Introductory steel design courses focus on the analysis and design of primary members, which typically include tension members and connections, compression members, flexural members, and beam-columns. Introducing structural steel design concepts to students presents its fair share of challenges. First, it is difficult for students to visualize and accurately predict the potential failure modes of a tension member: yielding of the gross section, rupture of the net section, and block shear. Second, it is also difficult for students to visualize the buckling modes of steel columns, which vary with shape and type of bracing. Students particularly struggle with the determination of buckling modes between strong and weak axes based on effective lengths. Third, flexural failure modes of steel beams are very difficult for students to visualize and understand when each mode controls. The failure modes are complex and fall into three categories for compact shapes: yielding of the cross section, inelastic lateral torsional buckling, and elastic lateral torsional buckling, which is dependent on the unbraced length of the compression flange. Non-compact sections also include local buckling of the flange or web, but identifying the relationship between the unbraced length and beam span and how the unbraced length affects the flexural capacity tends to be the most difficult concept for students to grasp.
This paper provides a detailed overview of the design, fabrication, and implementation of three large-scale experiential learning modules for an undergraduate steel design course. The first module focuses on the tension connections by providing physical models of various failure types including yielding of the gross section, rupture of the net section, and block shear; the second module focuses on the capacity of columns with different amounts of lateral bracing about the weak axis; and the third module focuses on the flexural strength of a beam with different unbraced lengths to illustrate the difference between lateral torsional buckling and flange local buckling/yielding of the gross section. The three modules were used throughout the steel design course at Saint Louis University and Rose-Hulman Institute of Technology to illustrate the failure mechanisms associated with the design of steel structures.
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Cross-sections of doubly curved sheets as confined elastica
Although thin films are typically manufactured in planar sheets or rolls, they are often forced into three-dimensional (3D) shapes, producing a plethora of structures across multiple length scales. To understand this complex response, previous studies have either focused on the overall gross shape or the small-scale buckling that decorates it. A geometric model, which considers the sheet as inextensible yet free to compress, has been shown to capture the gross shape of the sheet. However, the precise meaning of such predictions, and how the gross shape constrains the fine features, remains unclear. Here, we study a thin-membraned balloon as a prototypical system that involves a doubly curved gross shape with large amplitude undulations. By probing its side profiles and horizontal cross-sections, we discover that the mean behavior of the film is the physical observable that is predicted by the geometric model, even when the buckled structures atop it are large. We then propose a minimal model for the horizontal cross-sections of the balloon, as independent elastic filaments subjected to an effective pinning potential around the mean shape. Despite the simplicity of our model, it reproduces a broad range of phenomena seen in the experiments, from how the morphology changes with pressure to the detailed shape of the wrinkles and folds. Our results establish a route to combine global and local features consistently over an enclosed surface, which could aid the design of inflatable structures, or provide insight into biological patterns.
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- Award ID(s):
- 1654102
- NSF-PAR ID:
- 10421119
- Date Published:
- Journal Name:
- Proceedings of the National Academy of Sciences
- Volume:
- 120
- Issue:
- 11
- ISSN:
- 0027-8424
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1073/pnas.2216786120
