Shear and Moment diagrams/calculations

[frozenguy]

Homework Statement

Draw the shear and moment diagrams for the beam shown and find the bending moment M at section C.

The Attempt at a Solution

So I got the correct answer for M_c but I'm confused on a few things.
I get different answers using different techniques for different aspects of this problem. Take my shear diagrams for example. You can see two sections to the lower right trying to calculate shear in between forces (I wanted to confirm between techniques) but they aren't adding up. 1.5' to the right of the 1000lb downward force, the shear should be 1000 up right? If I cut it into a section? But it doesn't coincide with my diagram.

Also, if I add up all the areas under my shear lines, I get -730.9. Shouldn't I get 0?

BTW, I know my moment diagram is off, I have since changed it but don't have the copy to scan, this is an old copy.

 

[PhanthomJay]

Homework Statement

Draw the shear and moment diagrams for the beam shown and find the bending moment M at section C.

The Attempt at a Solution

So I got the correct answer for M_c but I'm confused on a few things.
I get different answers using different techniques for different aspects of this problem. Take my shear diagrams for example. You can see two sections to the lower right trying to calculate shear in between forces (I wanted to confirm between techniques) but they aren't adding up. 1.5' to the right of the 1000lb downward force, the shear should be 1000 up right?

No. When you cut the section, there are forces and moments on that section. Draw a free body diagram of the section between the cut and one end of the beam. Then sum forces in the y direction to get the shear on the cut section. Your shear diagram is correct.

Also, if I add up all the areas under my shear lines, I get -730.9. Shouldn't I get 0?

did you properly take into account the plus and minus values, and check the shear values at the height of the rectangles? The areas do sum to zero.

 

[frozenguy]

No. When you cut the section, there are forces and moments on that section. Draw a free body diagram of the section between the cut and one end of the beam. Then sum forces in the y direction to get the shear on the cut section. Your shear diagram is correct. did you properly take into account the plus and minus values, and check the shear values at the height of the rectangles? The areas do sum to zero.

Hey thanks for your help!

Ok so when I cut a section, I have to make sure it includes one end of the beam? I can't just take a cut from the middle?

Because if I cut at 6' and cut again at 7.5 feet so I have a section representing 1.5 feet with 1000lb concentrated force acting downwards on the left portion, summing up y gives me 1000. So I do i have to include the rest of the beam to the right or left?

 

[PhanthomJay]

Hey thanks for your help!

Ok so when I cut a section, I have to make sure it includes one end of the beam? I can't just take a cut from the middle?

you could, but then you would have unknown forces and moments at each end of the cut 'middle' section, and you would not be able to directly solve for the shear without doing another step first. When you include one end of the beam, you know the reaction or applied force at those points, so it's a one step operation to get the shear at the cut section.

Because if I cut at 6' and cut again at 7.5 feet so I have a section representing 1.5 feet with 1000lb concentrated force acting downwards on the left portion, summing up y gives me 1000. So I do i have to include the rest of the beam to the right or left?

Never cut directly at a concentrated force, you get into singularities where the shear is changing over 0 distance. Instead, cut to right or left of the load, even if the cut is just an infinitesimal distance away.

 

[frozenguy]

you could, but then you would have unknown forces and moments at each end of the cut 'middle' section, and you would not be able to directly solve for the shear without doing another step first. When you include one end of the beam, you know the reaction or applied force at those points, so it's a one step operation to get the shear at the cut section.Never cut directly at a concentrated force, you get into singularities where the shear is changing over 0 distance. Instead, cut to right or left of the load, even if the cut is just an infinitesimal distance away.

Ok I'm almost there i think haha.

So to just do it in one step, I must include one end of the beam.

If I take a cut without including an end piece, i must take it away/around a concentrated load and apply an initial step? I don't remember learning another steps. Do you know if this is a step that might be taught in a statics class? I guess as long as I include an end I'll be fine..

Thanks for your help again!

 

[PhanthomJay]

Ok I'm almost there i think haha.

So to just do it in one step, I must include one end of the beam.

generally speaking, yes.

If I take a cut without including an end piece, i must take it away/around a concentrated load and apply an initial step?

Yes, because you get unknown shears and moments at each end of the cut section when you do it that way. So it gets you nowhere, unless, from a prior step, you know the value of one of the moments at one end of the cut.

I don't remember learning another steps. Do you know if this is a step that might be taught in a statics class? I guess as long as I include an end I'll be fine..

Thanks for your help again!

That other step would be to determine the moment at one end of the cut from another free body of a different section. Just forget about it, and include an end.