Canadian Seismic Design of Steel Structures

Canadian Seismic Design of Steel Structures

Design of Steel Structures of the Canadian Standards Association (CSA) governs the design of the majority of steel structures in Canada. Clause 27 of the standard includes the earthquake design provisions for seismic force resisting systems for which ductile seismic response is expected. Technical changes and new requirements have been incorporated in the 2009 edition of CSA S16, including modifications of the expected material properties for HSS members, consideration of protected zones, definitions of brace probable compressive and tensile resistances for capacity design and special requirements for braces intersecting columns between floors for concentrically braced steel frames, new seismic provisions for buckling restrained braced steel frames, design and detailing requirements for built-up tubular ductile links in eccentrically braced steel frames, changes to the requirements for ductile steel plate walls and for plate walls with limited ductility, including allowances for perforations and corner cut-outs in infill plates, and special provisions for steel frames of the Conventional Construction category above 15 m in height. These modifications were developed in parallel with the 2010 National Building Code of Canada (NBCC). The paper summarizes the new CSA S16-09 seismic design requirements with reference to NBCC 2010.

Basic capacity design provisions are given in CSA S16 to ascertain that minimum strength hierarchy exists along the lateral load path such that the intended ductile energy dissipation mechanism is mobilized and the integrity of the structure is maintained under strong ground shaking. In the design process, the yielding components of the SFRS may be oversized compared to the specified design seismic forces, as would be the case when drift limits, minimum member sizes or non-seismic load combinations govern the design. In this case, it is specified both in NBCC 2010 and CSA S16 that the design forces in capacity-protected elements need not exceed those induced by a storey shear determined with RoRd = 1.3. This upper bound essentially corresponds to the elastic seismic force demand reduced by 1.3, recognizing that nonyielding components will likely possess minimum overstrength. This 1.3 reduction factor only applies if the governing failure mode is ductile, and RoRd = 1.0 must be used otherwise.

This file contains formatted spreadsheets to perform the following calculations:
 - Section 1: Area of equivalent diagonal brace for plate wall analysis (Walls).
 - Section 2: Design of link in eccentrically braced frames (EBF).
 - Section 3: Design of Bolted Unstiffened End Plate Connection (BUEP).
 - Section 4: Design of Bolted Stiffened End Plate Connection (BSEP).
 - Section 5: Design of Reduced Beam Section Connection (RBS).
 - Section 6: Force reduction factor for friction-damped systems (Rd_friction).

 Additionally, this file contains the following tables:
 - Valid beam sections for moment-resisting connections (B_sections).
 - Valid column sections for moment-resisting connections (C_sections).
 - Valid bolt types for moment-resisting connections (Bolts).
 - Database of properties of all sections (Sections Table).


Modern Experimental Stress Analysis

Modern Experimental Stress Analysis

This book is based on the assertion that, in modern stress analysis, constructing the model
is constructing the solution—that the model is the solution. But all model representations
of real structures must be incomplete; after all, we cannot be completely aware of every
material property, every aspect of the loading, and every condition of the environment,
for any particular structure. Therefore, as a corollary to the assertion, we posit that a
very important role of modern experimental stress analysis is to aid in completing the
construction of the model.

What has brought us to this point? On the one hand, there is the phenomenal growth
of finite element methods (FEM); because of the quality and versatility of the commercial
packages, it seems as though all analyses are now done with FEM. In companies
doing product development and in engineering schools, there has been a corresponding
diminishing of experimental methods and experimental stress analysis (ESA) in particular.
On the other hand, the nature of the problems has changed. In product development,
there was a time when ESA provided the solution directly, for example, the stress at a
point or the failure load. In research, there was a time when ESA gave insight into the
phenomenon, for example, dynamic crack initiation and arrest. What they both had in
common is that they attempted to give “the answer”; in short, we identified an unknown
and designed an experiment to measure it. Modern problems are far more complex, and
the solutions required are not amenable to simple or discrete answers.

In truth, experimental engineers have always been involved in model building, but the
nature of the model has changed. It was once sufficient to make a table, listing dimensions
and material properties, and so on, or make a graph of the relationship between quantities,
and these were the models. In some cases, a scaled physical construction was the model.
Nowadays the model is the FEM model, because, like its physical counterpart, it is a
dynamic model in the sense that if stresses or strains or displacements are required, these
are computed on the fly for different loads; it is not just a database of numbers or graphs.
Actually, it is even more than this; it is a disciplined way of organizing our current
knowledge about the structure or component. Once the model is in order or complete, it
can be used to provide any desired information like no enormous data bank could ever
do; it can be used, in Hamilton’s words, “to utter its revelations of the future”. It is this
predictive and prognostic capability that the current generation of models afford us and
that traditional experimental stress analysis is incapable of giving.

