ADVANCED STRUCTURAL ANALYSIS
5 MARKS:
1.
Structural analysis is the determination of the effects of loads on physical structures and their
components. Structures subject to this type of analysis include all that must withstand loads,
such as buildings,
bridges, vehicles, machinery, furniture, attire, soil strata, prostheses and
biological tissue. Structural analysis incorporates the fields of applied mechanics, materials
science and applied mathematics to compute a structure's deformations, internal forc
es,
stresses, support reactions, accelerations, and stability. The results of the analysis are used to
verify a structure's fitness for use, often saving physical tests. Structural analysis is thus a key
part of the engineering design of structures.
2.
A
nalytical methods
To perform an accurate analysis a structural engineer must determine such information as
structural loads, geometry, support conditions, and materials properties. The results of such an
analysis typically include support reactions, stres
ses and displacements. This information is then
compared to criteria that indicate the conditions of failure. Advanced structural analysis may
examine dynamic response, stability and non

linear behavior.
There are three approaches to the analysis: the mec
hanics of materials approach (also known as
strength of materials), the elasticity theory approach (which is actually a special case of the
more general field of continuum mechanics), and the finite element approach. The first two
make use of analytical fo
rmulations which apply mostly to simple linear elastic models, lead to
closed

form solutions, and can often be solved by hand. The finite element approach is actually
a numerical method for solving differential equations generated by theories of mechanics
such
as elasticity theory and strength of materials. However, the finite

element method depends
heavily on the processing power of computers and is more applicable to structures of arbitrary
size and complexity.
Regardless of approach, the formulation is
based on the same three fundamental relations:
equilibrium, constitutive, and compatibility. The solutions are approximate when any of these
relations are only approximately satisfied, or only an approximation of reality
3.
Limitations
Each method has no
teworthy limitations. The method of mechanics of materials is limited to
very simple structural elements under relatively simple loading conditions. The structural
elements and loading conditions allowed, however, are sufficient to solve many useful
engine
ering problems. The theory of elasticity allows the solution of structural elements of
general geometry under general loading conditions, in principle. Analytical solution, however, is
limited to relatively simple cases. The solution of elasticity problems
also requires the solution
of a system of partial differential equations, which is considerably more mathematically
demanding than the solution of mechanics of materials problems, which require at most the
solution of an ordinary differential equation. Th
e finite element method is perhaps the most
restrictive and most useful at the same time. This method itself relies upon other structural
theories (such as the other two discussed here) for equations to solve. It does, however, make it
generally possible t
o solve these equations, even with highly complex geometry and loading
conditions, with the restriction that there is always some numerical error. Effective and reliable
use of this method requires a solid understanding of its limitations.
20 marks:
1.
Methods using numerical approximation
It is common practice to use approximate solutions of differential equations as the basis for
structural analysis. This is usually done using numerical approximation techniques. The most
commonly used numerical approx
imation in structural analysis is the Finite Element Method.
The finite element method approximates a structure as an assembly of elements or components
with various forms of connection between them. Thus, a continuous system such as a plate or
shell is m
odeled as a discrete system with a finite number of elements interconnected at finite
number of nodes. The behaviour of individual elements is characterised by the element's
stiffness or flexibility relation, which altogether leads to the system's stiffnes
s or flexibility
relation. To establish the element's stiffness or flexibility relation, we can use the mechanics of
materials approach for simple one

dimensional bar elements, and the elasticity approach for
more complex two

and three

dimensional element
s. The analytical and computational
development are best effected throughout by means of matrix algebra, solving partial
differential equations.
Early applications of matrix methods were for articulated frameworks with truss, beam and
column elements; later and more advanced matrix methods, referred to as "finite element
analysis," model an entire structure with one

, two

, and three

dimensional el
ements and can
be used for articulated systems together with continuous systems such as a pressure vessel,
plates, shells, and three

dimensional solids. Commercial computer software for structural
analysis typically uses matrix finite

element analysis, whi
ch can be further classified into two
main approaches: the displacement or stiffness method and the force or flexibility method. The
stiffness method is the most popular by far thanks to its ease of implementation as well as of
formulation for advanced app
lications. The finite

element technology is now sophisticated
enough to handle just about any system as long as sufficient computing power is available. Its
applicability includes, but is not limited to, linear and non

