Curved panels constructed of laminated graphite-epoxy composite material are of potential interest in airframe fuselage applications. An understanding of structural response at elevated temperatures is required for anticipated future high speed aircraft applications. This study concentrates on the response of unstiffened, curved composite panels subjected to combinations of thermal and mechanical loading conditions. Mechanical loading is due to compressive end-shortening and thermal loading is due to a uniform temperature increase. Thermal stresses, which are induced by mechanical restraints against thermal expansions or contractions, cause buckling and postbuckling panel responses. Panels with three different lamination sequences are considered, including a quasi-isotropic laminate, an axially soft laminate, and an axially stiff laminate. These panels were chosen because they exhibit a range of stiffnesses and a wide variation in laminate coefficients of thermal expansion. The panels have dimensions of 10 in. by 10 in. with a base radius of 60 in. The base boundary conditions are clamped along the curved ends, and simply supported along the straight edges. Three methods are employed to study the panel response, including a geometrically nonlinear Rayleigh-Ritz solution, a finite element solution using the commercially available code STAGS, and an experimental program. The effects of inplane boundary conditions and radius of curvature are studied analytically, along with consideration of order of application in combined loading. A substantial difference is noted in the nonlinear load vs. axial strain responses of panels loaded in end-shortening and panels loaded with uniform temperature change, depending on the specific lamination sequence, boundary conditions, and radius of curvature. Experiments are conducted and results are presented for both room temperature end-shortening tests and elevated temperature tests with accompanying end-shortening. The base finite element model is modified to include measured panel thicknesses, boundary conditions representative of the experimental apparatus, measured initial geometric imperfections, and measured temperature gradients. With these modifications, and including an inherent end displacement of the panel present during thermal loading, good correlation is obtained between the experimental and numerically predicted load vs. axial strain responses from initial loading through postbuckling. / Ph. D.

Presently, the industry accepted method for the determination of the governing buckling strength for cold-formed purlins supporting a standing seam metal roof system is the 1996 AISI Specification for the Design of Cold-Formed Steel Structural Members, which contains provisions for local and lateral buckling. Previous research has determined that the AISI provisions for local buckling strength predictions of cold-formed purlins are highly unconservative and that the AISI provisions for lateral buckling strength predictions of cold-formed purlins are overly conservative. Therefore, a more accurate "hand" method is needed to predict the buckling strengths of cold-formed purlins supporting standing seam roof systems. The primary objective of this study is to investigate the accuracy of the Hancock Method, which predicts distortional buckling strengths, as compared to the 1996 AISI Specification provisions for local and lateral buckling. This study used the experimental results of 62 third point laterally braced tests and 12 laterally unbraced tests. All tests were simple span, cold-formed Z-section supported standing seam roof systems. The local, lateral, and distortional buckling strengths were predicted for each test using the aforementioned methods. These results were compared to the experimentally obtained data and then to each other to determine the most accurate strength prediction method. Based on the results of this study, the Hancock Method for the prediction of distortional buckling strength was the most accurate method for third point braced purlins supporting standing seam roof systems. In addition, a resistance factor was developed to account for the variation between the experimental and the Hancock Method's predicted strengths. / Master of Science

