- #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.
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:
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).
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!
