WEBVTT
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So, welcome to the lecture number 3, that
Different Methods of Design of Reinforced
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Concrete Structures. Today, I shall give you
the brief idea of the different methods. So
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far, we have done the introduction, why you
are going for concrete, what is the limitation
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of the materials, show the permissible stresses,
those things, and also stress-strength curve
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- that we have seen in the last two classes.
So, today we shall start with the design.
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First, let us over view the different design
methods. For that, one is called that working
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stress method. The first one that is the working
stress method. Let me first give the list
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of different methods, then we shall come,
and then finally, we shall come to the one,
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which one we shall study in this particular
class. So, first one that is working stress
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method. There is another one, that is load
factor method; we shall come again in brief
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each of the methods. Third one, the strength
and serviceability method. We shall consider
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strength as well as serviceability. The first
two we can say only we are considering strength,
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but for the third one we shall consider strength
and serviceability both.
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And finally, we have that limit state method;
that is the one, which is the present day
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practice. We do this particular one, the limit
state method, that we use it extensively for
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our design reinforced concrete design, and
that, we shall study in this particular course.
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So, I repeat, working stress method, load
factor method, strength and serviceability
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method, and finally, the limit state method.
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So, what is working stress method? This has
evolved say around 1900 or the late nineties
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of the, or close of the, say, nineteenth century,
and this is the basic concept of modular ratio.
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So, what is modular ratio? Ratio between two
modulus, that elasticity of steel and concrete.
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This is one, I can explain, this particular
one, that we are considering, say, particularly,
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we are starting with the beam. We have to
find out the dimension of say beam. If we
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have to find out the dimension of the beam,
what we can do, let us forget the reinforced
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concrete for the time being; let us consider
that we would like to provide a section, may
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be a rectangular, may be a rectangular, which
is having
the width b and depth D. We would like to
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provide this particular section for a beam.
Since it is homogenous, so, permissible stresses
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at the top, permissible stresses at the top,
and the permissible stresses at the bottom
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- both are same.
We are considering a beam where the permissible,
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that means, the section will fail with certain
limit; maybe we can consider that one, say,
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sigma; permissible stress, say, sigma; that
means, if it is more than that, then we shall
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consider the section failed; that is the thing
we are considering here. So, what is the…
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and if we consider this one, this is the section
of a beam; this is the section of a beam;
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we can consider a simply supported beam also.
So, a simply supported beam. So, a simply
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supported beam having certain length, a span,
let us consider L. So, we would like to provide
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this particular one. We can consider different
kinds of load; we can consider say concentrated
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load at the centre; we can consider UDL; whatever
the arbitrary load we can consider. So, what
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we have to find out what is the design philosophy,
we have to find out the maximum moment.
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The beam has two parts: one is that one that
bending moment - that is the governing one
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- and shear force. So, for the time being,
we are considering that only for the bending;
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that means, we shall check the bending, we
shall resist bending only. So, beam will…
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so, whatever section we shall provide, that
section will resist the bending whatever coming
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due to external load as well as including
the self-weight.
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So, considering that, if you would like to
provide this simple section, say rectangular
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section, homogenous section, may be, say,
made of steel, aluminum, may be made of wood
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also, we can consider. So, if we consider
this particular one, then what we shall find
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out? For this particular case, we know, let
us say that we are applying certain load to
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be more specific say P. So, bending moment
M equal to P L by 4.
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So, what we can do it here, we would like
to find out… let us go little more specific
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also, that we will elaborate, the bending
moment diagram will be like that. So, this
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is your P L by 4. So, we have to resist this
particular moment, providing this particular
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section. That means we have to give certain
dimension of b and certain dimension of D.
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b, generally it is governed by the wall thickness;
generally not always. If you consider that
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any building, you will find out that beam
or column that is projected from the wall,
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that means, we cannot provide that one within
the wall, we cannot keep it, that is why you
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will find out that thickness is coming little
more. But generally, it comes with the wall
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thickness or you can consider brick thickness.
Generally, it comes say a width of the brick
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or length of the brick that is 250 millimeter,
and wall thickness also we provide that, and
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we can also keep the beam, we always keep
the beam within that particular 250, but sometimes
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if it is not possible due to other reason,
we go a little more, but generally we keep
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it 250 millimeter.
So, this one we can restrict it; so, that
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means, we have another one that is D. Now,
coming… since I have told this beam that
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is governed by dominating one that bending,
we have to check that one whether we can resist
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that bending moment. So, what is the equation?
Our equation is M by I equal to, say, f by
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uI or sigma by uI whatever it is. So, M is
the moment, that all you know, I think from
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the your first year or second year class.
So, M is the moment; I is the moment of inertia
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or second moment of area to be more specific;
f is the stress; and y that where you are
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going to find out the stress.
