Structural Mechanics Problem - Reaction Forces, Shear, Moment

[civilrobot PE etc etc]

Can someone help me to solve this problem? I don't have the full solution. I tried solving on my own but I only solved the first one. 

@NJHHEngineer @leggo PE @youngmotivatedengineer and anyone else who could help...

 

[NJHHEngineer P.E.]

Can someone help me to solve this problem? I don't have the full solution. I tried solving on my own but I only solved the first one. 

@NJHHEngineer @leggo PE @youngmotivatedengineer and anyone else who could help...

View attachment 20512

I'm tied up right now with some work - but what I can offer to help at the moment (no pun intended):

1.  How confident are you in your reaction force calculation? If you're confident, see next step.

2. Draw Shear Diagram to find Shear At B. (Note, since B is a hinge, you can break the beam into two sections for stability analysis)

3. Draw Moment Diagram to find Moment @ C (remember, internal moment at a hinge is 0)

If I have some time today, I'll see if I can work through this.

 

[NJHHEngineer P.E.]

@civilrobot

Check these out.  Maybe these will help.  Almost identical to your problem.  Watch the first video and then the second.

 

[leggo PE]

Hi @civilrobot! I agree with what @NJHHEngineer stated. I haven't watched the videos he posted, but I imagine they are good references.

Because of the hinge, I would definitely break the beam up into two sections (divided at that hinge) and use the conjugate beam method to solve the overall beam. Are you familiar with this method? One key thing about the hinge, is that, the beam on one side of the hinge will deflect in one direction, and the beam on the other side of the hinge will deflect in the opposite direction.

Also, yes! Moment at a hinge is always zero, which is very important to remember. That also corresponds to a point of zero slope of the shear at the hinge location in the shear diagram. Remembering those two tips will help you get the shape of your shear and moment diagrams correct when dealing with hinges.

 

[NJHHEngineer P.E.]

One key thing about the hinge, is that, the beam on one side of the hinge will deflect in one direction, and the beam on the other side of the hinge will deflect in the opposite direction.

^^^ that too.  I did work this out by hand last night.  But, I initially drew the FBD of each beam left and right hinge reactions in the same direction.  Took a second to realize why the math wasn't working out.

 

[civilrobot PE etc etc]

@NJHHEngineer and @leggo PE thank you! Both of these videos and your descriptions were very helpful. I now have the solution. I'll add this one and the problem in the video to my example problems. 

I haven't worked one of these problems in 20 years. I'm not kidding. After undergrad, I never used it. I didn't even use it on the last PE exam back in Oct 19 because I chose to wing it on this subject. But when I sat down and looked at the problems, I got so mad at myself. The problems weren't that complicated but the memories were too foggy and too distant to conjure up, and I wasn't going to sit in the exam and spend an hour trying to re-learn something I used to have the ability to do in my sleep. I figure if I put in a bit of effort this time around, I can pick up a few of these that I gave up on last time. They were so simple. 

So thanks again!

 

[leggo PE]

You're gonna rock the structural stuff this time around, @civilrobot! I just know it. You're preparing yourself very well, I can tell!

 

[NJHHEngineer P.E.]

@NJHHEngineer and @leggo PE thank you! Both of these videos and your descriptions were very helpful. I now have the solution. I'll add this one and the problem in the video to my example problems.

I haven't worked one of these problems in 20 years. I'm not kidding. After undergrad, I never used it. I didn't even use it on the last PE exam back in Oct 19 because I chose to wing it on this subject. But when I sat down and looked at the problems, I got so mad at myself. The problems weren't that complicated but the memories were too foggy and too distant to conjure up, and I wasn't going to sit in the exam and spend an hour trying to re-learn something I used to have the ability to do in my sleep. I figure if I put in a bit of effort this time around, I can pick up a few of these that I gave up on last time. They were so simple.

So thanks again!

@civilrobot You're welcome. One other thing to point out - in the AISC Steel Manual there's the beam diagrams and equations for various loading scenarios. Sometimes you might just be able to pick out the equation you need to solve direct for a variable. Rather than having to solve in a few steps. Might save a few minutes here and there.