Collapse Load Research Articles

Generatrix shape optimization of stiffened shells for low imperfection sensitivity

According to previous studies, stiffened shells with convex hyperbolic generatrix shape are less sensitive to imperfections. In this study, the effects of generatrix shape on the performances of elastic and plastic buckling in stiffened shells are investigated. Then, a more general description of generatrix shape is proposed, which can simply be expressed as a convex B-spline curve (controlled by four key points). An optimization framework of stiffened shells with a convex B-spline generatrix is established, with optimization objective being measured in terms of nominal collapse load, which can be expressed as a weighted sum of geometrically imperfect shells. The effectiveness of the proposed framework is demonstrated by a detailed comparison of the optimum designs for the B-spline and hyperbolic generatrix shapes. The decrease of imperfection sensitivity allows for a significant weight saving, which is particularly important in the development of future heavy-lift launch vehicles.

A procedure for the identification of the seismic vulnerability at territorial scale. Application to the Casbah of Algiers

One of the objectives of the PERPETUATE EU-FP7 project was to determine a sound approach to the quantification of the seismic vulnerability of historic centres at territorial scale. The procedure presented herein provides a ten steps guideline from how to select building samples in the area of study, to how to compute the buildings’ seismic performance and finally how to evaluate rehabilitation decisions to reduce the seismic fragility of the studied typologies over an entire district or city. The procedure is illustrated in this paper by way of application to The Casbah of Algiers, a world heritage site composed of building clusters from the Ottoman to the French period. Pre-existing seismic damage, decay due to lack of maintenance and environmental factor and a urban irregular and complex lay-out make this application particularly challenging. A total number of around 150 houses, characterised by the most representative features of the Algerian historic construction, have been selected in collaboration with the Directorate of the Office for Management of Cultural Property of the Ministry of Culture,. The seismic Vulnerability Assessment Method (VAM) underpinning the 10-step procedure is is FaMIVE (Failure Mechanism Identification and Vulnerability Evaluation), a mechanical approach based on limit state analysis and kinematics, which allows computing collapse load factor, deriving capacity curves and determining fragility functions. As the approach identifies also the collapse mechanisms, it provides a base for choosing and evaluating the effects of strengthening interventions, which are rolled out at territorial level to improve the seismic performance of the whole sample. The effectiveness of the present procedure for the identification of the seismic vulnerability at territorial scale is discussed in the conclusions.

Análisis plástico y Ensayos de Losas multidireccionales de HRFA

This paper presents a theoretical and experimental study of multidirectional steel fibers reinforced concrete slabs (SFRC). The study is based on a real building application using SFRC flag slabs. For the evaluation of the slabs bearing capacity, plastic calculations are performed both at section and structure levels. The section analysis uses the perfect plastic stress-strain diagram, with reference to the values of the strength characteristics of SFRC based on previous jobs that used similar fibers and dosages. In the structure analysis the plastic yield lines method has been used. This method relates the section last bearing moment and the plastic collapse load. The experimental campaign has consisted of the testing of six 2 m. diameter circular shaped slabs prototypes, and has allowed to verify the reference resistance used in the calculations.

Determination of collapse loads in pipe bends with ovality and variable wall thickness under internal pressure and in-plane opening moment

The combined effect of ovality and variable wall thickness on collapse load of pipe bends under in-plane opening bending moment with internal pressure was investigated using finite element limit analysis considering large geometric change effect. The material was assumed to be elastic–perfectly plastic. The collapse moments were obtained from moment-rotation curves drawn for each bend using twice-elastic-slope method. Thickening/thinning effect on collapse load is very minimal and can be neglected. The effect of ovality is significant with the reduction of collapse load by a maximum of 39.1% for the maximum internal pressure and ovality considered. Based on the finite element results, a mathematical expression is proposed to determine collapse load of the pipe bends with ovality and this equation has been verified with experimental collapse loads.

Interval Limit Analysis of Rigid Perfectly Plastic Structures

This article presents a novel extended limit analysis approach that determines the sharp maximum and minimum bounds on the collapse load of rigid perfectly plastic structures simultaneously subject to uncertain but bounded loading magnitudes and plastic material capacities. The governing formulation is cast as a linear programming problem with interval coefficients. Linearity is achieved by a suitable piecewise linearization of nonlinear yield surfaces. The proposed algorithm is founded on a characteristic formula concept and an appropriate interval arithmetic interpretation to transform the interval limit analysis problem into two deterministic linear programming problems that can be solved by any available linear programming solver.

