Abstract

     In order to obtain stable and realistic truss structures in practical applications, it is essential to include nodal and local buckling stability in truss topology optimization. There have been several approaches to address the challenges including nodal stability or local buckling stability. However, these approaches often lead to ill-conditioned optimization problems, such as convergence problems due to the concavity of the problem or high computational costs. In this study, two novel but conceptually simple methodologies, the nominal perturbing force (NPF) approach, and the allowable stress iteration (ASI) approach, are proposed to address nodal instability and local buckling instability problems in truss topology optimization, respectively. Initially, in the NPF approach, an infinite number of disturbing forces that a node may suffer are incorporated into the truss topology optimization problem in the form of nominal perturbing force conditions, whose magnitude and direction are discussed to capture the worst case. In the ASI approach, the allowable stress for each compressive bar is redefined in each iteration to ensure that the Euler critical buckling constraint is active. In this way, the concave local buckling instability problem is linearized in each iteration and can be solved efficiently by a linear programming solver. Finally, based on the finite element limit analysis (FELA) method, a truss topology optimization formulation incorporating the NPF and ASI approaches is proposed to solve the nodal stability and local buckling stability problems simultaneously. The proposed formulation is demonstrated through several numerical examples showing significant effects of including nodal stability and local buckling stability in the optimized designs, while at the same time demonstrating the validity and potential of the proposed approaches.

Introduction

     The pin-jointed truss topology (or “layout”) optimization problem is concerned with finding an optimal arrangement of structural bars subject to prescribed constraints. A typical truss topology optimization problem might comprise a design domain containing an array of fixed nodal points connected by potential members, called the ground structure [4,11,33,37,42]. The optimization objective might typically then be to minimize the total volume, mass [21,37], or compliance[28] of structure, with constraints ensuring that each node is in static equilibrium and that bar stresses are within predefined limits [22,47,48]. The optimal cross-sectional areas for all the bars in the ground structure are then determined as part of the optimization process; typically, many of these will be zero, leaving the optimal topology comprising only of bars with non-zero cross-sectional areas[20].

     Mathematically, the ground structure provides a feasible domain for the truss structure optimization problem. Typically, the truss topology optimization based on the ground structure method is mainly divided into four steps [19]. Firstly, as shown in Fig. 1a, the design domain with appropriate supports and loads is determined. Secondly, as shown in Fig. 1b, the nodes are arranged, usually evenly, to discrete the design domain. Thirdly, as shown in Fig. 1c, these nodes are connected with potential bars to generate the ground structure. Finally, as shown in Fig. 1d, some optimization algorithms are used to remove the redundant bars to generate the optimal structure.

Conclusions

     The main contribution of this study is the development of a truss topology optimization formulation including nodal and local buckling stability constraints. A brief review of literature has shown that a convenient approach to state the basic plastic problem of truss topology optimization relies on the FELA method.

     The novel nominal perturbing force (NPF) approach has been proposed to address the nodal instability in the truss topology optimization problem. In the NPF approach, nominal perturbing forces consistent with the directions of the Cartesian axes are used to model the possible perturbations of the unstable nodes. Compared with the conventional nominal lateral force (NLF) approach, (a) the NPF approach has higher computational efficiency because it contains fewer optimization variables; (b) the effect of tension bars connected to the nodes is considered in determining the unstable nodes, which can lead to a better optimization result.

     In addition, the novel nominal allowable stress iteration (ASI) approach is proposed to address the local buckling instability in the truss topology optimization problem. In this way, the concave local buckling instability problem is linearized in each iteration and can be solved efficiently by a linear programming solver. Numerical examples have shown the practical applicability of the proposed method for the preliminary design of truss structures.

