A new and free buckling mode identification tool (Buckling Cracker 1.0) is now available online at: http://www.moen.cee.vt.edu/category/tools/.

Developed by Junle Cai from Dr. Moen’s research group at Virginia Tech, this tool is dedicated to free researchers from subjective and tedious process of determining mode participation visually. Hopefully, this is helpful for strength prediction and design code development of thin-walled structures.

Based on genuine generalized beam theory (GBT), the software uses a novel algorithm to extracts modal amplitudes and modal participation factors quantitatively from 3d displacements field gained by either FEA or experiment for thin-walled members with an open cross-section. Taking advantage of GBT kinematics, the software is applicable to different boundary and loading conditions.


Junle Cai
Virginia Polytechnic Institute and State University (Virginia Tech)
Blacksburg, VA

A modeling approach for simulating steel axial cyclic response including local buckling deformations is in development. Two methods are proposed – (1) a nonlinear spring model with concentrated nonlinear axial load-displacement (P-δ) behavior, and (2) a nonlinear beam-column with distributed nonlinear section axial load-strain (P-ε) behavior (Fig. 1). The models are implemented in OpenSees using Pinching4 as the underlying material model with parameters derived as a function of the dissipated energy, member slenderness, and buckling half-wavelength. Parameter relationships have been shown by recent lipped C- section cold-formed steel cyclic experiments and finite element simulations [1-4]. The presented models would provide means to explore limit states associated to thin-walled member behavior and its application to light steel framed building systems (e.g., shear wall in Fig. 1a).

The proposed methodology is established for thin-walled cold-formed steel members, however the Pinching4 parameters are posed generally as a function of member slenderness and could be extend-ed to hot-rolled steel members and cross-sections with future validation.


David A. Padilla-Llano, Cristopher D. Moen and Matthew R. Eatherton
Virginia Polytechnic Institute and State University (Virginia Tech)
Blacksburg, VA

The prediction of collapse of structures has gained growing attention in recent years to enable the structural engineering community to predict possible extreme loads that precipitate collapse. To predict collapse of steel structures, finite element deletions strategies have been used successfully in the past to account for fracture in steel members. Prior work has of-ten used a constant critical strain approach (CS), which deletes an element when it achieves a specific level of strain (e.g., 0.2, which is used in this work), typically without modeling of material softening. This approach requires frequent re-calibration depending on the configuration of the structural components and systems. This research proposes a more robust and general-purpose approach to collapse modeling of steel structures through the use of a Void Growth Model (VGM) to simulate the initiation of softening and the Hillerborg model for modeling the subsequent material softening, followed by an element deletion strategy that is developed in this work. In addition, a second approach is investigated that adds a Bao-Wierzbicki model to the VGM strategy (VGM-BW) in order to better account for lower and negative triaxiality regions in determining softening. The parameters of the VGM strategy were calibrated to a comprehensive set of experimental test results of circumferentially notched tensile (CNT) coupon specimens, while the Bao-Wierzbicki parameters in VGM-BW strategy were deter-mined analytically. These strategies were then validated without recalibration through comparison with a comprehensive range of experimental test results of material characterization specimens and full-scale structural steel connection tests (Figures 1 and 2), moment resisting frame experiments (Figure 3), and multi-story braced frame experiments. The VGM strategy provided most accurate prediction, while VGM-BW has better potential if it is calibrated to experimental results directly in the low and negative triaxiality range (Figures 1 and 2). In general, the constant strain strategy did not compare well to experiments (Figures 1 and 2). The VGM and VGM-BW approaches thus enable high-fidelity parametric simulation capabilities of interest to researchers, practitioners, and code developers who address collapse of structures.


