Collapse Load Research Articles

Progressive axial crushing behaviour of Al6061-T6 alloy tubes with geometrical modifications under impact loading

Axial crushing of tubes with multiple patterns of cut-outs is studied using numerical analysis. Commercially available finite element ABAQUS/Explicit® package is used to simulate the model under impact loading condition. Split-Hopkinson Pressure Bar (SHPB) is modelled to dynamically test the tube specimens with and without cut-outs. Number, size, and shape of cut-outs are kept constant in all specimens to have a constant weight reduction. In order to improve the crashworthiness characteristics of tubes, cut-outs are arranged on a tube surface along the circumferential and longitudinal direction in multiple rows. Crashworthiness parameters i.e., peak and mean collapse load, crushing efficiency, energy absorption characteristics are studied. The results revealed that a moderate weight reduction of tube can significantly affect the crushing characteristics of tube. In terms of load characteristic values, only 1% of weight reduction in modified tube samples has helped in 4.46% peak load reduction as compared to the normal tube, and crushing efficiency of the modified tube (T2) is found to be 2.17% higher than normal tube (T). In terms of energy absorption characteristic values, 1% of weight reduction in modified tube samples has helped in 1.95% reduction in energy absorption capacity as compared to the normal tube, and energy efficiency of modified tube (T2) is found to be 2.56% higher than the normal tube (T). After arranging the cut-outs in a multiple pattern, the location of cut-out is also seen to be influencing on the tube behaviour. It helps the tube to reduce the initial peak collapse load and optimize the mean collapse load. Further, force–deformation characteristics are also discussed to improve the crashworthiness characteristics of tube under impact load.

Restoring force model of end-plate bolted shear links in eccentrically braced frames

The eccentrically braced frame with end-plate bolted shear links provides both the necessary seismic performance and a cost-effective post-earthquake repair system. In this paper a more accurate and sophisticated restoring force model was developed to describe the mechanical properties and hysteresis behavior of widely stiffened I-shape shear links with bolted end-plate connections. Cyclic loading tests were performed on 18 link specimens to investigate the post-buckling behavior and ultimate capacity of this type of members. The key observations concerning the characteristic diagonal shear buckling of the web and the development of plastic hinges in the flanges exhibited by the web panel at failure were discussed, and the key factors affecting the mechanical properties of shear links were also investigated. Further, the forms of tension field distribution and failure modes for framing web panels of the specimens with different stiffener layouts were determined. The Cardiff's tension field method was employed to predict the post-buckling strength and collapse loads of link models, and the regression analysis integrating link major configurations was used to give the stiffness expressions of multi-linear model. The hysteresis curve parameters were calibrated based on the experimental results and given by simple expressions. The comparison between numerical and laboratory results shows an accurate evaluation of the response of the widely stiffened I-shape shear links. Finally, the applicability of the proposed model is shown by means of comparing with other link models often used in eccentrically braced frames.

Theoretical study on progressive collapse of truss string structures under cable rupture

Cables are critical components of truss string structures and cable failure can cause serious damage to the structure or even progressive collapse. However, little theoretical research work deals with this phenomenon. In this study, a rapid analysis method for the progressive collapse of truss string structures based on the nonlinear buckling material model was proposed. The results showed that the rapid analysis method could reduce the computational time by at least 30% and effectively improve computational efficiency. Based on the validated rapid analysis method, the progressive collapse failure mechanism of truss string structures under cable rupture was analyzed. The results showed that progressive collapse failure mechanisms could be divided into two categories. In one category, compression buckling of the upper chord member leads to a loss of load capacity and a rapid increase in deflection without convergence, resulting in progressive collapse of the structure. In the other category, tensile yielding of the lower chord member results in a gradual loss of stiffness and a slow increase in deflection without convergence, leading to progressive collapse of the structure. Moreover, a series of assumptions and simplifications were made, followed by the establishment of calculation equations for the progressive collapse load capacity and deflection of truss string structures under cable rupture. By comparing the theoretical values with the finite element values as well as test values, the accuracy of the equations proposed in this study for calculating the progressive collapse load capacity and deflection of truss string structures was verified.