1- Introduction

2- Designing and modeling diagrid archetype models

3- Equipping the diagrid structural models with BRBs

4- Nonlinear static analyses

5- Nonlinear dynamic analyses

6- Conclusion

References

Abstract

The seismic performance of diagrids equipped with buckling restrained braces (BRBs) is investigated. In that regard, the effects of BRBs on the seismic performance characteristics of diagrids such as response modification factor, R, overstrength factor, Ω0, ductility ratio, μ, and median collapse capacity, ^ SCT, are evaluated. To this end, 6 three dimensional diagrid structures with various heights and diagonal angles are modeled using OpenSees program and are equipped with BRBs in a novel arrangement. Utilizing nonlinear static analysis, the seismic performance factors of models are evaluated. Subsequently, the median collapse capacity (^ SCT) of the models are determined by performing nonlinear dynamic analyses. The results indicate that using BRBs improve the seismic performance of the considered models due to accumulation of plastic damages in BRBs and a better distribution of plastic hinges over those models. The nonlinear static analyses indicate that for the original diagrid models, the response modification factor, R, ranges from 1.7–2.5, while the ductility ratio, μ, varies between 1.2 and 2.5, depending on the diagonal angles. Also, the results show that the Ω0 remains fairly constant. However, in BRB equipped diagrids, the range of R increases to 2.4–3.3, while the ductility ratio μ varies in the range 2.1–3.1. Similar to regular diagrids, Ω0 remains constant for BRB equipped models. Furthermore, the output of the dynamic analyses indicates that the ^ SCT, which is a function of diagonal angles and generally increases by growing the diagonal angles, could rise up to 60% for diagrids equipped with BRB.

Introduction

After a long period of ignoring aesthetic aspects of brace elements in building constructions, now, the engineering societies are convinced to benefit from the appearance of these components as a symbol of concinnity in urban construction. One of the manifest examples of this trend is the diagrid system which has emerged as an innovative and adoptable approach to create not only the building structures but also constructions with various functionalities. Over time people learnt how to increase the resistance of the building structures against lateral forces such as wind, soil pressure, water pressure, and earthquakes, by “use of oblique elements” [1]. Nonetheless, utilizing only pure triangulate modules to build a structure commenced in 20th century by Vladimir Shukhov in designing a radio tower (opened 1922). After that, triangulation concept assisted Walther Bauersfeld to construct the first geodesic dome, for a planetarium (opened 1926). Some years later, in 1953, Goldsmith [2], who majored civil engineering at the Illinois Institute of Technology, probably was the first person that academically investigated the diagrids. He proposed three different diagrid shapes that did not receive much attention, until one of them was utilized by Fazlur Khan [1] in designing the John Hancock Center in Chicago. In 1963, IBM building in Pittsburgh was constructed which can be considered as the most prominent example of shifting to diagrid structures. Fig. 1 shows some important diagrid structures built around the world [1].

1. Introduction

2. Seismic analysis of 3-D steel structures

3. Seismic response results

4. Synopsis and conclusions

Acknowledgement

Appendix A. Supplementary data

Research Data

References

Abstract

A numerical comparison study of the interstorey and the residual interstorey seismic drifts of steel structures equipped with the seesaw system and buckling-restrained braces is carried out. This investigation involves inelastic time-history seismic analyses of 2-, 5- and 8-storey 3-D steel structures, with specific orientation of columns and configuration of braces, for the design basis earthquake. The effects of soil-structure interaction and seismic incident angle are also considered in these analyses. Comparison of the seismic drift responses experienced by the seesaw-braced and the buckling-restrained braced steel structures, reveals different peak interstorey drift values but in many cases similar drift concentration along the height of the structures. Furthermore, the seesaw-braced steel structures exhibit, in general, larger peak residual drifts than buckling-restrained braced steel structures.