There are two main types of stress analyses. The first is conceptual, where the structure
does not yet exist and the analyst is given reasonable leeway to define geometry, material,
loads, and so on. The preeminent way of doing this nowadays is with the finite element
method (FEM). The second analysis is where the structure (or a prototype) exists, and it
is this particular structure that must be analyzed. Situations involving real structures and
components are, by their very nature, only partially specified. After all, the analyst cannot
be completely aware of every material property, every aspect of the loading, and every
condition of the environment for this particular structure. And yet the results could be
profoundly affected by any one of these (and other) factors. These problems are usually
handled by an ad hoc combination of experimental and analytical methods—experiments
are used to measure some of the unknowns, and guesses/assumptions are used to fill in
the remaining unknowns. The central role of modern experimental stress analysis is to
help complete, through measurement and testing, the construction of an analytical model
for the problem. The central concern in this book is to establish formal methods for
achieving this.

Experimental methods do not provide a complete stress analysis solution without additional
processing of the data and/or assumptions about the structural system. Figure I.1

shows experimental whole-field data for some sample stress analysis problems—these
example problems were chosen because they represent a range of difficulties often encountered
when doing experimental stress analysis using whole-field optical methods. (Further
details of the experimental methods can be found in References [43, 48] and will be elaborated
in Chapter 2.) The photoelastic data of Figure I.1(b) can directly give the stresses
along a free edge; however, because of edge effects, machining effects, and loss of
contrast, the quality of photoelastic data is poorest along the edge, precisely where we
need good data. Furthermore, a good deal of additional data collection and processing is
required if the stresses away from the free edge is of interest (this would be the case in
contact and thermal problems). By contrast, the Moir´e methods give objective displacement
information over the whole field but suffer the drawback that the fringe data must be
spatially differentiated to give the strains and, subsequently, the stresses. It is clear from
Figure I.1(a) that the fringes are too sparse to allow for differentiation; this is especially
true if the stresses at the load application point are of interest. Also, the Moir´e methods
invariably have an initial fringe pattern that must be subtracted from the loaded pattern,
which leads to further deterioration of the computed strains. Double exposure holography
directly gives the deformed pattern but is so sensitive that fringe contrast is easily lost
(as is seen in Figure I.1(c)) and fringe localization can become a problem. The strains
in this case are obtained by double spatial differentiation of the measured data on the
assumption that the plate is correctly described by classical thin plate theory—otherwise

it is uncertain as to how the strains are to be obtained.


Advanced Stress and Stability Analysis: worked examples

Advanced Stress and Stability Analysis

This book is not a collection of problems in the ordinary sense. The exercises
are not intended for beginning students in a “Strength of Materials”
course but for those who have completed the course. Neither does the book
intend to interpret a full coursev, but it draws the reader’s attention either to
some speci…c problems that are not at all included in the course, or to such
problems that often escape the student’s attention not only in the process of
training but also in their further engineering activity.
The problem complexity is also di¤erent. Some are ordinary problems and
others are rather complicated. Some of them require only common knowledge
and quickness of wit and others require application of primary aspects of
the theory of elasticity. Many of them are complicated at …rst glance, but
their solution may be found to be unexpectedly simple. In other cases the
at …rst glance obvious solution may be incorrect. Even experienced readers
may …nd themselves making mistakes. That is why all problems are provided
with detailed solutions for those who are interested in the principles of the
problem-solving process, or to provide the possibility for testing the obtained
results in case the readers intend to solve the problems in their own manner.
Experience shows that students are often dissatis…ed with the solutions
of typical problems presented in ordinary textbooks. Many students have
questions that are beyond the training course and require more fundamental
understanding. They naturally want to test themselves in solving more complex
and more interesting problems where alertness, knowledge, and intuition
are required. The book is aimed at the demands of those students, most of all.

New problems appear not at a writing-table. They arise as a result of new
developments and sometimes simply by friendly conversations, as a result
of opinion exchange and creative search of suitable statements. The author
was fortunate for encountering such kind discussions with colleagues and

specialists and extremely thanks his lucky stars and friends for that.

