Well so far done up to design of columns that
means, the load that started from the slab then, your through beams it is transferred
to the column. And now, what we have to do that load we have to transfer to the ground.
So, that is we have to now design the footings or foundation. So, column will transfer the
load on the footings and we have to give sufficient area. So, that it will take that it will that
it will not cross the limit of the bearing capacity of soil.
So, your geotechnical engineers after the soil investigation they will provide us the
bearing capacity of soil that is the basic thing we need. And according to that, we have
to design that the base of the footing and also you have to provide the reinforcement.
So that, foundation of footing that 1 will not have any crack or it will not say kill.
Generally, it happens that when you are having say column here. Let us, say column these are the different
columns we are talking 1 frame we can go little further, it happens that we can also provide
that tie beam. It means we are providing here tie beams, we are not giving any separately
we are not giving any say foundation for masonry wall. Wall is generally, it is made of masonry.
So, for that we are giving any say foundation what we are doing as if the here if we have
the masonry wall, that load will be transferred to again column this masonry wall. And finally,
it will come to the ground. So, it may happen that there are so many ways
we can transfer the load depending on the situation it may happen that one. That generally,
it happens say it can start with say that 5 simply say 5 kilo newton per say square
meter. Then, we can have say your 10 like that this is the beam bearing capacity. So,
we can go to the different bearing capacity we can go and depending on the if the bearing
capacity is less and load is more on the column then, your footing size will be bigger.
So, if you have plan of a building where we are having so many columns and each of them we have different column
position. So, these are the column positions we are looking that say plan of a building
and these are all columns. We have to give certain dimension of the footing because,
directly that if we simple say 300 millimeter by 300 millimeter, 400 millimeter by 400 millimeter
that column. So, we can consider that 1 compared to the
dimension of the building you can almost consider that column dimension is just say a needle.
So, that means if we just keep it over the soil it will simply piers. So, because the
soil bearing capacity that how much it can take that 1 dependent on that whether, it
will piers or not. If it is hard soil or if it is rock then obviously, it will not penetrate
otherwise, it may penetrate. So, because of that we have give certain dimension here also
and that we shall find out. Or it is very simple if p is the and bearing
capacity say, I can consider say any bearing capacity say Sbc soil bearing capacity if
I consider. So, I can find out P by A; A is the footing area so, if I know may say 10
ton per square meter. So, if we have 10 ton per square meter is your say bearing capacity
of soil. So, depending on that we can find out say bearing capacity of soil if we know.
Then, I can find out what is the area of footing that will be equal to P by say bearing capacity
of soil. So, I can find out the area of the footing
that we can find out. And then, whether we shall provide that 1 say rectangular column,
rectangular footing, square footing. Or if this area comes say it may happen, this area
is coming such a way that if I consider the individual footing then, it may overlap that
is also possible. That means, here that whatever area we are getting for this column footing
and whatever area we are getting for this footing that it may overlap. Or we are having
very little, very small may be say 100 millimeter may be say 50 millimeter gap so, we can avoid
that. So, that way we can make it say full whole 1 as it say bridges wrapped 1 we call
wrapped type of foundation also we can make it.
So, for bridges particularly, also for say your high raised buildings for that also we
have say pile foundations. If it is so, particularly for bridges that we make it say pile foundation
also for buildings also we make it high raised buildings not for ordinary 1 say your say
3 storied or 5 storied or 5 storied not like that. But if the bearing capacity is less
then, we have to make pile foundation also that is also possible. Now, 1 case it may happen that is called say
isolated footing our objective in this class, just to introduce what are the different forces
come in the footing. Then how to design, what aspect you have to consider that is your objective.
If you know 1 or 2 cases then, immediately we can do for any other case. So, that is
our objective here. So, isolated footing it may be square, it may be rectangular, then
we can have combined footing, simple we can have only say 2; the 2 columns the columns
are so close we cannot give 1 any isolated footing.
In that case, I can give 1 combined footing; the combined footing may be for 3 or 4 also,
but generally we make it for at least for 2 generally we make it here. And what type
of that say that, footing size all those things you can find out for combined footing. The
other 1 say, footing on piles we shall mainly find out today at least say square footing,
but before that let me show you how it comes that piles. The pile footings it comes generally, say
this is the pile that say your I mean to say that where we provide the piles. Let us, say
we have provided piles of 3 1 so, there are say 5 into 3 15 piles may be say 20 meter
long, 10 meter long those piles. That means, it comes in this way this is the 1 plan I
am talking. So, we will have say 1 2 3 4 5 and over that these are called piles each
of them may be say 300 or 350. Just give you, some dimensions at least you should know what
is the dimension may be say 350 millimeter 400 millimeter that diameter over that this
is called pile cap So, over that we should have I am talking
for say bridges over that we should have may be say 3 a big 1 just a schematic 1 I am talking.
