DIRECT STRENGTH DESIGN FOR COLD-FORMED STEEL
MEMBERS WITH PERFORATIONS
Solicited proposal submitted to:
The American Iron and Steel Institute (AISI)
Principal Investigator:
Ben Schafer
Assistant Professor
Department of Civil Engineering
The Johns Hopkins University
Baltimore, Maryland
June 2004
Abstract
The recently adopted Direct Strength Method has opened the potential for the Specification to
encourage the creation of highly optimized and efficient cold-formed steel members by integrating
numerically determined elastic buckling loads directly into the design process. A significant current
shortcoming of Direct Strength design is that it does not apply to members with perforations (holes).
Perforations are commonly used in nearly all cold-formed steel applications and therefore extension of
Direct Strength design to members with holes is sorely needed. A three phase (year) proposal is
proposed herein to address this shortcoming. The first phase focuses on using existing data coupled
with finite element analysis to efficiently provide a means to bring conventional members with holes
into the Direct Strength procedures. Phases 2 and 3 focus on more in-depth theoretical challenges and
experimental validation so that a rational analysis method can be provided for any cold-formed steel
member with perforations, including unique configurations such as flanged holes, slotted holes, and the
like. Specific budgets are provided for the three separate phases. A rational analysis method for
designing any cold-formed steel member with holes stands to significantly increase the flexibility of
cold-formed steel applications and allow industry and practicing engineers to take full advantage of the
potentials of the Direct Strength design method.
Direct Strength Design for Cold-Formed Steel Members with Perforations
1
1. Background
Perforations in cold-formed steel members come in a variety of different forms, as shown in Figure 1.
The two most common types of perforations are isolated holes, and patterned holes. Isolated holes
include load bearing studs with holes for services and/or bridging (Figure 1a), and isolated holes in
joists, purlins, and girts (Figure 1a). Patterned holes include those in pallet rack post uprights for
tabbed beam connections (Figure 1b). Other more unique situations exist for cold-formed steel
members with perforations; including isolated holes that include formed-in flanges for increased
stiffness around the hole (Figure 1c) and new ideas for better thermal behavior using small patterned
perforations (Figure 1d).
(a) Isolated holes in studs, may also be found in joists,
purlins, and girts, several holes may exist along the length,
though spacing is generally far apart
(b) Patterned perforations in rack posts, and in some rack
beams, in addition other specialty industries include such
perforations (picture from UNARCO product catalog)
(c) Isolated flanged holes in joists, purlins; holes stiffened
through transverse and possibly longitudinal external
stiffeners also relevant (picture from Dietrich web site)
(d) Specialty perforations as found in slitted cross-sections
used in Europe for improved thermal performance (Sections
tested and analyzed in Kesti 2000, picture from Kesti 2000)
Figure 1 Examples of perforation patterns found in cold-formed steel systems
Current Specification (NAS 2001) methods for designing members with holes are limited. For isolated
circular holes in lipped channel columns the experiments of Ortiz and Peköz (1981) are used to define
a reduced effective width for geometries in the tested range only. Isolated holes in lipped channel
beams follow Shan et al. (1994), Langan et al. (1994), Uphoff (1996), and Deshmukh (1996) and are
used to define a hole size which is small enough to be ignored – design for other hole sizes
conservatively require the effective width to be calculated assuming the hole creates unstiffened
elements on either side, i.e., the classic solution for a long plate simply supported on three sides and
free on the third (the hole) is used for finding the effective width. Alternatively, and with much greater
accuracy for local buckling, stub column testing may be performed. This is common practice for
members with patterned perforations only. However, testing is only done at short lengths, and
distortional buckling which dominates at intermediate lengths, is problematically not considered
(Hancock et al. 1994). Thorough compilations of other relevant work are provided in Kesti (2000) and
Direct Strength Design for Cold-Formed Steel Members with Perforations
2
Shanmugam and Dhanalakshmi (2001). Existing methods have an intentionally limited range of
applicability, but may be excessively conservative in some situations and ignore important limit states
in other situations. A consistent design approach is needed.