• Rentschler, G. P., Chen, W.-F., and Driscoll, G. C. (1978). Tests of Beam-to-Column Web Moment Connections, Report #405.9, Fritz Engineering La-boratory, Bethlehem, PA.
• Sadek, F., Main, J. A., Lew, H. S., Rob-ert, S. D., Chiarito, V. P., and El-Tawil, S. (2010). An Experimental and Com-putational Study of Steel Moment Con-nections under a Column Removal Sce-nario, NIST Technical Note 1669, Na-tional Institute of Standards and Tech-nology, U.S. Department of Commerce, Gaithersburg, Maryland.
• Saykin, V. V. (2014). “A Validated Approach for Modeling Collapse of Steel Structures,” Ph.D. Dissertation, Civil and Environmental Engineering, Northeastern University, Boston, Mas-sachusetts.
• Schutz, F. W., Schilling, C. G. J., and Beedle, L. S. (1953). The Collapse Strength of a Welded Single Bay Frame, Report #205D.5, Fritz Engi-neering Laboratory, Lehigh University, Bethlehem, Pennsylvania.






Jerome F. Hajjar, Northeastern University
Junho Song, Seoul National University
Vitaliy Saykin, Wentworth Institute of Technology
Derya Deniz, University of Illinois at Urbana-Champaign
Tam Nguyen, KTP Consultants Pte Ltd.

Sponsored by National Science Foundation 

In the design of cold-formed steel buildings, shear walls are typically used to provide lateral resistance for seismic or wind load. The wood sheathing, such as oriented strand board, is screw-fastened to the cold-formed studs and tracks to develop shear stiffness as well as strength in the wall system.


The composite shear wall response is dominated by the local behavior at each steel-fastener-sheathing connection. Researchers from Johns Hopkins University and Bucknell University cur-rently conduct research addressing this topic. They extend the development of a mechanics-based approach to predict lateral response of wood sheathed cold-formed steel (CFS) framed shear walls.

An OpenSees model is developed that uses standard beam-column elements for the framing members and a rigid diaphragm for the sheathing. The stud-to-sheathing connections are represented as zero-length springs utilizing a Pinching04 material re-sponse developed based on isolated fastener tests. The OpenSees model is validated against previously conduct-ed, monotonic and cyclic full-scale shear wall tests, and shown to have good general agreement. In addition, the developed force distribution of the fasteners in the studs of a typical shear wall is explored. Work remains to further calibrate the OpenSees model, but the developed results demonstrate that the shear wall response relies on connection deformations and this is the critical nonlinearity. This observation makes the possibility of determining lateral response for gravity walls and wood-sheathed floor diaphragms a distinct possibility- and this capability is critical to better understanding the seismic system-level response of cold-formed steel framed buildings.


Guanbo Bian and Benjamin W. Schafer
Johns Hopkins University
Baltimore, MD

Stephen G. Buonopane
Bucknell University
Lewisburg, PA

O. Ozgur Egilmez
Izmir University of Economics
Izmir, Turkey

Mustafa Vardaroglu and Andac Akbaba
Izmir Institute of Technology
Izmir, Turkey

Lateral torsional buckling is a failure mode that often controls the design of steel I-beams during construction. During this critical stage, the buckling capacity of the beams can be increased by reducing the laterally unbraced length by providing bracing at either discrete locations or continuously along the length of the beam. Light gage metal decking, which is often used in the building and bridge constructions as concrete deck formwork, acts like a shear diaphragm and can provide continuous lateral bracing to the top flange of non-composite beams and girders by restraining the warping deformations along the beam/girder span. Past studies that investigated the stiffness and strength behavior of shear diaphragms used to brace steel beams mainly focused on the strength of the end connections (sheet to beam connections along the length of the beam). However, the strength of a diaphragm is generally controlled by either the shear strength of the end connections or shear strength at interior connections between panels. Therefore, strength requirements for shear diaphragm bracing should ad-dress both end and sidelap fasteners. This study investigates the stiffness and strength behavior of shear diaphrssrsdusbsis1agms used to brace stocky and slender beams/girders by taking into account both end and sidelap fastener connections. A simple finite element analytical model is utilized in the study that enables the end and sidelap fasteners to be separately modeled. The parameters that are investigated include diaphragm stiffness, thickness, and width, number of side-lap fasteners, web slenderness ratio, and section depth. The results indicate that web slenderness ratio is not as much effective as section depth on fastener forces. The findings of the study will be used to develop strength and stiffness requirements for shear diaphragms used to brace steel beams.


