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Russian
00:00:03
[applause]00:00:04
[music] [applause]00:00:09
[music]00:00:11
hello, dear listeners, here00:00:13
I am again with Tatyana00:00:15
today I will have a somewhat unusual00:00:18
topic since I was asked a question00:00:21
in the comments about the line of influence, I decided to00:00:25
record and post several videos with00:00:27
this topic00:00:28
I want to warn you right away that this topic00:00:31
is not studied by all specialties, I don’t know the00:00:35
curricula of all universities, but I can00:00:38
say with full confidence that such a00:00:40
specialty as architecture,00:00:42
engineer-economist at any university is unlikely to00:00:45
study this topic, so we have before us00:00:50
beam to beam and even frame to frame any00:00:56
structure can be subject to not only a00:01:00
stationary load, but also a moving one, for00:01:03
example, all moving transport, and that00:01:06
is, a moving load, lines of influence,00:01:10
this is also like diagrams, these are graphs, what is it,00:01:16
before explaining this00:01:23
topic, today I will explain the construction of lines of00:01:27
influence in simple beams, so here it is00:01:31
before explaining, I want to say what an00:01:35
influence line is, attention a line of influence00:01:41
is a graph that shows how00:01:47
this or that force changes00:01:52
depending on the position of a unit force,00:01:57
and what does this mean, that is,00:02:03
some force acts on our beam, it00:02:09
will always be a force equal to one s unit is00:02:13
simpler if we know about00:02:15
or from one then we can know the force00:02:18
and from ten from 15 by multiplying this whole00:02:23
force by 10 by 15 further, the00:02:27
distinctive feature of the course on the00:02:29
strength of materials was not studied in this topic; the00:02:32
distinctive feature is that the00:02:35
force is always equal to one, but00:02:40
the position and and non-constant, that is, x is00:02:45
not unknown, but a variable, when we are00:02:50
talking about an equation,00:02:51
then this is unknown to us x, and if we00:02:55
are talking about some kind of function, then this is00:02:57
a variable, and so the position of the force of a00:03:02
unit force is described by the ordinate x, I00:03:08
immediately want to draw your attention to a00:03:12
unit or 10 or 20 in supports, the00:03:16
same reactions occur in beams from a00:03:20
vertical load; the horizontal00:03:22
reaction is always zero and I won’t even00:03:26
show it, even though this support and hinge have a00:03:29
fixed horizontal reaction; I00:03:32
won’t show this is a support, which means I’ll00:03:35
draw00:03:36
this support b This is something else I would like to00:03:42
draw attention to: the force f is always00:03:45
oriented from top to bottom when constructing00:03:48
lines of influence, and the reactions are oriented from00:03:52
bottom to top, these are always not diagrams I will drink alcohol with00:03:56
my husband, the reaction is up, show and00:03:59
in the line of influence is always upward, so if00:04:05
we move along the beam,00:04:07
our force naturally, these reactions you00:04:11
would change their value regardless00:04:15
of what this force is equal to,00:04:18
imagine yourself if you are moving along a jar,00:04:21
then if you stand in the middle of the beam,00:04:24
the butterfly will bend more if you move00:04:29
closer to the support, that00:04:32
is, if the shell00:04:33
bends less, what such a jar, place a00:04:36
piece of board on 200:04:37
bricks and try to see how00:04:41
your board will sag and so the force00:04:48
f is equal to the unit of position and and changes00:04:52
as the origin of coordinates; always00:04:56
take the left support as the most convenient to take;00:05:00
attention, no matter what kind of support there is, it is00:05:05
hingedly fixed or hingedly00:05:08
movable left the most convenient support is not00:05:12
the end of the beam, namely the left support, so00:05:17
if we have a concentrated00:05:20
force that is applied somewhere in one place,00:05:22
and we are drawing up an equation of00:05:24
moments,00:05:26
let’s draw up here to determine the00:05:28
support reactions wi wi b we in the beams00:05:31
when constructing diagrams00:05:33
inserted the equation of moments around00:05:35
points a and so one we must multiply00:05:40
by x 1 multiply by x rotates this unit00:05:46
