Determine a suitable cross sectional area for strength

[dbag123]

Homework Statement

Determine a suitable cross section of a handle using von mises stress

Relevant Equations

equation in picture form bottom of page

Lenght=300mm, Force at the end of the handlebar is 200N

What i would like to know is: does that 20x20mm end piece affect the calculation process in any way? and whether there are more than 3 types of stresses in this case. First stress being moment created by the 200N and second stress is shear and 3rd the stress caused by torsion.
Homework equation:

 

[PhanthomJay]

Yes those are the 3 stress types acting (bending, Shear, and torsion), but you need to determine where in the handle lever is the critical cross section or sections for max von Mises stress. I am not sure if they are asking for a numerical answer.

 

[dbag123]

Yes a numerical answer is required, but the critical cross section is given by the problem and it is that small red arrow in picture 2 right after the bend

 

[PhanthomJay]

Oh, OK, but what is the handle thickness? What sort of handle is this? Is the 200 N load applied vertically down? Have you identified any torsion at this section?

 

[dbag123]

handle thickness is upto the designer, i am supposed to pick a crossection(rectangle) then calculate the stresses using that information.

200N load is vertical.

My thinking is that the lever does experience torsion at the cross section where i am supposed to examine it.

Torsion is calculated by dividing the moment with section modulus, section modulus for torsion is calculated S=Chb^2 where c is the ratio of h/b from handbook h is height and b is base.

My problem is figuring out if that 45 deg bend adds to the strain or not? Does it even matter? the handle bar is 90mm long so when calculating torsion do i calculate the acting moment with 90mm or 110mm?

 

[PhanthomJay]

handle thickness is upto the designer, i am supposed to pick a crossection(rectangle) then calculate the stresses using that information.

200N load is vertical.

My thinking is that the lever does experience torsion at the cross section where i am supposed to examine it.

Torsion is calculated by dividing the moment with section modulus, section modulus for torsion is calculated S=Chb^2 where c is the ratio of h/b from handbook h is height and b is base.

My problem is figuring out if that 45 deg bend adds to the strain or not? Does it even matter? the handle bar is 90mm long so when calculating torsion do i calculate the acting moment with 90mm or 110mm?

Yes there is torsion at the critical section and if you draw a free body diagram using a cut just to the left of the critical section and examine the right part of the cut handle, it should become evident that the lever moment arm for torsion is 110 mm. The 45 degree angle affects loading in that angled piece because there are torsional and bending components of the moments at that section. Otherwise it doesn’t really change the stresses to the left of the critical section. Incidentally, for torsion shear stresses of the flat bar, the constant ‘c’ comes from the h/b ratio from tables, it is not the h/b ratio itself, you probably understand that but said it wrong ( c is in the 0.2 to 0.3 range depending on that ratio).

 

[dbag123]

Thank you very much. I think i have everything i need to make to complete this assignment.