Abraham Lama-Salomon , Fannie Tao , Junle Cai and Cristopher D. Moen
Virginia Polytechnic Institute and State University (Virginia Tech)
Blacksburg, VA

Recebmicfsce3dibr1ntly developed thin-walled modal decomposition algorithms are merged with 3d image based reconstruction (Figure 1) to document and quantify buckling deformation throughout a cold-formed steel column experiment. The buckling deformation is recorded with strategically located high-definition video cameras. The video footage is decomposed into individual frames, and a gradient-based optimization algorithm, available in low cost commercial software packages, is applied that finds the 3d image coordinates and camera position by maximizing the number of matching (overlapping) features from frame to frame. Once the 3d coordinate system and camera locations are established, a dense point cloud is generated resulting in the 3d column representation throughout the experiment. The 3d point cloud is analyzed with a buckling mode identification tool that employs cross-sectional deformation modes from generalized beam theory. Local, distortional, and global buckling participation are documented, including contributions just prior to col-umn failure which can be useful for the development of future strength prediction design approaches, especially where buckling modes mix near an ultimate limit state.


David C. Fratamico
Johns Hopkins University
Baltimore, MD

Built-up cold-formed steel members are integral parts of shear walls and are frequently included in frames as king and corner studs. Current predictions for buckling capacity in AISI S100-12 Sec-tion D1.2 employ the modified flexural slenderness ratio, which reduces the buckling capacity of columns in part due to a loss of shear rigidity in the overall member’s interconnections (fasteners). There exist provisions for calculating fastener spacing and layout, whether screws or welds are used to connect two sections together. However, a detailed understanding of the effective section rigidities of these composite, thin-walled members does not yet exist.

Interestingly, connecting two standard CFS channel sections together does of-fer a boost in flexural capacity. Elastic flexural buckling loads of back-to-back channel sections frequently used in de-sign, for example, are theoretically more than twice the buckling load of the individual channel sections. A recent approach to understanding the behavior of built-up columns at Johns Hopkins University employs the concept of composite action, in which this boost in flexural capacity can begin to be quantified.

A parametric study using elastic buck-ling analysis was conducted on a representative population of built-up structural columns in ABAQUS (using discrete fasteners) and Finite Strip Method-based software CUFSM (using smeared constraint interconnections). Member cross-sections, fastener spacing, and fastener grouping at the column ends were varied. Prevailing buckling modes are shown in Figure 1. Buckling loads from the study are compared to code-based equation predictions and show considerable composite action (illustrated by the signature curve in Figure 2), which can increase a column’s flexural buckling load by up to 85% from its non-composite lower bound, for trials in both CUFSM and ABAQUS. Future work includes more accurate modeling of fastener stiffness and experimental studies.


Aritra Chatterjee and Cristopher D. Moen sbfcmss1
Virginia Polytechnic Institute and State University (Virginia Tech)
Blacksburg, VA

Yibing Xiang and Sanjay Arwade
University of Massachusetts, Amherst
Amherst, MA

Benjamin W. Schafer
Johns Hopkins University
Baltimore, MD 

Structural design continues to be a component based process, typically check-ing beam, column and connection capacities against design demands. However, end-user safety in the event of natural hazards hinges on system performance. The challenges in casting structural design as a ‘system-based’ process stems from a fundamental lack of understanding how component level properties, namely component ductility and uncertainty, propagate to system behavior —  redundancy, overstrength and system ductility.

