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00:00In this video, we are going to learn how to draw shear force and bending movement diagram
00:13for a cantilever beam as shown in figure.
00:17So the statement is given as, draw shear force and bending movement diagram for a cantilever
00:23beam AB, 2m long, carries a uniformly distributed load of 1.5 kN per meter over a length of
00:331.6 meter from the free end.
00:37So this is the cantilever beam of length 2 meter and carrying a uniformly distributed load of
00:431.5 kN per meter over a length of 1.6 meter.
00:50So for this setup, we have to draw the shear force and bending movement diagram.
00:56So first of all, I will draw the free body diagram for this beam section.
01:02Here first we have to convert this UDL into point load.
01:08So to convert this, I will multiply this UDL value that is 1.5 kN per meter with the length
01:16over which the UDL act, that is 1.6 meter.
01:22So by calculating this, I will get the point load of 2.4 kN.
01:28Now this calculated point load is acting on the beam on the midpoint of length over which
01:33the UDL act.
01:34Now this type of problem, we are going to solve in three steps.
01:39In the first step, we have to calculate the value of support reaction force RA.
01:48So to calculate this value, I will use the condition of equilibrium that is summation
01:54of Fy equal to 0.
01:56That means addition of all forces in the vertical axis equal to 0.
02:01While doing the addition of all vertical forces, I will consider upward forces as positive and
02:08downward forces as negative.
02:10Here R is the vertical reaction force.
02:14So I will add this force with positive sign.
02:18And there is uniformly distributed load that we had converted into point load is acting on
02:23the beam in the downward direction.
02:26So I will add this 2.4 kN with minus sign.
02:32So from this, I will get the value of reaction force RA equal to 2.4 kN.
02:39Now with the help of this calculated value of RA, I will further calculate the values of
02:45shear forces at all the points of the beam.
02:49So the next step is calculation of shear forces.
02:53And the sign convention for the shear force calculation is upward forces are considered
02:58as positive and downward forces are considered as negative.
03:04And here I will start the shear force calculation from the left hand side of the beam.
03:10So first to calculate shear force at point A to its left, that is SF at A to the left.
03:17So as we can see, there is no force acting at the left side of point A.
03:22Therefore, SF at A to the left is equal to 0.
03:28So to draw a shear force diagram, I will first draw a horizontal reference line of 0 kN shear force.
03:35So here I will mark the point of 0 kN on the reference line, that is shear force at point
03:41A to the left is 0.
03:45If I go to the right of point A, then there is reaction force RA in the upward direction.
03:52So as per the sign convention, I will consider upward forces as positive.
03:58So here the shear force is plus 2.4 kN.
04:02Here one thing you should remember, while calculating shear force at particular point load, you can
04:17calculate the shear force values for the left side and right side of that particular point
04:22load.
04:23But, while calculating the shear force at uniformly distributed load, that is UDL, you should calculate
04:30shear force values at start point and end point of UDL.
04:35That is shear force at point C and shear force at point B, we need to calculate.
04:40Shear force at point C, that is SF at point C.
04:44Now, there is no load on the beam between the right side of point A and point C.
04:51Therefore, shear force remains constant.
04:54That is shear force at point C equal to 2.4 kN.
04:58Here, as there is no variation in shear force value, so I will make the horizontal line with
05:05shear force value as 2.4 kN.
05:07Now, the point B is the end point of UDL.
05:13So, I am taking section to the point B and I will calculate shear force at point B, that
05:18is SF at point B.
05:21And here I will carry forward previous value of shear force up to point C, which is 2.4
05:26kN.
05:27And to the left side of point B, there is uniformly distributed load of 1.5 kN per meter that we
05:35had converted into point load of 2.4 kN in the downward direction.
05:41So, as per the sign convention, I will consider this downward force as negative.
05:46So, I will add this point load as minus 2.4 kN.
05:51So here, plus 2.4 kN minus 2.4 kN gives me the value of shear force as 0 kN.
