WEBVTT
00:20.199 --> 00:29.350
Hello everybody so we have just now we have
discussed on what is state method used in
00:29.350 --> 00:39.780
RC 21 and also IS456 also now, now we shall
go for working stress method we shall go for
00:39.780 --> 00:47.399
on that and then that is as per IS456 because
you are very much familiar with IS456 and
00:47.399 --> 00:55.920
then we shall go to IRC 112 that is for the
bridge we used that we shall go for that concrete
00:55.920 --> 01:01.020
bridges that we shall go for it.
And then we shall compare that the difference
01:01.020 --> 01:07.240
method that whatever we are going to use it
or whatever methods available so this is our
01:07.240 --> 01:17.740
lecture number 7 on reinforced concrete Road
bridges and then we are coming back to that
01:17.740 --> 01:28.380
limit State method and which will be as per
IS 456:2000 and we are again considering first
01:28.380 --> 01:35.490
limit state of collapse that is flexure because
our objective here in this particular course
01:35.490 --> 01:42.590
but mainly it will go on by your clicks or
and I have told it number of times.
01:42.590 --> 01:49.490
So let us click with the clicks are only and
again we are having certain assumptions and
01:49.490 --> 01:56.340
those assumptions again you see that on the
first assumption plane sections normal to
01:56.340 --> 02:03.079
the axis remain plane after bending the maximum
strain in concrete at the outermost compression
02:03.079 --> 02:11.450
fiber is taken as 0.0035 so please note to
this particular aspect that in working stress
02:11.450 --> 02:17.610
method we are totally silent only thing we
have told that strain profile will be linear
02:17.610 --> 02:22.690
straight line that much only we have told.
But we have never given you any number that
02:22.690 --> 02:27.670
how much will be the strain but here we are
giving certain limiting value of strain and
02:27.670 --> 02:35.140
that is 0.35 the tensile strength of the concrete
is ignored as usual because there is no such
02:35.140 --> 02:39.790
difference with the working stress method
elemental method here we are ignoring.
02:39.790 --> 02:49.750
That to the stress block may be assumed to
be rectangle trapezoid parabola or any other
02:49.750 --> 03:01.340
shape which results in prediction of strength
please note the next one the substantial agreement
03:01.340 --> 03:09.519
with the results of tests so that means the
code agrees that it will not exactly it will
03:09.519 --> 03:17.019
not match so that is why the code means you
that a very wise lead it has told the substantial
03:17.019 --> 03:22.799
agreement so this why that is the one issue
the understand that record on that at left
03:22.799 --> 03:26.690
on the substantial agreement.
So that means it should come very close no
03:26.690 --> 03:35.250
doubt so but otherwise you can use any other
one and I shall tell you that one also that's
03:35.250 --> 03:40.780
why I have taken this particular one that
working stress method limited as per IS-456
03:40.780 --> 03:47.810
and then we shall go for IRC 112 that we shall
go for it so that we can I can show you the
03:47.810 --> 03:53.110
one way that you evolution another way the
journey that how we are going from elastic
03:53.110 --> 03:59.659
to the beyond elastic that Parker 1 and real
it is very interesting to note those things.
03:59.659 --> 04:09.190
Only thing I would like to say that note triangular
as in the working stress method so this is
04:09.190 --> 04:15.829
the one we have taken that I have told you
rectangle trapezoid parabola like that but
04:15.829 --> 04:21.280
here we are taking say that triangular in
the working segment of this is the one difference
04:21.280 --> 04:27.070
that we are having the stresses in the reinforcement
are derived from the representative stress
04:27.070 --> 04:32.330
curve for the type of steel used so which
type of steel you have use it is dependent
04:32.330 --> 04:37.980
on that for design purposes the partial safety
factor because you see that one last time
04:37.980 --> 04:41.950
in working strength at all.
Suddenly I have told you for fuel but I will
04:41.950 --> 04:46.150
know that partial we are not going to use
it for work Lister's method but here we are
04:46.150 --> 04:53.390
going to use the term partial so the thing
is that in the fifth lecture just I have given
04:53.390 --> 05:02.490
you idea though it may look like to you that
why that particular that one lecture was given
05:02.490 --> 05:08.610
on the design principles where that problem
because I feel that the coal one the there
05:08.610 --> 05:16.930
is no such scope to understand the that you
say that how the code is made what is the
05:16.930 --> 05:21.280
basic principle the reliability index other
things so that's why I have given you that
05:21.280 --> 05:26.980
just only happen over one though it may look
like it is little bit very fast.