linear analysis, solid and fluid
inte
ractions, materials that are isotropic, orthotropic, or anisotropic, and external effects that
are static, dynamic, and environmental factors. This, however, does not imply that the
computed solution will automatically be reliable because much depends on t
he model and the
reliability of the data input.
2.
Limitations
Each method has noteworthy limitations. The method of mechanics of materials is limited to
very simple structural elements under relatively simple loading conditions. The structural
elements
and loading conditions allowed, however, are sufficient to solve many useful
engineering problems. The theory of elasticity allows the solution of structural elements of
general geometry under general loading conditions, in principle. Analytical solution,
however, is
limited to relatively simple cases. The solution of elasticity problems also requires the solution
of a system of partial differential equations, which is considerably more mathematically
demanding than the solution of mechanics of materials pr
oblems, which require at most the
solution of an ordinary differential equation. The finite element method is perhaps the most
restrictive and most useful at the same time. This method itself relies upon other structural
theories (such as the other two dis
cussed here) for equations to solve. It does, however, make it
generally possible to solve these equations, even with highly complex geometry and loading
conditions, with the restriction that there is always some numerical error. Effective and reliable
use
of this method requires a solid understanding of its limitations.
[edit]
Strength of materials methods (classical methods)
The simplest of the three methods here discussed, the mechanics of materials method is
available for simple structural members subj
ect to specific loadings such as axially loaded bars,
prismatic beams in a state of pure bending, and circular shafts subject to torsion. The solutions
can under certain conditions be superimposed using the superposition principle to analyze a
member under
going combined loading. Solutions for special cases exist for common structures
such as thin

walled pressure vessels.
For the analysis of entire systems, this approach can be used in conjunction with statics, giving
rise to the method of sections and meth
od of joints for truss analysis, moment distribution
method for small rigid frames, and portal frame and cantilever method for large rigid frames.
Except for moment distribution, which came into use in the 1930s, these methods were
developed in their curre
nt forms in the second half of the nineteenth century. They are still used
for small structures and for preliminary design of large structures.
The solutions are based on linear isotropic infinitesimal elasticity and Euler
–
Bernoulli beam
theory. In other
words, they contain the assumptions (among others) that the materials in
question are elastic, that stress is related linearly to strain, that the material (but not the
structure) behaves identically regardless of direction of the applied load, that all de
formations
are small, and that beams are long relative to their depth. As with any simplifying assumption in
engineering, the more the model strays from reality, the less useful (and more dangerous) the
result.
3.
Structures and Loads
A structure refers
to a body or system of connected parts used to support a load. Important
examples related to Civil Engineering include buildings, bridges, and towers; and in other
branches of engineering, ship and aircraft frames, tanks, pressure vessels, mechanical syste
ms,
and electrical supporting structures are important. In order to design a structure, one must
serve a specified function for public use, the engineer must account for its safety, aesthetics,
and serviceability, while taking into consideration economic a
nd environmental constraints.
Other branches of engineering work on a wide variety of nonbuilding structures.
[edit]
Classification of structures
It is important for a structural engineer to recognize the various types of elements composing a
structure an
d to be able to classify structures as to their form and function. Some of the
structural elements are tie rods, rod, bar, angle, channel, beams, and columns. Combination of
structural elements and the materials from which they are composed is referred to
as a
structural system. Each system is constructed of one or more basic types of structures such as
trusses, cables and arches, frames, and surface structures.
[edit]
Loads
Main article: Structural load
Once the dimensional requirement for a structure hav
e been defined, it becomes necessary to
determine the loads the structure must support. In order to design a structure, it is therefore
necessary to first specify the loads that act on it. The design loading for a structure is often
specified in building c
odes. There are two types of codes: general building codes and design
codes, engineer must satisfy all the codes requirements for a reliable structure.
There are two types of loads that structure engineering must encounter in the design. First type
of loa
d is called Dead loads that consist of the weights of the various structural members and
the weights of any objects that are permanently attached to the structure. For example,
columns, beams, girders, the floor slab, roofing, walls, windows, plumbing, ele
ctrical fixtures,
and other miscellaneous attachments. Second type of load is Live Loads which vary in their
magnitude and location. There are many different types of live loads like building loads, highway
bridge Loads, railroad bridge Loads, impact loads
, wind loads, snow loads, earthquake loads, and
other natural loads.
[edit]
Analytical methods
To perform an accurate analysis a structural engineer must determine such information as
structural loads, geometry, support conditions, and materials
properties. The results of such an
analysis typically include support reactions, stresses and displacements. This information is then
compared to criteria that indicate the conditions of failure. Advanced structural analysis may
examine dynamic response, s
tability and non