Perforations (holes) are a common need in cold-formed steel systems; whether for services in
buildings, for convenient connection of other members, or other uses. The main Specification (NAS
2001) covers specific cases of members with holes, but the use is effectively limited to the testing
performed. Further, in some cases the Specification methods are known to be overly conservative. The
Direct Strength Method (DSM) was created to provide a means to efficiently design highly optimized
cross-sections; cross-sections that could not be readily handled by the design method of the
Specification. Extension of the Direct Strength Method is needed in order to provide a general method
for the efficient design of members with perforations (holes).
2. Elastic buckling and the Direct Strength Method
The basic premise of the Direct Strength Method may be expressed for a column as:
Pn=f(Pcr,Pcrd,Pcre,Py)
(Eq. 1)
where:
Pn=nominal column strength
Pcr=axial load at which elastic local buckling occurs
Pcrd=axial load at which elastic distortional buckling occurs
Pcre=axial load at which global column buckling (flexural, torsional, flexural-torsional occurs)
Py=axial load at which yielding occurs (squash load).
The development of functional expressions (the “f” of Eq. 1) preceded from considering the large
amount of available experimental data and empirically fitting limit-state specific strength curves for
global buckling, distortional buckling, and local-global buckling.
For members without holes the primary means for examining the elastic buckling loads employed the
classical finite strip method (FSM), e.g., CUFSM. However, this method cannot discretely handle the
presence of holes without significant modifications. Thus, when considering members with holes the
more general finite element method (FEM) using shell elements is typically preferred. Recent work by
Sarawit (2003) on patterned perforations for rack posts (Figure 1b) and by Kesti (2000) on small
patterned perforations for a unique stud with better thermal properties (Figure 1d) has shown how the
finite element method may be used for elastic buckling prediction of members with holes. For
example, Figure 2 shows an open source tool developed by Sarawit for isolated plates and
demonstrates the reduction in the elastic local plate buckling coefficient. Figure 3 extends the analysis
to full members with a general purpose FE package, ABAQUS, for elastic buckling in the local,
distortional, and global buckling modes.
Figure 2 and Figure 3 demonstrate, at least visually, that members with holes have elastic buckling
modes similar to members without holes. But, what these figures fail to show is (1) many more
buckling modes may exist – particularly for larger holes and (2) determining which of the
myriad of buckling modes should be defined as “local” or “distortional” or “global” without the
aid of the half-wavelength vs. load factor plot that finite strip provides is difficult at best and
impossible at worst. The finite element method is less restricted than the finite strip method, with this
generality comes much complication. A methodology is needed to post-process finite element analysis
(FEA), similar to that used in finite strip analysis, so that specific modes can be identified and even
isolated. A consistent approach to identifying elastic buckling modes in members with holes is a key
challenge in the work proposed herein.
Direct Strength Design for Cold-Formed Steel Members with Perforations
3
Figure 2 FE predications of elastic plate buckling coefficients for isolated plates with rack post
patterned perforations completed by Sarawit 2003
Figure 3 FE predictions of the elastic buckling modes of rack post columns with patterned
perforations (a) Local (b) Distortional (c) Flexural-torsional, completed by Sarawit 2003
Direct Strength Design for Cold-Formed Steel Members with Perforations
4
3. Ultimate strength and the Direct Strength Method
Development of the Direct Strength Method relied on the wide body of available experimental data on
members without holes. Strength curves were selected that connected elastic buckling loads to ultimate
strength, for example, for a column in distortional buckling the expression is:
0.6
0.6

 Pcrd   Pcrd 

 
 P
(Eq. 2)
Pnd  1  0.25
 P   P  y
y
y

 


Consider the rack post of Figure 3b, the question for members with holes is, if Pcrd is properly
calculated to reflect the reduction due to the holes will the same strength expression (Eq. 2) be
applicable to this member? It is certainly possible that this will be the case, but it is not guaranteed, as
theoretically the presence of the hole will influence the elastic buckling response (represented by P crd)
and the post-buckling response (handled through Eq. 2). While a clear means exists to account for the
change in elastic buckling, and thus the reduced Pcrd due to the hole, needed modifications to the Direct
Strength expressions, such as Eq. 2, remain unknown.