If I would like find out the stress and where
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from it is let us recapitulate. If this is
the section, due to this beam, we have in
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the top we have compression and at the bottom
we have tension. If we consider, because this
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beam, that one will deflect like this, it
will deflect in this way. So, we shall get
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tension at the bottom and compression at the
top. Most of the cases, you will find out
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this type of nature of that, your say stresses,
in beam. Only in cantilever you remember,
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cantilever it will be different. So, cantilever
tension will be at the top and compression
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will be at the bottom. And that is why we
provide main reinforcement; please note, main
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reinforcement, I am talking; that means, there
is some secondary or some will also be there;
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that one due to other reasons; but let us
consider only we are considering the main
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reinforcement or we say that, call it, longitudinal
reinforcement. So, that one we have to provide
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in the top for cantilever, because tension
is being developed at the top.
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So, here if we consider this particular equation,
let us recapitulate. We should have one neutral
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axis. And from the neutral axis, we will have
that y, we are going up. So, at any point,
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we can find out the corresponding stress.
Generally, the stress diagram comes, in the
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neutral axis it will be zero and it will be
this one. So, we can find out the stress,
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which will be maximum at the edges on the
outer side - at the top at the bottom. We
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shall find out that stress and on the basis
of that we have to find out whether it is
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coming within permissible limit or not.
If it is say wood, it has a permissible limit;
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if it is say steel, it has a different value;
similarly, for aluminum, it has a different
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value; for any material, each material has
its own permissible limit. And that one, where,
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how we are getting that one? That one, we
are getting from the stress-strain curve of
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that particular material. If we can find out
the stress-strain curve of that material,
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we shall find out the yield strength; that
where that material will yield. That all we
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shall consider, that one like concept, that
is the failure part we can consider, for the
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time being let us say, and on the basis of
that we shall find out the permissible limit,
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permissible stress, and that stress, obviously,
it will be lower than the yield strength,
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because we have to provide the factor of safety.
So, if we provide say factor of safety, say
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one, then may be the yield stress we have
to consider. If it is, say, 2, then half;
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if it is 3, then one-third. So, that way we
consider in our design. So, now, we shall
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consider this particular one. This is the
equation M by I equal to f by y. So, M will
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be equal to f times I by y, and we shall get
it here. If we consider at the top, if we
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consider at the top, if we consider at the
top, then f b D cubed by 12 and y is D by
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2; y is D by 2, because we are considering
from the neutral axis, we are going top, this
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is D by 2; and similarly, here also D by 2.
So, we have to find out the moment that is
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the one governed by that; that is the maximum
limit; and we can find out here f b D squared
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by 6. So, this is the simple equation, and
which, will come in our all the calculations.
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We shall consider this simple equation, we
shall consider. So, we can find out even more
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clear way. So, I can say 0.16, let us say
go up to 7 f b D squared. So, this is the
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equation we shall get it. Please note, M equal
to 0.167 f b D squared; that is the one we
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shall consider and let me follow in the next
page.
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Just to recapitulate once more in this particular
diagram. I repeat once more, D and b, and
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we have found M; M equal to moment of resistance
we can consider 0.167 f b D squared. So, we
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can find out, say, the equation becomes very
simple, handy, and we can find out the moment
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of resistance of that particular section.
The section you are going to provide, if you
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know the moment, so you have to provide the
moment of resistance.
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What we can do it here, if I know f, permissible
limit f, permissible stress f, if I know;
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b also, I am assuming b depending on your,
say, practical difficulty, not difficulty,
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say from the practical consideration, you
are providing b 250, 300, whatever you consider
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the width of the section you are providing.
And so, we know everything, f and b. Only
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we do not know D, and that D - depth - we
can provide on the basis of that moment.
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In other way, there are two parts: one is
that one, that you can design you are providing;
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the other way, let us assume b and D, and
let us assume b and D, and find out the corresponding
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moment of resistance. And that moment of resistance
should be more than the moment developed due
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to external load and self-weight. It should
be moment of resistance of that particular
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section you are providing, that should be
more than the moment developed due to external
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load and self-weight. That way also you can
do it; that means, you can make a table also,
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with different sections, b and D different
sections, you can make a table, and from that
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we can already compute those moment of resistance,
you can keep it in a tabular form, and whenever
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you will find out that this is the external
moment, so let us provide this section, because
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we generally do not provide whenever we are
considering design, we do not provide, say,
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175 or 177.2 millimeters; not like that. We
always provide some regular number.
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If we consider in the say reinforced concrete
design, you will find 250 by 250, 250 by 200;
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250 by 300, like that we will provide, in
a multiple of may be 25 millimeter. So, since
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we provide, that means, we have very, very
few options; not the huge options we have.