05:59So, I will mark this point of 0 kN shear force at point B.
06:05And if you can see, on cantilever B, between point B and C, there is UDL.
06:11And to draw a shear force diagram, I will indicate UDL with an inclined line.
06:16So I will connect these two points with an inclined line.
06:21And here in shear force diagram, whatever the position above the reference line, I will
06:25show this with plus sign.
06:27So, here I have completed the shear force diagram.
06:31Now, the next step is calculation of bending moment.
06:37So, bending moment at a section of beam is calculated as the algebraic sum of the moment
06:43of all forces acting on one side of the section.
06:48So to calculate bending moments, I will start either from left end or from right end of beam.
06:55Here I will start from right side.
06:58So whenever you are calculating the bending moments at a section of a beam, you should remember
07:04these conditions.
07:07So here, for cantilever beam, the condition is, at the free end of beam, the value of bending
07:13moment will be 0.
07:16That is BM suffix B equal to 0 kNm.
07:20So to draw bending moment, firstly I will draw the reference line of bending moment 0 kNm.
07:28So here BM suffix B equal to 0 kNm.
07:33So now we have to calculate bending moment at point C.
07:36Here you should remember, in case of cantilever beam, while you are doing the calculations for
07:42bending moment, at a particular point, you should always add movement of all the forces present
07:49from free end of cantilever beam, up to that particular point at which you are calculating
07:54the bending moment.
07:57And for calculation of bending moment, our sign conversion is, for sagging effect of beam,
08:02the force is considered as positive.
08:05And for hugging effect of beam, the force is considered as negative.
08:09So here, UDL of 1.5 kNm per meter acting on the beam in the downward direction.
08:17And previously I have converted this UDL value into point load of 2.4 kNm which is acting
08:24on the beam in the downward direction.
08:26Hence, the beam shows hogging effect.
08:29And for hogging effect of beam, our sign conversion is negative.
08:35So, for bending moment, this will be the amount of force acting on the beam into distance from
08:42point of action of force, i.e. 0.8 m.
08:46So, this will get the value of bending moment at point C equal to minus 1.92 kNm.
08:55So as it is negative value of bending moment, hence I will mark the point of bending moment
09:01below the reference line of 0 kNm bending moment.
09:05And to draw bending moment, I will indicate this UDL with a parabolic curve.
09:11Hence, I will join these two points with a parabolic curve.
09:15Now, the next we have to calculate the bending moment at point A.
09:22That is BM suffix A equal to, algebraic sum of movement of all the forces at the right-hand
09:28side of point A.
09:31So here, at the right-hand side of point A, there is UDL force of 1.5 kNm per meter that
09:38we had converted into point load in the downward direction.
09:42Hence the beam shows hogging effect.
09:45And for hogging effect, our sign convention will be negative.
09:49Hence, the amount of force is minus 2.4 kNm into distance from point of action of force.
09:58That is 1.2 m.
09:59So, this will get the value of bending moment at point A equal to minus 2.88 kNm.
10:10So as it is negative value of bending moment, hence I will mark this point below the reference
10:15line of bending moment 0 kNm.
10:20And as there is no forces acting on the beam between point C and point A, therefore, to
10:26draw bending moment diagram, I will join these two points with a straight line.
10:33Now since I can see, this bending moment diagram is drawn below the reference line of 0 kNm bending
10:39moment, hence I will show this portion by minus sign.
10:44So here, we have completed the shear force diagram and bending moment diagram for this cantilever
10:48step.
10:49This has been about to pass by the end of the beam.
10:53We have completed the shear force diagram and this length of the beam, so we have completed
10:55that because the shear force diagram here is a soft structure of the beam.
10:58And as long as the shear force diagram here, we have put the thickness of the beam and here
11:01through the beam.
11:01Follow the beam.
11:02I will show you some more of the resistance at the border and this length, where the speed
11:03of the beam time is reversed.
11:04Click the beam then add the beam to the beam.
11:07I am going to show you some more of the temperature of the beam and then increase the beam.