Buckling of thin-walled torispherical heads in water heater tanks

The buckling strength of a thin-walled torispherical head in a residential electric water heater tank was investigated by both experimental and finite element analyses. Three water heater tanks pressurized with water were tested, and the strains on the heads and the pressure variations were measured and recorded. Finite element analysis was used to predict the buckling of the torispherical head. The effect of the imperfection induced by the contact nonuniformity between the torispherical head and the shell on the buckling of the structure is included. Good agreement between the test and finite element results shows that finite element models used in this paper are viable to predict the buckling pressure of a thin-walled torispherical head in a water heater tank. The results also show that the contact between the bottom head and the shell has a reinforcing effect on the buckling strength of the head. The contact imperfection will produce a dent adjacent to the knuckle region when the head buckles. The buckling pressure of the head perfectly contacting with the shell is 6.88% higher than that without contacting with the shell. The obtained results provide reference for the design and manufacture of water heater tanks.     

谐波沉降下开顶罐的屈曲分析

研究有关谐波沉降下开顶罐的屈曲性能。首先,研究各种谐波数下开顶罐的极限谐波沉降和屈曲性能。结果显示受小波数影响的上壳体发生屈曲,而受大波数影响时则在壳体的其他地方发生屈曲。随着谐波数的增加,在壳体底部也出现越来越多的屈曲点。此外,对开顶罐来说,受小波数影响时其极限谐波沉降大大降低,而受大波数影响时其极限谐波沉降降低极少。对开顶罐的屈曲性能进行数值研究,考察高径比(h/r)和径厚比(r/t)的影响。可知:在某种特定的谐波数下,极限谐波沉降与高径比(h/r)为单调递减的关系。同样的,随着谐波数的增加,极限谐波沉降的降低变化越来越小。而在某种特定的谐波数下,极限谐波沉降与径厚比(r/t)也为单调递减的关系。此外,随着谐波数的增加,极限谐波沉降的降低变化也越来越小。最后,将开顶罐和锥形顶罐的屈曲结果进行比较。结果显示,受小波数影响的开顶罐比不受锥形顶约束的锥形顶罐更能承受大的谐波沉降。然而,受大波数影响时,开顶罐与锥形顶罐的沉降持续能力有所不同。     

Modified Critical Temperatures for Steel Design Based on Simple Calculation Models in Eurocode 3

Critical temperature is defined as the temperature at which failure is expected to occur in a structural steel member given a uniform temperature distribution and load level. Determination of the critical temperature is a simple but efficient way for structural fire design. This paper proposed a new model which incorporated the buckling, load levels and non-dimensional slenderness to calculate the critical temperature of steel member under fire based on the simple calculation models in Eurocode 3. To advance the application of this new model, design charts for determining the critical temperatures were developed. The design charts showed that the critical temperature decreases with increasing load level, and increases as the buckling curve varies from “a₀” to “d”. It is also recommended to use higher grade steel in both normal and fire situations. The accuracy of this model was ascertained by comparing with the test results in available literature. The new model gave an average prediction-to-test ratio of 0.980 with a standard deviation of 0.077, indicating conservative and less scattered predictions. The percentage of over-prediction (i.e., prediction-to-test ratio >1.0) was less than 5.8% when the nominal yield strength of steel rather than its test strength was used for predictions. In general, reasonable agreements were obtained between the test results and the predictions.     

Design charts for the general instability of ring-stiffened conical shells under external hydrostatic pressure

The paper describes experimental tests carried out on three ring-stiffened circular conical shells that suffered plastic general instability under uniform external hydrostatic pressure. In this mode of failure, the entire ring–shell combination buckles bodily in its flank. The cones were carefully machined from EN1A mild steel to a very high degree of precision.Using the results obtained from these three vessels, together with the results obtained from elsewhere, the paper also provides two-design charts, which are much easier to use than older design charts. The design charts allow the possibility of obtaining a plastic knockdown factor, so that the theoretical elastic buckling pressures for perfect vessels, can be divided by the plastic knockdown factor, to give the predicted buckling pressures. Although similar design charts have been produced in the past, the design charts presented here are based on using the simpler ring-stiffened circular cylinder, which has been made equivalent to the much more complex ring-stiffened circular conical shell. The advantage of using this method is that it is simpler and the design time is reduced by a factor of about 10 with little loss of precision. This method can also be used for the design of full-scale vessels.     