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So, for all the cases, we can keep ready our
calculation, that moment of resistance for
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that particular section, and immediately we
can provide. That way also we can do it.
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And that now-a-days through computer, that
only we do it; that means, we have computed
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the moment from any analysis software; let
us choose this section; let us find out whether
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this one having more than that moment of resistance,
more than the moment computed. So, that way
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you can easily provide the section.
So, now what we shall do it here, this one
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very simple; this one we are considering for
the homogenous one, where top and bottom having
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the same that your, say, permissible stresses,
but for concrete we do not have that case.
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For concrete, we have, when we are considering
concrete, we are assuming the tensile 1 at
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the bottom. So, this is the concrete, say
section, and here, we are assuming that the
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concrete in the tensile part will not take
any load, that beyond neutral axis, they feel
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there should be a neutral axis also, so it
will not take any load. So, we have to consider
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this; it will be resisted by these two bars
only, for this particular example. For that
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what we do? We use this modular ratio concept;
that means, we know the modular ratio of the
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steel, that is modular of elasticity of steel
reinforcing bar, and modulus of elasticity
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of concrete.
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So, what are the assumptions? That both concrete
and steel act together; it will work simultaneously;
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there is no slip; there is no slipping, that
means, whatever you are considering that concrete
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and steel, the steel is embedded on concrete,
and there is no slipping. Perfectly elastic
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at all stages of loading; it is perfectly
elastic at all stages of loading - this one
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we are assuming.
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And we have to consider factor of safety.
Factor of safety, we consider for concrete,
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about 3, with respect to cube strength. The
cube strength that we have told, that cube
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strength, that cubes 150 by 150 by 150 - those
cubes. So, from the cube strength, you will
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get it, that we shall find out, and we shall
take factors up to 3.
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For steel, we consider about 1.8, with respect
to yield strength. So, for steel, the yield
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strength, so we have to divide by 1.8, and
then, we shall get the corresponding, say,
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permissible stress in steel. So, that is the
one, that much, that is the one freedom you
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are getting in your design. So, based on your
experiment of a definite sample, we shall
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get the yield stress or cube strength; from
there, we can find out the corresponding permissible
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stress.
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Now, obviously, each method has some defects.
It deals only with the elastic behavior of
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the member; it deals only with the elastic
behavior of the member. It results in larger
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percentage of compression steels. That one,
let me elaborate. Sometimes, we know that
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steel only will takes a tensile part, tensile
zone we are reinforcing with steel bars, to
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take care the tensile stress developed in
the concrete section, but what we do it, sometimes
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we provide reinforcement steel in the compression
zone also, that we provide. And this particular
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method, will result more compression steel,
because that whatever the compression will
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be, because, that means, due to other methods
you will get less, when you are telling that
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more, that means, it will be obviously; so
that one we shall find out in limit state;
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that we can compare that particular method.
So, we are not going to detail of that particular
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one now, but we shall come back when we shall
solve few problems, which has developed that
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particular theory, that time we shall come
in detail.
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Only thing I would like to tell for this particular
section here, we provide reinforcement, say
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if we reinforcement top also, that is you
would get compression one; that means, in
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the compression side also you are providing
reinforcement; in the compression side also
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you will provide the reinforcement.
Generally, what we do it actually, even if
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we provide the, even if we provide reinforcement
at the bottom, we also provide reinforcement
23:57.230 --> 24:08.490
at the top also, though it is not required,
but we provide this one to hold stirrups;
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the stirrups goes like this, that one will
resist shear, because stirrup resists shear.
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It looks like this; this shear it looks like
this. That one, when we shall design shear,
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that time we shall consider this stirrups,
but what I mean to say, we also provide the
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reinforcement at the top, but even if we provide
the reinforcement at the top - this longitudinal
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one I am talking - even if we provide that
longitudinal reinforcement at the top, even
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then we have not, we have not actually considered
in our design; we have only considered this
24:49.059 --> 24:54.320
one at the bottom.
So, that time, though it is in the compression
24:54.320 --> 24:59.460
zone, even then, we have not considered this
one in our design; this one we are just simply
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keeping this one to hold in this stirrups.
But compression steel is something different;
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generally, provide near the support.
See, if this is a support say your wall - brick
25:16.529 --> 25:29.460
wall; here is also a brick wall; compression
reinforcement, because bending moment, since
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we can consider this type of support, just
this is simply supported. We can consider
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this support as a simply supported, because
the moment will be here zero, but we can consider,
25:54.309 --> 26:05.880
this is your say column, and this is your
beam, this one beam, and this is column.
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What I mean to say here, the support condition
in this case, and the support condition in
26:14.270 --> 26:22.590
this case - two are different. That fixity
of this one, that means, the way it is hold
26:22.590 --> 26:29.490
here, the way, and the way it is placed here
- they are two different support conditions.