Many structures are sensitive to initial imperfections, sometimes leading to a great decrease in buckling load. Koiter showed that the effect of initial imperfections is largely determined by the initial post-buckling behavior of the perfect structure. The present work seeks to implement Koiter’s method of asymptotic post-buckling analysis on a finite element program Engineering Analysis Language (EAL). EAL is based on engineering strain measures. It is shown via examples that the predicted post-buckling behavior of a structure for engineering strain measure is approximately the same as that for Green’s strain measure provided the strains are small. To characterize the post-buckling behavior by Koiter’s method in the finite element form, the linear and incremental stiffness matrices are required. These matrices comprise the tangent stiffness matrix. As EAL uses the modified Newton-Raphson procedure to solve nonlinear structures, it calculates the tangent stiffness. The first and second order incremental stiffnesses are extracted by partial differentiation of the tangent stiffness using a second order central difference scheme. The linear stiffness is directly given by the EAL processor ”K”. These stiffnesses are then used to get the post-buckling load-displacement behavior close to the bifurcation point. Numerical results for the initial post-buckling behavior are obtained for truss and frame structures using the Koiter’s analysis procedure on EAL. It is compared to the nonlinear load-displacement behavior of the structures with small initial imperfections. The post-buckling load-displacement behavior for a knee frame is also compared to the behavior obtained experimentally by Roorda [19] and analytically by Koiter [13]. The asymptotic analysis procedure has given good asymptotic post-buckling results. / Master of Science

The buckling constant for neutron moderators in the shape of an elliptic cylinder, hemisphere, and"piggy-back" cylinder has been determined by experimental measurements using paraffin as a moderator. The pulsed neutron sources technique was used throughout the work; a fast neutron burst of short duration was injected into regular paraffin shapes (cylinders with diameter and height ratio equal approximately to one). An empirical curve of decay constant of the neutron population versus the buckling was obtained. The measured decay constant, λ, was fitted by the method of least square to a parabola in B² of the form: λ=Σ_av+ B²D - CB⁴ where λ= the decay constant B² = the buckling constant Σ_a = the macroscopic absorption cross section v = the neutron velocity D = diffusion coefficient C = diffusion cooling coefficient The resulting values of the diffusion parameters are: Σ_a v = 4858 ± 162 sec⁻¹ D = 25911 ± 202 sec⁻¹ cm² C = 1186 ± 2558 sec⁻¹ cm⁴ By measuring the decay constant, the buckling of the moderators with irregular shapes were determined from the above parameters. The result was in general accord with the theoretical approximations for such shapes. / Master of Science

The first purpose of the present paper is to provide an elastic theory from which problems involving coupling may be approached. Potential energy and equilibrium expressions will be derived for these are the components of the theory which are lacking. The potential energy expression may be used either in small- or large-deflection analysis. Equations of equilibrium are presented for both small- and large-deflection theory. The second purpose of the present paper is to determine the effect of coupling on deflections and buckling of a simple supported anisotropic plate in compression. A small deflection analysis of this problem is made using the theory presented herein. No large deflection analysis is attempted; however, an estimation of the large deflection effect of coupling is made. The electric theory presented herein forms a basis from which problems involving coupling may be treated. The significance of coupling is most apparent in problems which would involve stability considerations in the absence of coupling. The presence of deflections due to coupling prior to reaching the uncoupled buckling load forces the problem to be treated asa one of deflections rather than stability. Coupling has a general detrimental effect upon this type of problem in that it lowers the load at which deflections grow rapidly (that is, buckling in the uncoupled case). The effect of coupling on the buckling of plates of equal bending stiffnesses in their two orthogonal directions becomes negligible as the aspect ratio of the plate becomes large. Some lateral deflection prior to buckling will occur, however, even for large aspect ratios. The general anisotropic plate is considered in the small-deflections solution to the differential equation of equilibrium. Computations were made for cases in which the bending stiffness were equal. The equations and methods are applicable to cases in which the bending stiffness are not equal. / Master of Science

Tapered beams and columns are often used in single story gable framed steel buildings for reasons of economy. By varying the resistance to bending in similar proportion to the bending moments, more economical structures can be obtained. The beam and column connection, or knee area, is generally subject to the greatest bending moments. It is therefore comprised of the deepest sections of the tapered members, which also possess the least resistance to shear buckling. The web element's stress distribution in this region of relatively complicated geometry is unknown. For this reason, web stiffening plates are commonly used to brace the slender web elements against elastic shear buckling. The design and proper installation of these relatively small elements, while proven to be effective, is also costly. Because it is desirable to remove the stiffeners, the shear behavior of unstiffened tapered members near the moment connection was the primary focus of this study. Four knee area specimens were tested to failure under simulated gravity load conditions. The specimens were analyzed according to the AISC shear provisions for prismatic members. The appropriateness of a modified shear force, which accounts for the influence of inclined flanges, and the role of initial web imperfections were examined as well. Finally an analysis method which most consistently produces conservative results is proposed. / Master of Science