新型椭球网壳减震体系性能分析

本文利用非线性有限元理论,对附加屈曲约束支撑的单层组合椭球网壳的减震性能进行了初步研究.假设钢材为理想弹塑性模型,通过大型有限元分析软件ANSYS编程进行参数化建模和具体实例分析;模型中的结构杆件采用Beam188单元,而支撑部件用Link8单元代替.对结构进行三维El-centro波作用下的动力响应分析,结果表明,这种附加屈曲约束支撑的网壳结构的关键点位移响应明显减小.基于分析结果,本文提出此类网壳屈曲约束支撑的一种布置方法,并对具体的支撑布置形式进行了分析研究,得出相关结论.     

Tragverhalten und Bemessung windbelasteter Kreiszylinderschalen mit diskreter Verankerung

Structural behaviour and design of wind‐loaded cylindrical shells with discrete anchorage. Stubby cylindrical shells are often used as storage tanks. Because of their large diameters, in general they are not anchored continuously, but discretely. Nevertheless, the previous investigations of the stress and strain state of the shell were done almost exclusively by assuming a continuous anchorage. In the contribution, it is analyzed for the critical load case wind on the emptied tank, how the internal forces and the buckling strength verification are changed, if the discrete anchorage is realistically taken into consideration at the tensile zone of the base cross section. The differences are quantified. From it, it can be concluded, that a continuously anchorage may be used in the mechanical model, if the interaction buckling strength verification of the stress design is only exploited up to 90%.     

Parametric study on buckling behaviour of dented short carbon steel cylindrical shell subjected to uniform axial compression

Generally, thin cylindrical shells are susceptible for geometrical imperfections like non-circularity, non-cylindricity, dents, swellings, etc. All these geometrical imperfections decrease the static buckling strength of thin cylindrical shells, but in this paper only effect of a dent on strength of a short (Lc/Rc∼1, Rc/t=117, 175, 280) cylindrical shell is considered for analysis. The dent is modeled on the FE surface of perfect cylindrical shell for different angles of inclination and sizes at half the height of cylindrical shell. The cylindrical shells with a dent are analyzed using non-linear static buckling analysis. From the results it is found that in case of shorter dents, size and angle of inclination of dents do not have much effect on static buckling strength of thin cylindrical shells, whereas in the case of long dents, size and angle of inclination of dents have significant effect. But both short and long dents reduce the static buckling strength drastically. It is also found that the reduction in buckling strength of thin cylindrical shell with a dent of same size and orientation increases with increase in shell thickness.     

Dynamic buckling of anchored steel tanks subjected to horizontal earthquake excitation

We investigate dynamic buckling of aboveground steel tanks with conical roofs and anchored to the foundation, subjected to horizontal components of real earthquake records. The study attempts to estimate the critical horizontal peak ground acceleration (Critical PGA), which induces elastic buckling at the top of the cylindrical shell, for the impulsive hydrodynamic response of the tank-liquid system. Finite elements models of three cone roof tanks with height to diameter ratios (H/D) of 0.40, 0.63 and 0.95 and with a liquid level of 90% of the height of the cylinder were used in this study. The tank models were subjected to accelerograms recorded during the 1986 El Salvador and 1966 Parkfield earthquakes, and dynamic buckling computations (including material and geometric non-linearity) were carried out using the finite element package ABAQUS. For the El Salvador accelerogram, the critical PGA for buckling at the top of the cylindrical shell decreased with the H/D ratio of the tank, while similar critical PGAs regardless of the H/D ratio were obtained for the tanks subjected to the Parkfield accelerogram. The elastic buckling at the top occurred as a critical state for the medium height and tallest models regardless of the accelerogram considered, because plasticity was reached for a PGA larger than the critical PGA. For the shortest model (H/D=0.40), depending on the accelerogram considered, plasticity was reached at the shell before buckling at the top of the shell.     

