Instantaneous Center Method for Diaphragms

Hello!

This repository contains computational notebooks for the Instantaneous Center Method (ICM) to estimate the shear strength of steel diaphragms. It specifically considers diaphragms where different types of fasteners are employed for strength calculations. The North American Standard for the Design of Profiled Steel Diaphragm Panels, AISI S310-16, provides design rules for diaphragm shear strength, in Section D, based on the elastic analysis. The objective of this project is to ascertain whether the inelastic analysis of bare steel deck diaphragms using the ICM is a viable design method.

The AISC Steel Construction Manual, AISC 360, has incorporated inelastic analysis for both bolted and welded connections since its 8th Edition. The Instantaneous Center Method, as outlined in Brandt 1982a and 1982b, necessitates understanding the load versus deformation behavior of the fasteners. Data on these load-deformation characteristics can be found for arc-spot welds in Easterling and Snow (2008) and for sheet-to-sheet screws in Moen et al. (2014), among other sources.

The ICM solutions for this project are written in Python 3. Users can execute the "test.ipynb" file on Google Colab, a web-based user interface that eliminates the need for local software downloads, to test some example diaphragms. When using Google Colab with Github to run the 'test.ipynb' file, it operates through your Google Drive. As a result, you will receive a prompt requesting permission to access your Google Drive. The developed ICM codes have been tested against diaphragm test results provided in the SDII project (https://steeli.org/?p=71) and DDM 01 (Steel Deck Institute Diaphragm Design Manual, First Edition). Detailed procedures for the ICM are available in Brandt (1982a) and Brandt (1982b).

The repository features four main code files: 1. group.py - This code provides the coordinates of fasteners grouped by their locations, including the end, edge, interior supports, and side-lap fasteners. An illustration below offers a visual representation of the fastener labels. This project ignores the resistance of the corner fasteners associated with the overhanging welds, where pink X marks are present in the illustration. 2. force_function.py - This code calculates the forces exerted by fasteners and their respective moments about the instantaneous center. It considers different load-deformation relationships for arc-spot welds (used for end, edge, and interior fasteners) and screws (used for side-lap fasteners). The load-deformation relationships embedded in this code are derived from test results (Snow and Easterling 2008 and Moen et al. 2014) 3. IC.py - This code embodies an iteration process designed to estimate the final instantaneous center. 4. test.ipynb - Users can excute this file to calculate the shear strength of diaphragms using the three functions defined in the code files 1-3. Detailed annotations are provided line by line in the code.

References

• AISI S310, North American Specification for the Design of Profiled Steel Diaphragm Panels, AISI, 2016.
• ANSI/AISC 360, American Institute of Steel Construction, Specification for Structural Steel Buildings, Chicago, IL, 2022.
• Brandt, G. D. Rapid Determination of Ultimate Strength of Eccentrically Loaded Bolt Groups, 1982a.
• Brandt, G. D. A General Solution for Eccentric Loads on Weld Groups, 1982b.
• Snow, G. L. and W. S. Easterling. Section properties for cellular decks subjected to negative bending. 2008.
• Moen, C. D., D. A. Padilla-Llano, S. Corner, and C. Ding. Towards load-deformation models for screw-fastened cold-formed steel-to-steel shear connections. 2014.
• SDI DDM 01, Steel Deck Institute Diaphragm Design Manual, 1981.