The Modified Direct Analysis Method: an Extension of the Direct Analysis Method

The purpose of this research project is to study an innovative method for the stability assessment of structural steel systems, namely the Modified Direct Analysis Method (MDM). This method is intended to simplify an existing design method, the Direct Analysis Method (DM), by assuming a sophisticated second-order elastic structural analysis will be employed that can account for member and system instability, and thereby allow the design process to be reduced to confirming the capacity of member cross-sections. This last check can be easily completed by substituting an effective length of KL = 0 into existing member design equations. This simplification will be particularly useful for structural systems in which it is not clear how to define the member slenderness L/r when the laterally unbraced length L is not apparent, such as arches and the compression chord of an unbraced truss. To study the feasibility and accuracy of this new method, a set of 12 benchmark steel structural systems previously designed and analyzed by former Bucknell graduate student Jose Martinez-Garcia and a single column were modeled and analyzed using the nonlinear structural analysis software MASTAN2. A series of Matlab-based programs were prepared by the author to provide the code checking requirements for investigating the MDM. By comparing MDM and DM results against the more advanced distributed plasticity analysis results, it is concluded that the stability of structural systems can be adequately assessed in most cases using MDM, and that MDM often appears to be a more accurate but less conservative method in assessing stability.

Ability of the PM3 Quantum Mechanical Method to Model Intermolecular Hydrogen Bonding between Neutral Molecules

The PM3 semiempirical quantum-mechanical method was found to systematically describe intermolecular hydrogen bonding in small polar molecules. PM3 shows charge transfer from the donor to acceptor molecules on the order of 0.02-0.06 units of charge when strong hydrogen bonds are formed. The PM3 method is predictive; calculated hydrogen bond energies with an absolute magnitude greater than 2 kcal mol-' suggest that the global minimum is a hydrogen bonded complex; absolute energies less than 2 kcal mol-' imply that other van der Waals complexes are more stable. The geometries of the PM3 hydrogen bonded complexes agree with high-resolution spectroscopic observations, gas electron diffraction data, and high-level ab initio calculations. The main limitations in the PM3 method are the underestimation of hydrogen bond lengths by 0.1-0.2 for some systems and the underestimation of reliable experimental hydrogen bond energies by approximately 1-2 kcal mol-l. The PM3 method predicts that ammonia is a good hydrogen bond acceptor and a poor hydrogen donor when interacting with neutral molecules. Electronegativity differences between F, N, and 0 predict that donor strength follows the order F > 0 > N and acceptor strength follows the order N > 0 > F. In the calculations presented in this article, the PM3 method mirrors these electronegativity differences, predicting the F-H- - -N bond to be the strongest and the N-H- - -F bond the weakest. It appears that the PM3 Hamiltonian is able to model hydrogen bonding because of the reduction of two-center repulsive forces brought about by the parameterization of the Gaussian core-core interactions. The ability of the PM3 method to model intermolecular hydrogen bonding means reasonably accurate quantum-mechanical calculations can be applied to small biologic systems.

Study of the Compressive Strength of Aluminum Curved Elements

Currently, the Specification for Aluminum Structures (Aluminum Association, 2010) shows thin-walled aluminum plate sections with radii greater than eight inches have a lower compressive strength capacity than a flat plate with the same width and thickness. This inconsistency with intuition, which suggests any degree of folding a plate should increase its elastic buckling strength, inspired this study. A wide range of curvatures are studied—from a nearly flat plate to semi-circular. To quantify the curvature, a single non-dimensional parameter is used to represent all combinations of width, thickness and radius. Using the finite strip method (CU-FSM), elastic local buckling stresses are investigated. Using the ratio of stress values of curved plates compared to flat plates of the same size, equivalent plate-buckling coefficients are calculated. Using this data, nonlinear regression analyses are performed to develop closed form equations for five different edge support conditions. These equations can be used to calculate the elastic critical buckling stress for any curved aluminum section when the geometric properties (width, thickness, and radius) and the material properties (elastic modulus and Poisson’s ratio) are known. This procedure is illustrated in examples, each showing the applicability of the derived equations to geometries other than those investigated in this study and also providing comparisons with theoretically exact numerical analysis results.

Effective Length K-Factors For Flexural Buckling Strengths Of Web Members In Open Web Steel Joists

Open web steel joists are designed in the United States following the governing specification published by the Steel Joist Institute. For compression members in joists, this specification employs an effective length factor, or K-factor, in confirming their adequacy. In most cases, these K-factors have been conservatively assumed equal to 1.0 for compression web members, regardless of the fact that intuition and limited experimental work indicate that smaller values could be justified. Given that smaller K-factors could result in more economical designs without a loss in safety, the research presented in this thesis aims to suggest procedures for obtaining more rational values. Three different methods for computing in-plane and out-of-plane K-factors are investigated, including (1) a hand calculation method based on the use of alignment charts, (2) computational critical load (eigenvalue) analyses using uniformly distributed loads, and (3) computational analyses using a compressive strain approach. The latter method is novel and allows for computing the individual buckling load of a specific member within a system, such as a joist. Four different joist configurations are investigated, including an 18K3, 28K10, and two variations of a 32LH06. Based on these methods and the very limited number of joists studied, it appears promising that in-plane and out-of-plane K-factors of 0.75 and 0.85, respectively, could be used in computing the flexural buckling strength of web members in routine steel joist design. Recommendations for future work, which include systematically investigating a wider range of joist configurations and connection restraint, are provided.

Tributary and Mainstem Benthic Macroinvertebrate Communities Linked By Direct Dispersal and Indirect Habitat Alteration

Benthic communities in tributary-mainstem networks might interact via downstream drift of invertebrates or material from tributaries and adult dispersal from the mainstem. Depending on the strength of these interactions, mainstem downstream communities are expected to be more similar to tributary communities due to drift or habitat alteration. Communities not connected by flow are expected to be similar due to adult dispersal but decreasing in similarity with distance from the mainstem. We investigated interactions between invertebrate communities of a 7th order river and 5th order tributary by comparing benthic community structure in the river upstream and downstream of the tributary confluence and upstream in the tributary. Non-metric multidimensional scaling showed invertebrate communities and habitat traits from river locations directly downstream of the tributary clustered tightly, intermediate between tributary and mid-channel river locations. In addition, Bray-Curtis dissimilarity increased between the mainstem and tributary with distance upstream in the tributary. Our results indicate that similarities between mainstem and tributary communities are potentially caused by direct mass effects from tributary to downstream mainstem communities by invertebrate drift and indirect mass effects by habitat restructuring via material delivery from the tributary, as well as potential effects of adult dispersal from the river on proximal tributary communities.