The present paper studied the buckling phenomena of membranes under tensile load with and without central crack.  The studies of fracture mechanics are tested within certain conditions of membranes. The tensile test has been performed with Al-foil in different crack lengths, i.e. 0 mm, 12.5 mm, 25 mm and 50 mm. The numerical analysis has been carried out by Finite Element Analysis (FEA) and comparing with the theoretical and experimental results.  In this paper, the critical buckling behavior is tested, validated and compared. Same observation of patterns in experiments and the simulation are found. The influence of scale factor for imperfection setting are tested.

Civil Engineering thin cylindrical shells such as silos and tanks are normally subjected to axial compression that arises from a stored solid, wind, earthquake, self-weight or roof loads. The walls of these shells are very thin, generally of the order of 6 to 25 mm, and massively less than the radius, which is typically 5 to 30 m. They are thus very thin shell structures, like those of rockets, spacecraft, motor vehicles and aircraft. The commonest failure mode is elastic buckling under axial compression. It has long been known that the buckling strength of a thin cylindrical shell under axial compression is very sensitive to tiny deviations of geometry, reducing the buckling strength to perhaps 10 or 20% of the value for the perfect structure. A normal internal pressure usually accompanies the axial compression, caused by stored granular solids or fluids. At relatively low pressures, the elastic buckling strength under axial compression rises, but an elastic-plastic buckling phenomenon intervenes at higher pressures, causing a dramatic decrease in buckling resistance associated with an elephant’s foot collapse mode. To construct such large shells, the fabrication technique is generally the assembly of many rolled plates or panels, joined by short longitudinal welds and continuous circumferential welds. The process of welding produces a distinctive geometric imperfection form at each weld joint, which in turn is extremely detrimental to the shell axial buckling carrying capacity. The strength may be further reduced by slight misalignments between adjacent panels, or in bolted construction, by vertical and horizontal lap splices. Due to the pattern of loading, both the axial compression and internal pressure increase progressively down the wall. Accordingly, practical construction usually uses a stepped wall, formed from panels of uniform thickness, but with larger thicknesses at lower levels. Since the loading varies smoothly, but each panel has constant thickness, the critical location for buckling lies at the base of a panel. But the greater thickness of the lower panel can usefully enhance the buckling strength of the critical panel above it. This thesis presents an extensive computational study that examines all the above influences, divided into chapters that are outlined here. A full exploration of the effect of the cylinder length on the perfect and imperfect elastic buckling strength is presented in Chapter 3. In Chapter 4, the elastic-plastic buckling resistance of imperfect cylinders is described, including strain hardening. These lead to many capacity curves, for which the key parameters are extracted. The effect of internal pressure on the buckling resistance of imperfect elastic cylinders is explored in Chapter 5. Chapter 6 studies the effect of high pressures that produce elastic-plastic elephant’s foot buckling at circumferential welds in imperfect shells. Next, a step change in plate thickness is studied in Chapter 7 for imperfect butt jointed cylinders with and without the internal pressure. Chapter 8 presents an exploration of the effect of plate misalignments at a circumferential joint, as well as the full misalignment of a circumferential lap joint in bolted construction. These are investigated in both the elastic and elastic-plastic domains. The entire thesis is conceived in the context of EN 1993-1-6 (2007) and the ECCS Recommendations on Shell Buckling (2008). This research has shown significant weaknesses in both the concepts and the detailed rules of these standards. Many conditions are found where either the standard is unnecessarily conservative, or its safety margin may be too low. Thus, some new provisions are proposed for each of the above practical problems. These are expected to provide useful knowledge for the design of such structures against buckling in the future.