Use of the available experimental data on members with holes from Ortiz and Peköz (1981), Shan et
al. (1994), Langan et al. (1994), Uphoff (1996), Deshmukh (1996) and others available in the literature
will be crucial to initially evaluating the Direct Strength expressions. For each existing test (1) general
purpose finite element models will have to be built to determine the elastic buckling loads in the
presence of the holes (2) the FE elastic buckling modes will have to be mapped appropriately to local,
distortional, and global buckling values and only then can we (3) determine the accuracy of existing
Direct Strength expression and evaluate the necessity of potential modifications to those expressions.
4. Statement of Work and Work Plan
Objective: Development of a general design method for cold-formed steel members with perforations.
The developed design method is envisioned as an extension to the Direct Strength Method. While it is
believed that completion of the entire project plan is required in order to fully implement the Direct
Strength Method for members with perforations it is recognized that funding may not be available for
this complete effort immediately. Therefore, the project has been specifically broken into three years,
each year with separate tasks and goals so that the funding and effort levels can be matched
appropriately.
Year 1: Benefiting from existing experimental data
$66,056
Objective: Efficiently extend DSM to members with holes that are already covered in the Specification
and insure that DSM, at least in a limited sense, can be applied to products already on the market:
metal studs, rack posts, etc., at least where test data is already readily available.
Survey current industry use on members with perforations
Evaluation of existing experimental results
- Gather all existing experimental data
- Elastic FEA of existing experimental results
- Identification of local, distortional, and global modes for perforated members
- Evaluation of existing Direct Strength expressions
Design examples
Specification ballot on Direct Strength Method for conventional members with perforations
Direct Strength Design for Cold-Formed Steel Members with Perforations
5
Year 2: Tackling theoretical challenges and extending experiments
$62,617
Objective: Formalize identification of buckling modes for members with holes. Increase understanding
of post-buckling mechanisms for members with holes. Extend DSM as a rational analysis method for
any cold-formed member with holes; including unique members with flanged or stiffened holes.
Identification/isolation of buckling modes in a general FEA
- Extension of Adany and Schafer work on modal identification from finite strip to FEA
Extension of existing experimental results
- Nonlinear FEA models of experiments to verify and validate implemented FEA model
- Additional parametric studies for ultimate strength of members with perforations
(focus on unusually large holes, boundary between isolated holes and patterned holes, etc.)
- Examination/extension of Direct Strength expressions
- Detailed evaluation of post-buckling response (using nonlinear FEA)
Evaluation of flanged or stiffened holes
- Collection of existing experimental data, as available
- Complete elastic buckling and nonlinear FEA of typical sections
- Examination/extension of Direct Strength expressions
- Design examples
Specification ballot on members with flanged or stiffened holes
Research tool for the direct identification of buckling modes for members with holes
Draft ballot on rational analysis method for any member with holes
Year 3: Experimental validation and developing open-source tools
$81,104
Objective: Experimentally validate DSM as a rational analysis method for any cold-formed member
with holes; including unique members with flanged or stiffened holes. Develop open-source tools that
engineers may use for easy application of DSM to members with holes.
Experiments on beams and columns with holes
Beam testing would use the existing rig at JHU and column testing would employ the 100 kip
universal testing machine. If the DSM beam-column proposal is funded this work would have
significant synergy with that proposal – and the developed testing rig from that proposal could be used
for the testing here. Since only a 1 year testing program is envisioned the FEA work and existing tests
would be used to carefully select a small subset of cross-sections and hole patterns of interest. A total
of approximately 36 tests is envisioned, 3 tests at each of 3 lengths for four different cross-sections,
this allows the influence of a critical hole to be gauged for local, distortional, and global buckling.
Development of an open-source computational tool for members with perforations
- stand-alone tool for elastic buckling of members with perforations and/or
- post-processing tools for general purpose FE programs (ANSYS, ABAQUS, etc.)
- integrate work on modal identification work from year 2
Design examples
Ballot on rational analysis method for any member with holes
Open-source computational tool for members with holes
Direct Strength Design for Cold-Formed Steel Members with Perforations
6
The order of the work in years 2 and 3 is somewhat more flexible than year 1. The project may be
thought of as consisting of 3 phases, each with the proposed budget provided.