Robust design of composite cylindrical shells under axial compression — Simulation and validation

Thin-walled shell structures like circular cylindrical shells are prone to buckling. Imperfections, which are defined as deviations from perfect shape and perfect loading distributions, can reduce the buckling load drastically compared to that of the perfect shell. Design criteria monographs like NASA-SP 8007 recommend that the buckling load of the perfect shell shall be reduced by using a knock-down factor. The existing knock-down factors are very conservative and do not account for the structural behaviour of composite shells. To determine an improved knock-down factor, several authors consider realistic shapes of shells in numerical simulations using probabilistic methods. Each manufacturing process causes a specific imperfection pattern; hence for this probabilistic approach a large number of test data is needed, which is often not available. Motivated by this lack of data, a new deterministic approach is presented for determining the lower bound of the buckling load of thin-walled cylindrical composite shells, which is derived from phenomenological test data. For the present test series, a single pre-buckle is induced by a radial perturbation load, before the axial displacement controlled loading starts. The deformations are measured using the prototype of a high-speed optical measurement system with a frequency up to 3680 Hz. The observed structural behaviour leads to a new reasonable lower bound of the buckling load. Based on test results, the numerical model is validated and the shell design is optimized by virtual testing. The results of test and numerical analysis indicate that this new approach has the potential to provide an improved and less conservative shell design in order to reduce weight and cost of thin-walled shell structures made from composite material.     

Design procedure for stiffened water-filled steel conical tanks

Since the collapse of the steel liquid-filled conical tank located in Fredericton, Canada in December 1990, a concern has been raised about the safety of existing tanks. In a previous investigation, it was shown that welding longitudinal stiffeners to the bottom part of hydrostatically loaded conical tanks would provide a significant enhancement to the buckling capacity of this type of shell structure. In the current study, an attempt is made to develop a simple procedure that can be used in designing stiffened conical tanks. The procedure is based on the theory of orthotropic shells and design formulae for unstiffened tanks previously developed by Vandepitte.The study is conducted numerically using an in-house developed shell element model to simulate both the walls of the tank and the stiffeners. The study considers stiffening existing tanks and the design of newly stiffened ones. As the application of the orthotropic theory depends on the ratio between the stiffener spacing and the shell thickness, limiting values for such a ratio have been evaluated and are presented graphically. The orthotropic design procedure is then described and applied in two examples involving a retrofitted as well as a newly designed stiffened conical tanks.     

强冰雪灾害下大型薄壁圆柱钢壳结构稳定性研究

2008年我国南方地区发生强冰雪灾害,造成不少钢结构破坏。在化工、电力等工程中有很多作为整个系统关键设备的大型薄壁圆柱钢壳结构,柱壳内通常需设置一些横梁支承工艺设备,壳体既受到由上部壳体、顶盖和设备自重等荷载形成的沿环向均匀分布的整体轴向压力,又受到横梁支座传递来的局部轴向压力。在这些荷载作用下结构已经积累了一定的内力和变形,一旦再遭受强冰雪灾害,面积较大的顶盖和相连的其他管道上会快速积聚较大的雪荷载,导致结构发生失稳破坏。根据结构施工和使用过程,考虑加载路径的影响,先施加整体均布轴向压力,再施加局部轴向压力,然后施加模拟强积雪荷载的均布轴向压力,对112个带焊缝初始缺陷的薄壁圆柱壳结构进行了非线性稳定性数值分析。研究表明:随着初始整体荷载水平提高,柱壳承受积雪荷载的能力下降;随着缺陷幅值的增大,柱壳承受积雪荷载的稳定承载力与整体均布轴压下的稳定设计承载力的比值增大,其后屈曲承载能力也提高。柱壳下部储有浆液时;壳体承受积雪荷载的能力有小幅提高。根据大量计算结果,提出了考虑加载历史的遭受强冰雪荷载的圆柱壳稳定性设计建议。     

Structural optimization and dynamic analysis for double-layer spherical reticulated shell structures