These are called piers here each of them pier and this is called pier cap what could be
the dimension of this 1? It may happen, 1200 millimeter dia, 1500 millimeter dia of the
pears. Each of them because, just to give you certain dimension this 1 can come say
your 1000 millimeter, 800 millimeter the depth. Then, this pier cap it can come say 1000 millimeter
the depth of the pier cap and over that the bridge deck will come. We will provide the
bearing these are called bearing and over that, your Bridge Deck will come this is called
Bridge Deck. So, you can understand that now we transfer the load just though it is we
are going a little bit out of context. But even then, I shall tell you and that we
shall do it at least for multistoried building later on. We shall analysis as well as, design
that 1 and what are the different load cases. Different load cases: come 1 is the obviously,
your dead, the other 1 we call it say superimposed dead load. Then, live load in terms of say
vehicle load that means, different classes of vehicles here; what happens here, that
just for your reference I shall tell you 1. So, far you know that IS: Indian Standard
and another for roads that is IRC: Indian Road Code that IRC those codes are available
for say you’re for roads. And also, your say for pavement for bridges also. So, those
things it is available here as a structural engineer where we are interested. We are interested
here that, what is the soil condition say at least we should now what should be the
pile length. The length of the pile you should know then,
we shall provide the dimension of the piles may be say 350, 400 millimeter whatever it
is coming. So, that whatever load is coming at the top that, load should be safely transferred
to the ground that is our objective here. And since, you can understand this 1 that
we are having different piles over that your having 1 plate, over that your having piers,
generally 3 piers generally we provide. Then, over that we are having pier cap finally,
the bridge deck is coming that which is called superstructure.
So, 1 part is called superstructure, the other part is called foundation. So, up to the pier
cap that is your foundation I talking this 1 for piles though that is not in our scope.
Here in this beginners course, but I would like to say that 1 that how to design. But
here also, it is based on your say bending moment, shear force and axial load. In addition,
to that we will find out also torsion also so, far we have not covered mainly we have
covered say bending moment, shear force and axial. Now let us, come back to our say footing
and that 1 say your isolated footing. Then, what should be your loads it should
have load combination: number 1 dead load plus imposed load. So, it comes please note
for calculating size of the footing for size of the footing we do not take that 1.5. Because,
we are noting the limit state rather, we are taking that 1 say working stress. Because,
the bearing capacity of the soil is given as say you are working stress that 1 that
serviceable 1, not the 1 limit state or ultimate bearing capacity.
Because, ultimate bearing capacity divided by the certain factor of safety will give
me the safe bearing capacity of soil which is the serviceable 1. So, that is why here
we do not multiply with that 1.5 we multiply with say 1.0 that is for dead load plus 1.0
say live load that is 1 case. The other case that, dead load plus wind load which comes
as 1.0 dead load multiplication factor 1 plus 1.0 wind load it could be earthquake load
also. Number 3, dead load plus imposed load or live load plus wind load or earthquake.
So, it could be earthquake load or wind load which 1 is the governing 1 that we have to
find out we check it. So, here it comes as 1.0 dead load plus 0.8 live load we take it
when, we consider the live load as well as wind load we take that factor. Or 0.8 times
wind load or earthquake load what I would like to say here. These are the whenever,
you are doing analysis you have to find out different cases that which 1 is the governing
1. Then, you have to get different cases for
this say your building, we get these are the 3 different load cases we generally get. So
dead load, live load that is 1 case then, it may happen dead load also another 1 case
also it may happen dead load. And impose load, dead load and wind load, dead load, impose
load and wind load or earthquake load. Either, of them we shall take it we generally do analysis
and find out which 1 is the governing 1 and we take that load. So, what should be the now come back to the
area of footings we have to calculate. So, service load on column divided by safe bearing
capacity of soil below. So, if we know the service load that means, giving the proper
multiplication factor 1.0 this case or 0.8 with the live load and the wind when you are
talking. So, service load on column divided by say bearing capacity of soil whatever there
on the basis of that, you can get the area of footings.
So, up to this you will get your that service load, but now we have to give your say dimensional
thickness of the footing. So, when you have to give the thickness of the footing, in that
case what you have to do. Then, we shall go to the factored load. So, factored load to
check thickness of footing in this case we can have just simply, if this is your column
we can have like this I can make it that uniform thickness.
