HW5_1: REACTION AT SUPPORT AND INTERNAL AXIAL TORQUE RESULTANT

Question

We will use moment equilibrium around the x axis to calculate the x-component of the reaction torque at A, TAx, and the axial torque resultant at section C, TC=T(xC), for these two shafts in torsion.

HW5_1_1 : 15.0 POINTS

For Shaft (1), obtain the numerical value, in N⋅m, for:

TC=
N⋅m unanswered
TAx=
N⋅m unanswered

HW5_1_2 : 15.0 POINTS

For Shaft (2), obtain the numerical value, in N⋅m, for:

TC=
N⋅m unanswered
TAx=
N⋅m

HW5_2: THIN-WALL SHAFT UNDER CONCENTRATED TORQUES

The thin wall shaft ABCD is fixed at A and loaded by concentrated torques at sections B,C, and D of direction and magnitude indicated in the figure. The shaft is composed of three segments, AB,BC, and CD of equal lengths L=2 m, and diameters indicated in the figure. The three segments are hollow tubes made of steel with shear modulus G=70 GPa and have equal wall thickness t=1.5 mm.

Note that, for the given dimensions, so you can use the thin-wall approximations introduced in class.

HW5_2_1 : 20.0 POINTS

Obtain the numerical value, in N⋅m, for the internal axial torque resultant in the three segments TAB, TBC, and TAB, and for the x-component of the reaction torque at A,TAx:
TAB= N⋅m unanswered
TBC= N⋅m unanswered
TCD= N⋅m unanswered
TAx= N⋅m unanswered

HW5_2_2 : 5.0 POINTS

Obtain the numerical value, in radians, for total angle of twist of the shaft ΦAD:
rad unanswered

HW5_2_3 : 5.0 POINTS

Obtain the numerical value, in MPa, for the maximum shear stress in the wall of the shaft:
τmax= MPa unanswered

HW5_3: A DESIGN PROBLEM FOR A THIN-WALL SHAFT

For the shaft ABC in the figure, both segments AB and BC are hollow tubes made of the same material and have equal wall thickness t. Torques of magnitude T1 and T2 are applied in opposite directions at sections B and C as indicated in the figure. The relative dimensions of the two segments are:

d1d2=L1L2=1.5

HW5_3 : 30.0 POINTS

If you want the shaft to have zero rotation at point C (i.e. you want to have a total angle of twist for the shaft equal to zero), what ratio should you impose between T1 and T2?

T1T2=
unanswered

HW5_4: AXIAL TORQUE DIAGRAM FOR CONCENTRATED AND DISTRIBUTED LOADING

For the shaft ACB in the figure has length L=4 m and is fixed at section A. Concentrated torques of magnitude Q1=10 kN·m and Q2=5 kN·m act in opposite directions at sections C(x=L/2) and B(x=L) respectively, as indicated in the figure. A distributed torque of uniform magnitude q0=6 kN·m/m acts along the segment AC of the shaft, in the direction indicated in the figure:

tx(x)={−q0,0,0≤x<L/2,L/2<x≤L

HW5_4_1 : 20.0 POINTS

Obtain a symbolic expression (in terms of Q1, Q2, q0, x, L) for the axial torque resultant T(x) along the shaft:
0≤x<L/2, T(x)=
unanswered
L/2<x≤L, T(x)=
unanswered

HW5_4_2 : 5.0 POINTS

Obtain the numerical value, in kN⋅m, of the maximum magnitude for the axial torque resultant in the shaft, Tmax:
∥Tmax∥=
kN⋅m unanswered

HW5_4_3 : 5.0 POINTS

Obtain the numerical value, in kN⋅m, of the axial torque resultant at the midsection of segment AC, T(x=L4):
T(x=L4)=
kN⋅m unanswered

HW5_4_X : 0.0 POINTS

CHALLENGE QUESTION

This challenge question is just for fun: it gives you no points, so you do not NEED to get the right solution. Indeed it is not even graded.

See if you can plot the T(x) from E5_3 by writing MATLAB code in the blank command window below. If you succeed, take a screenshot of your plot (NOT THE CODE in the command window!) and post it in the discussion forum under the "Challenge!" thread.

Once you have succeeded in plotting T(x) from E5_3, click "Reset" to clear the window and then try to write the code to plot T(x) from HW5_4. Take a screenshot of the plot (NOT THE CODE) and post that as well. It is okay to do this just this once, even if it "gives away" the solution to HW5_4.

Note that, for reference, you can look at what we had in the command windows for the examples in axial loading and in the Introduction to MATLAB sequence. You will have to write all of the code, including lines similar to the ones in previous "do not edit" sections. Note that any text after the % sign is interpreted by MATLAB as a comment, and it is not executed.

Did you succeed? Pat yourself on the back!