05:26.980 --> 05:31.470
But anyway just to give you idea but the difference
book which I have given from there you can
05:31.470 --> 05:37.270
get more information if you are interested
and that is very interesting also but the
05:37.270 --> 05:42.600
basic idea they are there calibration of that
partial safety factor that one is important
05:42.600 --> 05:49.460
because this partial safety factor it is coming
for different materials for different cases
05:49.460 --> 05:53.700
were say loading you will get different actually
factor you will get it.
05:53.700 --> 05:58.250
It is not like working stress method you are
having only one value this is very important
05:58.250 --> 06:08.960
and here we shall get it say 1.15 that we
shall take it here then maximum strain in
06:08.960 --> 06:16.090
the tension reinforcement in the section at
failure shall not be less than if FY /1.15Ex+0.002
06:16.090 --> 06:23.680
what I would like to mention here for concrete
irrespective of grade of concrete we always
06:23.680 --> 06:31.870
give .035 that is the limiting value of strain
but in this case we are giving that value
06:31.870 --> 06:41.530
depending on the grade of steel so FY /1.15Ex+0.002
this is the value that we shall consider that
06:41.530 --> 06:43.260
means for different grade of steel.
06:43.260 --> 06:50.050
We shall get different values so this is the
one that figure which we have taken data here
06:50.050 --> 06:56.280
you are very much familiar with that so first
this is the one f-ck next we are having from
06:56.280 --> 07:01.640
that designer point of viewpoint six seven
f-ck which is nothing but 2/3 of that then
07:01.640 --> 07:08.310
you are getting .67 f-ck by gamma M gamma
we will give you 1.5 so we shall get which
07:08.310 --> 07:14.910
is nothing but 4 /9 f-ck 2/3 f ck into 2/3
of that will come here.
07:14.910 --> 07:22.750
So 4 /9 0.444 like that you will go so generally
we write down one .445 or .45 f ck that we
07:22.750 --> 07:27.370
write down that that means f ck is the strength
of the concrete and we are going for that
07:27.370 --> 07:33.760
point four five f ck that is the value we
take it here that for we can consider.
07:33.760 --> 07:38.680
Now this is the four fold over the deform
bar again he are getting this is the actual
07:38.680 --> 07:45.470
one and we are getting this one here FY /1.15
and that value we get it here.
07:45.470 --> 07:52.840
This is for mild steel so this Parker one
again you are getting FY /1.15 so this value
07:52.840 --> 08:01.720
we are getting up to the same after that we
are getting little less coming to this one
08:01.720 --> 08:04.780
here.
08:04.780 --> 08:10.990
So this one whenever I have shown that figure
I have shown you any value in working stress
08:10.990 --> 08:20.760
method here we are taking this factor on here
a D and D X this is the neutral axis so this
08:20.760 --> 08:25.640
portion only we are getting that value because
here we have not told or the value here but
08:25.640 --> 08:30.150
here I know how is the value this one for
steel what is the value for the concrete there
08:30.150 --> 08:36.519
is always next from point0 negative 3 5 this
is 0.45 f-ck we have considered this one.
08:36.519 --> 08:40.399
I am telling that what it wants okay to if
they are actually of told this is the X so
08:40.399 --> 08:46.720
X by 3that is very simple because this is
a triangle but in this case it is not a triangle
08:46.720 --> 08:51.300
so that is why you are getting that value
here that particular value you are getting
08:51.300 --> 08:57.950
here that you can find the that you are some
value will be there k2 that particular value
08:57.950 --> 09:05.460
we are to find out and this is the tensile
stress tension of course in steel and as usual
09:05.460 --> 09:10.960
that you will say tensile stress in the concrete.
09:10.960 --> 09:15.180
That is actually expert core portion ignored
so only we are having compression concrete
09:15.180 --> 09:22.840
will take the compression and reason we take
the tensile so k2 s is the distance of the
09:22.840 --> 09:28.650
center of compression in the concrete from
the top compression fiber.
09:28.650 --> 09:38.091
So we can find out that k1 and k2 this one
area of rectangle that one- area of outer
09:38.091 --> 09:43.160
parabola so you can make this by culinary
simple calculation then I can get it 0.364
09:43.160 --> 09:49.200
f ck X into B so q1means 0.364.