Evaluation of the mean crushing load of perforated circular tubes undergoing progressive collapse

Perforations have been successfully employed for reducing the initial collapse load of tubes undergoing axial collapse. Most of the available literature evaluates the reduction in the initial collapse load through either experiments or numerical simulations. Theoretical models for calculating the mean crushing load are available for tubes without any perforations. In this study, the theoretical model proposed by Abramowicz and Jones is adapted to calculate the mean crushing force of circular tubes, having multiple perforations, undergoing collapse in the concertina mode as a function of the number of perforations, their size, and radius to wall thickness ratio of the cylinder. The mean load predictions from the model compared well with results from finite element (FE) simulations with a maximum deviation of 10%. The FE results indicated that the peak load during initial collapse is correlated well with the mean crushing load. Therefore, the presented model can be used for obtaining an indirect initial estimate of the effect of number of perforations and their size in reducing the initial collapse load.

Limit analysis of locally reinforced masonry arches

The use of composite on the strengthening and retrofitting of masonry structures over the past few decades has gained considerable importance. In this paper, the influence of partial reinforcement on the structural response of masonry arches is studied. An upper bound limit analysis numerical approach has been implemented to compute the collapse multipliers and reproduce the collapse mechanisms of two different study cases by increasing the cohesion value of the reinforced inter-block joints. The results thus obtained, have been compared to numerical simulation outcomes reported by other authors on the literature. The numerical approach adopted on this work, which requires few input parameters, is relatively fast in comparison to alternative numerical simulation methods, provided good agreement in terms of collapse loads and mechanisms.

Semianalytical Lower-Bound Limit Analysis of Domes and Vaults

The calculation of the collapse load of spherical domes is addressed using a semianalytical approach under the hypothesis of small displacements and perfect plasticity. The procedure is based on the numerical approximation of the self-stress that represents the projection of the balance equilibrium null space on a finite dimensional manifold. The so-obtained self-equilibrated stress span is superimposed onto a finite-element linear elastic solution to the prescribed loads yielding to the statically admissible set accordingly to Melan’s theorem. The compatibility of the stress with the constitutive law of the material was enforced using a linearized limit domain in terms of generalized stress, namely, axial force and bending moment along the local spherical curvilinear coordinates. The procedure was tested with reference to numerical and experimental data from the literature, confirming the accuracy of the proposed method. A comparison with the literature confirms that the buckling load was much greater than the two plastic collapse loads calculated through the proposed procedure and reported in the quoted literature.

On the Modelling of “Fork” Supports Using geometrically Exact Thin‐walled Beam Finite Elements

AbstractThis paper discusses issues related to the modelling of so‐called “fork” supports using geometrically exact 3D thin‐walled beam finite elements whose rotations are parametrized using the rotation vector. This study is motivated by the fact that isolated members with “fork” supports are commonly employed in numerical and experimental studies, for the development of design rules for steel members. These supports are defined in the small displacement range, restraining the cross‐section in‐plane displacements and the torsional rotation of the beam (along the beam initial axis). This definition is usually extended to the large displacement case for beam finite element models, whereas in experimental tests and shell finite element models, a two‐axis gimbal‐type support is used instead. This paper thus aims at (i) showing how the two‐axis gimbal support may be modelled using beam elements which are based on a rotation vector parametrization of finite rotations and (ii) highlighting the differences between the two support types. Numerical examples are presented to illustrate the differences, which are quite significant for moderate‐to‐large displacements, but do not seem to affect the collapse load of standard steel members.