Advanced numerical models for the analysis of masonry cross vaults: A case-study in Italy

Aim of the present paper is the analysis of a series of existing masonry cross vaults exhibiting meaningful structural deterioration and diffused crack patterns, by means of an advanced non-linear and limit analysis software.The approach utilized is a non-standard and non-commercial one and bases both for the non-linear and limit analysis procedure on a FE discretization of the domain by means of rigid infinitely resistant wedges, where all the non-linearity is concentrated on interfaces between adjoining elements.When dealing with the non-linear code, a sequential quadratic programming scheme is used at each iteration in order to deal with the deterioration of mechanical properties of interfaces, provided that the actual non-linear behavior is approximated by means of a linear piecewise constant function.Several numerical simulations are performed varying constraint conditions, material properties, infill modeling and presence of FRP strips as reinforcement devices, comparing and discussing in detail the results obtained.From simulations results, it is found that the approach commonly used in practice to study cross vaults by means of the assemblage of single arches is not always reliable, providing failure loads and mechanism quite different from the real ones. Furthermore, similarly to what occurs for masonry arch bridges, it is found that the role played by the infill is crucial and that, depending on the actual mechanical properties of the infill, both the failure mechanisms and the collapse load may vary significantly.

Fundamentals of exact multi-load topology optimization – stress-based least-volume trusses (generalized Michell structures) – Part I: Plastic design

In this two-part paper, Michell’s century-old stress-based single-load truss topology optimization paper is extended to multiple load conditions. In Part I, so-called ‘optimal plastic design’ of multi-load trusses is reviewed, which is based on ultimate (limit or collapse) load principles and requires only statical admissibility of the solution. However, its connections to ‘optimal elastic design’ will be explained, and these will be used in Part II for the full extension of Michell’s theory to elastic multi-load problems, which will fill a significant gap in our knowledge.

Stability of dual square tunnels in cohesive-frictional soil subjected to surcharge loading

The stability of dual square tunnels in cohesive-frictional soils subjected to surcharge loading has been investigated theoretically and numerically assuming plane strain conditions. From the viewpoint of the efficient utilization of underground space for human activities, noncircular openings and tunnels should be preferred in the design stage. Despite the importance of this issue, previous research on the subject is very limited. At present, no generally accepted design or analysis method is available to evaluate the stability of multiple tunnels–openings in cohesive-frictional soils. In the design stage, it is important to consider the interaction effects of dual tunnels. Unlike the case of a single tunnel, the centre-to-centre distance appears as a new parameter that must be considered and plays a key role in tunnel stability. In this study, continuous loading is applied to the ground surface and a smooth interface condition is modelled. For a series of tunnel size-to-depth ratios and material properties, rigorous lower- and upper-bound solutions for the ultimate surcharge loading are obtained by applying finite element limit analysis techniques. For practical suitability, the results are presented in the form of dimensionless stability charts and a table with the actual tunnel stability numbers closely bracketed from above and below. As an additional verification of the solutions, upper-bound rigid-block mechanisms have been developed, and the predicted collapse loads from these mechanisms are compared with those from finite element limit analysis. Finally, a discussion is presented regarding the location of the critical tunnel spacing between dual square tunnels where interaction no longer occurs.

Numerical analysis of partly wrinkled cylindrical inflated beams under bending and shear

This paper is aimed at assessing the nonlinear elastic response of an inflatable cylindrical beam through a simple mechanical model recently proposed by the authors for studying the equilibrium configurations of highly pressurised elastic membranes with general shapes. The attention is focused on beams loaded at mid-span with two different constraints, corresponding to simply-supported ends and built-in ends. The geometrical nonlinearities due to both the cross-sectional ovalization and wrinkling are carefully considered. In particular, the wrinkling of the membrane, clearly visible for load values much lower than the collapse load, is taken into account by means of an equivalent physical non-linearity. A two-states constitutive law for the material is assumed: when a fibre is stretched (the active state), its response is elastic, while when the fibre is contracted, no compressive force can be engendered in it (the passive state). The evolution of the cross-sectional ovalization, the size of the wrinkled regions and the magnitude of longitudinal and transverse stresses in the membrane are accurately determined for increasing levels of loads, up to collapse. The numerical results for the corresponding values of load and internal pressure, obtained through an expressly developed incremental-iterative algorithm, are compared with the experimental ones available in the literature.

Experimental vertical compression tests on reinforced concrete panels made with wood blocks system and theoretical evaluation of critical load

The paper deals with the experimental and theoretical study of the behavior of panels made with Large Lightly Reinforced Concrete Walls–Wood Blocks System (LLRCW–WBS). The results of a series of centered axial compression tests performed on slender and squat panels made with the above mentioned system are presented. The theoretical studies carried out in order to estimate the local and global buckling collapse load as a function of significant parameters are then introduced. Theoretical analyses have been conducted on the basis of already established studies aiming to produce appropriate calculation methods for the design of LLRCW–WBS panels subjected to axial compressive actions. The results from theoretical analyses have been compared with those obtained from tests which resulted in an adequate correspondence.