26:29.490 --> 26:36.740
Simply for this case, simply you are placing
the beam on the top of the wall, but whereas,
26:36.740 --> 26:42.940
here you are fixing this one as if it is clamped.
I can consider this one as a fixed case. So
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that means, moment will be developed at the
two supports. So, you have to provide reinforcement,
26:50.650 --> 26:53.080
in the support; in both supports we have to
provide the reinforcement. That means, you
26:53.080 --> 27:00.200
have to design for the support moments also.
Where as in this case, we have to design only
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for the span moment, because that is the only
moment developed in this particular case.
27:05.789 --> 27:09.850
So, even if we consider the support condition
with some arrow, all those things, whatever
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you have done so far, now you have to find
out from your experience that what is the
27:14.740 --> 27:19.440
support condition you will consider, if it
is say, if it is say the column, both sides
27:19.440 --> 27:21.909
column, it may happen like this also.
27:21.909 --> 27:49.450
It may happen like this also. I can show you
one more example. So, this is your say RC
27:49.450 --> 28:18.490
column; this one beam; and this one brick
wall. So, what is the support condition, that
28:18.490 --> 28:24.779
what support condition should be suitable
for this type of problem? Because it is again
28:24.779 --> 28:30.440
different. So, we can consider this one as
a propped cantilever; that could be the more
28:30.440 --> 28:40.840
logical. We can assume this way; fixed and
it is propped. So, fixed and propped. So,
28:40.840 --> 28:49.460
that could be the solution, and if we have
say UDL; let us assume that we have UDL; UDL
28:49.460 --> 28:59.260
it may come if there are say live load as
well as your no that brick wall, and that
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one, we can consider that say W shape.
So, we can find out the bending moment diagram.
29:08.669 --> 29:15.330
This is the nature of… this should be the
nature of the bending moment diagram. Here
29:15.330 --> 29:20.350
this is zero, and we shall get support moment,
and we shall get span moment also. And we
29:20.350 --> 29:28.010
have to find out what is the maximum moment
between these two, and then, we have to design,
29:28.010 --> 29:35.350
first we have to design with the maximum moment,
and then check with the other moment. You
29:35.350 --> 29:42.880
provide reinforcement with the other moments
whatever found or developed in the beam section
29:42.880 --> 29:47.100
at different section; that is the general
philosophy we consider.
29:47.100 --> 29:54.200
So, that we shall again come back to this
percentage steel - on the compression steel
29:54.200 --> 30:04.330
- that we will find out what will be the percentage
steel, how all those things that we can compare.
30:04.330 --> 30:12.110
The other problem, the other problem, that
is concrete, does not have definite modulus
30:12.110 --> 30:25.320
of elasticity. This is one big problem. Though
we assume that concrete has a, say your, certain
30:25.320 --> 30:40.409
modulus of elasticity, roughly we can say,
say 25000 Newton per square millimeter.
30:40.409 --> 30:45.789
It is dependent on say your cube strength.
For different cubes you will have different
30:45.789 --> 30:54.330
values, but approximately, I can say 25000,
22000, those values which will come that definite
30:54.330 --> 31:00.890
formulas that 5700 root over FCT, that we
shall come back. So, that way also we can
31:00.890 --> 31:06.490
compute, that our what our code says. For
the time being, I am not telling that.
31:06.490 --> 31:11.610
So, this is because of say shrinkage, and
creep, because it is a time dependent phenomena
31:11.610 --> 31:16.409
that particular one concrete behaves. So,
that is why, because of that, the modulus
31:16.409 --> 31:20.950
of elasticity changes, because of particularly,
because of say creep and shrinkage, that we
31:20.950 --> 31:31.399
cannot get the definite value; the one we
can get it for is steel.
31:31.399 --> 31:37.769
We shall come back again with that working
stress method, with a small problem, we shall
31:37.769 --> 31:44.010
come back, but today just in this particular
class, let me tell you the overview of the
31:44.010 --> 31:50.360
different methods. So, one is the working
stress methods, that one I have told. Now
31:50.360 --> 32:13.330
let me teach the load factor method. This
was introduced in USA, in 1956; UK in 1957.
32:13.330 --> 32:22.549
The strength of the RC section at working
load is estimated from the ultimate strength
32:22.549 --> 32:34.440
of the section. So, we can find out the strength
of the RC section, that one due to your working
32:34.440 --> 32:39.059
load, whatever load actually given, we can
calculate from the ultimate strength of the
32:39.059 --> 32:45.700
section; we can find out from the ultimate
strength of the section; that means, we are
32:45.700 --> 32:51.230
going approaching towards a non-linear part
of the concrete; we are not assuming, no longer
32:51.230 --> 32:57.000
we are assuming the concrete that stress curve
is linear. We are going, we are also taking
32:57.000 --> 33:02.169
care of the non-linear part of that concrete
stressing curve.