Introduction

After a major seismic event, the integrity of a structure, e.g. its capacity for immediate occupancy, should be certified via the explicit consideration of seismic response indexes such as the peak drifts. Focusing on steel structures, several studies, e.g. Ref. [1], have demonstrated the necessity to consider residual (permanent) drifts after an earthquake. Residual drifts, i.e. permanent drifts caused by yielding, permit the evaluation of the seismic performance of a steel structure regarding deformation and damage to its elements. In regions where repeated earthquakes can take place in a short period of time, the occurrence of a second or a third earthquake (not necessarily aftershocks of the first earthquake), increases the collapse risk of a steel structure if its residual drifts are significant [2]. The importance of residual drift has been also recognized as a key design parameter of novel seismic force resisting systems for steel structures, e.g., Refs. [3,4]. The limit value of 0.5% for residual drifts has been established as the threshold beyond which any repair of a structure is unfeasible in comparison to its rebuilding [5].

Over the past 20 years, buckling-restrained braces (BRBs) have shown an increased popularity in China, Japan, Taiwan, United States and other countries, as a primary force-resisting system for steel structures [6]. More recently, BRBs have also been applied for the seismic retrofit of older non-ductile structures [7]. BRBs, due to their stable and symmetric cyclic hysteretic response, have the advantage of developing full plastic strength in both tension and compression, providing, thus, significant energy dissipation and ductility without exhibiting strength degradation. The main disadvantage associated with BRBs is their tendency to cause storey drift concentration, i.e. accumulation of significant storey drifts in a few storeys without a more or less “uniform” distribution along the height of a structure, which inevitably leads to large residual storey drifts [8].

1- Introduction

2- Employed higher-order beam theory (HoBT)

3- Buckling analysis based on HoBT

4- Finite element formulation

5- Numerical examples

6- Conclusions

References

Abstract

When a higher-order or generalized beam theory is used for the buckling analysis of thin-walled beams, the analysis accuracy critically depends on the number and shapes of the cross-sectional modes associated with warping and distortion. In the study, we propose to use the hierarchically-derived cross-sectional modes consistent with the higher-order beam theory for the analysis of pre-buckling stress and buckling load. The proposed formulation is applicable to any box beams subjected to arbitrary loads and general boundary conditions. We demonstrate the effectiveness of the proposed method by performing buckling analyses for axial, bending, torsional, and general loadings. Length-to-height ratios of the beams are also varied from 1 to 100. If up to fifty cross-sectional and rigid-body modes are employed, the calculated buckling loads are found to match favorably those predicted by the shell finite element analysis. In that a unified buckling analysis under general loads is developed for box beams, the present study is expected to contribute towards new possibilities for the efficient buckling analysis of more general box beam structures involving several joints.

Introduction

In contrast to solid beams, thin-walled beams involve global and local buckling modes when they buckle. Local modes involve localized cross-sectional deformations at several points along the beam axis. Specifically, these modes stem from the buckling of the wall plates of a thin-walled beam. A dominant deformation pattern in local modes is distortion, i.e., a sectional in-plane deformation. Cross-sectional deformations of box beams are developed even in global buckling, and thus the classical Euler or Timoshenko beam theories cannot accurately predict the buckling loads and modes of thin-walled beams. The accuracy by these classical beam theories becomes worse especially when the box beams are not long. In the case when a box beam is shorter than a certain length, a local buckling mode appears as the primary buckling mode because the buckling of wall plates forming a box beam is dominant. Prior to proposing a method to accurately predict the buckling phenomenon of thin-walled box beams with a higher-order beam theory, we will review related extant investigations to validate the need for an alternative approach as discussed in the study. If a thin-walled box beam is viewed as a plate structure, a discrete plate model can be employed as in Refs. [1-3]. In the aforementioned studies, a thin-walled beam is considered as an assembly of thin plates having various boundary conditions. Typically, different boundary conditions are considered based on loading and bonding conditions between the wall plates of a box beam. Because they used a plate theory, the analysis was more complicated than that using a (higher-order) beam theory. The finite strip methods were proposed by Refs. [4-8], in which the distortional deformations of the beam section were taken into account. Methods mainly considering warping were also proposed [9-12]. In these methods, nodal displacements at each corner were used as the beam degrees of freedom (DOFs) to describe warping deformation.

