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advanced structural analysis by devdas menon - pdf

Advanced Structural Analysis
Prof. Devdas Menon
Department of Civil Engineering
Indian Institute of Technology, Madras
Module - 1.1
Lecture - 01
Review of Basic Structural Analysis-1
Good morning to all of you. Welcome to this course on advanced structure analysis. This
is a course that we are offering on video through the auspices of NPTEL. We are starting
with the first module, where we will be reviewing basic structural analysis. This is a first
lecture in this entire series of about 45 lectures. Welcome once again to advanced
structural analysis.
(Refer Slide Time: 00:46)
So, these are the modules that we will cover in this course. There are seven modules the
first is review of basic structural analysis 1, which is what we will start with today, . we
will go fast over it because you already studied that. Review of basic structural analysis
2, part of it you studied will be looking at indeterminate structures. You have learnt
forced methods, but you have not learnt displacement methods, so we will study
displacement methods in some more detail and then we have basic matrix concepts.
This course is essentially a course which is matrix analysis of structural analysis and then
we will do axial elements first, they are truss elements both plane trusses and space
trusses. Then we look at beams, we look at grids, look at plane and space frames, and we
will also look at second order effects and elastic instability.
So, these are little advanced topics and I hope you will find it interesting, you are free to
ask questions at any point.
(Refer Slide Time: 01:59)
To start with, please note that the primary reference for this course will be the two books
which I have authored. Structural Analysis you have already been exposed to, except for
some chapters at the end which we will cover now and the main text is Advanced
Structural Analysis both are published by Narosa in India. they are paperback and abroad
it is Hardbound published by Alpha Science.
(Refer Slide Time: 02:24)
In the first module, we will basically cover introduction to structural analysis in statically
determinate structures, work and energy methods.
(Refer Slide Time: 02:40)
In the next module or in this module itself these are the topics but the last two, force
methods and displacement methods, we will cover in module two.
(Refer Slide Time: 02:52)
So, if you recall, in the book on Structural Analysis, we have five parts and today we will
quickly cover parts one and two. To begin with, let us refresh our understanding of what
Structural Analysis is all about.
(Refer Slide Time: 03:11)
Structural Analysis is the analysis of a given structure subject to some given loads and
the idea is to predict the response of the structure, as you may know that this is exactly
what is expected of all sciences. you can view it as a system.
There is some input to the system, which we call a stimulus and there is an output from
the system, which we call a response and Structural Analysis is the application of solid
mechanics to predict the response in terms of forces and displacements of a given
structure. It could be an existing structure or a new structure subject to specified loads.
Along with Structural Analysis, we have structural design. Your real objective is to do
structural design, but in order to do design, you need to do analysis. In design, we
proportion the structures, we identify the materials and you need to have some initial
proportions to do analysis in the first place, so it is an interactive process and there is
some requirements of any structure. Can you name some the main requirements of any
structure?
Strength. Yes, stability. Which should come first? Stability should come first. Structure
should first be stable. Strength and?
Durability?!
Durability will come as a party of serviceability. okay.
So, basically there are safety related issues and stability, strength and stiffness generally
cover the safety related issues. Strength and stiffness we have covered stability you all
know what it means and then it is not just enough to make a structure strong, stiff, and
stable, it must be also economical and it must look good, it must be aesthetic.
So you will find that economy is... There is a tradeoff between economy and safety,
because you need to invest more to make a structure more safe, but then someone has to
pay for it, so the real challenge for a structural engineer is to just about give the right
proportions, so that you do not spend too much money on the structure.
(Refer Slide Time: 05:36)
So, we have discussed this. The structure is really a system and we actually deal with the
mathematical model of the structure, so we reduce the complex three dimensional
structure to something that we can handle. So, we need to do structural idealization. We
have to reduce the structure to elements, and the elements are interconnected with joints
and there is something called internal stability of the structure.
The structure must also be externally stable especially terrestrial structure on the ground.
They should not fly off or move away, so we have to have adequate supports and that
raises the issue indeterminacy. We will look into that static and kinematic indeterminacy.
So, all these put together covers the structure and then loads that act on the structure are
of two kinds. We will come to that later.
(Refer Slide Time: 06:35)
Let us look at the structure properly. So, I have shown here the picture of a building. It is
pretty complicated. You have slabs, you have columns, you have beams, and you have
foundations. So, for our convenience, we try to separate out the slabs which we deal with
independently and separately and we transfer the loads of that slab to the frames. So you
end up dealing with the analysis of a space frame.
(Refer Slide Time: 07:09)
That space frame is made up of elements which are... or the structure as a whole is made
up of elements which are skeletal and which have also spatial elements. So, spatial
elements are those elements whose plan dimensions are large, but the thickness is small.
For example, a slab or a plate or a shell, they constitute spatial elements.
Whereas, the skeletal element like the human skeleton is made of line elements whose
length dimension is very large in comparison with the cross sectional dimensions and we
all know that the first course in Structural Analysis, we deal with the skeletal elements.
The spatial elements is little advanced to be taken up later.
So, the most general skeletal structure is a three dimensional space frame. I showed you
a picture in the earlier slide and special case of that structure is a planar structure. How is
a planar structure defined?
All those elements and loads are in the same plane.
All the elements that make up a structure must lie in one plane and the loads that act on
the structure must also lie on that same plane. So that is how you get a planar structure
and a special case of the planar structure is linear structure. For example, the chain where