Elastoplastic analysis of reinforced concrete space frames using the uniaxial and biaxial bending method

The scope of the work involves reinforced concrete frame structures with variations in structural design conception for columns with biaxial bending or uniaxial bending. The beams are designed with simple bending criteria for singly or doubly reinforced beams, or uniaxial bending. The analysis and design criteria are according to NBR 6118:2014. Structure analysis in elastoplastic regimen with the incremental analysis method is performed to detect plastic hinge formation order, collapse load factor, displacements, and rotation capacity of cross sections with the criteria established in the current building codes. The study evaluates the influence of the defined concepts on the structure’s elastoplastic behavior. The biaxial and uniaxial bending method is presented as an important formulation for obtaining the collapse load factor using the elastic stiffness matrix with modifications. The algorithms presented enable the development of research without the need for expensive commercial software licenses.

Nonlinear investigation of Gol’denveizer’s problem of a circular and elliptic elastic torus

The Gol’denveizer problem of a torus can be simply described as follows: the inner and outer equator of the torus shell is loaded by the vertical opposite balanced forces. Gol’denveizer proposed that the membrane theory of shells does not yield a valid solution to this problem. Following this, Audoly and Pomeau used a membrane theory of a toroidal shell and nonlinear boundary-layer to study the linear Gol’denveizer problem and gave a simple solution relating resultant force F and vertical displacement. Sun used the bending theory of shells to solve the linear Gol’denveizer problem, and demonstrated that the solution by Audoly and Pomeau for the linear Gol’denveizer problem is extremely accurate. However, to the best of our knowledge, no one has examined the nonlinear Gol’denveizer problem. In this study, the finite element method is used to observe the nonlinear mechanical property and buckling of the Gol’denveizer problem of a circular and elliptic torus. Investigations reveal that the radius ratios a/R and a/b have great influences on the deformation and force of a circular torus and elliptical torus, respectively, and that the negative Gaussian part of a torus has a stronger bearing than the positive Gaussian part. Additionally, when the vertical force is large enough, shear buckling may occur in the circular and elliptic tori. We propose the buckling failure modes of circular and elliptical torus. As a/b increases, the collapse load of an elliptic torus of the Gol’denveizer problem is enhanced gradually.

Buckling of Stiffened Cone–Cylinder Structures Under Axial Compression

This paper studies the instability behavior of stringer-stiffened cone–cylinder shells under axial compressive load via computational finite element (FE) code, ABAQUS. First, the FE model was validated using past experiments on four cone–cylinder specimens (two unstiffened and two stringer-stiffened) fabricated in pairs using mild steel. Results show that the comparison between numerical and experimental collapse loads was less than 10%. Second, parametric study was conducted using the validated FE model to investigate the effects of the location and number of stringers on the buckling behavior of axially compressed cone–cylinder structures. It has been found that reinforcing the cone–cylinder structures tends to produce higher buckling load when compared to the unstiffened ones. The presence of stringers changes the failure mode of the structure, and the initial post-buckling curves show a less steep negative slope when compared to that of the unstiffened counterpart. Externally stiffened structures were able to sustain more load as compared to the internally stiffened counterpart. Introducing longitudinal reinforcement on the conical section and ring reinforcement on the cone–cylinder junction produces a much higher buckling load compared to having stringer-stiffeners on the conical part only.

Robustness study of fabricated single-layer grid shell structures based on component sensitivity and vulnerability

Using discrete beam elements (DBE) to simulate the mechanical properties of assemble joints, the refined analysis model of fabricated single-layer grid shell structures for progressive collapse simulation was established. Based on the component sensitivity and vulnerability, the evaluation indexes of component importance and structural robustness were proposed. The effects of meshing sizes, rise-span ratios and connection behaviors on the collapse performance of K6 type spherical surface grid shell were also investigated. The following conclusions are mainly obtained: (1) By conducting the integral scaled model test, the accuracy of the refined analysis model was verified. (2) Considering the sensitivity and vulnerability of components, the evaluation indexes of component importance and structural robustness were proposed, and the reliability of the component importance coefficient was examined. (3) The effects of grid sizes, rise-span ratios and connection behaviors on the collapse performance of the gird shell were studied, and the rules of structural collapse loads changing with grid sizes and rise-span ratios were explained. (4) To ensure the structure with good collapse resistant capacity, the rise-span ratio should not be less than 1/4 for the K6 type spherical surface grid shell, and failure of the connection region should be avoided.

