MERM 13, Problem 51.10

[JHW 3d]

This is a combined stress problem, with a compressive stress and a shear stress as given. It asks for the stresses in an inclined plane. Problem is the inclined plane is at an angle where the compressive stress is not in plane.

The solution blindly combines the compressive stress and shear stress AS IF they were in plane. Am I crazy, or is this problem just poorly formulated and solved?

To do it right, I believe you'd have to calculate the triaxial stresses which is way more complicated, and not even covered in the MERM. Or, am I missing something?

 

[P-E]

Likely crazy. Can you put it up here. Might be able to help, just not tonight.

 

[loudog]

For others info, JHW is talking about the MERM Practice Problems 51.10, not example 51.10 in the MERM.

I don't see any issue with the solution. You're just applying Equations 51.17 and 51.18 with theta = 60 degrees.

It's still planar stress, just rotated by theta.

 

[denver1000 PE]

I also think the solution is ok - tool me a while to find it in the 12 ed.

 

[denver1000 PE]

JHW3 and loudog - I stand corrected - taking a look at the drawing again and yes it is actually triaxial loading shown in the sketch - I breezed through it when I did it and assumed it was biaxial loading shown as triaxial loading isn't covered. The compressive force should have been shown on the cross section view if it were to be treated as biaxial loading.

 

[denver1000 PE]

Good spot JHW3 btw.

 

[loudog]

I'm still not seeing the issue. Maybe this is like the blue dress / white dress thing, and we're interpreting the 3D drawing differently

Here is the problem in my version of the book, 13 (attached).

LP

 

[denver1000 PE]

The shear stress is in the x-y plane and the compressive acts in the z plane.

 

[loudog]

Ahhhhhhhhhhhhhhhh, thanks for bearing with me. I see now.

Yeah, I just powered right through that Bad Larry assuming the compressive force was acting on the long side of the sample (by mistake). Whoops.

 

[denver1000 PE]

Yes I made the same mistake. Thank you JHW3

 

[denver1000 PE]

Update to this, the same solution results if you calculated thr triaxial stress - I did it very quickly so open to correction!

 

[wopkins]

Diagram shows 18000 lbf compressive in the z-direction, but the solution treats it as stress in the x-direction.

So you guys are saying that the problem statement is unclear, or that JHW3 was missing something in his original question?