33:02.169 --> 33:10.510
Load factor is the ratio of the ultimate load
the section can carry to the working load
33:10.510 --> 33:16.649
it has to carry. So, this is the one; that
means, we can find out, from this particular
33:16.649 --> 33:19.850
load factor we can find out, that how much
maximum it can take.
33:19.850 --> 33:25.370
So, whatever that working load given, and
whatever the ultimate load that it can take,
33:25.370 --> 33:29.890
from the ratio we can find out, and that is
why you call it actually load factor. So,
33:29.890 --> 33:40.049
one is coming from the resistance of that
particular section, considering the ultimate
33:40.049 --> 33:44.110
strength, considering the non-linear part
of the stress-strain curve of the concrete,
33:44.110 --> 33:49.429
and from there, we can find out that load
factor method, because concrete behaves in
33:49.429 --> 33:58.010
a non-linear one, due to our… that is the
one, which governs the behavior of the concrete,
33:58.010 --> 34:05.279
and that is why it is worth considering that
you would, say, that non-linear part of the
34:05.279 --> 34:07.510
stress-strain curve.
34:07.510 --> 34:17.659
So, I have already told, but anyway let me
repeat once more. Reinforced concrete sections
34:17.659 --> 34:25.990
behave inelastically at high loads. So, if
you apply more load than it will behave in
34:25.990 --> 34:33.820
an inelastic manner; no longer it is elastic;
and which is logical also in our consideration.
34:33.820 --> 34:39.540
And that is why, we find that this is the
one, which we should consider. So, reinforced
34:39.540 --> 34:43.349
concrete sections behave inelastically at
high loads.
34:43.349 --> 34:52.770
Ultimate strength design allows a more rational
selection of the load factors. So, what we
34:52.770 --> 34:59.410
can do, that means, if we know the ultimate
strength of a particular section, so, from
34:59.410 --> 35:06.560
there, we can find out that how much maximum
load it can take; how much maximum load it
35:06.560 --> 35:12.829
can take. And that is why we can say that;
otherwise, say, that it allows us to go approaching
35:12.829 --> 35:20.480
the more closer one, that one is the maximum
strength it can take. And the stress-strain
35:20.480 --> 35:25.859
curve for concrete is non-linear and is time
dependent - already I have told - and that
35:25.859 --> 35:31.310
is because of creep and shrinkage only. And
that one, we use second kind of empirical
35:31.310 --> 35:37.210
formula; we shall do that, we shall find out
deflection, we shall find out due to creep
35:37.210 --> 35:41.300
and shrinkage, we shall find out, and that
one, we shall do with our code, give some
35:41.300 --> 35:51.099
empirical formula, that we shall use it, and
we shall find out the deflection.
35:51.099 --> 35:56.670
Now, because the ultimate load factor, the
load factor method is nothing but we shall
35:56.670 --> 36:01.339
come back to the limit state; that is why
I am just giving you a only a very simple
36:01.339 --> 36:05.250
introduction, because that is the one we are
going towards the limit states.
36:05.250 --> 36:17.230
Now, what we shall do it here, if sections
are designed for by ultimate strength requirements
36:17.230 --> 36:24.680
alone, if we just simply consider the strength
requirement with the ultimate load, that ultimate
36:24.680 --> 36:30.540
strength, the cracking and deflections at
the service loads may be excessive. This is
36:30.540 --> 36:40.079
another, you can call conflict, you can say;
we have just seen the philosophy, that we
36:40.079 --> 36:45.339
have started with the elastic method, then
we have found, that concrete, if we consider
36:45.339 --> 36:52.050
it behaves in a non-linear elastic one with
a high load. So, let us go for the ultimate
36:52.050 --> 37:00.079
load, because that one will give us more,
better estimate of the strength of the section;
37:00.079 --> 37:04.750
that is the one we have to consider.
We are providing a section, if we say that
37:04.750 --> 37:10.540
this section will take this much of load,
if we consider the modular stress-strain curve,
37:10.540 --> 37:16.970
then we can get the more that the capacity
of the section will be more, and obviously,
37:16.970 --> 37:24.349
it is a reasonable and good estimate, but
if we go to that level, then we are facing
37:24.349 --> 37:29.050
another problem, that it may happen, because
we have assumed that concrete will not take
37:29.050 --> 37:36.089
any tension; steel will only take tension.
