Simply Supported Beam Numerical 7: Draw Shear Force Diagram and Bending Moment Diagram
Subject - Strength of Materials
Chapter - Shear Force and Bending Moment Diagrams
Chapter - Shear Force and Bending Moment Diagrams
Transcript
00:07In this video
00:08we are going to learn
00:09how to draw shear force diagram
00:11and bending moment diagram
00:13for a simply supported beam AB
00:15as shown in figure
00:19so the statement is given as
00:21draw shear force
00:23and bending moment diagram
00:24for a simply supported beam AB
00:276 meter long
00:28is loaded
00:29as shown in figure
00:34so this is the simply supported beam AB
00:36of length 6 meter
00:38and carrying a uniformly distributed load
00:40of 2 kilo Newton per meter
00:43over a length of 6 meter
00:46so for this setup
00:47we have to draw the shear force diagram
00:50and bending moment diagram
00:55so first of all
00:56I will draw the free body diagram
00:58for this beam section
01:02so for solving this numerical problem
01:04first we have to convert
01:06this uniformly distributed load
01:08into point load
01:12so to convert this
01:14I will multiply
01:15this UDL value
01:17with the length
01:18over which
01:19their UDL acts
01:22so the point load equal to
01:24UDL of 2 kilo Newton per meter
01:27multiply by distance AB
01:28that is 6 meter
01:32so here I will get
01:33the converted point load of 12 kilo Newton
01:38now this converted point load
01:40is acting on the midpoint
01:42of the length
01:43over which this UDL acts
01:46that is 12 kilo Newton load
01:48is acting on the midpoint
01:50of length AB
01:55now this type of problem
01:56we are going to solve in 3 steps
02:01In the first step
02:03we have to calculate
02:04the values of support reaction forces
02:07Ra and Rb
02:09so to calculate these values
02:11I will use 2 equations of equilibrium
02:15where first equation is
02:17summation Fy equal to 0
02:21that means
02:22addition of forces
02:23in the vertical axis
02:25equal to 0
02:27and the second equation is
02:29summation of moment
02:31equal to 0
02:33that means
02:34addition of moments
02:36due to all the forces
02:37about any point
02:39must be zero
02:42so here in the first equation
02:44while I am doing the addition
02:45of all vertical forces
02:48I will consider
02:49upward forces as positive
02:51and downward forces as negative
02:56here Ra and Rb
02:57are the vertical reaction forces
03:00acting on the beam
03:01in the upward direction
03:03so as per the sign convention
03:05I will add these forces
03:07with positive sign
03:09and the converted point load
03:11of 12 kilo Newton
03:13is acting on the beam
03:14in downward direction
03:16so as per the sign convention
03:17I will add this force
03:19with negative sign
03:22therefore
03:23after calculating
03:25this will get the equation
03:27that is Ra plus Rb
03:28equal to 12 kilo Newton
03:31so I will give this as
03:32equation number 1
03:35now the next equation is
03:37summation of moment equal to 0
03:41so for calculating the moment
03:43either we can take moment
03:45at point A
03:47or at point B
03:49and here my sign convention would be
03:52clockwise moment as
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