09:49.200 --> 09:57.080
So this particular one please note this parker
1.36 for again this is a very, very important
09:57.080 --> 10:18.420
one for limited method and we are talking
here IS456: 2000 in this case we are taking
10:18.420 --> 10:49.230
second portion and C which is coming as 0.364
fck X*B so this is your X
10:49.230 --> 11:01.620
this is 0.45 f-ck and B is the width of the
beam so this particular one we shall note
11:01.620 --> 11:16.840
down this particular one and which we are
talking this one K1 Fcx X*B further we can
11:16.840 --> 11:21.839
make many more things we can do it that I
am not going to all detail all those things
11:21.839 --> 11:22.839
.
11:22.839 --> 11:27.870
But I am keeping this one for the time being
that particular value where we are telling
11:27.870 --> 11:37.480
that K1=0.364 because why I am looking down
this what color on again I shall show you
11:37.480 --> 11:47.251
this 4-1 the current coming to this one here
so another value of K1 and K2 so this K2 we
11:47.251 --> 11:54.870
have to find out what is that K2 x, K2X we
know taking moment our neutral axis you can
11:54.870 --> 12:02.860
find out all those things 0.36 for that area
of this one X *B X-K2 X 0.45 f-ck X this is
12:02.860 --> 12:10.570
a rectangular part and then we are finding
these four parabolic path this particular
12:10.570 --> 12:11.570
portion.
12:11.570 --> 12:37.010
We shall deduct so 1- K2 =0.584 so let us
go down that K2 =0.416=0.42 so it is very,
12:37.010 --> 12:44.230
very important here and K2 why I am try what
I am trying to say the specter on here so
12:44.230 --> 12:51.300
that means see this one that all equation
can be written in terms of K1 and K2 that
12:51.300 --> 12:55.900
is our objective that the current we have
taken a parabolic shape certain say parabolic
12:55.900 --> 12:59.880
rectangular shapes you can say more precise
way.
12:59.880 --> 13:05.850
So if we take a parabolic rectangular one
and there but code 1 we can define with the
13:05.850 --> 13:13.529
term sum 1and K2 then C will be equal to K1
fck x /d similarly we can find out your say
13:13.529 --> 13:30.200
value of NIEM also so C equal to K1 fck x/d
BD t =0.87 FY so let us write down that one
13:30.200 --> 13:46.060
here also t =0.87 FY ast so this is your C
and this compression in concrete and tensile
13:46.060 --> 13:55.480
in steel and this is called again I think
I have not told so far again I am killing
13:55.480 --> 14:13.110
this paper on here that a singly reinforced
section.
14:13.110 --> 14:20.060
So this is your single reinforced section
that compression side even though steel is
14:20.060 --> 14:24.890
there that on in ignore that means or that
it will contribute or not in your moment of
14:24.890 --> 14:31.330
resistance we do not know so but, but that
force are actually ignore that one so just
14:31.330 --> 14:35.830
to complete this worker on I would like to
say similarly we are having doubling and for
14:35.830 --> 14:40.880
section also reinforcement the compression
will the compression side also steel will
14:40.880 --> 14:46.300
be available all will be provided sometimes
we do it.
14:46.300 --> 14:52.310
So coming to this on here this is a situation
we are getting it here and as usual the C
14:52.310 --> 15:07.680
and T that one should be equal that C and
T that will be equal so C and T we know and
15:07.680 --> 15:16.360
we know this one equivalent 0.87 FY ast equal
to 0.36 for f ck b xu that parker one we can
15:16.360 --> 15:47.210
find out and then we can write down here Mu
equal to K1 f-ck in x/d 1-k2 x/d bd2 I have
15:47.210 --> 15:55.270
taken all of them to the virtually who are
your k1 fck x/d bd2 that economy can take
15:55.270 --> 15:59.550
it here.
So this one just to complete this packer on
15:59.550 --> 16:18.490
i can write down here what I can do .364 fck
x/d bd2 that is whatever take a one point
16:18.490 --> 16:28.110
three six fold is nothing but K1fck x/d bd2
and this portion is coming from the lever
16:28.110 --> 16:34.350
arm so this portion is coming from the lever
arm so that means actually whatever I am doing
16:34.350 --> 17:07.409
Mu equal to C times Z, C this much
C is this much into Z, Z means this Parker
17:07.409 --> 17:22.559
one here.
This is your Z so Z equal to D minus k2 X
17:22.559 --> 17:36.429
equal to 1 minus K2 x/d into D
so 1 minus K2 x/d into D a colonial here on
17:36.429 --> 17:40.149
there I am getting one D and from that I am
get another D so that is how it is coming
17:40.149 --> 17:52.320
any equal to this particular one bd2 so this
is the equation you are getting for in you
17:52.320 --> 18:01.950
so similarly just I would like to make it
in one page that is why I am becoming a little
18:01.950 --> 18:06.559
miser.
