For the beam shown, determine (a) the maximum tensile and...

For the beam shown, determine (a) the maximum tensile and compressive bending stresses, (b) the maximum shear stress due to V, and (c) the maximum shear stress in the beam. a. Draw the shear force and bending moment diagram. b. Find the locations and magnitudes of the maximum compressive bending stress due to M. c. Show the stress element at point D on the cross section of the beam located at x=35in. d. Draw the Mohr's circle for stress element at point D and find the principal stresses Show the principal stress element of point D correctly aligned with respect to the xy coordinates.

Transcript

00:01 High so we are given that a beam shown into the figure in which at point a you can see there is a force of 1800 of lbf and the constant reaction on the beam to that of bc is 300 of lbf per meter.

00:22 So in first part we have to draw the shear force and bending moment diagram.

00:27 So let's draw it down.

00:29 So for that we need to do some calculation.

00:31 So concept behind this will be we have to use the moment mb and this should be equals to 0.

00:41 We take this direction as positive.

00:43 So see the forces are minus of rc times of the distance 30 plus force 300 times of the distance 13 to 15 minus of 10 into 1800 this is going to be equals to 0.

01:01 This implies rc is equals to 3900 lbf.

01:06 In similar way we take the moment positive as anticlockwise for c point.

01:14 So this should be equals to 0 according to the concept.

01:17 So from the given diagram of beam rb times of this 40 should be equals to sorry minus of 300 into 30 into 15 minus of 1800 and the distance will become 40 should be equals to 0.

01:35 You will get reaction on b point 90 sorry 6900 of lbf.

01:42 Now at x is equals to 35 of inch you will get vd is equals to 3900 minus of this 300 multiplied by 5.

01:54 So that will comes out 2400 of lbf.

01:58 So v maximum will comes to 5100 which is at point b.

02:07 By using all this quantities let us draw that bending moment diagram and force shear diagram.

02:14 See here i'm writing down all of the reactions.

02:18 So basically at this point there is a force of 1800.

02:23 This is what the point a this is the point b where the reaction is rb and this is what the point d and here one of the reaction that is rc.

02:34 So corresponding to that we can draw first the shear diagram.

02:39 So it will be something like in this way that you can clearly see this will be at point c and for point d we will have to take a dash line for is further.

02:53 So this is what a and this much of region basically corresponds to the shear force.

02:59 Let's say this has point sorry the distance x this is point b.

03:04 This is b.

03:05 This is d.

03:07 This point is c.

03:08 So obviously this much of distance will become 30 minus of this and this is what that component of the force 3900 of l base.

03:16 Now secondly we have to draw the bending diagram.

03:19 So it can be something like in this way that i have drawn here.

03:23 So this will represent the positive region of it and this is the negative one.

03:31 This is the point a...

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