Effect of Shape Imperfections on Thin-Walled Pipe Bends under Out-Of-Plane Moment and Internal Pressure

This paper quantifies the effect of ovality and thinning/thickening of thin-wall pipe bend modeled using the geometric parameters of r/t=15 and 20 and λ=0.1 to 0.3. For each model the ovality and thinning is varied from 5% to 20 % in steps of 5 % .The collapse loads were obtained from twice-elastic-slope method of pipe bends subjected to out-of-plane moment with and without internal pressure. Large displacement analysis was performed on elastic-perfectly plastic material using the nonlinear FE package of ABAQUS. The analyzed shows that the thinning effect is insignificant and ovality produce the significant effect of upto 27.7% decrease in collapse load for pipe bend subjected to combined moment and internal pressure.

A Study on Effect of Shape Irregularities on Collapse Loads of Pipe Bends with Critical Circumferential Throughwall Crack under In-Plane Closing Bending

The presence of thorough wall circumferential cracks has a detrimental effect on collapse load of elbows. The existing theoretical solutions do not correctly quantify the weakening effect due to the presence of the circumferential through wall crack in shape imperfect pipe bends. The present study has been done to investigate the effect of ovality and thinning on the collapse moment of 90° elbow with critical throughwall circumferential crack under in-plane bending moment using elastic-plastic finite element analysis considering large geometry change.

A robustness-based design strategy for composite structures

Purpose – This paper aims to present a new robustness-based design strategy for thin-walled composite structures under compressive loading, which combines strength requirements in terms of the limit and ultimate load with robustness requirements evaluated from the structural energy until collapse. Design/methodology/approach – In order to assess the structural energy, the area under the load-shortening curve between several characteristic points such as local buckling, global buckling, onset of degradation and collapse load is calculated. In this context, a geometrically nonlinear finite element analysis is carried out, in which the ply properties are selectively degraded by progressive failure. Findings – The advantage of the proposed methodology is observed by analyzing unstiffened composite plates under compressive loading, wherein the lightest plate that satisfies both strength and robustness requirements can be attained. Practical implications – As a practical implication, this methodology gives a ne...

Buckling Analysis of Steel Semi-Spherical Shells with Square Cutout Under Axial Compression

Buckling of steel thin-walled semi-spherical shells with square cutout due to axial compressive loads has been studied by numerical simulations, and results were compared with those from the experiments. Three vertical compression loadings were applied to specimens using the following methods: a rigid flat plate and a rigid bar with circular and spherical cross sections. The main aim of this study is to determine the influence of the cut out size-to-location (a/H) and the thickness-todiameter (t/D) on the mean collapse load of the semi-spherical shells. The finite element models were analyzed using ABAQUS nonlinear buckling analysis and the experimental tests were performed using an INSTRON 8802 servo-hydraulic machine. Finally, the different results obtained using the two analysis methods were compared. The comparison reveals that experimental and numerical nonlinear model results match closely with each other.

적층구성이 CFRP 사이드 부재의 충돌안전성에 미치는 영향

The global demand for reduction in the weight of automobiles has led many countries to focus on the development of hybrid, eco-friendly, and electric cars. Reduction in the weight of materials can both increase fuel efficiency and maximize automobile performance. Therefore, the design of automobile should be inclined towards the safety aspects. but at the same time, it also consider reducing the structural weight of an automobile. In this study, CFRP side members with circular and double hat shaped section was manufactured. The impact collapse tests performed with change of the stacking condition, such as variation of interface number and outerlayer angle. The impact collapse load and absorbed energy were quantitatively analyzed according to the changes in section shapes and stacking condition. This analysis was performed to obtain design data that can be applied in the development of optimum lightweight members for automobiles.

Full 3D homogenization approach to investigate the behavior of masonry arch bridges: The Venice trans-lagoon railway bridge

Some different procedures for the evaluation of the non-linear behavior of masonry arch bridges are here proposed. In particular, the Venice trans-lagoon masonry arch bridge is numerically analyzed by means of several 3D FE numerical strategies. The three dimensional behavior of the structure when subjected to train loads and pile foundation settlement is investigated. Focus is also posed to the stabilizing role played by the backfill.Both a non-commercial code and a standard commercial FE software are utilized. The non-commercial code properly takes into account for the orthotropic behavior of the barrel vaults and the stone arches, and allows performing non-linear static and limit analyses on complex 3D structures. Within the non-commercial FE approach, each material of the bridge (barrel vault, external stone arches, spandrels, piers, backfill) is suitably modeled using rigid parallelepiped elements and quadrilateral interfaces exhibiting an orthotropic constitutive law with either softening or rigid-plastic behavior in the non-linear and limit analysis version respectively. In both FE codes, mechanical properties of each material of the bridge (barrel vault, external stone arches, spandrels, piers, backfill) are modeled starting from suitable homogenization procedures in the elastic range (commercial software) and also beyond the linear limit (non-commercial FEM).The bridge is studied under service loads and up to failure for the passage of a standard train on either a single or both tracks. In the analyses, the stabilizing role played by the backfill, the strength increase obtained with stiff lateral stone arches on the barrel vault and the 3D effects induced by both load configurations are discussed. Results obtained with the incremental non-linear procedures are always compared with limit analysis predictions of collapse loads and failure mechanisms.Finally a uniform foundation settlement of one of the piles is simulated.