As discussed in the elastic buckling section previously, a key theoretical challenge, addressed in year 2
of the work, is the identification/isolation of individual buckling modes from a general purpose FEA;
currently no tool exists for this purpose. Consider a simple model of a lipped channel (without holes)
as shown in Figure 4. At a given length, the number of total degrees of freedom determines the number
of possible modes. For Figure 4
FSM: 15 nodes × 4 DOF/node = 60 modes, and
FEA: 15 nodes in a section × 9 sections along the length × 4 DOF/node = 540 modes.
In general the situation is actually much worse than this calculation indicates, because FEA is
performed on a much longer length model with many more elements. Members with holes require the
convenience of FEA to incorporate discontinuities (like holes) along the length but methods are needed
for post-processing FEA runs to effectively deal with the large number of modes and to identify modes
of actual interest.
1,2
all-mode
global
dist.
local
(Pcr/Py)
1
0,8
0,6
0,4
0,2
finite element
finite strip
0
10
Figure 4 FEM/FEA vs. FSM
100
1000
buckling length (mm)
10000
Figure 5 FSM analysis with modal constraints
Recently Adany and Schafer (2004) have shown how to use the mechanical assumptions of
Generalized Beam Theory (Davies et al. 1994, Silvestre and Camotin 2002a,b) in order to restrain
general purpose analysis tools like FSM to the analysis of a single mode. As an example, FSM analysis
of a lipped channel in pure compression is shown in Figure 5, the “all-mode” curve is the traditional
FSM analysis; note that distortional buckling cannot be readily identified in this curve because no
minimum exists. However, in the subsequent curves we have restricted the FSM analysis via a series of
mechanical assumptions (deformation constraints) and generated curves which are unique to the
traditional buckling modes. These curves provide exact definitions for the individual buckling modes
and allow isolation of the modes.
Extension of the technique employed by Adany and Schafer to FEM is possible, and would provide a
means to isolate the FEA on individual modes. This would allow one to directly identify the influence
of a hole, or series of holes on a particular buckling mode. Without such a tool proper identification of
the modes, given a myriad of possible choices in the FEA and the subtle differences between the
modes, would rely solely on the experience of the analyst. Such a method is possible in some cases,
but can introduce significant approximation and a loss of transparency and generality for the approach.
Direct Strength Design for Cold-Formed Steel Members with Perforations
7
5. Impact on Industry
The metal stud and rack manufacturing industries, which use perforations in most of their products,
need this research to bring the potential short- and long-term advantages of the Direct Strength Method
to their industries. Unique innovations involved with perforations in members, such as flanged holes,
and slotted holes need this research to provide a recognized design approach in the Specification.
Cold-formed steel members require perforations. The development of the Direct Strength Method
provides a means to highly optimize cold-formed sections. Extending the application of the Direct
Strength Method to members with holes provides a means for industry to move towards highly
optimized sections, more readily embrace high strength steels, and increase the flexibility of coldformed steel applications.
6. Work Product
Progress reports will be provided to AISI every 6 months at the AISI-COS meetings. A report will be
provided upon completion of the project. Upon review and comments from the AISI a final report will
be provided. Test data and reports will be made available in electronic format to AISI and other
researchers.
7. Budget
A summary of the proposed budget is provided in Table 1. Support for a student and 1 month of
faculty salary is requested in all 3 years. In year 1, funding for a computer is requested, and in year 3
funding for performing experiments is requested. A detailed breakdown of the budget is provided in
the Appendix.
Table 1 Summary budget
BUDGET BREAKDOWN
Year 1
Year 2
Year 3
Total
Faculty
Student
Travel/Dissemination
Experiment
Computation
17,993
41,745
0
0
6,318
66,056
18,712
43,087
0
0
818
62,617
19,461
44,475
0
16,350
818
81,104
56,166
129,308
0
16,350
7,953
209,776
* Budget notes:
(1) Equipment costing greater than $5K is not subject to overhead
(2) The Department supports first-year graduate students, therefore the student on this project will be a second year student
when joining the research (this provides a means to fund a student for 4 years with only 3 years worth of money).
8. Facilities
Computer: Computing resources at Johns Hopkins University are nearly completely de-centralized.
Computers in current use in the PI’s research group were purchased through startup funds and other
grants. All of my current graduate students have Dell workstation class Intel machines varying from 1
to 2 years old. In addition I have 2 machines used primarily for finite element analysis with ABAQUS;
two 2 GHz Dell workstation with 2 GB of memory running Linux. Three computers with A/D boards
and 1 laptop have also been purchased to support efforts in the lab. These resources will be available to
support the research initiatives proposed herein. The proposed computational efforts will be aided by
purchasing a new Linux workstation for parametric studies using CUFSM and ABAQUS.
