Question

torsion

Answer 1

Looking through your work, I think you had a mishap with both values of J.
For J1,J3, the internal diameter should be Do-2t.
For J2, for some reason, you used d=60 instead of d=65.

Now about the approach.
I see that the problem is anti-symmetric, i.e. segments 1 and 3 are identical, and Tb and Tc are equal and opposite in directions, which means that the mid-segment of segment 2 does not rotate at all. Taking advantage of this, we will solve instead half the problem, with the mid-section of segment taken as fixed.
Hence
L1=305; do=75; di=75-2*5=65;G1=45000;
J1=(do^4-di^4)/32=1353830
L2=360/2;d2=65; G2=26000
J2=d2^4/32=1752481
Tb=10000000
Let
T1=portion of Tb resisted by segment 1
T2=portion of Tb resisted by segment 2 (=Tb-T1)

We then equate angles of twist of both sections, i.e.
T1*L1/(G1*J1) = (Tb-T1)*L2/(G2*J2)
and solve for T1=4410544 (hence T2=5589456).
Solve for tau_1, tau_2 using TRmax/G, and phi=TL/(GJ).
Please check all my assumptions and numerical data.
You can post your values for checking.

Answer 2

before I look at this I want to just discuss briefly this problem with you.. Let me post it. The image is just difficult to interpret.

Answer 3

where F is located would that be the bottom of the gate?

Answer 4

I was discussing this with a classmate and I believe the bottom of the gate is where the F is located.

Answer 5

Do-2t? what?

Answer 6

I see what you mean by 2t

Answer 7

why is it twice the thickness?

Answer 8

for j1 and j3 i got 1.752x10^6 mm^4

Answer 9

Okay that is what I thought I did originally but only subtracted one t, not 2.

Answer 10

I get
J1=J3=(75^4-65^4)\(\pi\)/32=1353830

Answer 11

okay I got it. Let me finish the other parts.

Answer 12

For the hydrostatic problem, I think either h1 extends to the bottom of the tank, or there is a separate dimension for the depth.
If h1 extends to the bottom, and since H2 >H1, then there is a chance that a force is required to keep the gate closed.
You may want to check with your teacher for the possible error in the drawing/dimensioning.

Answer 13

Yep, will compare notes when you finished the other parts.

Answer 14

@mathmate I am not understanding the analysis.

Answer 15

which one, torsion?

Answer 16

why Tb - T1? I see that they are rotating in opposite directions, but why didn't you use
-Tc + T2

Answer 17

we could have instead, right?

Answer 18

why did you say segment 2 won't twist? Is it because B and C have torques in opposite directions. The ends of segment 2 will twist.

Answer 19

Where do you get this equtions?

T1*L1/(G1*J1) = (Tb-T1)*L2/(G2*J2)

Answer 20

I did not consider Tc at all.
The first part of the analysis is to observe the symmetry of the system.
The geometric properties of segments 1 & 3 are identical (length, material, dimensions...). So there is symmetry.
The loads are anti-symmetric, Tb=-Tc.
Therefore the mid-segment of BC does NOT rotate.
I therefore simplify the shaft as half its length:
where BE=EC.
The torque Tb is then split into two components, one for AB (T1), and the remainder (Tb-T1) for BE, such that the angle of twist is equal.