WEBVTT
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Hello everybody so we have almost at the end
of the design of slab bridges that we would
00:26.710 --> 00:31.500
like to conclude today with the checking with
the bending moment.
00:31.500 --> 00:40.900
So let us quickly just to go to that one so
what we would you like to see this particular
00:40.900 --> 00:41.900
one.
00:41.900 --> 00:48.250
We have got that 7.327 that one we have got
it.
00:48.250 --> 00:54.989
So and also you have got this 5.69 also that
meter we have got it so let me keep to the
00:54.989 --> 00:56.730
shear, force first.
00:56.730 --> 01:04.580
So that one now I shall tell you one more
important aspect that is your say impact factor
01:04.580 --> 01:10.010
already we have discussed that impact factor
and that we have given that one that relevant
01:10.010 --> 01:16.750
clauses that we have given here, so impact
percentage for Class A loading and class 70L
01:16.750 --> 01:23.640
loading for spans less 9m the value of the
impact percentage shall be taken as follows,
01:23.640 --> 01:36.020
so 25% for spans up to 5m linearly reducing
to 10 then, so 5. So, that means here we can
01:36.020 --> 01:42.130
consider this particular one 5.9 meter.
So in that case it will fall to this particular
01:42.130 --> 01:48.260
category for this is not will wheel vehicle
so this is a first case will come case a will
01:48.260 --> 01:55.680
come this is for spans of greater than 9m
so 10% to up to span of 40 and then figure
01:55.680 --> 02:02.470
5 already we have shown you in one of the
that your lecture and then we are having this
02:02.470 --> 02:06.400
one so we will show our case will be here
this particular one.
02:06.400 --> 02:12.610
So how it comes let us see so their impact
percentage that we can say for span greater
02:12.610 --> 02:20.620
than 5 m but less than 9m, 25 – 5.9 – 5
so that means actually you know what we are
02:20.620 --> 02:28.690
doing this basically here.
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So this is 25% say and up to this we are considering
that particular one here somewhere here and
02:52.310 --> 03:04.390
which is linearly varying, so this is 5m this
is 9 m so how much is this one so it will
03:04.390 --> 03:15.680
be reduced to 15%and so for any kind of thing
we can find out that how much you are additional
03:15.680 --> 03:20.100
one from there you can find out and that is
what we have done basically here.
03:20.100 --> 03:27.739
So 5.9 – 5 / 9-5 x 25 – 10 so these particular
induction we are doing according to that clause.
03:27.739 --> 03:29.680
We are following this clause.
03:29.680 --> 03:36.630
And then we can find out this work role here
and which is coming as 21.625 that is in percentage
03:36.630 --> 03:44.879
so impact factor will be 1.216 so you will
get the impact factor of 1.216 that you can
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find out here.
03:47.950 --> 03:58.370
Now intensity of loading then here there is
the impact factor into 700 that is the kilo
03:58.370 --> 04:07.400
Newton the load 7.327 x 5.69 so 20. 421 so
let us add one more thing that I would d like
04:07.400 --> 04:12.900
to add let me add it here so that then you
can find out that how much we are getting
04:12.900 --> 04:14.780
that.
04:14.780 --> 04:25.199
Here we are getting it here so q sorry this
will be q live load q live load or vehicle
04:25.199 --> 04:49.069
load which will be equal to here 1. 216 x
700/ 7.327 x 5.69 = 20.421 kilo Newton/ m2
04:49.069 --> 04:54.559
so that means here from these particular one
if we come down, so it is coming down this
04:54.559 --> 04:58.639
particular one here there so how much if you
do this one that whatever section will come
04:58.639 --> 05:04.349
you can imagine then if you compare to there
to one that considering the both the tracks
05:04.349 --> 05:09.449
then coming down to the dispersion final you
are going down to a 20.421 that particular
05:09.449 --> 05:11.561
one here.
If we consider the effective develop will
05:11.561 --> 05:19.759
be little more, so this is the one that we
shall consider in our analysis that will find
05:19.759 --> 05:23.719
out the bending moment that because one we
shall consider here.
05:23.719 --> 05:31.669
So maximum live load bending moment this is
the maximum live load bending moment that
05:31.669 --> 05:36.999
particular one we are getting it here, so
how much that particular one we are getting
05:36.999 --> 05:39.150
it here let us find out here.