So; that means, here in the bottom, the crack
37:36.089 --> 37:43.030
may appear and crack may appear, and if the
crack that one width, if we find out the crack
37:43.030 --> 37:48.510
opening, then also the user of that particular,
say residents of that particular building,
37:48.510 --> 37:55.070
he may feel discomfort. If we have say excessive
say deformation, I can say that it will not
37:55.070 --> 38:00.550
fall, but even then, if you move through the
your say floor, and if it is a deforms, then
38:00.550 --> 38:05.150
also we shall feel discomfort, and that is
the reason that we have to consider the not
38:05.150 --> 38:12.200
only strength as well as that it should be
serviceable. And that is why your are considering
38:12.200 --> 38:19.579
that sales serviceability part. And so, if
sections are designed by ultimate strength
38:19.579 --> 38:24.510
requirements alone, the cracking and deflections
at the service loads, may be excessive, that
38:24.510 --> 38:32.609
may be excessive.
It is necessary to keep crack widths and deflections
38:32.609 --> 38:37.560
within reasonable limiting values. So, you
have to provide, that is obviously based on
38:37.560 --> 38:43.599
experiments. If the crack width is this much
or the deflection is this much, then we shall
38:43.599 --> 38:49.630
not feel any discomfort; the users will not
be panicked. So, those thingsm it will not
38:49.630 --> 38:54.430
be scary. So, those things also you have to
consider in your design; not only the strength
38:54.430 --> 39:04.950
as well as the serviceable condition.
So, these are the major two points what we
39:04.950 --> 39:09.980
consider, and we are we started with the strength,
and also we are considering the other part,
39:09.980 --> 39:12.310
that is your serviceable part also.
39:12.310 --> 39:20.890
So, coming to the final one, and which we
are going to study in this particular course,
39:20.890 --> 39:32.329
that is the limit state method. A limit state
corresponds to each of the states in which
39:32.329 --> 39:40.200
the structure becomes unfit. So, we should
have certain kind of… the one we have already
39:40.200 --> 39:46.190
told, that whether you are considering work
stress or ultimate strength, that is one side;
39:46.190 --> 39:51.560
whether you are considering say crack width,
deflection - that is another side; but the
39:51.560 --> 39:58.089
thing is, that these are two hands you have
to consider, and each of them, we can consider
39:58.089 --> 40:06.500
that is your say limit state. So, limit state,
it may be due to collapse, and limit state
40:06.500 --> 40:11.250
due to collapse, means we are talking from
the strength point of view, and limit state
40:11.250 --> 40:14.630
due to serviceability.
40:14.630 --> 40:23.520
So, limit state may be classified under two
broad categories. I have already pointed out.
40:23.520 --> 40:30.849
So, serviceability limit state of failure
in respect of deflection, cracking. So, this
40:30.849 --> 40:35.869
is the one we consider is a serviceability
limit state. The other one we consider limit
40:35.869 --> 40:45.700
state of failure in respect of strength, in
shear, flexure, torsion, bond or combined
40:45.700 --> 40:50.710
effects that axial also will come, when we
were talking, say your columns.
40:50.710 --> 40:56.000
So, these are the called limit states; one
part is from the serviceability point of view;
40:56.000 --> 41:01.619
other part is from the failure point of view
or we consider that one say collapse - limit
41:01.619 --> 41:11.000
state of collapse. And that is those two things
we shall consider in our case; those two things
41:11.000 --> 41:14.550
we shall consider.
41:14.550 --> 41:24.900
So, now we consider that characteristic strength.
I had told already, that it comes from the
41:24.900 --> 41:32.780
cube strength, cube strength of concrete.
The strengths that one can safely assume for
41:32.780 --> 41:40.200
materials are called their characteristic
strengths; the strengths that one can safely
41:40.200 --> 41:46.420
assume for materials are called their characteristic
strengths. So, this is the strength for each
41:46.420 --> 41:52.869
material it should have one characteristic
strength; that is the maximum limit we can
41:52.869 --> 41:58.720
consider for that particular material. We
shall not assume that one for our design,
41:58.720 --> 42:13.490
but we shall start from that particular, say,
strength.
42:13.490 --> 42:26.530
Now, let me find out in our IS 456, that our
design code, what, how it is defined. The
42:26.530 --> 42:33.599
term characteristic strength means that value
of the strength of the material below which
42:33.599 --> 42:40.900
5 percent of the test results are expected
to fail. That means, even if you consider
42:40.900 --> 42:45.849
a lot of say safety measurement all these
things, even then also, that means, about
42:45.849 --> 42:51.420
95 percent on the good faith, that way you
can consider, and that is the value we shall
42:51.420 --> 42:55.970
consider our characteristic strength; that
we shall consider.
42:55.970 --> 43:09.530
Similarly, we have the characteristic load
also. The maximum working load that the structure
43:09.530 --> 43:16.920
has to withstand and for which it is to be
designed is called the characteristic load.
