Benjamin W. Schafer

Computational modeling of cold-formed steel: characterizing geometric imperfections and residual stresses

Thin-walled, cold-formed steel members exhibit a complicated post-buckling regime that is difficult to predict. Today, advanced computational modeling supplements experimental investigation. Accuracy of computational models relies significantly on the characterization of selected inputs. No consensus exists on distributions or magnitudes to be used for modeling geometric imperfections and for modeling residual stresses of cold-formed steel members. In order to provide additional information existing data is collected and analyzed and new experiments performed. Simple rules of thumb and probabilistic concepts are advanced for characterization of both quantities. The importance of the modeling assumptions are shown in the examples. The ideas are summarized in a preliminary set of guidelines for computational modeling of imperfections and residual stresses.

Mechanics of Flexible Needles Robotically Steered through Soft Tissue

The tip asymmetry of a bevel-tip needle results in the needle naturally bending when it is inserted into soft tissue. This enables robotic needle steering, which can be used in medical procedures to reach subsurface targets inaccessible by straight-line trajectories. However, accurate path planning and control of needle steering require models of needle-tissue interaction. Previous kinematic models required empirical observations of each needle and tissue combination in order to fit model parameters. This study describes a mechanics-based model of robotic needle steering, which can be used to predict needle behavior and optimize system design based on fundamental mechanical and geometrical properties of the needle and tissue. We first present an analytical model for the loads developed at the tip, based on the geometry of the bevel edge and material properties of soft-tissue simulants (gels). We then present a mechanics-based model that calculates the deflection of a bevel-tipped needle inserted through a soft elastic medium. The model design is guided by microscopic observations of needle-gel interactions. The energy-based formulation incorporates tissue-specific parameters, and the geometry and material properties of the needle. Simulation results follow similar trends (deflection and radius of curvature) to those observed in experimental studies of robotic needle insertion.

Nuclear Envelope Breakdown Requires Overcoming the Mechanical Integrity of the Nuclear Lamina

In prophase cells, lamin B1 is the major component of the nuclear lamina, a filamentous network underlying the nucleoplasmic side of the nuclear membrane, whereas lamin A/C is dissociated from the scaffold. In vivo fluorescence microscopy studies have shown that, during the G2/M transition, the first gap in the nuclear envelope (NE) appears before lamin B1 disassembly and is caused by early spindle microtubules impinging on the NE. This result suggests that the mechanical tearing of the NE by microtubules plays a central role to the progression of mitosis. To investigate whether this microtubule-induced NE deformation is sufficient for NE breakdown, we assess the mechanical resilience of a reconstituted lamin B1 network. Quantitative rheological methods demonstrate that human lamin B1 filaments form stiff networks that can resist much greater deformations than those caused by microtubules impinging on the NE. Moreover, lamin B1 networks possess an elastic stiffness, which increases under tension, and an exceptional resilience against shear deformations. These results demonstrate that both mechanical tearing of the lamina and biochemical modification of lamin B1 filaments are required for NE breakdown.

Direct Strength Method for Design of Cold-Formed Steel Columns with Holes

In this paper, design expressions are derived that extend the American Iron and Steel Institute (AISI) direct strength method (DSM) to cold-formed steel columns with holes. For elastic buckling-controlled failures, column capacity is accurately predicted by using existing DSM design equations and the cross-section and global elastic buckling properties calculated including the influence of holes. For column failures in the inelastic regime, in which strength approaches the squash load, limits are imposed to restrict column capacity to that of the net cross section at a hole. The proposed design expressions are validated with a database of existing experiments on cold-formed steel columns with holes, and more than 200 nonlinear finite-element simulations that evaluate the strength prediction equations across a wide range of hole sizes, hole spacings, hole shapes, and column dimensions. The recommended DSM approach is demonstrated to provide a broad improvement in prediction accuracy and generality when com...

Buckling behavior of cold-formed zed-purlins partially restrained by steel sheeting

Abstract This paper presents a study on the buckling behaviour of purlin-sheeting systems under wind uplift loading. The restraint provided by the sheeting to the purlin is modeled by using two springs representing the translational and rotational restraints. The analysis is performed using finite strip methods in which the pre-buckling stress is calculated based on the same model used for the buckling analysis rather than taken as the ‘pure bending’ stress. The results obtained from this study show that, for both local and distortional buckling, the restraints have significant influence on the critical loads through their influence on the pre-buckling stress rather than directly on the buckling modes. While for lateral-torsional buckling, the influence of the restraints on the critical loads is mainly due to their influence on the buckling modes rather than the pre-buckling stress.