This is a book, written by the famous late Russian engineer and educator
Vsevolod I.Feodosiev, who formed the tradition of stress and stability analysis
for generations of engineers and researchers working in those …elds, where the
Soviet Union accomplished the greatest technological breakthrough of the
20th century – a race into space.
Prof. Feodosiev continued the best tradition of the Russian engineering
school with his innovative and unique concepts based on deep penetration
into the mechanical and practical nature of problems. Four times revised and
republished in Russia and translated into some languages, the book became
a classical desk text for training of top mechanical specialists. Written with
a great pedagogical skill, it gives to the reader a fresh and original outlook
on analysis of some advanced engineering problems.
The research and educational work of Prof. V.I. Feodosiev was carried
out in the Bauman Moscow State Technical University (BMSTU), where he
studied and worked for over 50 years. For a long time Prof. V.I. Feodosiev
was head of the Space Missile Engineering Department.
His outstanding ability, extraordinary memory and diligence revealed itself
quite early. Feodosiev’s …nal student project was quali…ed as a PhD thesis.
He was awarded his DSc degree for research in application of ‡exible shells
in machines when he was 27 years old.
For 50 years Prof. Feodosiev delivered in BMSTU his course of lectures
on strength of materials. His textbook of the course, republished more than
ten times, became the basic book on the subject for top Russian technical
universities and was awarded the State Prize. V.I. Feodosiev was awarded
also the Lenin Prize (the main scienti…c award in the Soviet Union) for his
contribution into fundamental tree-volume monograph ”Strength Analysis in
Mechanical Engineering”.
The fundamentals of strength and reliability in aero-space engineering
were published in his monographs: ”Elastic Elements of Precision Engineering”,
”Strength Analysis of High-Loaded Parts of Jet Engines”, ”Introduction
into Missile Engineering”.
Deep insight into engineering problems, clearness of concepts and elegance
of solutions enhanced by undoubted pedagogical talent are the main features
of Feodosiev’s style.


Reanalysis of Structures: A Unified Approach for Linear, Nonlinear, Static and Dynamic Systems

Reanalysis of Structures: A Unified Approach for Linear, Nonlinear, Static and Dynamic Systems

Structural analysis is a most exciting field of activity, but it is only a support
activity in the field of structural design. Analysis is a main part of the
formulation and the solution of any design problem, and it often must be
repeated many times during the design process. The analysis process helps
to identify improved designs with respect to performance and cost.
Referring to behavior under working loads, the objective of the analysis
of a given structure is to determine the internal forces, stresses and displacements
under application of the given loading conditions. In order to
evaluate the response of the structure it is necessary to establish an analytical
model, which represents the structural behavior under application of
the loadings. An acceptable model must describe the physical behavior of
the structure adequately, and yet be simple to analyze. That is, the basic
assumptions of the analysis will ensure that the model represents the problem
under consideration and that the idealizations and approximations used
result in a simplified solution. This latter property is essential particularly
in the design of complex or large systems.

The overall effectiveness of an analysis depends to a large degree on the
numerical procedures used for the solution of the equilibrium equations
[1]. The accuracy of the analysis can, in general, be improved if a more refined
model is used. In practice, there is a tendency to employ more and
more refined models to approximate the actual structure. This means that
the cost of an analysis and its practical feasibility depend to a considerable
degree on the algorithms available for the solution of the resulting equations.
The time required for solving the equilibrium equations can be a
high percentage of the total solution time, particularly in nonlinear analysis
or in dynamic analysis, when the solution must be repeated many times.
An analysis may not be possible if the solution procedures are too costly.
Because of the requirement to solve large systems, much research effort

has been invested in equation solution algorithms.

In elastic analysis we refer to behavior under working loads. The forces
must satisfy the conditions of equilibrium, and produce deformations compatible
with the continuity of the structure and the support conditions. That
is, any method must ensure that both conditions of equilibrium and compatibility
are satisfied. In linear analysis we assume that displacements
(translations or rotations) vary linearly with the applied forces. That is, any
increment in a displacement is proportional to the force causing it. This assumption
is based on the following two conditions:
The material of the structure is elastic and obeys Hooke's law.
All deformations are assumed to be small, so that the displacements do
not significantly affect the geometry of the structure and hence do not
alter the forces in the members. Thus, the changes in the geometry are

small and can be neglected.

Repeated analysis, or reanalysis, is needed in various problems of structural
analysis, design and optimization. In general, the structural response
cannot be expressed explicitly in terms of the structure properties, and
structural analysis involves solution of a set of simultaneous equations.
Reanalysis methods are intended to analyze efficiently structures that are
modified due to various changes in their properties. The object is to evaluate
the structural response (e.g. displacements, forces and stresses) for such
changes without solving the complete set of modified simultaneous equations.
The solution procedures usually use the response of the original
structure. Some common problems, where multiple repeated analyses are
needed, are described in the following.