This National Science Foundation sponsored Grant Opportunities for Academic Liaison with Industry (GOALI) project, coordinated through the Cold-Formed Steel Research Consortium , www.cfsrc.org, seeks to meet this challenge for typical building structural systems: roof, walls, and floors. Build-ings framed from cold-formed steel are targeted for initial application. The industry partner, the American Iron and Steel Institute (AISI), is working directly with the academic re-search team to insure the research has maximum impact on the practical design of cold-formed steel building sub-systems.

So far the focus has been on wood-sheathed cold-formed steel floor sub-systems under in-plane lateral loads (wind or seismic). High-fidelity finite element models have been developed in ABAQUS and shown to replicate real behavior previously seen in mon-otonic experiments. Surrogate models were generated to study system response in a computationally efficient manner, and dedicated experiments were used to determine component response and uncertainty. These were coupled together to generate system-level strength distributions at first yield and ultimate limit states, and it was shown that component load-deformation behavior has a great impact on system over-strength and ductility. The ongoing parallel efforts are focused on generalizing these methods, and building a full-scale experimental setup at Virginia Tech for testing floor diaphragm sub-systems in order to validate the computational models.


Delphine Sonck
Ghent University

Cellular and castellated members are usually made by performing thermal cutting and welding opera-tions on hot-rolled I-section members. The global buckling behavior of these members will be quali-tatively similar to that of I-section members. Howev-er, it is expected that the buckling resistance will be influenced by the different geometry and the modi-fication of the residual stress pattern during the production of the cellular and castellated members. Current design guidelines for the global buckling of these members are conflicting or lacking altogether and do not take into account the effect of the modi-fied residual stresses, which could possibly be very unsafe. Therefore, the lateral-torsional buckling and weak-axis flexural buckling behavior of castel-lated and cellular members were investigated in a recent PhD investigation at Ghent University.

A series of residual stress measurements demonstrat-ed the increase of the compressive residual stresses in the flanges during the production of these members, which is detrimental for the global buckling re-sistance. This was taken into account in the proposed modified residual stress pattern. The numerical model in which this residual stress pattern was introduced, was validated using the results of a series of lateral-torsional buckling experiments. Based on the results of the numerical parametric study of the global buckling behavior, a first design rule proposal was made. This proposal is similar to the currently used European guidelines for I-section members without openings, but with a different calculation of the cross-sectional properties and a modified buckling curve selection. The PhD dissertation can be downloaded from http://hdl.handle.net/1854/LU-4256332.


Mohammed A. Morovat, Michael D. Engelhardt, Todd A. Helwig and Eric M. Taleff
The University of Texas at Austin, Austin, TX

Sponsored by National Science Foundation 


The ability of steel columns to carry their design loads is greatly affected by time and temperature dependent mechanical properties of steel at high temperatures due to fire. It is well known that structural steel loses its strength and stiffness with temperature, especially at temperatures above 400 °C. Further, the reductions in strength of steel are also dependent on the duration of exposure to elevated temperatures. The time-dependent response or creep of steel plays a particularly important role in predicting the col-lapse load of steel columns subjected to fire temperatures.

Along with the main goal of developing a fundamental understanding of the phenomenon of creep buckling, this project has shown that time-dependent effects are significant in response of steel columns in fire. Now that the buckling tests on W4×13 columns have ended, the methodology devel-oped to account for the effect of material creep on the buckling of steel columns in fire can be further verified. An example of such veri-fications is shown where analytical and computational creep buckling predictions are compared against test results for W4×13 columns with KL/r of 51 at 600 °C. Analyt-ical solutions are based on the concept of time-dependent tan-gent modulus. Computational creep buckling analyses are per-formed in Abaqus®. A material creep model developed in this study for ASTM A992 steel is utilized in analytical and compu-tational buckling analyses. Con-sidering all the uncertainties in material creep models and buck-ling prediction methods, reasona-bly well agreements can be seen.