1
None
UnansweredUnsubmitted

Answer 1

HW5_1_1 : 15.0 points
-7
-17
HW5_1_2 : 15.0 points
-3
8
HW5_2_1 : 20.0 points
1600
5600
11600
-11600
HW5_3 : 30.0 points
3.2
HW5_4_2 : 5.0 points
7
HW5_4_3 : 5.0 points
-1

Answer 2

HW5_2_2 : 5.0 POINTS

Obtain the numerical value, in radians, for total angle of twist of the shaft ΦAD:
rad

HW5_2_3 : 5.0 POINTS

Obtain the numerical value, in MPa, for the maximum shear stress in the wall of the shaft:
τmax= MPa

Obtain a symbolic expression (in terms of Q1, Q2, q0, x, L) for the axial torque resultant T(x) along the shaft:
0≤x<L/2, T(x)=
unanswered
L/2<x≤L, T(x)=
unanswered

HW5_4_2 : 5.0 POINTS

Obtain the numerical value, in kN⋅m, of the maximum magnitude for the axial torque resultant in the shaft, Tmax:
∥Tmax∥=
kN⋅m unanswered

HW5_4_X : 0.0 POINTS

CHALLENGE QUESTION

This challenge question is just for fun: it gives you no points, so you do not NEED to get the right solution. Indeed it is not even graded.

See if you can plot the T(x) from E5_3 by writing MATLAB code in the blank command window below. If you succeed, take a screenshot of your plot (NOT THE CODE in the command window!) and post it in the discussion forum under the "Challenge!" thread.

Once you have succeeded in plotting T(x) from E5_3, click "Reset" to clear the window and then try to write the code to plot T(x) from HW5_4. Take a screenshot of the plot (NOT THE CODE) and post that as well. It is okay to do this just this once, even if it "gives away" the solution to HW5_4.

Note that, for reference, you can look at what we had in the command windows for the examples in axial loading and in the Introduction to MATLAB sequence. You will have to write all of the code, including lines similar to the ones in previous "do not edit" sections. Note that any text after the % sign is interpreted by MATLAB as a comment, and it is not executed.

Did you succeed? Pat yourself on the back!

Answer 3

5.2.2 0

Answer 4

Nope not Zero and I need help with the rest

Answer 5

HW5_4_1_b : ´Q_2 :

Answer 6

HW5_4_1_b : ´-Q_2 :

Answer 7

Ráááááá, more answers...

HW5_1_1
17
7

HW5_1_2
-21
16

Answer 8

Marcus this is wrong can you check?
HW5_4_1_b : ´Q_2 :

Answer 9

HW5_2_2
0.72

HW5_2_3
492.3

Answer 10

HW5_4_1

for 0≤x<L/2
-q_0*(L/2-x)+Q_1-Q_2

for L/2<x≤L
-Q_2

Answer 11

HW5_4_2 : 5.0 POINTS

Obtain the numerical value, in kN⋅m, of the maximum magnitude for the axial torque resultant in the shaft, Tmax:
∥Tmax∥=
kN⋅m
HW5_4_X : 0.0 POINTS

CHALLENGE QUESTION

This challenge question is just for fun: it gives you no points, so you do not NEED to get the right solution. Indeed it is not even graded.

See if you can plot the T(x) from E5_3 by writing MATLAB code in the blank command window below. If you succeed, take a screenshot of your plot (NOT THE CODE in the command window!) and post it in the discussion forum under the "Challenge!" thread.

Once you have succeeded in plotting T(x) from E5_3, click "Reset" to clear the window and then try to write the code to plot T(x) from HW5_4. Take a screenshot of the plot (NOT THE CODE) and post that as well. It is okay to do this just this once, even if it "gives away" the solution to HW5_4.

Note that, for reference, you can look at what we had in the command windows for the examples in axial loading and in the Introduction to MATLAB sequence. You will have to write all of the code, including lines similar to the ones in previous "do not edit" sections. Note that any text after the % sign is interpreted by MATLAB as a comment, and it is not executed.

Answer 12

5.3
% DO NOT EDIT % % % % % % % % % % % % % % % % % % % % % % % %
L=3; % in [m]
t_0=8; % in [kN]
x = linspace(0,L); %
t_x=t_0*(L-x)/L; % in [kN.m]
% DO NOT EDIT % % % % % % % % % % % % % % % % % % % % % % % %

T =((t_0/L)*(L-x).^2)/2;
% DO NOT EDIT % % % % % % % % % % % % % % % % % % % % % % % %
area(x,T,'LineWidth', 2.0, 'FaceColor', [0.7,0.9,0.9]) %
xlabel('x [m]') %
ylabel('T(x) [kN.m]'); %
% DO NOT EDIT % % % % % % % % % % % % % % % % % % % % % % % %

Answer 13

Obtain the numerical value, in kN⋅m, of the maximum magnitude for the axial torque resultant in the shaft, Tmax:
∥Tmax∥=

Answer 14

5.4.2. 7kN.m

Answer 15

HW5_2_1 : 20.0 points
11600
5600
1600
-11600