In structural optimization the solution is iterative and consists of
repeated analyses followed by redesign steps. The high computational
cost involved in repeated analyses of large-scale problems is one of the
main obstacles in the solution process. In many problems the analysis
part will require most of the computational effort, therefore only
methods that do not involve numerous time-consuming implicit analyses
might prove useful. Reanalysis methods, intended to reduce the
computational cost, have been motivated by some typical difficulties
involved in the solution process. The number of design variables is
usually large, and various failure modes under each of several load
conditions are often considered. The constraints are implicit functions of
the design variables, and evaluation of the constraint values for any
assumed design requires the solution of a set of simultaneous analysis

In structural damage analysis it is necessary to analyze the structure for
various changes due to deterioration, poor maintenance, damage, or
accidents. In general many hypothetical damage scenarios, describing
various types of damage, should be considered. These include partial or
complete damage in various elements of the structure and changes in the
support conditions. Numerous analyses are required to assess the
adequacy of redundancy and to evaluate various hypothetical damage
scenarios for different types of damage.


Retaining Wall with Anchors Analysis and Design Spreadsheet

Retaining Wall with Anchors Analysis and Design Spreadsheet

This spreadsheet provides the design and analysis of retaining wall with anchors.
Retaining walls with anchors shall be dimensioned to ensure that the total lateral
load, Ptotal, plus any additional horizontal loads, are resisted by the horizontal component
of the anchor Factored Design Load Thi, of all the anchors and the reaction, R, at or below
the bottom of the wall. The embedded vertical elements shall ensure stability and sufficient
passive resistance against translation. The calculated embedment length shall be the greater
of that calculated by the Designer or Geotechnical Services.

Typical design steps for retaining walls with ground anchors are as follows:

Step 1 : Establish project requirements including all geometry, external loading conditions
(temporary and/ or permanent, seismic, etc.), performance criteria, and construction
constraints. Consult with Geotechnical Services for the requirements.

Step 2 : Evaluate site subsurface conditions and relevant properties of the in situ soil or
rock; and any specifications controlled fill materials including all materials strength
parameters, ground water levels, etc. This step is to be performed by Geotechnical Services.

Step 3 : Evaluate material engineering properties, establish design load and resistance
factors, and select level of corrosion protection. Consult with Geotechnical
Services for soil and rock engineering properties and design issues.

Step 4 : Consult with Geotechnical Services to select the lateral earth pressure distribution
acting on back of wall for final wall height. Add appropriate water, surcharge, and
seismic pressures to evaluate total lateral pressure. Check stability at intermediate
steps during contruction. Geotechnical numerical analysis may be required to
simulate staged construction. Consult Geotechnical Services for the task, should it be required.

Step 5 : Space the anchors vertically and horizontally based upon wall type and wall height.
Calculate individual anchor loads. Revise anchor spacing and geometry if necessary.

Step 6 : Determine required anchor inclination and horizontal angle based on right-of-way
limitations, location of appropriate anchoring strata, and location of underground structures.

Step 7 : Resolve each horizontal anchor load into a vertical force component and a force
along the anchor.

Step 8 : Structure Design checks the internal stability and Geotechnical Services checks the
external stability of anchored system. Revise ground anchor geometry if necessary.

Step 9 : When adjacent structures are sensitive to movements Structure Design and
Geotechical Services shall jointly decide the appropriate level and method of
analysis required. Revise design if necessary. For the estimate of lateral wall
movements and ground surface settlements, geotechnical numerical analysis is
most likely required. Consult with Geotechnical Services for the task, should it be required.

Step 10 : Structure Design analyzes lateral capacity of pile section below excavation subgrade.
Geotechnical Services analyzes vertical capacity. Revise pile section if necessary.

Step 11 : Design connection details, concrete facing, lagging, walers, drainage systems, etc.
Consult with Geotechnical Services for the design of additional drainage needs.

Step 12 : Design the wall facing architectural treatment as required by the Architect.


Aboveground Storage Tanks

Aboveground Storage Tanks

Aboveground storage tanks (ASTs) have been around since the inception
of industrial processing, but surprisingly, very little practical
engineering or general information is readily available to the tank
inspector, engineer, or operator. Why this is can only be speculated
on. Perhaps, the concept of a tank is so simple that it fosters a belief
that there is little complexity to them and they do not warrant expenditures
of resources. Perhaps, the tank owner believes that it is
appropriate to relegate all tank issues to the care of the manufacturer.
Perhaps, it is because they are generally reliable pieces of equipment
or are considered infrastructure.