1- Introduction

2- Geometrical description of shells with special shapes

3- Geometrical description of shells with special shapes with corrugated middle surfaces

4- Linear buckling

5- Nonlinear buckling

6- Conclusions

References

Abstract

The problem of elastic stability of the shells with special shapes with corrugated middle surfaces under external pressure is debated in the presented paper. Solution of the problem is based on FEM study. Corrugated barrelled, pseudo-barrelled, and cylindrical shells of constant mass are considered. Geometrical modification of the middle surface geometry is based on sine wave along principal directions. Middle surface of the corrugated shells are described referring to differential geometry of surfaces by parametric functions in three-dimensional Euclidean space. Linear and nonlinear buckling analyses are conducted. Examples of buckling modes are presented, which differ significantly from those typical for shells of revolution with positive or zero Gaussian curvature. It is proven that corrugation may lead to serious increase or decrease of critical load for all types of presented shells.

Introduction

Continuous search for optimal technical solutions creates the need to develop more efficient structures. Due to the wide spectrum of shells applications in the industry, many authors devoted their efforts towards description of stress state and stability analysis of shells. In conjunction with thin-walled nature of those structures the most vivid branch of structural analysis of shells is stability problem. Among many monographs concerning structural stability one can distinguish the following: [1–5]. There are also many papers devoted to analytical and numerical solutions of buckling behaviour, concerning shells with unique geometrical forms. Due to practical limitations, shapes are usually narrowed to cylinders [6,7], spheres [8], and cones [9,10]. However, more often further complex shapes are being topics of consideration, for example: barrels [11], pseudo-barrels [12], pseudo-spheres [13], bi-segmented spherical shells [14], multi-segmented spherical shells [15], clothoidal-spherical shells [16] and egg-shaped shells [17]. Zingoni [18] presented a review work concerning liquid-containment shells of revolution including non-conventional shapes. Additionally various shell panels are being objects of intensive studies. Post-buckling problems of multiple shell panels are discussed in [19,20] using higherorder theories. The most effective way of increasing load-carrying ability of shell structures is modification of their geometrical form. This fact can be assumed due to the number of diverse types of shells shapes that have been developed in recent decades. In this work the effect of corrugation of shells with positive, negative, and zero Gaussian curvature on stability is considered. Some of corrugated structures, mainly longitudinally corrugated cylinders have been already studied. Malinowski et al. [21] presented the buckling problem of sandwich cylindrical shell with corrugated main core, subjected to uniformly distributed external pressure. Iwicki et al. [22,23] investigated numerous stability problems of silos composed of corrugated sheets and columns. Jongpradist et al. [24] considered a corrugated food can design in terms of stability and strength, by experimental studies and response surface method. Dickson et al. [25] performed an analytical study of buckling problem of ringstiffened corrugated cylinders and compared results with experimental data. Liu et al. [26] studied numerically the problem of axial-impact on meridionally corrugated tubes with a view to improve the energy absorption aspect of standard circular tubes. Hao et al. [27,28] performed an analytical study to resolve a similar problem considering progressive buckling and dynamic response of such structures. The Authors verified the analytical solution with a numerical FEM study. Ghazijahani et al. [29] performed an experimental study on equivalent structures and compared obtained results with theoretical predictions. Ning and Pellegrino [30] extensively described the problem of axially compressed, circumferentially corrugated cylindrical shells. Malek [31] et al. investigated the effect of corrugation along two directions of the surface of barrelled vault. The authors have proven such modification can lead to a great increase of the buckling load. Malek and Williams [32] presented conceptual design of corrugated plates and shells. Using analytical approach, a closed-form solution of equilibrium state of such structures was obtained.

Introduction

The buckling-restrained brace (BRB) is a seismic device consisting of an axially yielding core and axially decoupled restraining mechanism, which suppresses the overall buckling. The hysteretic characteristics are stable and nearly symmetric once the full cross section of the core has yielded, differing only slightly from the base material hysteresis. Because buckling is restrained, no associated degradation should be appeared during the compression cycles. For this unique behavior, BRBs can be modeled using truss elements and uniaxial material hysteresis rules, assuming strain is distributed along the full plastic core length.

