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.

A MICROFLUIDIC METHOD TO MEASURE DIFFUSION IN HYDROGELS

A novel microfluidic method is proposed for studying diffusion of small molecules in a hydrogel. Microfluidic devices were prepared with semi-permeable microchannels defined by crosslinked poly(ethylene glycol) (PEG). Uptake of dye molecules from aqueous solutions flowing through the microchannels was observedoptically and diffusion of the dye into the hydrogel was quantified. To complement the diffusion measurements from the microfluidic studies, nuclear magnetic resonance(NMR) characterization of the diffusion of dye in the PEG hydrogels was performed. The diffusion of small molecules in a hydrogel is relevant to applications such asdrug delivery and modeling transport for tissue-engineering applications. The diffusion of small molecules in a hydrogel is dependent on the extent of crosslinking within the gel, gel structure, and interactions between the diffusive species and the hydrogel network. These effects were studied in a model environment (semi-infinite slab) at the hydrogelfluid boundary in a microfluidic device. The microfluidic devices containing PEG microchannels were fabricated using photolithography. The unsteady diffusion of small molecules (dyes) within the microfluidic device was monitored and recorded using a digital microscope. The information was analyzed with techniques drawn from digital microscopy and image analysis to obtain concentration profiles with time. Using a diffusion model to fit this concentration vs. position data, a diffusion coefficient was obtained. This diffusion coefficient was compared to those from complementary NMR analysis. A pulsed field gradient (PFG) method was used to investigate and quantify small molecule diffusion in gradient (PFG) method was used to investigate and quantify small molecule diffusion in hydrogels. There is good agreement between the diffusion coefficients obtained from the microfluidic methods and those found from the NMR studies. The microfluidic approachused in this research enables the study of diffusion at length scales that approach those of vasculature, facilitating models for studying drug elution from hydrogels in blood-contacting applications.