Torsion in thin-walled cold-formed steel beams

Thin-walled cold-formed steel members have wide applications in building structures. They can be used as individual structural framing members or as panels and decks. In general, cold-formed steel beams have open sections where centroid and shear center do not coincide. When a transverse load is applied away from the shear center it causes torque. Because of the open nature of the sections, torsion induces warping in the beam. This paper summarizes the research on the behavior of cold-formed steel beams subject to torsion and bending. The attention is focused on beams subject to torque, because of the effect of transverse loads not applied at the shear center. A simple geometric nonlinear analysis method, based on satisfying equilibrium in the deformed configuration, is examined and used to predict the behavior of the beams. Simple geometric analyses, finite element analyses and finite strip analyses are performed and compared with experimental results. The influence of typical support conditions is studied and they are found to produce partial warping restraint at the ends. This effect is accounted for by introducing hypothetical springs. The magnitude of the spring stiffness is assessed for commonly used connections. Other factors that affect the behavior of cold-formed steel members, such as local buckling, are also studied.

Inelastic Bending Capacity of Cold-Formed Steel Members

AbstractThe objective of this paper is to provide and verify a general design method for prediction of inelastic bending capacity in cold-formed steel members potentially subject to local, distortional, and/or lateral-torsional buckling modes. An extensive experimental database of tested cold-formed steel beams is collected and indicates that inelastic reserve in the bending capacity of thin-walled cold-formed steel members is more common than typically assumed. Elementary mechanics for inelastic reserve are reviewed and simplified expressions provided for connecting the strain demand to the inelastic bending capacity in the range between the yield moment and the fully plastic moment. The strain capacity that can be sustained in inelastic local and inelastic distortional buckling is investigated through existing experiments coupled with nonlinear finite-element (FE) analysis. The nonlinear FE models provide a comprehensive means to investigate the relationship between cross-section slenderness, normalized...

STOCHASTIC POST-BUCKLING OF FRAMES USING KOITER'S METHOD

The objective of this paper is to explore the impact of stochastic inputs on the buckling and post-buckling response of structural frames. In particular, we examine the impact of random member stiffness on the buckling load, and the initial slope and curvature of the post-buckling response of three example frames. A finite element implementation of Koiters perturbation method is employed to efficiently examine the post-buckling response. Monte Carlo simulations where the member stiffness is treated as a random variable, as well as correlated and uncorrelated random fields, are completed. The efficiency of Koiters perturbation method is the key to the feasibility of applying Monte Carlo simulation techniques, which typically requires a large number of sample simulations. In an attempt to curtail the need for multiple sample calculations, an alternative first-order perturbation expansion is proposed for approximating the mean and variance of the post-buckling behavior. However, the limitations of this first-order perturbation approximation are demonstrated to be significant. The simulations indicate that deterministic characteristics of the post-buckling response can be inadequate in the face of input randomness. In one case, a frame that is stable symmetric in the deterministic case is found to be asymmetric when randomness in the input is incorporated; therefore, this frame has real potential for imperfection sensitivity. The importance of random field models for the member stiffness as opposed to random variable models is highlighted. The simulations indicate that the post-buckling response can magnify input randomness, as variability in the post-buckling parameters can be greater than the variability in the input parameters.

A Probabilistic Examination of the Ultimate Strength of Cold-formed Steel Elements

The statistical characteristics (mean and variance) of the ultimate strength of cold-formed steel plates in uniform compression and pure bending are calculated and compared to deterministic approximations. Three quantities: plate thickness, longitudinal flexural residual stress magnitude and first mode imperfection magnitude, are treated as random variables. Based on existing experimental data, appropriate probability distributions are determined for the three random variables. The ultimate strength calculations are performed numerically using the finite element method (FEM). The statistical characteristics are calculated using two methods: Monte Carlo simulation and Taylor series approximation. The results are compared to the deterministic design approach of the American Iron and Steel Institute (AISI) Specification for the design of cold-formed structural members.

Behavior and Design of Sheathed Cold-Formed Steel Stud Walls under Compression

AbstractCurrently, there is a need for a design method for cold-formed steel (CFS) stud and track walls that use traditional sheathing materials to brace against compressive load. The objective of this paper is to provide a robust design method for these walls. Existing design methods are unable to handle dissimilar sheathing attached to the CFS stud flanges [e.g., oriented strand board (OSB) on the exterior face and gypsum board on the interior face] and provide no clarity on the impact of key properties including sheathing shear rigidity and stud spacing. A series of tests on axially loaded sheathed single studs and sheathed full walls using OSB, gypsum board, or an unsheathed face (and combinations thereof) is performed to elucidate the basic behavior and limit states. The stiffness that the fastener-sheathing system supplies to the stud as bracing is characterized analytically and experimentally. The characterization clarifies how both local fastener deformations and global sheathing deformations cont...