NURBS solid modeling for the three-dimensional limit analysis of curved rigid block structures

In this paper, we present a novel computational approach for the generalized three-dimensional upper bound limit analysis of curved rigid block structures. This approach allows to discretize structures with complex geometries into a finite number of curved blocks, while retaining an overall exact description of the structural geometry and improving the accuracy of the solution in terms of both collapse load multiplier and failure mechanism. To this aim, the discretization of a given spatial curved structure is obtained by using NURBS solids, where NURBS stands for Non-Uniform Rational B-Spline. A NURBS solid is a closed region of space delimited by NURBS boundary surfaces: no information is provided about the space within the volume, except for the mathematical expression of the boundary surfaces. NURBS solids allow to discretize a complex spatial structure into a finite number of solid elements while maintaining unaffected the initial geometry, independently on the number of elements used. Each NURBS solid element is considered as a rigid and infinitely resistant block and an upper bound limit analysis is applied to the obtained assembly. The external power is evaluated on the original geometry: the resultants of surface and volume forces, and the coordinates of the corresponding loaded points are evaluated through a new boundary integration formula, which allows avoiding any additional discretization based on standard regular elements (voxel or tetrahedral). On the other hand, the internal power is evaluated according to an associated flow rule on the common boundary NURBS surfaces between adjacent solid elements, thus representing zero-thickness interfaces. The upper-bound formulation stems into a linear programming problem, from which the kinematic load multiplier, the generalized velocities of each block, and contact forces at interfaces are obtained. Finally, the Gothic arches with curved cross-sections located within the Carmo Convent (Lisbon, Portugal) and a double curvature groin vault from the St John Hospital (Jerusalem) are studied to prove the effectiveness of the proposed NURBS solid-based approach for the three-dimensional limit analysis of generally shaped rigid block structures.

Determination of bend angle and shape imperfection effect on collapse load of pipe bends under in-plane opening moment

This study uses a three-dimensional nonlinear finite-element method to investigate the effects of bend angle ([Formula: see text]) and shape imperfection on the collapse load of pipe bends subjected to in-plane opening bending moment using large displacement analysis. ABAQUS was used to create a pipe bend model, whereas by virtue of symmetry about the longitudinal axis, half of the pipe bend model was built. The bend angle was varied from 30° to 180° with an interval of 30°, and shape imperfections, namely ovality ( Co) and thinning ( Ct), were varied from 0% to 20% each at 5% intervals. Elastic-perfectly plastic is thought to be the material of choice for the pipe bend. The results show that the bend angle has a significant impact on the collapse load of pipe bends between 30° and 120°, after which a significant decline was observed. The ovality impact increases with an increase in bend angle for pipe bends with a large thickness, whereas the opposite effect was found for smaller thicknesses with a small bend radius. The effect of bend radius and thickness was significant for large bend angles. Thinning ( Ct) and thickening ( Cth) have no effect on collapse load. A new mathematical equation has been proposed to predict the integrated effect of bend angle and shape imperfection.