05:39.150 --> 05:59.610
So if you really see this one here
this is how much span so 5.9m how much is
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this one the load 5.69m so if we consider
this one here and the intensity we have got
06:20.270 --> 06:49.499
it after adding impact factor q that particular
one we can get it here 20.421 kN/m/m width
06:49.499 --> 07:00.159
so we can get this one q 20.421 x 5.69 / 2
x that movement 5.9/2 – 20.421 so you can
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get this one here.
07:06.240 --> 07:16.680
So you can get this one here that particular
one here 5.9 x 5.9 that particular one here.
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82.533 kNm that we are getting it here this
particular one we can find out, so this is
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the one that we can find out here so design
bending moment dead load bending moment, class
07:30.110 --> 07:35.449
live load bending moment already we have got
this one this class this which is coming as
07:35.449 --> 07:44.999
140.143 kNm, so this is the one the total
bending moment that you will get it here,
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so this is the one we can find out here first
you are getting there that means you can find
07:49.680 --> 07:57.159
out the reaction and then you can find out
that and then you can get the value.
07:57.159 --> 08:05.060
Now coming to this one here we shall come
back later on.
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So now we have two design you have to check
there are two ways to check that one is that
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you can find out the depth of the beam maybe
you want alternative alternatively you can
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check that you just you are providing the
dispersion of the zip that means I have already
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taken that one say 460mm that overall depth,
so we can find out the effective depth also,
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so on the basis of that you can find out from
the effective depth you can find out that
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whether the section is alright or not that
capacity of the section we can find out that
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means either you can find out the effective
depth and you can find out that your what
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is called that overall depth.
That we can that way also you can check alternatively
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you can check with the moment capacity that
means the moment applied here we are getting
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140.143 kNm and concrete grade obviously M25
steel grade Fe415 then overall the flow hybrid
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460 so our objective is that whether this
overall depth provided is alright or not that
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is the one we are covered you have taken say
30mm diameter of longitudinal bus 25mm that
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we have assumed that means we shall give that
one say 25mm bar scbc we are considering now
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working stress method.
That this particular one we are considering
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here the very simple one that working stress
method we are considering here you know that
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way you can consider that scbc which is coming
8. 5 N/ square meter and this one let me tell
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you again it is according to IS 456 8.5 now
here I would like to mention this vector on
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here that IRC 21 that because one it gives
one third of this way that means it will be
09:56.150 --> 10:02.330
8.33 they are very particular they can make
it simple one that 8.33 they consider that
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one and one third of XK they consider here.
So that way we can find out here it will sst
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again I have taken according to IS 456190
because the thing is that I would like to
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give you problem, so that you can compare
and you can see that you are from one code
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to another code with little value of changes
how much actually difference you are getting
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that is more important rather than just using
only formula using that certain value not
10:29.700 --> 10:34.620
like that you just feel it the particular
value whatever we are providing that particular
10:34.620 --> 10:39.770
one somewhere they are providing say 0.48
somewhere they are providing 0.58 like that
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you consider and that particular one can find
out here. So whenever we are talking to here,
10:49.250 --> 11:02.330
190 so if we consider that one just to give
you idea 190.
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So sst / 415 so 190 / 415 so which I am getting
here say 0.457 so this factor is very, very
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important I personally feel this factor is
more important here that means even shall
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we consider 0.46 or shall you consider 0.45
so as I have given you that on the fifth lecture
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that we have told you certain kind of say
your probability probabilistic one so this
11:43.370 --> 11:49.200
is very, very important here this particular
one we have to consider that one, so that
11:49.200 --> 11:54.860
means in absence of that without knowing that
value is 190 or 200 or something like that.
11:54.860 --> 12:00.470
So if even if you take say 0.45 that is actually
good enough that particular one you can consider
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and on the basis of that you can check the
value and you can go ahead with that your
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computation you will get a reasonable result
that we can find out, so the code we shall
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follow but at the same time you should understand
that how much percentage you are using with
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respect to that FCK Or FY that is more important
to me I personally feel that then only you
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can understand that whether the depth given
that it can take care or not this is the one
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you understand not like that the computer
program is giving you certain results.
12:33.150 --> 12:38.010
And it is alright or not that one so you just
think of a probabilistic manner hat whether
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it is coming all right with a small variation
so in this case at I have out 0.457 or 0.45
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that means I can use 0.45 also for to remembering
it easily instead of going for 0.46 like that
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we can say.