This paper is concerned with the geometrical optimum design and the aseismic analysis of double-layer reticulated shell structures. The characteristic of free vibration of reticulated shell structures, with respect to geometric parameter, is investigated. The variations of the eigenfrequency of shell structures, with respect to the ratio of height-to-span, span, grid division frequency and thickness of shell, are discussed. The Newmark method is used to calculate the stresses and displacements of the reticulated shell structure under earthquake action. The analysis results show that under a specified span, the eigenfrequency of the structure increases with the increase of the height-to-span ratio and then decreases afterwards. Therefore, there exists an optimum height-to-span ratio resulting in an optimum stiffness at the specified span. The optimum value of the ratio is found to be between 1/3 and 1/4 from the simulation study presented in this paper. At a specified height-to-span ratio, the increase of the value of structural span greatly reduces the eigenfrequency of the structure and then decreases the global stiffness of the structure. At the specified span and the specified height-to-span ratio, the eigenfrequency of the structure has a minor increase with the increase of the thickness and the grid division frequency of the reticulated shell structure. The partial double-layer reticulated shell structures have less stability compared with double-layer reticulated shell structures, but more stability in comparison with single-layer reticulated shell structures. The 1/6 partial double-layer reticulated shell structure has a best performance-to-price ratio. In other words, it has a higher buckling load, with smaller material consumption, compared with other partial double-layer reticulated shell structures. It is proposed to adopt the 1/6 partial double-layer reticulated shell structure in engineering if a double layer reticulated shell structure is required.     

Ultimate capacity of battened columns composed of four equal slender angles

Cold-formed steel structural members play a great role in modern steel structures due to their high strength and light weight. The behavior and strength of battened column members composed of slender angle sections are mainly governed by local buckling of angle legs or torsional buckling of the angle between batten plates. Moreover, local buckling depends on the interaction between the width–thickness ratio of angle leg, overall slenderness ratio of angle between batten plates and overall slenderness of column. Theoretical study has been carried out by a nonlinear material and geometrical finite element model. Numerous cases of slender battened column sections having different width–thickness angle leg ratios, overall slenderness ratios between batten plates and overall slenderness ratios are chosen in this study. Complete ultimate strength curves are drawn and different failure modes are studied by taking different member lengths, which produce local or torsional buckling of single angles between batten plates or overall buckling of the member. Empirical equations for the effect of shear deformation factor and the ultimate axial load capacities of members formed of battened slender angle sections are proposed. Strengths of axially loaded battened members predicted using finite element as well as the proposed empirical equations is compared with the design strengths obtained using North American and European codes. It is concluded that the design strengths predicted by North American and European codes are generally conservative, and these design rules have been shown to be reliable using reliability analysis.     

实腹圆弧钢拱的平面内稳定极限承载力设计理论及方法

拱的平面内稳定极限承载力设计一直没有成熟的规范指导。本文用有限壳单元模型先分析了工形截面两铰圆弧钢拱的平面内弹性屈曲性能,与拱的经典屈曲理论作了对比,指出了必须同时考虑长细比和矢跨比对屈曲荷载的影响。然后分析了两铰圆弧钢拱受静水压力和其它荷载作用下的弹塑性屈曲性能,指出了典型破坏机理为拱两侧1/4跨附近形成塑性铰导致结构失效。利用拱的弹性屈曲荷载定义了拱的正则化长细比,用Perry-Robertson公式的形式,建立了拱的稳定系数与正则化长细比的关系,提出了受静水压力的两铰圆弧钢拱的平面内稳定极限承载力设计方法,并用轴力和弯矩的两项相关公式提出了受其它荷载作用下的平面内稳定极限承载力设计方法。     

常州市体育馆椭圆抛物面弦支穹顶稳定性研究

常州市体育馆椭圆抛物面钢屋盖采用由Levy索杆系和单层网壳构成的弦支穹顶结构,与已研究的常规弦支穹顶相比,其具有体量大,矢跨比高和外形为椭圆抛物面的特点。将弦支穹顶与单层网壳进行稳定性对比研究,包括构件屈曲、线性屈曲和几何非线性屈曲等,分析了高矢跨比弦支穹顶中索杆系的作用以及对结构设计起控制作用的破坏形式。研究结果表明,索杆系增加了弦支穹顶的整体性,降低了其对初始几何缺陷的敏感性,但对结构刚度、基本自振周期和模态、构件屈曲荷载、线性屈曲荷载、无初始缺陷的非线性屈曲荷载、屈曲模态等影响不大。高矢跨比弦支穹顶仍对初始缺陷较为敏感,稳定性仍是结构设计控制因素之一。此外,由于椭圆抛物面外形,活荷载布置形式对结构屈曲模态影响较大,且满跨活荷载并不一定是最不利的活荷载布置形式。     