The basic concepts of buckling-restrained braces appeared from the 1970s, when limited successes were reported by several researchers in Japan and India [1–3]. The first practical BRB was achieved by Saeki, Wada, et al. [4, 5] in 1988. They employed rectangular steel tubes with in-filled mortar for the restrainer, and determined the optimal debonding material specifications to obtain stable and symmetric hysteretic behavior. In addition, the basic theory to design the restrainer was established and the first project application soon followed. In 1989, these BRBs (unbonded braces) were applied to two 10- and 15-story steel frame office buildings, in the first project to use BRBs [6]. BRBs increased in popularity and other configurations soon followed, notably the all steel tube-in-tube type

This paper describes a series of compression tests of circular hollow steel (CHS) sections and circular concrete-filled tubular (CFT) sections. The diameter to thickness ratios of the test specimens ranged 45–140. This range was set to investigate the effect of local buckling in the circular steel skin on the ultimate strength of CFT columns. The confining effect against filled-in concrete was also studied. A squash load formula for CFT stub columns is proposed to account for the post-local-buckling strength of steel skin. The ultimate strength of steel skin was predicted by a kind of Direct Strength Method (DSM). The proposed DSM does not require the computation of the effective area of the steel skin, but uses the gross area of the steel skin and the design strength formula based on various test results. The compressive strength formula of the filled-in concrete accounting for the strength ratio of steel skin to filled-in concrete is also proposed to consider the increase in compressive strength of the filled-in concrete, due to the confining effect of the steel skin. The design strengths of CFT columns were compared with the test results for verification.

Introduction

The attractive way to solve the local instability and the low ductility of thin hollow steel tubes is filling them with concrete. The concrete-filled tubular (CFT) composite sections are being widely used as columns of high-rise buildings and bridge piers in recent years. Since the steel skin confines the filled-in concrete tri-axially and the concrete resists against the inward deformation of steel skin, both steel and concrete contribute to the strength enhancement of the CFT column.

Elastic buckling properties of thin-walled storage rack columns under compression, e.g., critical buckling loads, are often the input parameters for analytical design solutions (e.g., the direct strength method in AISI_S100 2016). This paper deals with the accurate estimation of the elastic buckling properties of Σ-shaped rack sections with patterned holes. The investigation of the elastic buckling behaviour of three different Σ-shaped rack sections (with and without patterned holes) under compression is presented. More than 4000 finite element simulations were performed on these rack sections using the finite element program, ANSYS 18.1. The influences of the holes, perforation pattern, number of buckling half-wavelengths, and boundary conditions on the section’ buckling behaviour were studied. An alternative method is proposed to generate signature curves for solid rack sections, and its effectiveness has been tested to generate signature curves for perforated rack sections. Multihalf-wavelengths method is proposed to determine the critical buckling loads and critical buckling half-wavelengths of perforated rack sections, which has been proved to be unbiased and accurate. The results show that by considering the holes, the critical buckling loads of the rack sections decreased while the critical buckling halfwavelengths increased. The alternative method failed to generate the signature curves of perforated rack sections accurately since the shape functions used for describing the shapes of buckling modes of perforated rack columns are significantly different from those used for solid rack sections.

Introduction

Rack columns are generally made of thin-walled steel sheets, and the steel sheets are cold-formed into the desired sections of the columns. The columns are used to form the upright frames of a storage system and serve as compression members. To simplify the assembly of the upright frames and make the intervals of shelf panels adjustable, holes are often made at webs or flanges of rack columns along the length uniformly. Most rack columns have open and singly symmetric cross-sections. It imposes difficulties on structural designers for designing such columns, especially for perforated rack columns. This is because multiple buckling modes need to be considered for rack columns in the design. The common buckling modes of Local (L), Distortional (D), Torsional + Flexural (TF), and Flexural (F) buckling are shown in Fig. 1, and their definitions are given in the AISI_S100 [1]. The flexural buckling mode around the strong principal axis of the rack section is not available since the flexural buckling modes around the strong principal axis are always accompanied by torsional buckling mode due to the singly symmetric cross-section. TF and F buckling usually jointly termed as Global (G) buckling.