12:55.180 --> 13:06.900
Now coming to this one here modular ratio
m 280/ 3 scbc = 280/3 x 8.5 so 11 that value
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we can get it here 11 that particular one
here if you consider 8.33 there is obviously
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a little more that will be come to 11.5 also
and this one very interesting thing you can
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say that as I have told you for IRC code so
if you consider that m.
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Just to give you idea 280 /3 scbc and where
as you can see 3 scbc = /3 that means m is
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nothing but 280 by fck so that is the one
can consume that means what you can say you
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can express it in terms fck also initiative
remembering 3 scbc all those things that means
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in working stress method also you can go ahead
without 280 / fck and on the basis of that
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everything can be in terms of fck only that
is quite possible.
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Effective depth provided D – cc - ? t / 2
I we have assumed 25/2 so then you are given
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400 17.5 from the service this is the one
you have provided for balanced section kb
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=xd which is equal to m scbc / sst + m scbc
that way you can find out this particular
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one you can find out here you can do it very
easily also you can do it that means here.
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If you really consider
this is the one we can consider here so I
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can consider here scbc/ Ec this will give
me the strain this one sst / Es this length
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is kb and this one is
d so you can find out that this one that kb
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/d will be equal to this length make this
one so scbc / Ec / sst / Es + scbc / Ec and
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from there you will get that formula which
is equal to that way, so that means here what
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I mean to say you can easily you can remember
that no need of going every time that all
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those things, so if you multiply with the
ES / EC this ES will go. So you get that M
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s CBC here M, so that means you multiplied
with that ES here ES here this ES will go
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so will get M s CBC M s C which exactly this
particular value you can get it here.
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So again very interesting thing again M actually
again you can get it 280 /3 s CBC so 280 / 3
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s CBC I can write down here m2 HT / 3 so that
means here it will be in terms of 280 / 3
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280 / 3 and that means KB is dependent on
s s T and Jb = 1 – kV / 3, so which is equal
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to 1 - 0.329 = 3.89 that you can take it that
workers.
16:54.250 --> 17:06.640
So moment of resistance of concrete 1/2 s
CBC JB JB x BD2, so ½ x H 1 5 x 0.329 x 0.89
17:06.640 --> 17:17.660
x 1000 because I have taken that one say in
a parameter weight x 4 17.52 x 10-6, so 216.914.
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So we are getting here 140.143 and we are
getting that moment of resistance due to concrete
17:25.909 --> 17:32.990
216 that particular one is doing quite high
that particular one here that way you can
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find out. So we can consider this vector one
here.
17:39.019 --> 18:03.440
So MC 216.914Knm in which we have got it aim
apply it 140.143knm, now we have to provide
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the steel reinforcement that we have to provide
the steel reinforcement later because the
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thing is that this is the one requirement
and this is the one that concrete is giving
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that the core one here the section we are
providing this is the section. So overall
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depth 46mm and this one 1000 so 1000 mm and
460 mm we are getting it here.
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So what we can go do 460 and 1000, now we
have to provide that d c--reinforcement and
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that for that the moments should be in between
m and MC in between that moment it should
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be in between then all I can say get under
reinforce it should not be above that it should
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not be below that the reinforcement provided
due to that whatever moment of resistance
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due to steel that should be in between that
particular one here. So coming to that particular
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one here whatever we can do it here.
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So I can calculate that a compressive force
in balance section and which is coming else
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that because I have taken 1/2 s CBC B x X
because we are considering the section as
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a this particular one we are considering this
is your say KB, this is your say s CBC and
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then B so we are getting this per core value
here which is coming here into D particular
19:55.809 --> 20:01.340
one because 0.329 into that particular one
we are getting kV x D that particular one
20:01.340 --> 20:05.259
here.
So we can get it here K B x D we can find
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out here which is coming as 583.769, so from
there because the section will be in your
20:14.730 --> 20:19.549
equilibrium condition so Ast B = 3072 that
way this is the one balance percentage of
20:19.549 --> 20:29.240
Steel that particular one. So that means 3772.52
mm that is the steel required to go up to
20:29.240 --> 20:34.919
the valance section that means that time what
will happen that your steel in for steel will
20:34.919 --> 20:39.669
also take sSt quantity we also take s CBC
that is the balance section.