Then, It is also possible to make it sloped slopping because, I do not want I know that
here bending moment here 0 because, after all it is a cantilever 1 I can say. So, bending
moment 0 here bending moment maximum. So, I can reduce my thickness. So, this way make
it this is uniform then, slopped slopping and the third 1 also possible we can make
certain kind of step like this we can provide. That means we can up to certain distance we
can provide that 1 say some kind of say pedestal or say step 1. And then, after that we can
give uniform or we can give slope also. So, depending on the situation that we can
make it, but this is the very simplest 1 if we can make it because, here only thing here
we have to find out, what load cases say what type of say stresses will develop. When, you
are talking say your footing what type of stresses will develop. If you look this 1
let us, take this simple 1. Let us, say the load applied P and moment
say M and the plan of the footing let us, say this B that width and this is length L.
Since, we are having moment here so, we shall get it will not be uniformly stressed since,
we are having moment. So, because of that we shall if we have axially loaded 1 then,
we shall get uniform all along. But here since, we are having moment what we shall get we
may get something like this. So, this 1 let us say q1 maximum stressed
this 1 your say q2. So, q I can write down here P by B into L and let us say, plus minus
M by z; z is the section modulus I can say. So, 6M by BL square I equal to BL cube by
12 I of this 1 with respect to this axis BL cube by 12. So, My by I we are talking L by
2 and here another L by 2 because, with respect to this in other way I can say the z equal
to I by L by 2 which comes as BL square by 6.
So, I can get q that is this side that q let us write down q1 or 2. So, q1 will be P by
BL plus minus 6M by BL square and this side q2 P by BL minus 6M by BL square. That means,
depending on and another way also we can make it we can do 1 trick what we can do since,
we are having this 1. So, that means, say e equal to M by P I would
to make it uniform. I would to make this 1 uniform this stress what we can do. So, we shall do it this we shall have little
upset or in other way, I can say instead of having M here. I am not providing M here,
what I am doing as if it is at a distance say I should make it here little bit. Let, make it clearly then we write down. So,
I want this your P and let us say, I can have as
per my this drawing so, I can have this is your e. So, e equal to M by P and then, what
we shall get; we shall get the uniform. Uniform soil pressure that q this way also we can
make it. So, this 1 way generally we have acquired this 1 we generally, keep the central
line of the column and the central line of the footing same.
Generally because, this way makes it that we should not have any that in this case you
are getting uniform soil pressure whereas, in the other case, the 1 I have told in this
case we are getting that 1 side maximum and the other side less. So, it means that if
we get P by BL plus minus 6M by BL square see in 1 case it may happen that, I shall
get this side 0 that q2 equal to 0 I shall get depending on the value that e.
So, I can get q2 equal to 0 1 case it may happen if we further we go. Then, also it
may happen that, I shall get only certain portion, but not fully it is in contact that
is also possible. So, if we write down here P by BL minus 6M
by BL square equal to 0. So, what shall we get here M equal to P times e the other way
I can write down M equal to P times e. So, I can write down or. So, equal to e equal
L by 6 that means, if we get e equal to L by 6 in that case what will happen, it will
happen that you will get only on 1 side. That means, if this is the length L of the footing
so, in 1 end we shall get 0. So, if the P or e exceeds that L by 6 value
then, what will happen we shall get we may get certain lengths say this. That means certain
portion not in contact with the soil, this is if e greater than L by 6 this means, e
equal to L by 6. So, these are the different cases we only consider that e equal to L by
6 greater than L by 6 all those this so, generally we have. So, let us come back the thickness of the
foundation or footing what should be the thickness of footing, how shall be what is the governing
criteria. It should be sufficient to resist the shear force without shear steel. So, our
case here that we have to provide the thickness of footing such that, it will resist the shear
force without shear steel. That means, stirrup we do not provide any stirrup. That means,
in this case for M20 grade of concrete we have give; that means, your tau c for M20,
tau c equal to 0.35 Newton per square millimeter. So, that means, that value shear stress should
come less than 0.35 Newton per square meter minimum critical 1. If I say just for your
let us, check it that will be available that is your say 0.28. But depending on that
is your 0.28 that is the minimum, as per Table 19 of IS: 456. But if we know the area of
steel the area of tensile steel depending on that, we can take that is say 0.35 that
is why i have told 0.35. So that means, as if we are giving certain
say tensile steel on the basis of that, your critical stress of the shear stress that is
actually we have to find out. So, that is why i am telling say 0.35, but as per Table19
for M15 0.28 M20 also 0.28 M25 0.29, but that is less than equal to 0.15 percent. But if
we provide say 0.25 then, we are getting 0.35 0.36 like that. So, we can take say 0.35 Newton
per square millimeter. Now, also it should be sufficient to resist
the bending moment and here also we impose, another criteria
without compression steel. So that means, shear force without shear steel that means,
there was no stirrup and bending moment without compression steel. That means, only we are
providing 1 side the tensile 1. So, in footing we shall get the tensile 1 at the bottom that
1 we shall get it. So, here we are getting that also without
compression steel we shall do it. And also we can note another 1 number 3, that to withstand
the corrosion that can be caused from ground. So, at least you should have these 3 cases
at least you should have for that you have to provide the thickness. So, what about the minimum percentage of steel?