43:16.920 --> 43:23.230
So, we have one part the characteristic strength,
the other one the load point of view; that
43:23.230 --> 43:27.859
will be maximum safe load, maximum load it
can take. So, that one also you have to consider.
43:27.859 --> 43:32.150
So, these are the two parts we have to consider
in our design.
43:32.150 --> 43:38.940
So, load and your strength - those two things
only will give you that one proper design,
43:38.940 --> 43:44.030
because if you underestimate the load, that
is dangerous; and if you over estimate the
43:44.030 --> 43:49.819
load, it is safe, but at the same time it
is not economy. So, this is, these are the…
43:49.819 --> 43:56.190
and some times in the design of this we face
problem also, because if the structure is
43:56.190 --> 44:04.140
not a usual regular one, sometimes the structure
could be, say little bit say different, that
44:04.140 --> 44:09.109
the people used to not used to design it regular
manner. So, obviously, there we face a lot
44:09.109 --> 44:13.619
of problems - what should be the design load.
That particular case we can consider.
44:13.619 --> 44:22.060
Say, for example, I can give you one example,
we have done say ISRO, that they are having
44:22.060 --> 44:30.500
one that second launching pad, and they are
having two arms - they call it cryo arms - which
44:30.500 --> 44:38.349
is holding the vehicle - the rocket vehicle
- and that is 18 meter. You can imagine the
44:38.349 --> 44:48.010
18 meter. The cantilever having 18 meter.
And this one will be just removed, immediately
44:48.010 --> 44:54.160
that when the zero position will come, the
zero time, and it will go to this limit within
44:54.160 --> 45:02.630
3 seconds. So, and then, the vehicle will
start moving up. This is the one that, obviously,
45:02.630 --> 45:08.030
it is not a standard design, though it is
made of steel, but it is not a standard design.
45:08.030 --> 45:15.950
So, what should be the load? What should be
the load? And also not only that, it is dynamic.
45:15.950 --> 45:20.420
You can imagine that one, that immediately
that when that minus 10, minus 9, in this
45:20.420 --> 45:25.900
way and when that zero will come, then immediately
it will just simply move to this level, and
45:25.900 --> 45:30.720
that you have to do it within 3 seconds. We
have just last year only we have completed
45:30.720 --> 45:37.920
that work, and so you can imagine that even
you know the material properties, lot of things,
45:37.920 --> 45:41.990
but you do not - what about the loading, because
there loading one can argue no loading will
45:41.990 --> 45:45.540
be this much the loading will be other one.
So, you have to consider here the dynamic
45:45.540 --> 45:51.069
analysis also; the dynamic analysis also you
have to do it; and from there you can find
45:51.069 --> 45:55.990
out what is the load, you can find out. When
we shall come back to your, say earthquake
45:55.990 --> 46:00.869
resistance, design of earthquake resistant
structures, in the later part of our of this
46:00.869 --> 46:06.010
course, that time I shall tell you that, what
is that dynamic load, that we shall discuss
46:06.010 --> 46:10.660
in detail.
So, the load also, another important factor
46:10.660 --> 46:20.589
in your design. So, according to IS 456, what
they have mentioned, the characteristic load,
46:20.589 --> 46:29.579
means that value of load which has 95 percent
probability of not being exceeded during the
46:29.579 --> 46:34.190
life of the structure.
So, even then, we are considering one limiting
46:34.190 --> 46:45.089
value, even then, we are assuming that few
cases it may go up, it may cross that particular
46:45.089 --> 46:52.160
limit, that is also possible. So, that way
we are assuming that your say load.
46:52.160 --> 47:04.809
So, what are the different loads? The just
to summarize the thing dead load, live load
47:04.809 --> 47:13.940
- that I have already told, wind load, earthquake
load. So, these are the there are so many
47:13.940 --> 47:23.089
other loads also we will may come, but these
are the four loads generally we consider.
47:23.089 --> 47:30.450
Even if you consider say the leaves of that
the tree - tree leaves actually accumulated
47:30.450 --> 47:36.240
on the roof that one also sometimes you
may have to consider; that may be it is unusual,
47:36.240 --> 47:41.200
but some time also it creates problem. So,
because this is coming that with the water,
47:41.200 --> 47:47.020
and it will be thick, that it is under, people
they are not going to check it in a regular
47:47.020 --> 47:51.650
manner. So, may be 5 years something like
that it may go, but it may happen some other
47:51.650 --> 47:54.730
problem also.
But anyway, we shall consider in our case,
47:54.730 --> 47:58.010
that these are the four loads we shall consider.