Laboratory: The Department of Civil Engineering maintains a structural testing laboratory in the
building. The structural laboratory is approximately 20 ft x 40 ft in plan and has a 20 ft. ceiling. The
laboratory includes regularly spaced floor tie-downs, an electric over head crane, and a large adaptable
reaction frame consisting of heavy hot-rolled steel sections. Additionally, the laboratory includes sinks,
Direct Strength Design for Cold-Formed Steel Members with Perforations
8
gas and vacuum lines, and is served by an MTS hydraulic pump for running either of the 2,000 lbf or
20,000 lbf actuators or one 100,000 lbf universal testing machine – all controlled by the same MTS
407 controller. An adjoining laboratory of approximately the same size includes an additional 8,000 lbf
hydraulic universal testing machine for dynamic testing, and a 10,000 lbf screw-driven universal
testing machine – all available for use in this proposal. Laboratory sensors include, load cells, LVDTs,
position transducers, extensometers, accelerometers and other sensors. Data acquisition capabilities
include 3 computers with National Instruments A/D boards, 1 laptop with an A/D PCMCIA card, and a
National Instruments SCXI system for conditioning and reading strain gauges, LVDTs, accelerometers
and 20 other analog channels along with LabView. Miscellaneous supporting equipment for field
instrumentation is also available. The PI has experience using this equipment in his research efforts to
date. In addition, the department was recently donated 10 Parker Series 2HX Actuators with 42 in.
stroke, along with 2 enclosed pumps which can be used in the development of unique testing rigs. The
Department shares an on-site machine and wood shop with Mechanical Engineering.
Technician and admin. support: The Department has a full-time lab technician available to support
the experimental testing proposed herein. Additionally the department has a part-time staff member in
the machine shop available to aid in the manufacturing of fixtures and specimens. The Department
hires a private consultant for computational support. The Department also has two full-time
administrative staff which are available for help on an as-needed basis.
9. Personnel
In addition to the principal investigator one graduate student is requested for supporting the research
proposed herein. The Department of Civil Engineering supports all first-year graduate students,
therefore the student selected for this work would not be brought on to the project until their second
year of research. This insures far greater productivity for the research and is a form of cost sharing that
the Department extends to all funded research projects. A three year project would allow the graduate
student to completely focus their efforts on this work and provide funding towards a Ph.D. A one page
resume of the PI is attached.
10. References
ABAQUS (2003). ABAQUS/Standard Users Manual version 6.3, ABAQUS, Inc. (formerly Hibbitt,
Karlsson Sorensen, Inc.) www.abaqus.com (referenced on 21 July 2003).
Ádány, S., Schafer, B.W. (2004). “Buckling mode classification of members with open thin-walled
cross-sections.” CIMS ’04, Fourth International Conference on Coupled Instabilities in Metal
Structures, Rome, Italy, 27-29 September, 2004
Davies, J.M., Leach, P., Heinz, D. (1994). “Second-order Generalized Beam Theory.” J. of
Constructional Steel Research, Elsevier. 31 (2-3) 221-241.
Deshmukh, S.U. (1996). Behavior of Cold-Formed Steel Web Elements with Web Openings Subjected
to Web Crippling and Combination of Bending and Web Crippling for Interior-One-Flange
Loading. M.S. Thesis. University of Missouri-Rolla. Rolla, MO.
Hancock, G.J., Y.B. Kwon, E.S. Bernard, (1994). “Strength Design Curves for Thin-Walled Sections
Undergoing Distortional Buckling.” J. of Constructional Steel Research, Elsevier. 31 (2-3) 169-186.
Kesti, J. (2000). Local and Distortional Buckling of Perforated Steel Wall Studs. Ph.D. Thesis,
Helsinki University of Technology, Espoo, Finland.
Langan, J.E., LaBoube, R.A., Yu, W.W. (1994). Structural Behavior of Perforated Web Elements of
Cold-Formed Steel Flexural Members Subjected to Web Crippling and a Combination of Web
Crippling and Bending. Cold-Formed Steel Series, Department of Civil Engineering, University of
Missouri-Rolla, 94 (3).