Whatever the case, for those who have had to deal with ASTs,
understanding the complex issues and problems and implementing
good design, inspection, operational or environmental solutions to
AST problems have been all but simple. Well-intentioned individuals
and companies in need of sound engineering information frequently
make major blunders in areas of design, inspection, or safety. This
often results in high costs, shortened equipment life, ineffective inspection
programs, environmental damage, or accidents and injuries

as well as the threats of more national and state legislation.

In recent years there has been an increasing polarization between
industry, environmental groups, regulators, and the public. Each
facility which operates with tanks carries much more risk than just
damaging its equipment. Regardless of cause, injuries, fatalities, and
incidents all create a kind of press that can be used against the entire
industry with no real benefit. So rather than proper application of
industry standards to maintain facility integrity on a site-specific
basis, we are seeing a trend where the design, inspection, and operation
of facilities is being politically controlled or regnlated. This is the
worst possible way of running these facilities because it does not
address the fundamental causes of the problems and it creates inefficiencies

of mammoth proportion. It also directs resources away from where they are more needed for the public good such as higher risk
operations or in other places in the facility. The political approach to
controlling tank facilities penalizes the companies willing to do things
right while not really fIxing the fundamental problems. However, this
is not to say that there should be no responsibility to operate these
facilities carefully, safely, and in accordance with recogoized and generally
accepted good practices. In large part the situation we are in
now is a result of the industrial reticence to speak up on issues, to
promote information such as contained in this book to reduce the incidents
which form the basis of regulations, and to be more proactive in
the regulatory process than simply writing industry-recommended
practices or standards.

The purpose of the book then is to help break the cycle described
above by introducing appropriate information that will make any
tank facilities safer, more reliable, and not in need of more stringent
regulations. SpecifIcally, this book can help any individual, company,
or industry using ASTs to improve their performance in the areas of
safety (both employee and the public), environmentally responsible
operations, and implementation of good practices. Fortunately, this
can be done with relatively small expenditures of time and effort
when armed with knowledge and experience.

This book covers fundamental principles of aboveground storage
tanks as well as more advanced principles such as seismic engineering
needed for work in susceptible areas. It will be of interest to engineers,
inspectors, desigoers, regulators, and owners as well as to any
other person involved in any of the many specialized topics related to
tanks. Each topic is treated from a perspective that the reader knows
nothing and works up to a fairly advanced level so that the reading
may be selective as appropriate and as needed. Where the topic
becomes extremely advanced or where only unproved theories exist,
then this is noted and further references are made available. One of
the best sources of information about tanks, petroleum related issues,
and all kinds of problems associated with the petroleum business is
the American Petroleum Institute (API). This organization has produced
numerous high-quality standards, recommended practices, and
publications from which the reader may have access to the state of

the art in these topics.

Although the word tank identifIes only a single type or piece of equipment
in an industrial facility, tanks have been used in innumerable
ways both to store every conceivable liquid, vapor, or even solid and
in a number of interesting processing applications. For example, they
perform various unit operations in processing such as settling, mixing,
crystallization, phase separation, heat exchange, and as reactors.
Here we address the tank primarily as a liquid storage vessel with
occasional discussion regarding specialized applications. However, the
principles outlined here will, in many ways, apply generally to tanks

in other applications as well as to other equipment.


Footing Design of Shear Wall Based on ACI 318-14

Footing Design of Shear Wall Based on ACI 318-14

The criterion for the design of foundations of earthquake resisting
structures is that the foundation system should be capable of supporting the
design gravity loads while maintaining the chosen seismic energy dissipating
mechanisms of the structure. The foundation system in this context includes
the foundation structure, consisting of reinforced concrete construction, piles,
caissons and the supporting soil.

It is evident that for this criterion a suitable foundation system for a given
superstructure can be conceived only if the mechanisms by which earthquake actions
are disposed of are clearly defined. In most structures inelastic deformations
during large earthquakes are expected. Consequently for these
structures provisions are to be made for energy dissipation, usually by flexural
yielding. It is vital that energy dissipation be assigned by the designer
to areas within the superstructure or within the foundation structure in such
a manner that the expected ductility demands will remain within recognized
capabilities of the selected components. It is particularly important to ensure that
any damage that might result in the foundation structure does not lead to a
reduction of strength that might affect gravity load carrying capacity.

After defining design criteria in general for foundations
of earthquake resisting reinforced concrete structures, principles
are set out which govern the choice of suitable foundation systems
for various types of shear wall structures. The choice of
foundation systems depends on whether the seismic response of the
superstructure during the largest expected earthquake is to be elastic
or inelastic. For inelastically responding superstructures, preferably
the foundation system should be designed to remain elastic.
For elastically responding superstructures, suitable foundation systems
may be energy dissipating, elastic or of the rocking type. Design

criteria for each of these three foundation types are suggested.