The aim of this thesis is to investigate buckling, post-buckling behaviors and failure characteristics of composite laminated plates under compressive loading with the help of finite element method and experiments. In the finite element analyses, eigen value extraction method is used to determine the critical buckling loads and nonlinear Riks and Newton-Raphson methods are employed to obtain post-buckling behaviors and failure loads. The effects of geometric imperfection amplitude on buckling and post-buckling are discussed. Buckling load, post buckling loaddisplacement relations, out of plane displacements and end shortening of the plates are determined numerically. Furthermore, the numerical results are compared with experimental findings for two different laminates made of woven fabric and unidirectional tapes where buckling, post-buckling behavior and structural failure of laminated plates were determined. The comparisons show that there is a good agreement between numerical and experimental results obtained for buckling load and post-buckling range. However, 15 % - 22 % differences are predicted between the experimental and numerical results for failure of laminates made of woven fabric whereas the laminates with uni-directional tapes show good agreement.

Slender structures are elegant aesthetically. The insufficiency in knowledge of the real resistance to buckling of very slender reinforced concrete columns leads to an exaggeration of the sizes of the columns. _The examples of concrete compression members cited and constructed in Industry on a global basis suggest that very slender columns have inherent safety both from the point of view of the ultimate strength and stability. The strengths of columns given. by the British codes would seem to be exceeded by many of the long slender reinforced concrete columns and struts which have been used Internationally. Both the theoretical and the experimental short term investigations have been carried out to establish the behaviour of hinged, very slender reinforced concrete columns at various stages'of axial loading. Forty three very slender reinforced concrete columns of two different square cross sections with two sizes of longitudinal reinforcements with lateral ties were cast. Slenderness rates, L A, were varied from 30 to 79. Special factors were obtained to relate the actual modulus of elasticity of concrete in columns at buckling failure to a knowledge of the initial modulus of elasticity of concrete in control cylinder specimens. Both theoretical and experimental graphs of load against moment, made dimensionless for critical sections of columns have been obtained. Dimensionless load-moment interaction diagrams using material failure as the criterion have been superimposed on these graphs to show considerable inherent material strength of the tested columns near buckling collapse failures. A theory using the fundamental approach has, been developed to predict the deflected shape and moments along the, heights of the columns at various stages of loading. The proposed theory predicts with good correlations the experimental deflections and moments of any loading stages of the columns. The theory has been used to obtain the required variables, to arrive at the initial predicted design loads of the investigated columns. Good correlations of the moments derived from observed strains have also been obtained. The developed theory predicts satisfactorily the buckling collapse loads of the columns. Although the theory has been derived for axially I loaded very slender reinforced concrete-columns, it seems to accept satisfactorily eccentricities of up to about 10 mm. This was confirmed after extensive comparisons of the theoretical buckling collapse loads with the applicable tests of other authors. Creep In the columns investigated was discovered to be one of the major factors for serious consideration. This was conclusively revealed from the observations on the last two very long term creep tests on columns. The actual safe sustained loads for these very slender columns of slenderness ratios, L/H, between 40 and 79 seem to be between 33% and 19% of the short term buckling collapse loads. The reduced modulus approach to predict the safe long term sustained loads seems to give reasonable values for L/H ratios of 40 and 50. The recommendations given for the proposed design of very slender reinforced concrete columns seem to be adequate and simple to use in practice. They are further simplified by the derivation of two equations for the reduction factors, R, for the slenderness ratios between 36 and 40 and between 40 and 79 respectively. The investigation has proved that very slender reinforced concrete columns are very dangerous structural members, as they tend to have violent buckling failures. Nevertheless, It must be prudent not to design against disaster at any cost. This Investigation seemed to have enhanced considerably knowledge of the design of very slender reinforced concrete columns.