20:39.669 --> 20:45.230
But if it will if we provide little more of
that together then it will become over reinforced
20:45.230 --> 20:51.019
that means that case concrete will fail first
and which we do not want, so that way whenever
20:51.019 --> 21:00.320
you are getting here now est required for
M that we can say roughly 140 .143 in 2006,
21:00.320 --> 21:07.970
so 1985.1 that is for this moment we require
this much of steel and we are providing 25mm
21:07.970 --> 21:21.429
bar. So 1000 x 1985.1 / 490.9 so 247.3mm that
is the one let us provide 25mm dia at 200mm
21:21.429 --> 21:32.450
CC which will provide 2454.42mm.
So we shall provide that one say your steel
21:32.450 --> 21:43.009
we are providing 2454.4 ? 372 that means that
one the balance section or in other way to
21:43.009 --> 22:09.879
get these 216.914, we require corresponding
steel 372.52mm for this moment we are getting
22:09.879 --> 22:31.590
steel 1985.1 we are providing in between 2454.4
area of steel 2454.42 mm. So that means we
22:31.590 --> 22:39.340
can provide this particular one 2454.42mm,
so which will be in between that much we can
22:39.340 --> 22:44.210
say.
So this is the one we can find out actually
22:44.210 --> 22:50.899
here that we can we can say that particular
one here that we can say that particular one
22:50.899 --> 22:56.659
that means the section is shape with respect
to bending. Now we have to check the one which
22:56.659 --> 23:04.049
we shall get it here for that your shear forces,
so let us consider the shear, force part.
23:04.049 --> 23:10.769
So that then we can complete that one at this
force with the working stress method.
23:10.769 --> 23:26.520
Now regarding shear force we shall equally
we shall find out that one say effective length
23:26.520 --> 23:32.119
of dispersion for live load that shear force
so it will be same actually this one there
23:32.119 --> 23:37.090
is no problem with respect to that effective
length there is no problem we shall get the
23:37.090 --> 23:38.740
same.
23:38.740 --> 23:46.610
But for width of deck slab that particular
one CM a also we shall get same value because
23:46.610 --> 23:51.889
there will no change because B / L will not
change, so we shall not get any change there
23:51.889 --> 23:54.340
this one also shall get the same value.
23:54.340 --> 24:04.950
There is no such problem only problem we shall
get that x value support because we are considering
24:04.950 --> 24:15.870
in the shear, force.
24:15.870 --> 24:25.739
We shall provide that one near the support
because then only I shall get the maximum
24:25.739 --> 24:32.610
shear force here, so the load will be placed
from the late supper whistle for getting maximum
24:32.610 --> 24:38.850
shear force in the left support so that X
will no longer be L /2 that value will be
24:38.850 --> 24:45.249
change with that 5.692 this is the one effective
length so that X is reduced, so this is your
24:45.249 --> 25:01.750
say 5.69. So X will be half of that so this
is the one 5.69/ 2 that particular one we
25:01.750 --> 25:06.590
shall get it here, so B will be same.
25:06.590 --> 25:14.809
B effective we shall get it here, so that
will B effective is now change so 5.138 for
25:14.809 --> 25:20.950
a one case one track we are getting here 5.138
we are getting this particular value.
25:20.950 --> 25:26.980
Similarly we can find out the same way we
can get it here, here there is no problem
25:26.980 --> 25:32.379
2 .62 that is the one that end from the centerline
of that one and I am getting here 2.569, so
25:32.379 --> 25:38.739
that means I shall get go to the full extent
on the left side we shall go.
25:38.739 --> 25:44.080
In the right hand side also same passion 2.569
we shall go 4.82 so that particular one we
25:44.080 --> 25:50.559
shall go so we can find out the three parts
5.569 in the left side like the previous one
25:50.559 --> 25:57.019
this is the middle one this is the one again
5 + so if we add it so we shall get is 7.198.
25:57.019 --> 26:06.080
So value that particular one that you are
effective with that one reduced a little bit.
26:06.080 --> 26:23.080
So coming to this particular one here we can
find out.
26:23.080 --> 26:28.940
So this is the one we are getting intensity
of loading due to vehicle load, so we shall
26:28.940 --> 26:37.850
get this much for the shear force 7.198 x
5.69 maximum line load shear force so then
26:37.850 --> 26:45.149
we shall get it here 61.245kn design shear
forcing of dead load shear force which already
26:45.149 --> 26:53.590
calculated live load shear force now calculated
so this is coming as 100.303 kn. So we are
26:53.590 --> 27:08.739
getting here VDL which is equal to 39.058kn
Vll = 61.245kn and V = 100.303kn B = 1000
27:08.739 --> 27:40.080
D = 417.5mm.
