Full article

A general formulation is considered for the free vibration of curved laminated composite beams (CLCBs) with alterable curvatures and diverse boundary restraints. In accordance with higher-order shear deformation theory (HSDT), an improved variational approach is introduced for the numerical modeling. Besides, the multi-segment partitioning strategy is exploited for the derivation of motion equations, where the CLCBs are separated into several segments. Penalty parameters are considered to handle the arbitrary boundary conditions. The admissible functions of each separated beam segment are expanded in terms of Jacobi polynomials. The solutions are achieved through the variational approach. The proposed methodology can deal with arbitrary boundary restraints in a unified way by conveniently changing correlated parameters without interfering with the solution procedure. Full article

Load-bearing laminated glass (LG) elements take the form of simple members in buildings (i.e., columns, beams, and plates) or realize stand-alone assemblies, where glass and other traditional constructional materials can interact. Among several relevant aspects, the dynamic response of LG structures requires dedicated methods of analysis, towards the fulfilment of safe design purposes. A combination of multiple aspects must be taken into account for dynamic calculations of even simple LG elements when compared to static conditions, first of all the sensitivity of common interlayers to the imposed vibration frequency. The challenge is even more complex for the vibration serviceability assessment of in-service LG structures, where the degradation of materials and possible delamination effects could manifest, hence resulting in structural performances that can markedly differ from early-design conditions. Major uncertainties can be associated to the actual mechanical characterization of materials in use (especially the viscoelastic interlayers), as well as the contribution of restraints (as compared to ideal boundaries) and the possible degradation of the bonding layers (i.e., delaminations). All of these aspects are examined in the paper, with the support of extended analytical calculations, on-site experimental measurements, and parametric Finite Element (FE) numerical analyses. When compared to literature efforts accounting for ideal boundaries only, an analytical formulation is proposed to include the effects of flexible restraints in the dynamic performance of general (double) LG beams. Special care is also spent for the presence of possible delaminations, including size and position effects. In the latter case, existing formulations for composite laminates are preliminarily adapted to LG beams. Their reliability and accuracy is assessed with the support of test predictions and parametric FE simulations. Full article

Many types of engineering structures can be effectively modelled as orthotropic plates with opposite free edges such as bridge decks. The other two edges, however, are usually treated as simply supported or fully clamped in current design practice, although the practical boundary conditions are intermediate between these two limiting cases. Frequent applications of orthotropic plates in structures have generated the need for a better understanding of the dynamic behaviour of orthotropic plates with non-classical boundary conditions. In the present study, the transverse vibration of rectangular orthotropic plates with two opposite edges rotationally restrained with the remaining others free was studied by applying the method of finite integral transforms. A new alternative formulation was developed for vibration analysis, which provides much easier solutions. Exact series solutions were derived, and the excellent accuracy and efficiency of the method are demonstrated through considerable numerical studies and comparisons with existing results. Some new results have been presented. In addition, the effect of different degrees of rotational restraints on the mode shapes was also demonstrated. The present analytical method is straightforward and systematic, and the derived characteristic equation for eigenvalues can be easily adapted for broad applications. Full article

In this paper, a modified Fourier series method is presented for the free vibration of moderately thick orthotropic functionally graded plates with general boundary restraints based on the first-order shear deformation theory. Regardless of boundary restraints, displacements and rotations of each plate are described as an improved form of double Fourier cosine series and several closed-form auxiliary functions to eliminate all the boundary discontinuities and jumps. Exact solutions are obtained by the energy functions of the plates based on Rayleigh-Ritz method. The convergence and reliability of the current method and the corresponding theoretical formulations are verified by comparing the present results with those available in the literature, and numerous new results for orthotropic functionally graded (OFG) plates with general boundary restraints are presented. In addition, the effects of gradient index, volume fraction and geometric parameters on frequencies with general boundary restraints are illustrated. Full article