Direct Strength Design for Cold-Formed Steel Members with Perforations
9
NAS (2001). North American Specification for the Design of Cold-Formed Steel Structures. American
Iron and Steel Institute, Washington, DC.
Ortiz-Colberg, R., Peköz, T. (1981). Load Carrying Capacity of Perforated Cold-Formed Steel
Columns. Department of Structural Engineering Report, Cornell University, 81 (12).
Sarawit, T.P. (2003). Cold-Formed Steel Frame and Beam-Column Design. Ph.D. Dissertation.
Cornell University, Ithaca, NY.
Schafer, B.W. (2003) “CUFSM – Elastic Buckling Prediction” www.ce.jhu.edu/bschafer/cufsm
(referenced on 21 July 2003).
Shan, M., LaBoube, R.A., Yu, W. (1994). Behavior of Web Elements with Openings Subjected to
Bending, Shear and the Combination of Bending and Shear. Civil Eng. Study Structural Series,
University of Missouri-Rolla. 94 (2).
Shanmugam, N.E., Dhanalakshmi, M. (2001). “State-of-art review and compilation of studies on
perforated thin-walled structures.” International J. of Structural Stability and Dynamics, World
Scientific. 1 (1) 59-81
Silvestre, N., Camotim, D. (2002a). “First-order generalised beam theory for arbitrary orthotropic
materials.” Thin-Walled Structures, Elsevier. 40 (9) 755-789.
Silvestre, N., Camotim, D. (2002b). “Second-order generalised beam theory for arbitrary orthotropic
materials.” Thin-Walled Structures, Elsevier. 40 (9) 791-820.
Uphoff, C.A. (1996). Structural Behavior of Circular Holes in Web Elements of Cold-Formed Steel
Flexural Members. M.S. Thesis. University of Missouri-Rolla. Rolla, MO.
Direct Strength Design for Cold-Formed Steel Members with Perforations
10
APPENDIX: BUDGET BREAKDOWN
BUDGET - SPONSORED PROJECT
3 Years - Start Date 06/01/05
YEAR1
06/1/05 -05/31/06
YEAR 2
YEAR 3
06/1/06 - 05/31/07 06/01/07 - 05/31/08
Total
Faculty
Ben Schafer (1 month)
Benefits (33%)
Total Direct Salary & Benefits
Total F&A Base
F&A (63.5%)
Total Faculty Costs
8,274
2,730
11,005
11,005
6,988
17,993
8,605
2,840
11,445
11,445
7,268
18,712
8,949
2,953
11,903
11,903
7,558
19,461
25,829
8,524
34,352
34,352
21,814
56,166
20,964
6,269
1,200
28,433
20,964
13,312
41,745
21,593
6,583
1,200
29,375
21,593
13,712
43,087
22,241
6,912
1,200
30,352
22,241
14,123
44,475
64,798
19,763
3,600
88,161
64,798
41,146
129,308
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
10,000
10,000
10,000
6,350
16,350
0
10,000
10,000
10,000
6,350
16,350
Computer (no F&A)*
Software
Total Direct Equipment & Supplies
F&A Base
F&A (63.5%)
Total Equipment & Supplies
5,500
500
6,000
500
318
6,318
0
500
500
500
318
818
0
500
500
500
318
818
5,500
1,500
7,000
1,500
953
7,953
Total Direct
Total F&A base
Total F&A
Total Budget
Total All Major Items
45,438
32,469
20,618
66,056
66,056
41,320
33,538
21,297
62,617
62,617
52,755
44,643
28,349
81,104
81,104
139,513
110,650
70,263
209,776
209,776
Graduate Student
Graduate Student Salary (1 @12 months)
Tuition (for graduate students) (no F&A)
Health insurance (for graduate students) (no F&A)
Total Direct Graduate Student Costs
F&A Base
F&A (63.5%)
Total Graduate Student Costs
Travel
Dissemination of research results (conferences, etc.)