So let me write down that one Mu equal to
18:06.559 --> 18:31.380
get 0.87 FY ast into Z, Z again will be equal
to 1 minus a K2 x/d so this is the one term
18:31.380 --> 18:37.679
which you are getting due to steel so this
one you are getting so now what I would like
18:37.679 --> 18:47.159
to say that k1 f ck x/d all these equations
whatever you are writing that one you will
18:47.159 --> 18:52.960
find out later on that it will be independent
of any method.
18:52.960 --> 18:56.619
Whether it is working stress method or it
will limit State method whether you be IS
18:56.619 --> 19:04.530
456 IRC 112 you will get this type of that
equation that format of equation in you get
19:04.530 --> 19:10.870
it every time that is what I would like to
say and that one we shall come back later
19:10.870 --> 19:17.239
on if we get time because the main objective
will find out that is not just only a formula
19:17.239 --> 19:23.700
you are using you try to understand the formula
and from there you find out the little difference
19:23.700 --> 19:25.360
little modification.
19:25.360 --> 19:30.080
And how it actually affects or how which the
particular parameter actually affects that
19:30.080 --> 19:39.419
also you can find out this one is very, very
important this particular one you can say
19:39.419 --> 19:52.539
very, very important here that J equal to
0.5 plus root over point to 5minus nu by 0.87
19:52.539 --> 20:07.529
fck bd2 so I think this particular one we
can find out from
20:07.529 --> 20:08.600
the equation.
20:08.600 --> 20:32.529
In Mu = 0.36 we can write down here fck x/d
1-0.416 x/d bd2 these equation it will give
20:32.529 --> 21:03.840
you a fck bd2 so I am rearranging this particular
equation and from there you can find out here
21:03.840 --> 21:35.389
so I am taking these equation in one place
plus fck I could omit this portion but I feel
21:35.389 --> 21:42.600
that one that whenever you are going through
a problem so it is wise to go for that that
21:42.600 --> 21:47.509
is why I have taken this particle one.
I could refer this one to your reinforced-concrete
21:47.509 --> 22:22.190
one that way we can find out but any way so
we can find out this one here
22:22.190 --> 22:33.619
taking this particular one here we get it
here
22:33.619 --> 22:39.230
I am not going to show you are advised to
go in detail you can get this particular one
22:39.230 --> 22:52.919
in PC verges book of limit State design of
concrete and this one will give you just I
22:52.919 --> 23:14.700
am writing the final
23:14.700 --> 23:30.159
one 6.68 Mu / fck bd 2, so this is the one
you will get it this particular one you will
23:30.159 --> 23:31.759
get here.
23:31.759 --> 23:59.499
Now harder I would like to do it the j=1-0.416
x/d equal to 1-0.416into one point 2 plus
23:59.499 --> 24:29.690
0.416 root over one point two whole square
minus 6.668 Mu / f-ck bd2 which comes as 1-
24:29.690 --> 24:57.889
.499 plus if we just inside if you take it
.249-1.156 Mu/ bd2 which is nothing but you
24:57.889 --> 25:15.169
can say .5 plus 0.25 minus 1.15 I am writing
down Mu/fck bd2 this particular one we can
25:15.169 --> 25:29.690
write down here so J further that very interesting
way I can write down 0.5 plus root over 0.25-Mu
25:29.690 --> 25:45.490
1.15 divided by that one.
So 0.87 fck bd2 so Mu /fck bd2 that Mu which
25:45.490 --> 25:53.360
over the force over the moment actually applied
well due to load and fck b&d on the basis
25:53.360 --> 25:59.200
of that I can find out and then I can decide
the value of j and whenever we shall decide
25:59.200 --> 26:06.009
the j and then on the basis of that we can
find out there many more things so this particular
26:06.009 --> 26:12.380
one j we can find out so j is equal to this
one so that means here point five plus root
26:12.380 --> 26:18.789
over point two five very interesting that
beautiful number easier to remember also.
26:18.789 --> 26:23.269
And we did like to see that particular one
whether it is valid for other cases also so
26:23.269 --> 26:31.679
only these portion we change that will change
in lot of things will influence the whole
26:31.679 --> 26:39.269
idea Mu/fck bd2 this parker 1 we can tell
something this Mu/fck bd2 so we can say this
26:39.269 --> 27:02.539
one as you say k=Mu/fck bd2 so we can write
down this one as j 1 plus just let us distinguish
27:02.539 --> 27:28.070
this 1.5+0.25-1.15/K so k by k by 0.87 or
we can write down 1.15 k also.