clockwise we took this00:05:48
product with a plus reaction you would00:05:51
rotate counterclockwise in b multiplied00:05:54
by 5 expressing in from here v.v.00:05:57
we get that you can equal 1 5 x00:06:02
what does this mean we didn’t get a number we00:06:07
got a function00:06:09
function vb depends on x and that is,00:06:13
imagine if I wrote you00:06:15
y equals 1 5 x00:06:18
you should immediately answer me that this00:06:22
function is a straight line that is, a function00:06:26
that depends on their game site, in00:06:28
this case, a function that depends on00:06:31
X is our reaction to GDP, how would we00:06:35
build this graph, set the value00:06:37
of X, well, let’s assume x is equal to zero, then00:06:41
here it would be equal to zero in b00:06:44
and in Y the same thing, it would be00:06:48
one point with coordinates 0 0 and 2.00:06:51
which is more convenient to take x equal to 500:06:54
correctly because the00:06:56
five is reduced, then in b it is equal to one and00:07:01
so on the graph here is our00:07:09
coordinate system, that is, here we have our00:07:12
x going, as it were, and this is our y or the00:07:17
ordinate00:07:19
value in in is plotted along the y axis only this is how00:07:23
influence lines are drawn, this is how we draw the line of00:07:27
origin, I remind you at this00:07:30
point and the first point with coordinates 00 is00:07:34
here 0 2. x equals 5x equals 5 here is our00:07:39
origin of coordinates 5 means here00:07:42
and y is equal to or in b is equal to one,00:07:45
that is, here we have one we got00:07:49
two points through which we can00:07:51
draw an absolutely straight line00:07:54
since we got a00:07:57
linear relationship one to the first power,00:08:02
please remember algebra and now we00:08:06
have a graph that reflects the00:08:14
change in our reaction, you would00:08:19
call it the line of influence v.b.00:08:23
that is, on this graph, each00:08:30
ordinate k, that is, this little stroke, what does it00:08:33
mean,00:08:35
it means that if this one00:08:38
moves to this point, then the value of00:08:42
the reaction b will not be one, but this00:08:46
value really is if you take a00:08:48
1 multiplied by this and divide on 500:08:52
you are completely 1.400:08:55
from them that is, this is the length of the segment this00:08:58
on a scale00:08:59
means the value of the reaction in would be00:09:03
this unit again this value is still the00:09:07
same you would when the force stopped00:09:11
and here temporarily this zero means00:09:14
that if the force becomes in from this point to00:09:18
the full, imagine that you have become on the00:09:21
left support of the right support is inactive, then the00:09:23
value of the reaction in b will be equal to zero, why did00:09:26
the minus appear here, but00:09:29
because if the force moves to this00:09:31
console,00:09:32
then in order to balance the beam, this00:09:36
reaction must be directed downwards, that00:09:38
is not top to bottom, but we said at the beginning of00:09:41
the video that the reaction vb reaction is00:09:46
always shown by default from bottom to top00:09:49
on the lines of influence, and so every00:09:52
stroke, every ordinate k00:09:55
is the entire value of 1 of the same force,00:09:59
that is, you would accordingly if we00:10:05
need to build lines influence in the JSC00:10:09
line of influence in the same way,00:10:15
exactly the opposite, sometimes it is necessary and this00:10:18
can also be derived from this dependence, I00:10:21
won’t do this, the unit will need to be00:10:25
under the support and here it will be 0 and then we00:10:28
will get this straight line again00:10:34
here plus a here minus the line of influence00:10:42
once again I want to draw attention to each00:10:45
stroke this is the value of the reaction in and00:10:51
please remember the lines of influence00:10:54
they will all be the same they will be similar00:10:58
to each other it looks like if we build an00:11:01
influence line for a beam on two supports00:11:04
we build a line of influence for the00:11:06
left support reaction does not matter some kind of00:11:10
support is hingedly stationary00:11:12
or movable, I repeat once again if we00:11:15
build for the left support reaction, then00:11:18
under the left support the unit under the right one00:11:21
will always be 0 and finally, if we00:11:26
build a line of influence, the right support00:11:29
