Asked by MAN
tapered thin-wall circular shaft has constant wall thickness, t, length L, and diameters linearly varying between dA at the support A(x=0) and dB at its free end B(x=L). The shaft is homogeneous with shear modulus G
HW6_1A : 20.0 POINTS
Obtain a symbolic expression for the torsional stiffness of the shaft KT=Q/Φ, in terms of t, L, G, dA (you will have factors of π in your answers: enter π as "pi" ):
KT=
unanswered
HW6_1B : 20.0 POINTS
Obtain a symbolic expression for the maximum shear strain on the generic x-section along the shaft, γmax(x), in terms of t, L, G, Q, x, dA (you will have factors of π in your answers: enter π as "pi" ):
γmax(x)=
unanswered
HW6_1CX : 0.0 POINTS
CHALLENGE QUESTION! (no points, just for fun!)
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.
For L=0.5 m, t=2 mm, dA=4 cm, and G=70 GPa, obtain the torque Q0 that you need to apply to the shaft if you want to obtain a maximum value of 2% strain.
Then, use these values to plot γmax(x) by writing MATLAB code in the blank command window below. If you succeed, take a screenshot of your plot (NOT THE CODE) and post it in the discussion forum under the "Gamma- Challenge!" thread.
Note: be careful when you write your expression for γmax(x) in MATLAB. Remember that element-wise division needs the period, so if you need to define a vector y = 1/x where you want to obtain each element of y as the inverse of the corresponding element of x, you need to define y as: y = 1./x
1
None
UnansweredUnsubmitted
HW6_2: SOLID COMPOSITE SHAFT SUBJECTED TO DISTRIBUTED TORQUE
A composite shaft of length L is constructed from an inner core of radius R and modulus Gc=5G0, and a sleeve of outer radius 2√R and modulus Gs=G0, bonded together. One end of the shaft, B, is fixed and the other, A, is free to rotate as shown in the figure. A uniform distributed torque, tx(x)=t0 (t0 = constant with units of N⋅m/m), is applied to the shaft in the direction shown in the figure.
Obtain symbolic expressions in terms of R0, G0, L, t0, x for the following quantities.
(NOTE: you will have factors of π in your answers: enter π as "pi".)
HW6_2A : 10.0 POINTS
The axial torque resultant:
T(x)=
unanswered
HW6_2B : 10.0 POINTS
The rotation field φ(x) along the shaft:
φ(x)=
unanswered
HW6_2C : 10.0 POINTS
The angle of twist:
ΦAB=
unanswered
HW6_2D : 10.0 POINTS
The maximum magnitude of shear stress, τmax, in the shaft:
τmax=
unanswered
HW6_3: STATICALLY INDETERMINATE SHAFT UNDER DISTRIBUTED LOADING
The round shaft in the figure has length L and is fixed at both ends. The shaft is loaded by a constant distributed torque t0. The modulus of the material, G, and the polar moment of inertia of the cross section, Ip, are known.
HW6_3 : 40.0 POINTS
If we want to limit the rotation of the midsection of the shaft to a maximum value, φ(L2)=φm, what is the maximum value of the distributed load, t0,m, that can be applied to the shaft?
Provide your answer as a symbolic expression in terms of L, G, Ip, φm (write as "I_p" and "phi_m"):
t0,m=
unanswered
HW6_1A : 20.0 POINTS
Obtain a symbolic expression for the torsional stiffness of the shaft KT=Q/Φ, in terms of t, L, G, dA (you will have factors of π in your answers: enter π as "pi" ):
KT=
unanswered
HW6_1B : 20.0 POINTS
Obtain a symbolic expression for the maximum shear strain on the generic x-section along the shaft, γmax(x), in terms of t, L, G, Q, x, dA (you will have factors of π in your answers: enter π as "pi" ):
γmax(x)=
unanswered
HW6_1CX : 0.0 POINTS
CHALLENGE QUESTION! (no points, just for fun!)
