Mechanical Engineering - Strength of Materials - Discussion
Discussion Forum : Strength of Materials - Section 5 (Q.No. 8)
8.
A circular shaft fixed at, A has diameter D for half of its length and diameter D/2 over the other half, as shown in the below figure. If the rotation of B relative to A is 0.1 radian, the rotation of C relative to B will be
Discussion:
10 comments Page 1 of 1.
Amit Palve said:
5 years ago
As shown in figure 2 shafts are in series.
So their torques are equal, by equating torques of shafts AB and BC,
TAB= TBC.
Since, T/J= Gθ/L.
θ1 J1 = θ2 J2 .( Since G, T and L are same for both shafts).
θ1/θ2 = J2/J1 = π(D/2)^4/π(D)^4 = 1/16 and θ1=0.1 radian.
Therefore, θBC = θ2=0.1 * 16 = 1.6 radian.
So their torques are equal, by equating torques of shafts AB and BC,
TAB= TBC.
Since, T/J= Gθ/L.
θ1 J1 = θ2 J2 .( Since G, T and L are same for both shafts).
θ1/θ2 = J2/J1 = π(D/2)^4/π(D)^4 = 1/16 and θ1=0.1 radian.
Therefore, θBC = θ2=0.1 * 16 = 1.6 radian.
(2)
Rohit Koundal said:
7 years ago
@Karthik here is detailed answer
Acc to torsional equations:
The Polar moment is inversely proportional to the twisting angle.
That is
J =1\θ
Now J = π D^4/32
Therefore D^4 =1/θ
θ 1/θ2= D2^4/D1^4.
By putting values you will get the answer.
Acc to torsional equations:
The Polar moment is inversely proportional to the twisting angle.
That is
J =1\θ
Now J = π D^4/32
Therefore D^4 =1/θ
θ 1/θ2= D2^4/D1^4.
By putting values you will get the answer.
(1)
Jayesh said:
7 years ago
Can anyone explain it?
Karthik said:
7 years ago
Anybody explain this in step by step. I don't understand this problem.
B.Rajesh said:
8 years ago
From the Tortion equation we have T/J = G * (&theta)/length.
In the question, they have mentioned T, I and G are constant.
By equating the torques we can get answer as 1.6.
In the question, they have mentioned T, I and G are constant.
By equating the torques we can get answer as 1.6.
Ashwin said:
9 years ago
How could you say that 'Theta' is directly proportional to the polar moment of inertia? The relation between them is inversely proportional. So please give correct explanation.
Senthilkumar said:
9 years ago
I don't understand please explain as 1.6.
Mithlesh said:
9 years ago
It should be like this :
c1/l1 = c2/l2.
t/ip*theta 1-t*ip*theta 2.
On putting values theta 2 comes out to be 1.6.
c1/l1 = c2/l2.
t/ip*theta 1-t*ip*theta 2.
On putting values theta 2 comes out to be 1.6.
Expert's Advice said:
10 years ago
Theta 1*J1 = Theta 2*J2.
Theta 1 = 0.1.
J1 = pi*d^4 /32.
J2 = pi*d^4 /32*16.
=> Theta 2 = 1.6.
Theta 1 = 0.1.
J1 = pi*d^4 /32.
J2 = pi*d^4 /32*16.
=> Theta 2 = 1.6.
Gaurav said:
1 decade ago
Theta is inversely proportional to D^4
But 1.6 is coming out to be relative to A not B.
Answer should be 1.6-0.1 = 1.5
But 1.6 is coming out to be relative to A not B.
Answer should be 1.6-0.1 = 1.5
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