压弯钢构件在循环荷载作用下的非线性弯扭屈曲

本文根据非线性有限元的基本理论,采用基于修正的拉格朗日法描述的八节点超参数壳体单元,考虑几何非线性和材料非线性,结合混合强化本构关系,编制了非线性有限元计算程序。对压弯钢构件在循环荷载作用下的弹塑性弯扭屈曲进行计算机模拟,系统分析了H形截面压弯钢构件的滞回特性,以及翼缘宽厚比、腹板高厚比、构件轴压比和长细比对压弯钢构件弯扭屈曲的影响规律。通过对计算结果的比较,提出了强烈地震条件下,H形截面压弯钢构件在循环荷载作用下保持整体稳定,满足延性要求,具有较高屈曲后强度的长细比和板件宽厚比限值。     

Buckling of rings in column-supported bins and tanks

Theories for the out-of-plane buckling of rings under uniform circumferential compression are well established. However these theories are not applicable to rings in column-supported bins where the circumferential stress in the ring varies significantly over the cross-section and around the circumference.

This paper deals with the out-of-plane buckling of annular plate rings in column-supported bins and tanks. The stress distributions in such rings are first examined using a finite element shell analysis. A closed-form solution for the buckling of rings under non-uniform circumferential stresses is then derived. Numerical results from the closed-form solution are compared with those from a finite element shell buckling analysis, and close agreement is found. The significant effect of stress non-uniformity on the buckling predictions is demonstrated. Finally, simplified equations are given which are suitable for structural design purposes, and which closely model the predictions of the more rigorous solution.     

交叉加劲钢板深梁弹性屈曲分析

以交叉加劲钢板深梁为研究对象,利用有限元软件ANSYS分析其弹性屈曲性能,讨论了抗弯刚度比、跨高比、钢板深梁厚度对其弹性屈曲性能的影响;考虑钢板深梁在钢框架的弯剪受力特性,根据板的经典理论建立了交叉加劲钢板深梁屈曲荷载计算公式,提出了等效屈曲系数。结果表明:交叉加劲钢板深梁的临界屈曲荷载随抗弯刚度比增大而增大,但达到门槛刚度比后,增大幅度急剧减小,得到门槛刚度比约为10;临界屈曲荷载随跨高比和板厚的减小而减小,等效屈曲系数随板厚减小而增大;等效屈曲系数与跨高比关系曲线由二次抛物线形向波浪形渐变,交叉加劲钢板深梁受力特性由剪切主导向弯曲主导过渡。     

双参数弹性地基上的FGM壳体的热屈曲性能

分析双参数弹性地基上的FGM壳体的热屈曲性能。根据幂律分布,从厚度方向对各个构件的材料性能进行分级。周边的弹性介质被模拟为Pasternak弹性地基。在假定基本关系之后,对温度荷载下及位于双参数弹性地基上的FGM截顶圆锥壳体的稳定性和相容方程式进行分析。通过求解特征值,得到沿壳体厚度方向非线性分布的温度荷载下的基于或不基于弹性地基上的FGM截顶圆锥壳体临界温差。作为一个特殊案例,提出基于或不基于弹性地基上的FGM截顶圆锥壳体的方程。为了保证目前研究的正确性,详细地评价了临界温度的收敛性。     

钢管自应力自密实高强混凝土中长柱受压性能试验研究

为提高钢管内混凝土的密实度,减小混凝土的收缩,以保证钢管与混凝土更好地工作,满足实际工程需要,文中提出采用钢管自应力自密实高强混凝土柱,考虑初始自应力、长细比和混凝土强度等因素的影响,设计制作16个钢管自应力自密实高强混凝土中长柱试件,通过轴心受压试验,考察试件的破坏形态,实测试件的荷载-纵向变形曲线、荷载-挠度曲线和极限承载力,分析了各参数对试件轴心受压力学性能的影响。研究表明：大部分中长柱的破坏形态均为弯曲失稳破坏;初始自应力提高5MPa,钢管自应力自密实高强混凝土中长柱极限承载力提高19%,并改善了延性;长细比由5增大至12,试件的极限承载力降低16.9%;混凝土强度提高36.3%,钢管自应力自密实高强混凝土中长柱极限承载力提高16.3%。基于试验结果,参考国内相关规范,建立钢管自应力自密实高强混凝土中长柱轴心受压稳定承载力计算公式,可供工程设计参考。