Dealing with Stress in Homework: Understanding Normal and Shear Stress

[Suitengu]

Homework Statement

Took a picture from the book and attatched it.

Homework Equations

The Attempt at a Solution

Dont I only need either the U normal stress or the U shear stress? Not even sure where to start. Thats just my problem.

 

[PhanthomJay]

Start by taking moments about C and summing forces to determime the reactions at the pins. Then you've got to check the shear stresses at the pins, and the normal stress in the link, to see which governs when determining the max load. Note that one of the pins is in double shear.

 

[Suitengu]

I knew the statics behind it to get the stress. I was just wondering how to apply it further in finding those stresses in the link. Though you did point out to me that I need to check the pins as well.

 

[PhanthomJay]

The max stress in the link is the force in the link divided by the net area of its cross section (you must subtract the bolt hole width from the total width).

 

[Suitengu]

btw, what would di cross section be? the 8x36mm area or the 36x0.2*10^3 mm area?

 

[PhanthomJay]

I don't follow where you're numbers are coming from. Are you talking the net cross section of the link at the pin hole? The cross section for tension applications is the area perpendicular to the load.

 

[Suitengu]

yea my mistake mon. i was quoting a different question i was doing simultaneously. However I will make an attempt now with the given information and let you know what i did.

 

[Suitengu]

I tried doing it like this but it seems I am still not following the correct steps to get the solution as mine does not add up.

Factor of Safety = Ultimate stress / Allowable stress

A.S. = 400/3
= 133.3 MPa

Stress = Force/Cross-sectional Area
133.3 = F/(6(18-10))

I subtracted the bolt's diameter from width of BD.

F = 6398.4 N

Sum of the moments about C (anticlockwise +ve) = P(120+160) - 6398.4(120) = 0
P = 2.742kN (which is so wrong)

 

[PhanthomJay]

I tried doing it like this but it seems I am still not following the correct steps to get the solution as mine does not add up.

Factor of Safety = Ultimate stress / Allowable stress

A.S. = 400/3
= 133.3 MPa

Stress = Force/Cross-sectional Area
133.3 = F/(6(18-10))

I subtracted the bolt's diameter from width of BD.

F = 6398.4 N

Sum of the moments about C (anticlockwise +ve) = P(120+160) - 6398.4(120) = 0
P = 2.742kN (which is so wrong)

A couple of points here. First, you didn't check the shear stress in the pins. That might limit the load to less than what you calculated based on the allowable tensile stress in the link. For example, if the link can withstand 6398N, the shear stress in the 10mm diameter pin is F/A = 6398/(pi)(.0005)^2 = 81.5MPa which exceeds the allowable 50MPa shear stress in the pins. You've got to check that 6mm dia pin also (the one in double shear) to see if that may govern.

Secondly, I don't know if you are using a steel code for the net area calculation in the ternsion member. A 10mm pin has a slightly higher hole size, such that this fact combined with a code adder my be reduce the effective width of the 18mm link down to say 5 or 6mm instead of the 8mm you used. It might make a difference as to what governs, but if the problem does not state a hole size and does not reference a Code, then I guess its OK to assume just a 10mm hole for a 10mm pin, which may not be realistic.

 

[Suitengu]

Hmmm...I am at a lost then mon on what to try out. As this is my first week in the class I am not very certain about the steps to follow and so on and so forth. Also that last part you said came as a shock to me as its the first I am hearing of this.

Like how do you test for pins in double shear? Sorry for asking these questions but I am also without a textbook and I am just going off of what little I got in notes. I plan to get one this week however so this won't happen again. But in your shoes, walk me through the first step you would do? Also I subtracted that 10mm bolt hole diameter from the link's cross-sectional area. How is that justified as I don't see it affecting the area in any way and if so why didnt we subtract two bolt holes although that would be more than possible to do?

Oh you also made a mistake, for you to get MPa you should have left the 5mm as it is. You converted it to meters and N per meter squared is not MPa

 

[PhanthomJay]

Hmmm...I am at a lost then mon on what to try out. As this is my first week in the class I am not very certain about the steps to follow and so on and so forth. Also that last part you said came as a shock to me as its the first I am hearing of this.

Well just forget it and your calc for net area is correct.

Like how do you test for pins in double shear? Sorry for asking these questions but I am also without a textbook and I am just going off of what little I got in notes. I plan to get one this week however so this won't happen again. But in your shoes, walk me through the first step you would do?

If you look at your sketch, can you visualize that the 10mm pins are in single shear because there is only one shear plane across the pin, whereas at the 6 mm pin, there are 2 shear planes? This means that when analyzing a bolt or pin for double shear, you can double the area of the bolt when calculating the average shear stress in that bolt.

