Machine Elements: are both of these constructions basically the same?

In summary, the conversation revolved around two constructions that were believed to have different free-body diagrams, but it was later discovered that they were actually identical. The speaker had initially questioned if the two constructions had the same stresses and bolt requirements, and the expert confirmed that they should be the same as long as the free-body diagrams are identical. The expert also suggested that the teacher may have been confused about the positions of T1 and T2 in the diagrams. Eventually, it was confirmed that the two constructions were indeed the same and the solution to both problems were identical.
  • #1
manareus
20
4
Homework Statement
1. Draw free-body diagram of the construction.
2. Find the diameter of bolt required for the load stated.
3. Identify stresses that occur at the weld.
Relevant Equations
Stress equation and combined stress equation.
1683382862315.png

1683382817494.png


The construction just basically a bracket that is being held in place by welds and bolts and there is a force acting on it.
The textbook answered the first construction and the free-body diagram is shown like this below:

1683383213678.png


I apologize for the picture not being in English, here's the translations that can help: geser = shear, las = weld, baut = bolt, t subscript = tensile. So I tried to draw the free-body diagram for the second construction and found no difference. (I don't know a good software to draw free-body diagrams for images so I just used Paint).

1683383466728.png


Now if the free-body diagram is the same, to my knowledge the stresses acting on both of the constructions are also the same. But here's my calculation anyway for question number two: (##x## is for core bolt diameter)

$$τ_{shear} = \frac {20000} {4\frac {\pi} {4} x^2}$$
$$c_{bolt} = \frac {(20000)(350)} {(2)(500^2 + 100^2)} = 13,4615$$
$$Ft_2 = (13,4615)(500) = 6730,769$$
$$σ_{tensile} = \frac {6730,769} {\frac {\pi} {4} x^2}$$
So using combined stress equation, we can get the value of x:
$$8400 = \frac {6730,769} {2\frac {\pi} {4} x^2} + \frac 1 2 \sqrt {(\frac {6730,769} {\frac {\pi} {4} x^2})^2 + 4(\frac {20000} {4\frac {\pi} {4} x^2})^2}$$

The value of x is ##1,1932##. Now this is exactly the same as for the value for the first construction which is provided by the textbook. Appreciate if you can help me with this!
 
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  • #2
Sorry, what specific help do you need?
 
  • #3
Lnewqban said:
Sorry, what specific help do you need?
Sorry, I thought my title is sufficient, I want to know mainly if these two constructions have the same free-body diagram is correct or not. From the first construction, the textbook provided the free-body diagram as shown above.
I tried to draw the free-body diagram from the second construction and the result are same. So I thought I might be wrong because my teacher insist that the second construction is different than the first, albeit only rotated 90 degrees clockwise. So I wonder where my mistake is by drawing the free-body diagram for the second construction?
The calculations I provided just to show that the the diameter of bolt required for the second construction is the same as the first.
 
  • #4
manareus said:
Sorry, I thought my title is sufficient, I want to know mainly if these two constructions have the same free-body diagram is correct or not.
Apologies, I am old and slow.
manareus said:
So I thought I might be wrong because my teacher insist that the second construction is different than the first, albeit only rotated 90 degrees clockwise.
Dimensionally both assemblies seem to be identical.
Unless weigh of it is to be considered (mass not provided), the free body diagrams should be identical as well.
I don't understand the reason behind your teacher's statement.
 
Last edited:
  • #5
Lnewqban said:
Apologies, I am old and slow.
Ah it's okay :D

Lnewqban said:
Dimensionally both assemblies seem to be identical.
Unless weigh of it is to be considered (mass not provided), the free body diagrams should be identical as well.
I don't understand the reason behind your teacher's statement.
So my suspicion appears to be true, so if the free body diagrams of both constructions are same, then the diameter of the bolt required and the stresses acting on the weld should be the same right?
 
  • #6
manareus said:
Ah it's okay :DSo my suspicion appears to be true, so if the free body diagrams of both constructions are same, then the diameter of the bolt required and the stresses acting on the weld should be the same right?
I believe so.
May your teacher's reasoning be that you have switched positions for T1 and T2?
Also, each of the four bolts is resisting shearing and tension simultaneously.
 
  • #7
Lnewqban said:
May your teacher's reasoning be that you have switched positions for T1 and T2?
It's just a symbol and doesn't affect the answer for the t1 and t2 so I don't believe that it's the case.
Lnewqban said:
Also, each of the four bolts is resisting shearing and tension simultaneously.
Yes, and I take the biggest shear and tension force acting on one of the bolts and find the core diameter of the bolt required from there.

Later I will get an answer from my teacher about this problem and after that I can give an update where the differences are according to my teacher. Thank you very much for your help haha gives me some comfort to my mind about this problem.
 
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  • #8
manareus said:
Later I will get an answer from my teacher about this problem and after that I can give an update where the differences are according to my teacher.
So just to provide a quick update, it turns out it's the same construction after all and the solution to both problem are identically are same too he explained. I don't know why he said earlier it's different, it just makes me and other students confused lol.
 
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  • #9
manareus said:
I don't know why he said earlier it's different, it just makes me and other students confused lol.
In some circles his earlier response would be considered "A brain fart." :oops:
 
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