F&A Base
F&A (63.5%)
Total Travel
Experimental Support - Equipment & Supplies
Testing Equipment (no F&A)*
Materials/Supplies (Testing)
Total Direct Equipment & Supplies
F&A Base
F&A (63.5%)
Total Equipment & Supplies
Computational Support - Equipment & Supplies
Direct Strength Design for Cold-Formed Steel Members with Perforations
11
BENJAMIN WILLIAM SCHAFER
203 Latrobe Hall
Department of Civil Engineering
The Johns Hopkins University
Baltimore, MD 21218
e-mail: schafer@jhu.edu
voice: (410) 516-7801
fax: (410) 516-7473
web: www.ce.jhu.edu/bschafer
EDUCATION
Ph.D / M.S.
B.S.E.
Cornell University (1995–1997) Civil/Structural Eng., Minor: Theoretical and Applied Mech.
Thesis: Cold-Formed Steel Behavior and Design: Analytical and Numerical Modeling of Elements
and Members with Longitudinal Stiffeners. Advisor: Teoman Peköz
University of Iowa (1989–1993) Civil Engineering
HONORS
Research
Teaching
Service
Collingwood Prize (2003) (For paper on Distortional Buckling of Columns)
Best Presentation at the ASCE-SEI Structures Congress (2003) – tied for1st Place
Robert S. Pond, Sr. Excellence in Teaching Award (2004)
Dunn Family Award – from the JHU Student Council (2004)
PROFESSIONAL
Senior
Engineer
Simpson Gumpertz & Heger, Inc., Arlington, MA (1998 – 2000) Eng. Mech. & Infrastructure Division.
Failure Investigations, Buried Structures, Seismic Consulting
RESEARCH
Assistant
Professor
Postdoc
The Johns Hopkins University (2000 – Present)
Active Projects: Design of Structural Systems for Unforeseen Catastrophic Events, Cold-Formed Steel
Design Guide for the Direct Strength Method, Experimental Study of Distortional Buckling on C and
Z Members in Bending, Historic American Engineering Record: Covered Wooden Bridge Studies
Completed Projects: Test Verification of the Effect of Stress Gradient on Webs of C and Z Sections,
Distortional Buckling of Cold-Formed Steel Columns
Cornell University (1997–1998)
TEACHING
Asst. Prof.
Instructor
The Johns Hopkins University (2000 – Present) What is Engineering?, Steel Structures, Structural
Stability, Perspectives on the Evolution of Structures
Cornell University (1997-1998) Structural Behavior, Modern Structures
SERVICE & ACTIVITIES
Committees
American Iron and Steel Institute - Committee on Specifications (AISI-COS) (1995–Present)
ASCE-SEI Committee on Cold-Formed Steel, member (1997-2000) Chairmen (2001–Present)
ASCE-SEI Committee on Compression and Flexural Members, member (2001–Present)
SSRC TG 13, Thin-Walled Metal Construction, member (2001–2003) Chairmen (2004–Present)
SELECTED PUBLICATIONS:
Liu, H., Igusa, T., Schafer, B.W. (2004). “Global Optimization of Cold-Formed Steel Columns by an Original
Knowledge-Based
Optimization
Method.”
Elsevier,
Thin-walled
Structures
Journal
(In
Press)
(doi:10.1016/j.tws.2004.01.001)
Schafer, B.W. (2003). “Advances in Direct Strength Design of Thin-Walled Members.” Advances in Structures: Steel,
Concrete, Composite and Aluminum - ASSCCA’03, Sydney, Australia, June 23 - 25, 2003
Yu, C., Schafer, B.W. (2003). “Local Buckling Tests on Cold-Formed Steel Beams.” ASCE, Journal of Structural
Engineering. 129 (12) 1596-1606. (doi:10.1061/(ASCE)0733-9445(2003)129:12(1596))
Schafer, B.W. (2002). “Local, Distortional, and Euler Buckling in Thin-walled Columns.” ASCE, Journal of Structural
Engineering. 128 (3) 289-299. (doi:10.1061/(ASCE)0733-9445(2002)128:3(289))
Schafer, B.W., Peköz, T. (1999). “Laterally Braced Cold-Formed Steel Flexural Members with Edge Stiffened Flanges.”
ASCE, Journal of Structural Engineering. 125 (2) 118-127. (doi:10.1061/(ASCE)0733-9445(1999)125:2(118))
Direct Strength Design for Cold-Formed Steel Members with Perforations
12