---

Abstract In this paper the effect of two types of common initial geometric imperfections on the reliability of steel frames is investigated. These imperfections are the coordinates of connection nodes and crookedness of members. Most finite element reliability analyses in past literature neglect this source of uncertainty. For this purpose static nonlinear pushover structural analysis is used from which reliabilities are estimated based on FORM and Monte Carlo sampling methods. Furthermore to investigate the importance of uncertain parameters, reliability sensitivity analysis is performed by use of the direct differentiation method which has been implemented in the object oriented software framework Open Sees. It is demonstrated that some of these geometric imperfections have significant influence on reliability assessment of steel frames.

---

Abstract: The effect of two types of common initial geometric imperfections on the reliability of steel frames was investigated. These imperfections are the coordinates of connection nodes and crookedness of members. Most of the finite element reliability analyses in the past haveneglect this source of uncertainty. For this purpose, static non-linear pushover structural analysis was used in the present work from which reliabilities were estimated based on the FORM and Monte Carlo sampling methods. Furthermore, to investigate the importance of uncertain parameters, reliability sensitivity analysis was performed by the use of direct differentiation method, which was implemented in the object oriented framework of OpenSees software. It was demonstrated that some of these geometric imperfections have significant influence on the reliability assessment of steel frames.

---

When a cylindrical shell subject to a compressive load, because of various imperfections happened during processes as manufacturing, handling, assembling and machining, buckling occurs in loads lower than corresponding static failure load. Still many of cylindrical shell structures are designed against buckling based on experimental data introduced by NASA SP-8007 as conservative lower bound curves. In the manuscript, non-linear methods of Modified Linear Buckling Modeshape Imperfections (M-LBMI) and Simple Perturbation Load Imperfections (SPLI) for composite cylindrical shell with and without cutout are investigated. In order to evaluate the numerical results composite cylinder with stacking sequence of [90/+23/-23/90] are manufactured by using filament winding method and buckling tests are performed under axial loading. Non-linear numerical results in cylinder with and without cutout are close together and have good agreement with experimental data. . It was concluded that buckling load predicted by SPLI and modified LBMI method on cylinder with cutout is close to result of case without apply geometric imperfections. In summary, it was concluded that cutout on the cylinder body act as an imperfection to trigger buckling of the structures so there is no need to apply geometrical imperfections.

---

Steel cylindrical silos are key storages in many industries. They can be composed of flat or corrugated sheets. To construct these structures, steel sheets may be welded or bolted to each other. This study addresses steel welded silos with flat sheets. Different loads, such as, filling and discharge loads, wind load, seismic load and thermal loads should be considered in design of silos. Nevertheless, during the life cycle of a silo, filling and discharge of particulate solids exert the most frequent loads on the silo walls. Due to larger values of discharge pressures as compared with those of filling pressures, discharge loads are primarily considered for structural design of silos.
Due to small wall thickness, buckling resistance is of vital importance in steel silos design. Ensiled materials exert normal pressures and frictional tractions on silo walls. Accordingly, during discharge process, meridional buckling resistance of shell walls concurrent with internal pressures should be assessed. It is well known that buckling strength is very sensitive to geometric imperfections in shell structures. In welded silos, the most regular and well-defined imperfection is local depressions existing in circumferential welded joints due to the plate rolling process and shrinkage of the weld. The assumed shape given for this type of imperfection in the literature were adopted throughout the paper.
Eurocode as the most advanced and pioneering standard on the design of steel silos, provides a hand design procedure for buckling evaluation of steel silos under discharge loads. To assess the procedure, a full suite of computational shell buckling calculations was performed with special emphasis on the effect of aforementioned geometric imperfection. A slender, an intermediate slender and a squat silo were considered for the assessments. Linear elastic Bifurcation Analysis with Imperfections (LBIA) and Geometrically and Materially Non-linear Analysis with Imperfections (GMNIA) were carried out for each structure. Sample silos were loaded in accordance to the pressure distribution proposed in the Eurocode. By assuming strake’s height of 2 meters, uniform depressions were simulated in circumferential welded joints of each silo. Three different Fabrication Quality Classes (FQCs) denoted by FQC A, B and C in a descending order from Excellent to Normal Class were introduced in the Standard. The imposed depression amplitudes were calculated in accordance to FQCs of the silos.
Considering the results obtained, the LBIA buckling modes show several circumferential buckling waves at the first welded joint of each silo from the base. Lowering the FQC leads to the decrease in number of circumferential waves and to the development of buckling waves at the location of second and third welded joints. Nevertheless, the more sophisticated GMNIA analyses predict elastic-plastic buckling mode in the form of diamond pattern concentered at the first welded joint of the silos from the base, irrespective of selected FCQ. However, for the slender silo the two upper welded joints are also interact during buckling. With respect to the design buckling resistance ratios (r_Rd) obtained by hand calculations and through non-linear analyses, the former method has predicted r_Rd values in the range from 13% to 32% lower than those of GMNIA. Therefore, hand design procedure of Eurocode produced satisfactory results, without high conservatism. However, more researches on this issue can enhance the reliability of conclusions made with respect to the Eurocode provisions.