27:28.070 --> 27:34.370
We can write down this one so that all together
I do not either 1.15 K or point okay by0.87
27:34.370 --> 27:39.889
that well so you can write down this work
on equation so this key is a very, very important
27:39.889 --> 27:46.460
one because that it depends on that whether
this one is going to be negative or that negative
27:46.460 --> 27:52.320
I fit becomes negative so we shall not be
able to solve it so that is why this Mu /fck
27:52.320 --> 27:58.809
bd2 s this is a very, very important aspect
because I know Mu because it is coming from
27:58.809 --> 28:03.700
the load I know x EK because which grade of
concrete you are going to use is also already
28:03.700 --> 28:09.549
or beside it b also we know only thing that
one that you can change it that is the depth
28:09.549 --> 28:13.590
of the beam.
So this changing this depth d so that one
28:13.590 --> 28:19.379
should be always less than 0.25 if it is greater
than 0.25 then it will be a complex number
28:19.379 --> 28:26.349
and which is then means it is not possible
it is not feasible so this particular aspect
28:26.349 --> 28:32.020
we have to find out such a way so that i can
get certain value of j so that means here
28:32.020 --> 28:39.909
J can be0.5 because if we make such I that
point over 0 so that means you can get same
28:39.909 --> 28:45.470
minimum there is a J value of that point 5
here.
28:45.470 --> 28:55.269
So coming to this here just to give you idea
as per IS 456 mild steel 250 0.0031, 0.53
28:55.269 --> 29:05.389
high yield strength is 415 and yield strength
is 0.0038 and 0.48 high yield strength 500
29:05.389 --> 29:11.980
0.0042 and 0.46 we are getting this one FY
by 1.15 yes, yes that modulus of elasticity
29:11.980 --> 29:20.820
of steel that one we consider here all the
same 2 into 10 to 5 Newton per square millimeter
29:20.820 --> 29:26.590
X Y D it changes with respect to the respect
to steel.
29:26.590 --> 29:38.999
That X Y this changes and then x/d that your
FY/fck this value it gives you me or that
29:38.999 --> 29:43.519
that value it will give you that balance x
later on whenever we solve the problem that
29:43.519 --> 29:48.799
time we shall come comeback to that work for
one here and the maximum limiting values of
29:48.799 --> 29:56.299
compression this four column we can say so
we can say steel for our Xu /d k1 same for
29:56.299 --> 30:04.279
all of them k2 and if that occur one we can
find out x/d is varies with respect to that
30:04.279 --> 30:08.549
similarly F will also vary with respect to
that.
30:08.549 --> 30:13.559
So as usual the same thing balance sections
already i have told we have already told so
30:13.559 --> 30:20.840
that i do not want to come to that under reinforced
sections and that also we have discussed that
30:20.840 --> 30:26.159
an over reinforce section that particular
one we have considered already we have told
30:26.159 --> 30:32.229
these values so this is very, very important
here so that means here whatever we are considering
30:32.229 --> 30:38.250
here why I have chosen that IS 456 because
it will because since you are familiar with
30:38.250 --> 30:44.909
that may be that you are not familiar with
working stress method those who are taking
30:44.909 --> 30:48.940
but that is also another important actually
method.
30:48.940 --> 30:53.820
That we should never forget because there
is a very, very basic one after that we have
30:53.820 --> 31:00.029
come and considering all these aspect you
know what I can say that what want from the
31:00.029 --> 31:08.190
linear triangular one to the parabolic rectangular
one we have considered and because then finally
31:08.190 --> 31:15.149
we shall come to that IRC 112 and not only
that you will find out that code that is actually
31:15.149 --> 31:20.820
you know code where you will find out that
per core 1 or 0 code there will be get also
31:20.820 --> 31:25.720
similar kind of thing.
Whatever is when you will find out in IRC
31:25.720 --> 31:31.330
112 so considering all aspects oh I thought
I can tell you together CL but also that we
31:31.330 --> 31:37.859
shall tell you the you know when we shall
solve the problem that time we shall discuss
31:37.859 --> 31:45.359
so with this you know I think whatever we
can say that factor I would like to actually
31:45.359 --> 31:52.769
conclude this particular one with respect
to Is 456 the next one we shall go for it
31:52.769 --> 32:00.450
and that is IRC 112 and what is the difference
that we shall find out so with this we conclude
32:00.450 --> 32:02.899
this particular session thank you very much.