So tV V / BD = you
27:40.080 --> 27:54.970
can
say 100.303 / 1000 x 417.5 x 103 kn, so we
27:54.970 --> 28:17.789
can write down here 0.303 /417.5 0.24 if you
go back to the stable and with respect to
28:17.789 --> 28:24.489
the percentage of steel you will find out
this value is very less so that means we do
28:24.489 --> 28:29.710
not require any shear reinforcement. Now coming
to this particular one here that is the other
28:29.710 --> 28:35.600
two checks we generally do it for the slab
which that main reinforcement we provide that
28:35.600 --> 28:40.039
overall depth we provide mineral crystal wood
and we check the shear, force.
28:40.039 --> 28:44.609
Now there is a present trend you will find
out that one that people used to give that
28:44.609 --> 28:49.990
reinforcement overall depth list and if you
give the overall a list they obviously that
28:49.990 --> 28:56.659
effect would be that in the shear, force or
shear stress and in that case whatever we
28:56.659 --> 29:03.639
do whenever we consider for the shear stress
whatever we do here their per color one here
29:03.639 --> 29:09.779
then we have to provide the share reinforcement.
Now this is the one designers choice and generally
29:09.779 --> 29:17.070
that it happens for the slab we avoid the
slab we avoid giving actually shear reinforcement
29:17.070 --> 29:23.529
if it is at all required that one then we
provide but it is better not to give actually
29:23.529 --> 29:28.999
your shear reinforcement in slab whenever
you are considering that vertical slab if
29:28.999 --> 29:34.690
we consider this one as a beam then obviously
you can provide that one say shear. So that
29:34.690 --> 29:43.340
means slab means only bending and beam means
bending and shear.
29:43.340 --> 29:47.899
So this is the totally a design philosophy
that how you are considering that whether
29:47.899 --> 29:53.850
you will go for only bending that means it
is created a slab and you provide your reinforcement
29:53.850 --> 29:59.169
accordingly and if you consider that one as
a beam that means you are providing again
29:59.169 --> 30:05.759
shear reinforcement and that also you have
to provide. So considering that aspect that
30:05.759 --> 30:11.899
is the thing there is a designer choice but
I personally feel actually that it is better
30:11.899 --> 30:19.759
to give up for your just to give you IDI to
is better to go for on your say load more
30:19.759 --> 30:26.690
depth then you will have more cousin.
So that it will be more cousins with there
30:26.690 --> 30:34.570
with respect that enforcement the basic objective
is that it is this one.
30:34.570 --> 30:46.229
Then you are getting Ms and then you are getting
MC, so then only your under reinforce case
30:46.229 --> 31:03.240
condition can be full filled. So this is the
one just we have given so we shall solve we
31:03.240 --> 31:08.220
shall give few problems also we shall give
on the other methods also easily we have taken
31:08.220 --> 31:14.499
little more time on that to elaborate that
because I would like to give you idea that
31:14.499 --> 31:20.729
how we feel regarding design is not like that
a formula or using any software you just try
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to fill it and then it will then you can understand
that whether the structure is safe or not.
31:26.720 --> 31:32.289
There are many more other things also just
quickly I would like to give you just will
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be getting the slab whenever you are talking
slab.
31:37.580 --> 31:45.299
Just I am taking the cross section here there
is certain person the middle portion where
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that you are say carriageway other the load
they can load more you can also design like
31:53.470 --> 32:04.460
this also let mean this portion here the bearing
the two ends it may be like this so these
32:04.460 --> 32:13.629
portion that your footpath other things are
there which can come here and these portion
32:13.629 --> 32:19.990
may be after second level it can come and
where the load is less.
32:19.990 --> 32:26.549
So we can also design in that person that
and it will look very good also that is also
32:26.549 --> 32:31.099
another but that case if this portion will
become actually a continuous function it will
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not be your say longitudinal via these portion
is longitudinal and personal, so that will
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be the another one it can happen and one can
think of it also that how can you do it. So
32:42.799 --> 32:45.719
with this we conclude this particular one,
so thank you very much.