Bending behavior of lightweight sandwich-walled shells with pyramidal truss cores

A study on the bending response of a composite curved panel with pyramidal metallic truss cores suitable for functional applications is presented using a combination of analytical modeling, three-point bending experiments and finite element (FE) based simulations. The aluminum pyramidal cores were constructed using an interlocking method before curing with composite face sheets to fabricate the final structure. A theoretical model was developed to analyze the experiments and develop failure criteria. Three failure modes: (i) face wrinkling, (ii) face crushing, and (iii) debonding between face sheet and truss cores, were considered and theoretical relationships for predicting the collapse load associated with each mode were developed. The experiments were carried out on two sets of specimens with differing face sheet thickness which clearly indicated the important role played by core debonding in determining the peak load of the structure. Localized buckling instabilities were also reported for samples with thinner face sheets. The role of debonding in determining strength was further highlighted by a comparison with FE simulations with suppressed debonding.

Bearing Capacity of Strip Footings near Slopes Using Lower Bound Limit Analysis

Stability of foundations near slopes is one of the important and complicated problems in geotechnical engineering, which has been investigated by various methods such as limit equilibrium, limit analysis, slip-line, finite element and discrete element. The complexity of this problem is resulted from the combination of two probable failures: foundation failure and overall slope failure. The current paper describes a lower bound solution for estimation of bearing capacity of strip footings near slopes. The solution is based on the finite element formulation and linear programming technique, which lead to a collapse load throughout a statically admissible stress field. Three-nodded triangular stress elements are used for meshing the domain of the problem, and stress discontinuities occur at common edges of adjacent elements. The Mohr-Coulomb yield function and an associated flow rule are adopted for the soil behavior. In this paper, the average limit pressure of strip footings, which are adjacent to slopes, is considered as a function of dimensionless parameters affecting the stability of the footing-on-slope system. These parameters, particularly the friction angle of the soil, are investigated separately and relevant charts are presented consequently. The results are compared to some other solutions that are available in the literature in order to verify the suitability of the methodology used in this research.

Quasi-static response and multi-objective crashworthiness optimization of oblong tube under lateral loading

This paper addresses the energy absorption responses and crashworthiness optimization of thin-walled oblong tubes under quasi-static lateral loading. The oblong tubes were experimentally compressed using three various forms of indenters named as the flat plate, cylindrical and a point load indenter. The oblong tubes were subjected to inclined and vertical constraints to increase the energy absorption capacity of these structures. The variation in responses due to these indenters and external constraints were demonstrated. Various indicators which describe the effectiveness of energy absorbing systems were used as a marker to compare the various systems. It was found that unconstrained oblong tube (FIU) exhibited an almost ideal response when a flat plate indenter was used. The design information for such oblong tubes as energy absorbers can be generated through performing parametric study. To this end, the response surface methodology (RSM) for the design of experiments (DOE) was employed along with finite element modeling (FEM) to explore the effects of geometrical parameters on the responses of oblong tubes and to construct models for the specific energy absorption capacity (SEA) and collapse load (F) as functions of geometrical parameters. The FE model of the oblong tube was constructed and experimentally calibrated. In addition, based on the developed models of the SEA and F, multi-objective optimization design (MOD) of the oblong tube system is carried out by adopting a desirability approach to achieve maximum SEA capacity and minimum F. It is found that the optimal design of FIU can be achieved if the tube diameter and tube width are set at their minimum limits and the maximum tube thickness is chosen.

Influence of Friction Stir Welding Effects on the Compressive Strength of Aluminium Alloy Thin-Walled Structures

The main objective of the present work is to investigate the effect of the residual stresses originated by the friction stir welding (FSW) process in the compressive strength of aluminium alloy plates. The finite element method (FEM) is used to simulate the welding process and calculate the distribution of the residual stresses. The model is validated using a residual stress map obtained by means of the contour method from a friction stir welded AA2024-24 plate. The results from the welding simulation were then used to numerically assess the influence of the residual stresses on the collapse load of the plate.