Stability of members under static and dynamic loading conditions has been studied in the past.1-3 Studies on dynamic stability of compression elements such as columns and rods can be broadly categorized into 2 main subcategories3 : parametric resonance and stability under impulsive actions. A rod might experience parametric resonance when it is subjected to a harmonic axial force with an oscillation frequency that has a certain relation to the natural frequency of the member.3-7 The second subclass is concerned with the stability of compression members under impulsive actions such as the impact of a mass, a rapidly applied axial force, or an imposed boundary velocity.8-20 A brief summary of these studies, which are mostly conducted prior to the 1980s, can be found in Galambos3 and Simitses,21 while more recent studies in this active field of research can be found in Hao et al, Ji and Waas, Mimura et al, Motamarri and Suryanarayan, Morozov et al, and Kuzkin and Dannert.22-28 The common consensus in the above studies is that, under impulsive actions, the axial force of a member can easily exceed its static critical load. External impulsive actions that can cause axial strain rates of the order of 10−1 to 102 s −1 in a rod are generally considered as low‐velocity excitations while actions with a resulting axial strain rate of 102 to 106 s −1 as high‐velocity excitations. 3 Investigation of high‐velocity excitations, which are typically encountered under impact or blast conditions, is out of the scope of the current study. Previous studies9,13,19,26,29-32 have shown that, in low‐velocity excitations with low to moderate compression speeds, the expected buckled shape is identical to the fundamental buckling mode observed in a quasi‐static case; however, for high compression speeds, higher buckling modes might also be excited. During strong ground motions, brace members in steel concentrically braced frames (CBFs) exhibit rapid shortenings and elongations leading to repeated cycles of buckling in compression and yielding in tension. When a rod is subjected to rapid shortening, due to the inertia effect of the rod’s mass, it will take a certain amount of time for the member to deflect laterally and buckle, and within this time period, the axial force of the rod can exceed its Euler load significantly.9 Similarly, it is possible for braces of a CBF to exhibit loads above their static buckling load (ie, to experience dynamic overshoot). Previous experimental and analytical results9,25,26,28,32 have shown that such dynamic overshoots can range from a few percent to hundreds of times the Euler buckling load. In a brief study by Tada and Suito,33 it was also demonstrated that the buckling and postbuckling behaviors of truss structures could notably differ under dynamic and static analysis. It is worth noting that the study was, however, conducted considering monotonic loads and rather low compressions speeds (<15 mm/s).

Studies on enhancing the strength and usability of steel members for high-rise buildings and long-span bridges have been conducted (Xiong and Liew, 2015; Khan et al., 2015; Mikkola et al., 2015). Furthermore, numerous experiments and numerical analyses of the damage assessment of steel columns, beams, bracings, and other structural members under repeated loading such as an earthquake load have been conducted (Nguyen et al., 2015; Park, 1993; Gao and Usami, 2000). Owing to the emergence of ultrahigh-strength steels, structural steel shapes are a very important design parameter considering the local buckling, and buckling expressions according to the structural steel shapes and load conditions have been proposed (Seif and Schafer, 2010). In addition, a trilinear kinematic hardening model was proposed to simulate the behavior of ultrahigh-strength steel columns with an H-section under cyclic loading (Wang et al., 2015; Chen et al., 2016). A steel member that has a low slenderness ratio is less affected by additional flexure owing to the axial force, and lateral buckling is caused by local buckling. Therefore, the local buckling of plate elements is the major reason for failure. According to an experimental study by Park (1993), a steel member accumulates damage during repeated loading, and local buckling leads to buckling of the entire member (Park, 1993). As a very large amount of plastic deformation repetitively occurs in the steel member, the steel member will eventually fracture. It was found that a steel member element can fail when such a large amount of plastic deformation occurs in a steel member element damaged by local buckling, even when the number of repeated loading cycles is low. In this study, a damage index is developed to quantitatively comprehend the degree of damage due to a large amount of plastic deformation under the repeated loading of steel members. By using this damage index, a method for analyzing the damage to box-type steel members is developed.