In this case, we shall use that slab that whatever we provide the minimum reinforcement
for slab that is 0.15 percent for Fe 250 and 0.12 percent for Fe 415 and these we will
get in just for your reference clause 26.5.2.1 of page 48 IS 456 : 2000 the
same clause for slabs. What about your cover? Generally, we provide say 40 millimeter not
less than 40 millimeter. So, let us say 50 millimeter we shall provide
50 millimeter if we have certain say lean concrete. That means, we are providing not
directly on soil or say 75 millimeter if it is directly on soil. That means, if we
provide that so if then, you have to provide 75 millimeter. Generally we provide say sand
then, we are having lean concrete then, you provide that say foundation.
So, 40 millimeter or 50 millimeter let us say we shall provide for clear cover when,
you are providing with on lean concrete. Otherwise, if it is directly on the soil on the ground
then, we have to take say 75 millimeter. Now, let us come now I think what we can do instead
of coming say let us, take 1 problem I think that could be easier. That we can do it, but before that let us
take that we have shear and bending we take it say if this
is the plan of the footing. The bending we consider
at the face of the column. So, bending we shall consider at the face of the column.
That means, if this your length L, this is your say B, a is the say column and let us
take this is square. So, this length is equal to L minus a by 2 so that means, we shall
take this portion L minus a by 2. So, we shall take due to bending we shall
find out the bending moment at this position and which will be taken care of as you say
your cantilever beam. So, if q is the load that means, in other way if it comes this.
So, this your say q and this length is L minus a by 2. So, bending moment will be equal to
q times that is B this way and L minus a by 2 whole square.
So, I shall get this particular 1 here times half, this length we shall get it here. So,
this is will be your that whatever the bending moment we shall get it, we shall get this
bending moment here. And we have to check that thickness of this 1 we have to check
it with this bending moment. So, for footing we have to check the bending moment due to
the soil pressure whatever your getting. Next 1 we shall get it so that shear, we have
2 cases: 1 we call it 1 way shear, the other 1 is called 2 ways or punching shear. What
about this 1 way shear? 1 way shear means, if this is the column position if effective
depth of footing d. Then, we have to take a section
at a distance d. So this your d that means, shear force we have to compute where this
section compared to the bending moment. So, we are getting the shear force at this
section which is at a distance d from the face of the column, not immediately on the
face of the column which we have done it for bending moment. Here we have to find out at
a distance d that means, in other way I can say as if we are having 45 degree dispersion
of the load. So, we are going 45 degree dispersion of the load. So, we are going to that up to
say d; that means we are calculating the section here.
In other way, I can say as if we are having we are going here this
your d and this is your d. So, I am going; that means, I taking this section this is
45 degree so, this your effective depth d. So, we are calculating here at this section
and this is called 1 way, either we can compute here or we can compute here, but if it is
rectangular obviously, you have to take the longer direction, not the width. Because,
that there the shear force obviously, will be less. What about the punching shear or
2 ways or both ways? It means, if this is a column position. So,
we shall go all along in all side and this 1 will give you at a
distance d by 2; d is the effective depth of footing. What does it mean? What we are
doing basically? We are doing here because, punching means simply it will piers that means,
as if this portion we are applying load like this. That means, as if this portion simply
break and it will just simply insert that 1.
So that means, having that 1 say plate and it will just simply your are piercing through
that that is called the punching shear or 2 way shear. Or both ways, all sides your
are having. So, what is the effective area that means, what is the area which is actually
concerned with the shear if this is the length this is also. So, a column dimension say square.
