professor ben schafer's thin-walled structures research group - johns hopkins university


AISC Faculty Fellowship


Cross-section Stability of Structural Steel




Investigate the application of the Direct Strength Method (DSM) to structural steel shapes, and to provide the necessary research advances to make this a viable option for the design of noncompact and slender structural steel shapes. A goal of DSM is to provide a design method which is robust enough to allow engineers to realistically explore novel cross-sections, yet make this exploration simple. Investigate the potential of DSM to take a fresh look at hot-rolled steel structural shapes.


Work Products

Proposal (pdf - February 2005)

Progress Report #1 (pdf - June 2007)

Progress Report #2 (pdf - April 2008)

AISC Comm. on Resaerch talk (pdf - April 2008)

SSRC Stability Conference (paper talk - April 2008)

Progress Report #3 (pdf - April 2009)

SSRC Stability Conference (paper - April 2009)

Structures Congress (paper - April 2009)

Progress Report #4 (pdf - May 2010)

SSRC Stability Conference (paper - May 2010)

Eng. Mech Inst. Conf  (talk - August 2010)

JCSR Paper (link to journal page)

please email if doc or ppt files are needed insted of pdf


Related Links


constrained Finite Strip Method

Direct Strength Method for Cold-Formed Steel

Reliability and Advanced Analysis of Steel Frames

Frame design/robustness under unforeseen events





Provide tools, tutorials, and educational aids related to cross-section stability of structural steel shapes so that educators, students, and engineers may explore these concepts more readily. Provide educational aids appropriate for courses in steel design using structural steel at the undergraduate and graduate levels.


Work Products

CUFSM, software for cross-section stability analysis


Example files for structural steel shapes
W36x150, W14x120, C5x9, L4x4x1/2, WT 18x150,
HSS 4x4x1/2 (all example files in a zip folder)

Tutorial 1: Cross-section stability of a W36x150 using

                   the finite strip method (ppt) (pdf)

                   Learning objectives: (1) Identify all the buckling modes in a W-section, for columns explore flexural (Euler) buckling and local buckling, for beams explore lateral-torsional buckling and local buckling; (2) Predict the buckling stress (load or moment) for identified buckling modes, (3) Learn the interface of a simple program for exploring cross-section stability of any AISC section and learn finite strip method concepts such as half-wavelength of the bucking mode buckling load factor associated with the applied stresses. (see below for related exercises)


Tutorial 2: Cross-section stability of a W36x150

                   exploring higher modes and the

                   interaction of modes (ppt) (pdf)

                   Learning objectives: (1) understand the role of “higher” buckling modes in the analysis of a W-section, including how higher buckling modes relate to strong-axis, weak-axis, and torsional buckling in columns, what higher buckling modes mean for local buckling, and when knowledge of higher buckling modes may be useful in design; (2) Understand how interaction of modes may be identified and quantified using CUFSM for a W-section (note target audience of this tutorial is advanced undergrad/beginning grad).


Tutorial 3: Exploring how cross-section changes

                   influence cross-section stability - an

                   extension to Tutorial #1 (ppt) (pdf)

                   Learning objectives: study the impact of flange width, web thickness, and flange-to-web fillet size on a W36x150 section, learn how to change the cross-section in CUFSM, learn how to compare analysis results to study the impact of changing the cross-section. (see below for related exercises)


Exercises: Homework exercises related to Tutorials 1

                  and 3 on cross-section stability (doc)

Exercises include simple homework problems that cover tutorials 1 and 3, as well as homework problems that require the student to apply the knowledge from tutorials 1 and 3, in addition homework exercises related to the other W, C, L, WT, and HSS are provided and some simple group problems that require a fuller exploration of cross-section stability of structural shapes.


Related Links

Professor Schafer's Undergraduate Steel Course

    Course web site

    Learning Objectives

    Lecture Materials





last updated 08/16/10