oriol
Well-Known Member
Hi!
I had a small bicycle crash that has grounded me for at least a week. The good thing about it, is that I can focus on learning more about structures for a week!
I think that it would be good, to have a dedicated thread to Timoshenko, or other structures theory books. So that anyone can ask their doubts, about how to use the formulas, or how to analize problems. To be able to self study with some necessary guidance.
I am trying to solve Example 8.4 of the spanish edition.
The Exercise is intended to learn how to analize combined loads over a structure. The problem is about a heli solid shaft, of 50mm diameter, producing a torque T of 2.4Kn, and generating Lift equal to 125Kn. One has to find Sigma (W/area)? Maximum traction and compression (Mohr's circles formulas)? And maximum shear using torque formula (Tau = (T*r/Ip))?
It seems all very straightforward, at first glance.
Sigma = 125Kn/TT*0,025^2 = 63,66 Mpa
Tau = 2,4Kn*0,025*2/(TT*0,025^4) = - 97,78 Mpa
In the book tau is negative as in the diagram of the example. However I can not tell why the direction of shear stress over the element is negative and not positive?
It is action against reaction so perhaps you can pick any direction? It is like in thermodynamics, in were one asumes that the shaft is consuming power? How can you pick apositive or negative value form the torque?
Regarding shear stress. Sometimes it is confusing to dissociate shear loads from axial loads, given that a beam under pure axial load is under shear loads that result from compression or traction. When the elements of the beam are tilted and part of the horizontal or vertical load becomes shear. It is to assume that the sign of shear is taken from torque not from lift?
For finding maximum compression and traction one has to use the formula for the "Main tensions";
sigma1,2 = (sigmax+sigmay)/2+-((sigmax^2+sigmay^2)/2-tau max)^(1/2)
sigmax is zero, and thus the formula becomes simplified using the results calculated before;
sigma1,2 = 63,66*10^6/2+-((-63,66*10^6/2)^2-97,78*10^6)^(1/2)
As such;
sigma1,2 =31,83*10^6+-(1.01315*10^15-2,97.78*10^6)^(1/2)
The first term inside the square is much bigger than the second one. Which makes little difference in picking the positive or negative result of the square.
Inside the square I get (1.01315*10^15)^(1/2) = 3,183*10^7 which is almost like the first term in the equation.
Nothing makes sense, if I compare my result with the one in the book!?
According to the book, the result is;
sigma1,2 =32Mpa+-103Mpa
Any suggestion or advice would be greatly appreciated.
Thanks for taking the time to review my numbers!
Oriol
I had a small bicycle crash that has grounded me for at least a week. The good thing about it, is that I can focus on learning more about structures for a week!
I think that it would be good, to have a dedicated thread to Timoshenko, or other structures theory books. So that anyone can ask their doubts, about how to use the formulas, or how to analize problems. To be able to self study with some necessary guidance.
I am trying to solve Example 8.4 of the spanish edition.
The Exercise is intended to learn how to analize combined loads over a structure. The problem is about a heli solid shaft, of 50mm diameter, producing a torque T of 2.4Kn, and generating Lift equal to 125Kn. One has to find Sigma (W/area)? Maximum traction and compression (Mohr's circles formulas)? And maximum shear using torque formula (Tau = (T*r/Ip))?
It seems all very straightforward, at first glance.
Sigma = 125Kn/TT*0,025^2 = 63,66 Mpa
Tau = 2,4Kn*0,025*2/(TT*0,025^4) = - 97,78 Mpa
In the book tau is negative as in the diagram of the example. However I can not tell why the direction of shear stress over the element is negative and not positive?
It is action against reaction so perhaps you can pick any direction? It is like in thermodynamics, in were one asumes that the shaft is consuming power? How can you pick apositive or negative value form the torque?
Regarding shear stress. Sometimes it is confusing to dissociate shear loads from axial loads, given that a beam under pure axial load is under shear loads that result from compression or traction. When the elements of the beam are tilted and part of the horizontal or vertical load becomes shear. It is to assume that the sign of shear is taken from torque not from lift?
For finding maximum compression and traction one has to use the formula for the "Main tensions";
sigma1,2 = (sigmax+sigmay)/2+-((sigmax^2+sigmay^2)/2-tau max)^(1/2)
sigmax is zero, and thus the formula becomes simplified using the results calculated before;
sigma1,2 = 63,66*10^6/2+-((-63,66*10^6/2)^2-97,78*10^6)^(1/2)
As such;
sigma1,2 =31,83*10^6+-(1.01315*10^15-2,97.78*10^6)^(1/2)
The first term inside the square is much bigger than the second one. Which makes little difference in picking the positive or negative result of the square.
Inside the square I get (1.01315*10^15)^(1/2) = 3,183*10^7 which is almost like the first term in the equation.
Nothing makes sense, if I compare my result with the one in the book!?
According to the book, the result is;
sigma1,2 =32Mpa+-103Mpa
Any suggestion or advice would be greatly appreciated.
Thanks for taking the time to review my numbers!
Oriol
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