Statics questions for point loaded cables - PE exam studying

[hemiv]

Hi y'all.

I'm getting tripped up on a PE exam study problem that hopefully you can provide some help with. It's from the Goswami All-in-One guide, 3rd ed., problem 102-001.

In a nutshell, it's this problem: Link

The differences are:
y between A & B = 4'
x between A & B = 4'
y between B & C = 2'
x between B & C = 8'
y between C & D = 5'
x between C & D = 3'
D is 1' below A
3kN load is 20kip in my problem
8kN load is 30k

So in the Goswami problem, all lengths including sag are known.

Is there any reason I can't sum moment about A, get an equation in the form of:

aDx + bDy = c

where a, b and c are known values. Then substitute Dx and Dy with Dcosθ and Dsinθ, so long as θ is known? Then I would have an equation in the form of

aDcosθ + bDsinθ = c

Then solve for the resultant reaction at D, which for cables is also simply the tension load in the cable. For this problem, I'm getting 32.9k. The only problem is, Goswami does it with a different method and comes up with 51.9. I realize that my method is a bit of a long way around, instead of just starting with cutting around joints B and C. But you know, this is for the PE exam and I'd rather be able to just rely on my gut even if it takes 30 seconds longer to solve.

In fact, there are three different ways I'm trying to and coming up with different tension in cable CD every time. Is there some rule I'm missing on this one? I can solve the cables with supports on the same level easily, but for some reason this difference in height between support A and D is throwing me for a loop.

 

[straub46]

You're missing a number in the problem statement, but what you're doing should work.

Take the example problem you posted. It's straight out of Hibbeler's "Structural Analysis" textbook. What do you get for the tension in C-D?

Sum Ma = 0 --> 2(3) + 4(8) = 2Dx + 5.5Dy. Dx = (1.5/2.5)*T and Dy = (2/2.5)*t

38 = 2(0.6)T + 5.5(0.8)T --> T = 6.78.

In that example, cos(theta) = 1.5/2.5 and sin(theta) = 2/2.5

As long as the angle your using is correct it should be fine. Did you flip cos/sin?

Go Bucks!

 

[hemiv]

Corrected, thanks.

I'm getting 6.7857, so I'm right on with the given answer on that problem. Good to know that my method should be fine.

I don't know what the hell is going on with the Goswami problem. I've even worked through the entire problem 6 here and got the whole thing right. Maybe it's an error. I've found a few in that book, but they were more obvious. Maybe I should stop studying with it, the problems are tending to be very complicated, so if you mix in the unexpected errata or two they can be very frustrating.

 

[straub46]

I got the 32.9 k you mentioned in your original post as well based off the geometry above. I have an older copy of that Goswami book, but it's at home so I can't look through it now.

If you have the CERM from PPI, that should be all you need (besides the structural codes). I bought the Goswami book because it covered a few extra topics, but I don't think I actually opened it during the exam.

Getting to study crunch time, good luck!

Go Bucks!

 

[hemiv]

Ok, thanks. That's a relief. My thoughts are that he made an error giving the sag distances. In other words, given the loads and distances, the cable wouldn't actually take the shape he's saying it does.

Wish me luck. It's me second go on this thing, and it's getting to be a pain. All the advice I hear is to take time off the week before, but no way. I'm studying until the last minute. At least just working problems.

 

[straub46]

I took the day before off when I took the PE, and I'm doing the same thing before the SE next week, both studying and professionally. Giving yourself a break before mentally taxing yourself as much as you will has it's benefits, if only for your sanity.

Hopefully you do better this time than last!

Go Bucks!

 

[hemiv]

I've got to do some traveling on Thursday to get to the testing city, and I'll be carpooling. So I imagine we'll both probably take it a bit easy on that day. If I keep up my schedule, I should have a pretty light study load on Wednesday, as well.

Good luck on your exam. Taking the SE is (sometimes) a goal of mine. We'll see.

 

[BAretired]

The differences are:
y between A & B = 4'
x between A & B = 4'
y between B & C = 2'
x between B & C = 8'
y between C & D = 5'
x between C & D = 3'
D is 1' below A
3kN load is 20kip in my problem
8kN load is 30k

So in the Goswami problem, all lengths including sag are known.

Actually, all lengths including sag are not known. If the Goswami book says they are known, it is in error. If points A, C and D are positioned and the applied loads are specified, the location of point B will be determined using statics.

If points C and D are assumed to be correctly positioned, then Fcd = 32.9k, Vcd = 28.2k and Hcd = 16.9k. The vertical reaction at point A is 21.8k for equilibrium. As there are no horizontally applied loads, Ha = Hcd where H is the horizontal reaction at A; in fact the horizontal component of the cable is 16.9k from A to D.

If point B is 4' below and 4' to the right of point A, then Mb = 21.8(4) - 16.9(4) = 19.6k', but this cannot be correct as Mb must be zero. Tangent of slope AB is 21.8/16.9 = 1.29, so AB makes an angle of 52.2^o to the horizontal.

Good luck in the exam. I hope I haven't confused you.

BA

 

[BAretired]

If points A, B and D are deemed to be correct, then point C will need to shift in order to maintain equilibrium.

BA

 

[hemiv]

Thanks for the input! Yes, I figured that out after solving about 3 or 4 other cable problems and getting them all right. I realized none of them had all dimensions given. So Goswami's cable shape is just wrong for the given loads.