linear behavior.
There are three approaches to the analysis: the mechanics of materials approach (also known as
strength of materials), the elasticity theory approach (which is actually a special case of the
more general field of continuu
m mechanics), and the finite element approach. The first two
make use of analytical formulations which apply mostly to simple linear elastic models, lead to
closed

form solutions, and can often be solved by hand. The finite element approach is actually
a n
umerical method for solving differential equations generated by theories of mechanics such
as elasticity theory and strength of materials. However, the finite

element method depends
heavily on the processing power of computers and is more applicable to str
uctures of arbitrary
size and complexity.
Regardless of approach, the formulation is based on the same three fundamental relations:
equilibrium, constitutive, and compatibility. The solutions are approximate when any of these
relations are only approximat
ely satisfied, or only an approximation of reality.
4.
Service in Informatics and Analysis (SIA Ltd.) was one of the pioneering time

sharing service
bureau companies in the late 1960s, later known as SIA Computer Services. Its head office was
located at L
ower Belgrave Street, close to Victoria Station in London, and the company had
branch offices in Edinburgh, Manchester, the West End, Paris and (much later) in Hong Kong. SIA
offered terminal services via the Post Office telephone network at speeds of 10,
15, 30, 60 and
120 characters per second for Teletype

style terminals and of 1200 baud, 2400 baud and 4800
baud for Remote Job Entry terminals. Later with the release of the IBM PC, systems were
developed to emulate the Remote Batch and interactive termina
ls. Clients could also visit the
head or branch offices to submit their jobs personally or have them accepted and supervised by
the production department.
In 1968 the company installed a Control Data Corporation CDC 6600 mainframe computer
–
the
first CDC
6600 installed in the United Kingdom.[1] It was generally considered to be the first
successful supercomputer, outperforming its fastest predecessor, IBM 7030 Stretch, by about
three times. It remained the world's fastest computer from 1964 to 1969, when
it relinquished
that status to its successor, the CDC 7600. By 1974 SIA added more processing power by
installing a Control Data Cyber

72 at Victoria.
SIA had assembled a comprehensive library of proven software packages drawn from all over
the world. The
y covered a range of disciplines: electronics, management science, integrated
survey and statistical, integrated cluster analysis, segmentation analysis, simulation, financial
planning, production planning and control systems, civil and structural engineer
ing, finite
element stress analysis, box girder bridge design, highway engineering, business systems,
business data processing, database management and many others.
Client support groups
SIA's client support groups included:
Technical services
Supporte
d clients writing and running their own programs, whether written in ALGOL, BASIC,
COBOL, or Fortran. They provided training in all user aspects of the Kronos

75 service and on
operating various types of terminal.
Commercial team
Supported the SIA sales a
ccounting package and the database management system SYSTEM
2000. They also developed computer systems to meet various business applications to meet the
individual needs of client organisations. Applications covered included invoicing, sales ledger,
sales
analysis, stock control, bill of material processing, library information retrieval and a wide
range of database implementations characterised by the need to store quantities of data and to
retrieve from it in a number of differing ways.
Management science
s team
Supported the statistics, linear programming, depot location and financial modelling packages
offered. Production scheduling, warehouse siting, cash flow modelling and survey analysis are
typical applications.
Engineering
Civil and structural
support packages for bridge and building design and detailing, for soil
mechanics and for other civil engineering applications.
Offshore engineering
Concentrated on the business of designing structures for use in offshore oil production.
Waveloading, stat
ic and dynamic analyses, towing studies and stability problems were also
covered.
Advanced structural analysis
Supported clients tackling problems with the help of finite element techniques and other
analyses. Examples are drawn mostly from mechanical eng
ineering
—
from nuclear power
stations through aircraft and satellites to diesel engines.
Chemical engineering
Assisted process designers to use a powerful flowsheet simulator program, arguably the best in
the world.
[edit]
Highway engineering and mapping
Supported and developed a range of programs for use in highway design and in ground
modelling and mapping. Programs developed by this team have helped British and foreign
consultants to win highway design contracts in the Middle East since the design tim
escale is
dramatically shortened by their use.
Transportation
Developed and maintained the TFA suite of programs for transportation planning studies and
provided consultancy services.
Systems
The operating systems running on the Control Data 6600, Cyber

72 and later Cyber

175 included
SCOPE, Kronos and later NOS. The source code was heavily modified for the business needs of
the company by a team of systems programmers. Many of the ground

breaking ideas[peacock
term] developed at SIA were incorporated in
Control Data's later systems. SIA was a member of
J.U.N.K (Joint Users of NOS and Kronos), a user group formed to share ideas and experiences
using Control Data's software.[2]
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