So, we shall get 4 times a plus d by 2 the total perimeter. perimeter equal to 4 times
a plus d by 2 plus a plus d by 2. Because, this is the a and d by 2 this side
d and by 2 to this side and 4 times if it say square. So, we shall get the perimeter
of this 1 that is 4 times this 1 which comes as 4 times a plus d. What about the shear
force? The shear force will be equal to total shear force 4 times a plus d times the depth
d please note we are talking the Perimeter this is the perimeter.
So, what about the area; area means along the I can say like this area means this 1.
Because, this is the 1 say if this is your say d by 2 we are putting the I can say this
is the column say, your that calculator that we are putting here that is the column. And
we are going say at the distance d by 2 in all sides. So, we shall get the perimeter
that we can compute. So, this dimension if it is rectangular so, it is a and it is small
b say. So, a plus d by 2 d by 2 and this side may be b plus d by 2 d by 2 we can go. So,
we can get the perimeter and we have to find out that which will resist the shear.
The shear will be resisted by this area because, if this is the depth of the footing shear
will be resisted by this area. So, these area what will be the shear this will be the depth.
So, perimeter times the depth that we shall get it. So, that is what I have written here
4 times a plus d we are talking say square footing so, 4 times a plus d times d times
the allowable punching shear. So, that is say tau p; tau p is the allowable
punching shear. So, this 1 will be given that 1 say shear force and that should be equal
to or greater than whatever, the your say column load. So, that should be equal to that
means, not only column load including that also we have to add the self weight of the
footing. So, self weight of the footing plus the load whatever is coming from the column.
Then, from there whatever, you are getting say total load, design load that 1 from there
you will get the shear force that is the shear force that should be equal to or less than
this value. Then, you can say it is safe. So, if I now since I have come to this 1 let
us, come this 1 here if this your B or L. So, if I now since I have come to this 1 let
us, come this 1 here if this your B or L. Let us, say this your B then, in that case
what will happen here. I can find out the shear force here also shear force here. What
will be the shear force here? Again, here B times the d and due to this load.
Because, that you have to resist this portion what about shear force will come due to this
load, the left side at this section that we have resist. Here again, we are talking that
1 say the vertical section the 1 section overload whatever, we consider. That section we have
resist so, depth times this length that you have resist. So, these are the different cases
we get here. This 1 I mean to say that since, I am taking say d is the distance I can say
as if this load dispersed at say 45 degree. So that means, if this is your d this 1 also
will be d. So, that is why taking that 1 say at a distance say d; that means, in the other
way I can argue that as if we are taking a section and as if your having say 45 degree
load dispersion that we can say. So that means, if you have to design the your say thickness
of the footing we are having 3 cases: 1 case is the bending, another case shear; shear
having 2: 1 is called 1 way shear and another 1 is caller say punching shear or 2 way shear.
On the basis of that, only we can provide the thickness what we generally do, we generally
find shear in that your footing that is mores. So, we can calculate depth that generally
the usual procedural in design you calculate depth from any 1 of the 3. Either shear from
punching, shear from way or bending you can calculate the depth and you check for other
whether it is satisfied. So, that is the usual procedural here what we can do, you can find
out the depth from 1 way shear and then, we can calculate for others. So, let us check here I think we can start
solving 1 problem, but before that I think we shall actually we get time. So, we shall
take may be say let us keep it for the next class. So, let us at least tell say minimum
depth so, let us at least write down depth should be safe in whatever I have told just
let us, just simply enlist it. The depth should be safe in 1 way and 2 way shear I have already
told. But let us, just write down without shear
reinforcement. The depth should be safe for the bending moment without compression reinforcement.
So, we can take this 1 and I have already told 0.15 percent for Fe 250 0.12 percent
for Fe 415 as well as 500. So, this depth we have to provide and also we can say 150
millimeter at by the age of the 150 millimeter at the age of footing that should be the minimum
depth. So, I can write down here 150 millimeter the
age of the footing. So, and but 300 millimeter if it is 1 pile foundation 300 millimeter
that is the minimum. This 1 I am talking minimum. So, minimum 150 millimeter at the age of the
footing if it say minimum say 300 millimeter if it is on the pile. So, I think I can stop
here today. So, next class we shall solve problem at least
1 square footing and because, our main objective here that we have to finish it that all the
different components this footing because, we have done slab, we have done beam, we have
done say columns and we have done say your now we are doing footing and 1 more we have
that is your say staircase. So, that at least for at least building we
shall have all the components. Then, only we shall we shall start with at least 1 multistoried
frame, multistoried building we shall design for all the components starting from the analysis
and then design. Thank you