Strengthening of existing stone arch bridges using UHPC: Theoretical analysis and case study

Ultrahigh-performance concrete (UHPC) is widely used in retrofitting damaged structures, but few studies on the reinforcement of stone arch bridges have been reported. This paper presents a simplified analysis and its application for a damaged stone arch bridge. The finite strength of the masonry, the friction and rotation between voussoirs and the bond shear strength between UHPC and stone were considered. A double-sided shear test was carried out to determine the bond shear strength where stones were taken from the considered bridge. Four UHPC strengthening configurations, including intrados, extrados, U-hoop (wrapping for three sides) and □-hoop (wrapping for four sides) reinforcement configurations were discussed. The collapse mechanisms and load collapse multipliers were analyzed in their original and strengthened configurations. The analyses performed indicate that the interface strategies of scabbling and post-installed rebar can ensure ductility and interface bonding strength. The considered non-reinforced bridge shows a lack of load-carrying capacity of approximately 40% with respect to that required by the demand of local heavy traffic. To obtain load collapse multiplier values greater than one, the respective thicknesses of the UHPC reinforcement layer required by the four UHPC reinforcement configurations are 10 cm, 8.3 cm, 6.8 cm and 6.0 cm. The structural stiffness and carrying capacity have been significantly improved after reinforcement, which shows that UHPC is reliable for reinforcing a stone arch bridge and offers the value of popularization and application.

Multiscale modeling of 3D nano-architected materials under large deformations

Micro- and nano-architected lattice materials present a vast design space to achieve unique and highly tunable properties under large deformations. While computational models have the potential to significantly accelerate the exploration of this design space, current modeling capabilities are limited, particularly in their ability to capture cell collapse and post-collapse load increases due to densification. In this work, we present a multiscale, FE2 approach to modeling nano-architected materials that captures geometric nonlinearities of buckling, post-buckling softening, and densification. It also captures material nonlinearities of plastic yield and hardening. The homogenization scheme and coupling framework are developed to be compatible with widely available, general-purpose finite element analysis tools.

Development of a new improved closed-form plastic collapse moment solution for structurally distorted and through-wall axially cracked 90° pipe bends subjected to in-plane closing bending moment

Plastic collapse loads of 90° pipe bends with structural defects subjected to in-plane closing bending are systematically examined in this study using three dimensional nonlinear finite element (FE) analyses. The analyses consider the large strain formulation option with the pipe bend material assumed to be of the elastic perfectly plastic (EPP) type. Pipe bends are analyzed by changing the ovality at the mid-section which is varied from 0% to 20% by 5% per step. The through-wall axial crack (TAC) parameter at the pipe bend's crown is varied from 0 to 1 by 0.2 per step. Moment rotation curves are drawn for all simulated pipe bend models and plastic collapse moment (PCM) loads are determined from the corresponding moment rotation curves using the Twice-Elastic-Slope (TES) methodology as recommended by clause NB-3213.25 in section III of ASME B&PV code. Both ovality and TAC of pipe bends significantly affects their plastic collapse moments (PCM) and this almost doubles when ovality and TAC act together. The observed effect of ovality and TAC on pipe bends having thin walled and short bend radius does not significantly change with increasing wall thickness and bend radius. The present FE analysis is validated using experimental PCM loads of pipe bends available in open literature. The crack closing effect of pipe bends during closing bending is examined. Based on the analysis, an improved structural integrity assessment equation for shape imperfect pipe bends with TAC is developed for in-plane closing bending moment loads.

Experimental, numerical and analytical investigations of masonry corners: Influence of the horizontal pseudo-static load orientation

The present work aims to expand the knowledge of the behaviour of masonry corners, which are capital to obtain an integral seismic response in masonry buildings. In particular, the influence of the seismic load orientation (from π/4 to π/2) is investigated experimentally, numerically and analytically. Both units and interfaces have been subjected to a material characterisation process, following which pseudo-static 1:4 scaled experiments on a tilting table have been conducted on a symmetric dry-joint masonry corner. The experimental results have also been simulated using a discrete element model. Finally, a new analytical limit analysis model has been developed, which considers both experimental and numerical observations and accounts for rocking-sliding and flexural mechanisms. In general, a good agreement is found between the three approaches, both in terms of collapse mechanism and load multiplier.