Also I subtracted that 10mm bolt hole diameter from the link's cross-sectional area. How is that justified as I don't see it affecting the area in any way

I don't know what you mean. Without the hole, the area of the link is 18*6 = 108mm^2. With the hole, the net area is (18-10)*6 = 48mm^2

and if so why didnt we subtract two bolt holes although that would be more than possible to do?

If you and I were to pull on a bar at each end, with you pulling on one end and me pulling on the other end, with each of us pulling with a force of 100N, the bar sees 100N of force, and the tensile stress is uniform throughout. Similarly, the end of each link with the hole sees the same force, and the reduction in area at the hole is just for the one hole, not two holes. If there were 2 bolt holes side by side at one end, then you'd have to subtract them both from the width to get the net width, but this is not the case.

Oh you also made a mistake, for you to get MPa you should have left the 5mm as it is. You converted it to meters and N per meter squared is not MPa

Well now being from the States I'm not into this metric and Pascal stuff, and I slipped a decimal point as a typo when converting 5mm to meters, but the result is correct

 

[Suitengu]

I am not from the states either mon. Jamaica is where I hail from so I see what your saying. And now I finally understand the concept on why they subtract the bolt hole.

Okay so since we are sure that F cannot be 6398 N, how does one go back and calculate a different force there. I'm still not sure where to go from here. Oh and to check the 6mm diamter bolt, I would:

Allowable shear stress = Force/(2*A)

Force = (50*2(1/4)(6)^2*pi)
= 2,827N

But how does that help me and where would I go from there?

I think you may need to just walk me through this problem from start to finish as I am more confused than ever although I now understand why the bolt was subtracted in finding the net area. Sorry for the stress mon. No pun intended.

 

[PhanthomJay]

I am not from the states either mon. Jamaica is where I hail from so I see what your saying. And now I finally understand the concept on why they subtract the bolt hole.

Your use of the word 'mon' should have been an easy giveaway of your Jamaican roots, but I tend to be naive in these matters, and thought it was a misspelling.

Okay so since we are sure that F cannot be 6398 N, how does one go back and calculate a different force there. I'm still not sure where to go from here. Oh and to check the 6mm diamter bolt, I would:

Allowable shear stress = Force/(2*A)

Force = (50*2(1/4)(6)^2*pi)
= 2,827N

This is good. Now proceed as you did in the beginning when you did the tensile link force calc and backtracked in the statics by taking moments to solve for what the applied P force would be if link tension controlled. If you have a 2827N force at C, what is P? If its less than the value you arrived at for the link tension case, then the pin force at at C controls over it. BUT, you still need to look at the case where the 10mm pin shear stresses may govern the value of P. The lowest P wins.

I think you may need to just walk me through this problem from start to finish as I am more confused than ever although I now understand why the bolt was subtracted in finding the net area. Sorry for the stress mon. No pun intended.

No stress, man.

 

[Suitengu]

lol. Alright I did it also for the shear stress in the 10mm diameter pins and then use it also to find P and found that it produced the lowest value for P so yes it does win. I got it to be 1,683 kN. Thank you for your help mon. I got it in the nick of time as well as I almost gave up.

P's were; 2,742N, 2,120N and 1683N

Btw, why wouldn't the P obtained for checking the pin at C be used when its the biggest P and I guess it wouldn't break at that value?

 

[PhanthomJay]

lol. Alright I did it also for the shear stress in the 10mm diameter pins and then use it also to find P and found that it produced the lowest value for P so yes it does win. I got it to be 1,683 kN. Thank you for your help mon. I got it in the nick of time as well as I almost gave up.

P's were; 4,487 N, 2827N and 1683N

Thank you again

You are welcome, nice work.

 

[Suitengu]

Didnt even notice that you were posting while I was editing.

Btw, why wouldn't the P obtained for checking the pin at C be used when its the biggest P?

 

[PhanthomJay]

Didnt even notice that you were posting while I was editing.

Btw, why wouldn't the P obtained for checking the pin at C be used when its the biggest P?

I didn't notice you were editing while I was posting.
I checked all your numbers, and you have now correctly identified the 'P' loadings. P would be 2742N if you were just looking at the link max allowable tensile stress and paying no heed to the pins; P would be 2120N if you were just looking at the pin at C max allowable stress, paying no heed to the other pin or the link; and P would be 1683N if you were just looking at the 10mm pins and paying no attention to the 6mm pin or the link. But now you must compare all three values and pick the lowest. If you choose P as 2742N, the link holds up fine, but the pins get overstressed; if you choose 2120N for the P load, then the pin at C and the link are fine, but the 10 mm pins are overstressed. If you choose P as 1683N, then all pins and the link are within their allowable stresses. That's why you pick the lowest P as your answer. OK?