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.
For L=0.5 m, t=2 mm, dA=4 cm, and G=70 GPa, obtain the torque Q0 that you need to apply to the shaft if you want to obtain a maximum value of 2% strain.
Then, use these values to plot γmax(x) by writing MATLAB code in the blank command window below. If you succeed, take a screenshot of your plot (NOT THE CODE) and post it in the discussion forum under the "Gamma- Challenge!" thread.
Note: be careful when you write your expression for γmax(x) in MATLAB. Remember that element-wise division needs the period, so if you need to define a vector y = 1/x where you want to obtain each element of y as the inverse of the corresponding element of x, you need to define y as: y = 1./x
1
None
UnansweredUnsubmitted
HW6_2: SOLID COMPOSITE SHAFT SUBJECTED TO DISTRIBUTED TORQUE
A composite shaft of length L is constructed from an inner core of radius R and modulus Gc=5G0, and a sleeve of outer radius 2√R and modulus Gs=G0, bonded together. One end of the shaft, B, is fixed and the other, A, is free to rotate as shown in the figure. A uniform distributed torque, tx(x)=t0 (t0 = constant with units of N⋅m/m), is applied to the shaft in the direction shown in the figure.
Obtain symbolic expressions in terms of R0, G0, L, t0, x for the following quantities.
(NOTE: you will have factors of π in your answers: enter π as "pi".)
HW6_2A : 10.0 POINTS
The axial torque resultant:
T(x)=
unanswered
HW6_2B : 10.0 POINTS
The rotation field φ(x) along the shaft:
φ(x)=
unanswered
HW6_2C : 10.0 POINTS
The angle of twist:
ΦAB=
unanswered
HW6_2D : 10.0 POINTS
The maximum magnitude of shear stress, τmax, in the shaft:
τmax=
unanswered
HW6_3: STATICALLY INDETERMINATE SHAFT UNDER DISTRIBUTED LOADING
The round shaft in the figure has length L and is fixed at both ends. The shaft is loaded by a constant distributed torque t0. The modulus of the material, G, and the polar moment of inertia of the cross section, Ip, are known.
HW6_3 : 40.0 POINTS
If we want to limit the rotation of the midsection of the shaft to a maximum value, φ(L2)=φm, what is the maximum value of the distributed load, t0,m, that can be applied to the shaft?
Provide your answer as a symbolic expression in terms of L, G, Ip, φm (write as "I_p" and "phi_m"):
t0,m=
unanswered
Answers
Answered by
simonsay
HW6_1A
2*d_A^3*pi*t*G/(3*L )
2*d_A^3*pi*t*G/(3*L )
Answered by
MAN
6.1B, 6.1C, 6_2a to 6_2d, 6_3
Answered by
Phy
anyone got the 2nd answer???
Answered by
simonsay
6_2A= -t_0*x
6_2B= -t_0*(x^2-L^2)/(8*pi*G_0*R^4)
6_2C= -L^2*t_0/(8*pi*G_0*R^4)
6_2D= 5*t_0*L/(4*pi*R^3)
6_2B= -t_0*(x^2-L^2)/(8*pi*G_0*R^4)
6_2C= -L^2*t_0/(8*pi*G_0*R^4)
6_2D= 5*t_0*L/(4*pi*R^3)
Answered by
simonsay
6_3 8*phi_m*G*I_p/(L^2)
Answered by
nonomono
anyone has 6_1B solution?
Answered by
MAN
6-1B, 6-2C?
Answered by
simonsay
6_1B
(2*Q*L^2)/(G*pi*t*d_A^2*(L+x)^2)
(2*Q*L^2)/(G*pi*t*d_A^2*(L+x)^2)
Answered by
MAN
6-2C
Answered by
simonsay
6_2C= -L^2*t_0/(8*pi*G_0*R^4)
Answered by
MAN
6-1C
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.