00:01
In this question you are given this setup.
00:03
So there's a counterweight w at the right side.
00:07
It's supporting the beam, b, b, b, a, d.
00:11
And then on the beam ad, there are two loads at points a and c, 40 pounds each.
00:19
You want to find a reaction at d, when w is 100 pounds and 90 pounds.
00:25
So to solve this problem, and one thing the beam is at, static equilibrium.
00:32
Okay.
00:33
So the first thing we need to do is to draw the freeball diagram of the beam ad.
00:43
Okay.
00:45
So we have this is the beam and then we have 40 pounds of load at point a at point a and then at the center we have another 40 pound load and then we have point b here we have a w so at point d so maybe we assume that there's a force to the right and the x as the x component i'm going to assume that there's a downward component of force and then from the diagram just assume that there's a moment, okay, counterclockwise moment at point d, okay? in this case, just assume a particular direction, okay, and then the conditions for equilibrium, it is summation of forces along the x direction is zero, summation of forces along the y is zero, and then the summation of the moments, point d about point d is zero, okay, okay, so based on a diagram, okay, with summation of fx equals to zero, this means that d x equals to zero, okay, with summation of f y equals to zero, okay, just going to define, going right is positive, going up is positive.
02:40
So we have w minus 40 minus 40 minus dy minus dy.
02:49
Goes to 0.
02:51
Okay, and you know that w is 100, kw is 100 pounds.
02:56
Okay, so the y is is 100 minus 80, you get 20 pounds.
03:04
Okay, so this is downward and then summation of the moment about point d is zero.
03:16
So we have md.
03:20
So this is the i'm going to take clockwise to be positive.
03:28
Okay...