47:58.010 --> 48:06.210
Actually, I am developing one program actually
based on that, that one I have given a name
48:06.210 --> 48:13.760
also. So, that one, depending on the four
loads dead, wind, earthquake, and live load
48:13.760 --> 48:19.000
the program actually it analyses as well
as design also. I shall try to give it in
48:19.000 --> 48:27.160
a that I shall make it a little bit say
good at least. So, that you can also use it.
48:27.160 --> 48:35.400
So, on the basis of that, that program actually
I am developing, and this one, we use it that
48:35.400 --> 48:41.380
one analysis, and also it will show you the
deformed shape, and also you can get the bending
48:41.380 --> 48:49.349
moment, shear force, and then, you can design
your section.
48:49.349 --> 48:58.760
The partial safety factors for load. So, factored
load, we do not only check the load, whatever
48:58.760 --> 49:04.010
load we are getting, that is your that load
whatever is coming, in our limit state design
49:04.010 --> 49:11.950
particularly what we do, that load multiplied
by certain factor, that one will give you
49:11.950 --> 49:18.240
the factored load or the design load. So,
when you will design the structure, the load
49:18.240 --> 49:22.950
which is coming, you multiply with certain
factor, that one will give you the design
49:22.950 --> 49:27.940
load, and then, on the basis of that, you
have to compute moment, shear force, all those
49:27.940 --> 49:31.510
things.
Or other way you can analyze the one with
49:31.510 --> 49:37.369
the actual load, and later on, at the time
of design, you multiply with the factor given
49:37.369 --> 49:43.230
for different load, and do your design.
49:43.230 --> 49:48.790
And these are the different values. There
are different combination. If we considered
49:48.790 --> 49:54.099
say dead load and live load only, then you
have to multiply that load with 1.5 onward;
49:54.099 --> 50:01.460
dead load means, say your say slab, if you
consider slab, the self weight of the slab
50:01.460 --> 50:07.260
you have to multiply it with 1.5; and live
load also whatever you are getting, that you
50:07.260 --> 50:12.660
have to multiply it with again 1.5.
If it is due to say.. if you consider dead
50:12.660 --> 50:19.099
load and wind load, then, you consider that
one dead load contributes to stability, when
50:19.099 --> 50:25.930
you are considering that aspect. So, you are
assuming little less, on the stability, because
50:25.930 --> 50:31.200
as if that… so, that it will be more you
are considering from the safety point of view,
50:31.200 --> 50:37.480
you are in the other side. I mean to say,
that means, if you take less dead load, so
50:37.480 --> 50:41.829
from the stability point of view what will
happen, that means, that wind is more, so
50:41.829 --> 50:45.040
that means, it becomes say unstable; it may
be unstable. So, that part you are considering,
50:45.040 --> 50:49.710
that is why you are reducing that load. And
wind load that you are even multiplied with
50:49.710 --> 51:14.200
say 1.5.
So, similarly, for dead load and wind load
51:14.200 --> 51:18.339
also, we are having this one, which shall
come in detail, I think there is no point
51:18.339 --> 51:23.410
of discussing, just because we shall again
come back in detail at the time of say your
51:23.410 --> 51:23.730
design.
51:23.730 --> 51:32.030
Just to give you just an estimate that how
that factor comes. Now, we can have dead load,
51:32.030 --> 51:36.740
live load, and wind load also, when we consider
that, then we reduce the value 1.2, all of
51:36.740 --> 51:41.260
them, it comes 1.2
51:41.260 --> 51:46.390
We come here for the similarly, for the earthquake
load also, the similar fashion it is the almost
51:46.390 --> 51:50.910
same thing, similar fashion; that means, we
consider wind load and we consider earthquake
51:50.910 --> 51:55.500
load separately, but that the combination
comes in this manner.
51:55.500 --> 52:05.290
And similarly, dead load, live load, and earthquake
load, we consider.
52:05.290 --> 52:09.380
And this is for serviceability. Whenever we
consider serviceability, I mean to say that
52:09.380 --> 52:14.859
when we consider for, say cracking and deflection,
that time we do not multiply with any factor,
52:14.859 --> 52:21.040
the we just simply take the same that load.
52:21.040 --> 52:30.440
And this is your say for dead load, live load,
and wind load, that we consider.
52:30.440 --> 52:37.960
And the other one, when we consider, say earthquake
load, we consider. So, there is no point of
52:37.960 --> 52:45.460
coming to all those things in detail, because
whenever we shall solve the problem, we shall
52:45.460 --> 52:52.780
come to this values. Whenever we shall solve
problems that we shall come, and that time
52:52.780 --> 52:58.690
it will be easier to remember also. So, we
shall, the first part of our lecture, let
52:58.690 --> 53:00.710
us conclude here now.
Let us take a five minutes break and then
53:00.710 --> 53:02.480
we shall come to the next part.