مقاله سال 2016

در این مقاله مدل کمانش دقیقی برای تعیین طول موثر خمشی ستون فولادی تحت بارهای ثقلی میانی برای کاربردهای تحلیل ارتجاعی مرتبه دوم دوبعدی برپایه روش طراحی نشان داده می‌شود. مدل کمانش پیشنهادی دارای قیود افقی «موهومی» است که در آنها نیروهای افقی معادل اعمال می‌شوند و به راحتی می‌توان آنها را برای نرم‌افزار تحلیل و طراحی سازه برنامه‌نویسی کرد. تعداد ۳۰ ستون با قیود انتهایی مختلف و تحت بارهای ثقلی هم‌محور در طول غیرتکیه‌گاهی‌شان تحلیل می‌شوند تا مزیت‌های مدل کمانش پیشنهادی نشان داده شود. در این مقاله ثابت می‌شود که در اغلب موارد تحلیل، مدل کمانش پیشنهادی در مقایسه با حالت استفاده از طول موثر واحد یا مدل کمانشی که در آئین‌نامه طراحی قفسه متحرک اروپا آمده است ظرفیت قابل‌توجه‌تری برای ستون حاصل می‌کند. ظرفیت‌های قابل‌توجه‌تر به بارهای نهایی که از طریق تحلیل ناحیه پلاستیک مرتبه دوم تعیین می‌شوند بسیار نزدیکترند.

در مطالعه قبلی یک سیستم جدید قاب با بادبند کمانش ناپذیر برای قاب‌های بتن مسلح پیشنهاد شد که ویژگی‌اش استفاده از آرایش زیگزاگی بادبندهای کمانش ناپذیر جهت سهولت اتصال فولاد به بتن بود. آزمایش‌های آزمایشگاهی به منظور ساخت مدل‌های عددی واقعی اتصالات بادبندی در سیستم پیشنهادی انجام شدند. با این مدل‌های عددی، یک تحلیل غیرخطی برای نمونه اصلی ساختمان انجام شد تا رفتار لرزه‌ای سیستم قاب بادبندی جدید بررسی شود. نتایج نشان دادند که بادبندهای کمانش‌ناپذیر در این سیستم جدید در کاهش پاسخ ساختمان، حتی اگر غیرخطی بودن اتصال بادبند لحاظ شود، کارآمدند. علاوه بر این، مقاومت موردنیاز اتصالات بادبند حساسیت زیادی به مودهای بالای سیستم پس از تسلیم بادبندها دارد.

مقاله ارائه شده با آنالیز تاثیرات عیوب تصادفی بر روی ظرفیت حمل بار یک تیر فولادی سروکار دارد، که در معرض تاثیرات کمانش جانبی- پیچشی ناشی از گشتاور خمشی انتها برابر یا متضاد قرار دارد. ظرفیت حمل بار تیر فولاد گرم نورد بصورت تحلیلی آنالیز می شود. نمودارهای مستطیلی به دست آمده از تحقیقات تجربی برای اغلب عیوب (ناکاملی ها) در دسترس است. تحققات عیوب ورودی با استفاده از روش نمونه¬برداری ابرمکعب لاتین محاسبه می شود. آنالیز حساسیت جهانی به منظور شناسایی این عیوب استفاده می شود، که تغییرپذیری آن تاثیر غالبی روی ظرفیت حمل بار دارد. آنالیز حساسیت سه مسافت پیوسته از باریکی تیر را شناسایی می-کند که در آن ظرفیت حمل بار به انواع مختلفی از عیوب حساس است. قابلیت اطمینان طراحی با توجه به استاندارد یوروکد 3 با انجام آنالیز آماری حالت محدود نهائی تائید می شود.