reaction means under the right support there00:11:31
will always be a unit with a plus under the left the support00:11:35
will be zero not at the end of the stick not here00:11:41
not here but we are always tied to the00:11:43
supports, that is, always under the supports00:11:46
if we have a stick without the left00:11:49
console, then of course the line of influence will look00:11:52
like this if there is a point00:11:54
without the right console the lines of influence in00:11:58
will be look exactly like this in addition to a beam00:12:01
on 2 hinged supports, we have also00:12:05
encountered a stick with a rigid00:12:07
pinching, it doesn’t matter whether the rigid00:12:09
pinching is on the right or the left, we know that00:12:12
in a rigid pinching a moment arises and a00:12:18
vertical reaction, what will the00:12:25
value of the reaction look like? return the line of influence of the00:12:29
reaction, depending on where00:12:34
our load will be located, I draw your00:12:38
attention to the fact that this force f is equal to00:12:41
one and is very often called a load,00:12:46
this force has no dimension, a00:12:50
dimensionless quantity, it has no00:12:53
dimension, not kilonewtons and newtons, not00:12:56
kilograms, just an abstract unit, and00:12:59
so the force f is equal to one and the force you are in00:13:06
beam with rigid pinching, we know that00:13:08
to determine the reaction we must00:13:10
draw up an equation for the projection of forces on the00:13:12
y axis, if we draw up this equation then you00:13:17
will have a00:13:18
plus sign because y will be00:13:21
directed upward and one downward, I will00:13:25
repeat again the reaction is always shown from00:13:28
bottom to top force is always unitly00:13:30
oriented to the revolution, equating the culem,00:13:33
we get equal to one, that is, the line of00:13:37
influence of this support reaction, you00:13:40
don’t care whether it will be hard pinching00:13:44
on the right or hard pinching on the left, the00:13:47
line of influence will look like a vein, then the00:13:52
constant value is one sign plus00:14:01
this is the line of influence of the reaction you will be it00:14:06
rigid pinching on the right or rigid00:14:09
pinching on the left,00:14:11
it doesn’t matter, this reaction is the sum of y va00:14:15
up plus one down, which means one00:14:20
will always be constant + 1, this is what the00:14:24
lines of influence of support reactions will look like in00:14:29
wolves, as usual, let’s move on to generalizing00:14:34
once again the lines of influence of support reactions00:14:38
for simple beams always will look00:14:42
the same if we build an influence line00:14:45
for a beam on two supports, then these two00:14:48
influence lines will look exactly like this00:14:50
for a roll with rigid pinching, just like this,00:14:54
attention if you do00:14:58
the test work or do the00:15:00
test work, you most likely have a00:15:02
multi-span composite beam composite00:15:06
beam00:15:07
in In any case, you need to be able to build00:15:10
lines of influence in simple beams, just like00:15:14
in order to build a diagram of a multi-00:15:18
span beam, we break it down into00:15:21
simple ones and build for a simple one in the same way00:15:25
lines of influence, only then the separation is00:15:28
not extended, maybe they say they00:15:31
also extend to the overlying00:15:33
beams I’ll talk about this a little later,00:15:38
I’m finishing the video today, I will,00:15:42
of course, be very pleased if you like it,00:15:44
write comments, I will be00:15:48
grateful to you, as usual, at the end of the video I00:15:54
will have a task and an answer to the task. Have a00:15:59
great dateDescription:
как строить линии влияния опорных реакций в балках, понятие о линии влияния. 00:00 - начало 00:53 - условие задачи 01:09 - понятие о подвижной нагрузке и линии влияния 01:39 - определение "линия влияния усилия" 03:45 - направление реакций и единичной силы 05:27 - уравнения для определения реакции 06:35 - построение линии влияния реакции Vb 10:05 - построение линии влияния реакции Vа 12:00 - построение линии влияния реакции для консольной балки 14:30 - обобщение задание: https://drive.google.com/file/d/1T7p3HNAjDzXjvFpqKAZdYcQIbWQGTO16/view?usp=sharing ответы: https://drive.google.com/file/d/1T8l0__AEotO8tuNHrEBoftHepoVqzhnW/view?usp=sharing
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