A novel progressive collapse design concept for structural systems based on regional behaviors

To actively control the failure mode of structural systems, an anti-collapse design method considering the interaction between structural regions, called the region sacrifice (RS) method, is proposed in this paper. This approach divides a steel frame into regions separated by partition frames designed to prevent the transmission of failure response throughout the structure while ensuring structural stability. The transmission of the failure response through a steel frame structural system was investigated by considering the instability of the columns as a typical critical failure mode. The spatial effect of the unbalanced load resulting from column failure on the stability bearing capacity of adjacent columns was transformed into two plane load effects (unbalanced moment and horizontal tie force). The maximum collapse load for considering the most adverse effects of unexpected loads was then calculated based on this plane calculation model, and the most adverse impact of the sacrificed region on the other regions was considered using this load. Then, based on the relationship between different load effects and the ultimate stability bearing capacity of the adjacent regional edge columns, partition frames were designed to prevent the transmission of failure beyond the sacrificed region. Finally, detailed design strategies were obtained that can be used for any region partition scheme. Based on an analysis of reliable examples, the RS method was shown to prevent the structural failure from crossing beyond the sacrificed region. Notably, after the columns in the sacrificed region lost their stable bearing capacity, the adjacent regional edge columns still exhibited a certain capacity. Thus, the design concept underlying the RS method provides a new approach for the anti-collapse design of structures.

Improvement of Force History Pattern in Composite Tubular Structures by Developed Trigger Mechanisms

This paper investigates the effect of various trigger mechanisms on the force history pattern, initial collapse load, mean force and specific energy absorption of CFRP composite tubular absorbers. These trigger mechanisms are bevel with angles of 15°, 30°, 45° and 60° and tulip with angles of 60° and 90° and tip numbers of 4 and 6. Experimental studies were performed for three trigger mechanisms of Bevel (B30° and B60°) and tulip with four tips and angle of 60°, 4T60. It was shown that tulip mechanisms significantly change the force–displacement pattern in comparison with bevel triggers. In this case, the initial collapse load decreases, which leads to improving the crush force efficiency (CFE) and progressive energy absorption. This analysis also contains numerical modelling, which investigates other designs of bevel and tulip trigger mechanisms with different angles. Finally, numerical results are validated against experimental results using advanced finite element techniques in LS-Dyna. The developed tulip trigger mechanisms indicated a significant change of crushing force history, which results in improvement of crashworthiness parameters.

A novel Lower Bound Limit Analysis model with hexahedron elements for the failure analysis of laboratory and thin infill masonry walls in two-way bending

A novel Lower Bound (LB) Limit Analysis (LA) Finite Element (FE) model for the study at failure of laboratory and thin infill masonry walls in two-way bending is presented. In the model, a masonry plate is discretized into infinitely resistant hexahedrons and quadrilateral interfaces where all plastic dissipation occurs. Three internal static variables act on interfaces, namely bending moment, out-of-plane Kirchhoff shear and torque. Equilibrium is imposed on hexahedrons, whereas admissibility is enforced exclusively on interfaces between adjoining elements. The admissibility of the internal actions on masonry interfaces is imposed with a strength domain obtained by means of an already existing LB homogenization technique where joints are reduced to interfaces. The resultant Linear Programming (LP) problem - which allows to estimate collapse loads and distribution of internal actions at collapse - is characterized by a number of variables and constraints relatively limited, which requires little computational burden to be solved through standard interior point LP software. Failure mechanisms are obtained solving the dual LP problem. The procedure is validated against two existing experimental datasets of walls in two-way bending, namely three series of panels with and without perforations tested at collapse at the University of Adelaide Australia and four series of solid and perforated panels tested at the University of Plymouth UK. Comparing the results in terms of collapse loads, active failure mechanisms and distribution of internal actions with both experimental evidence and previously presented numerical models, excellent results are found, an outcome showing the reliability of the procedure proposed.