Can shear be ignored in a situation like this

[wahaj]

The situation I am looking at involves a round beam that goes through two rigid round holes (top beam in the image). The holes are meant to fix the beam. The beam length is between 1m and 2m and the diameter is less than 2 cm. If the beam was attached at the end with only one holes fixing it I would ignore the shear stress but in this case I am concerned about the region in between the two supporting holes. Is it ok to ignore shear stress in the beam?
When doing bending calculations would it be a bad approximation if I were to separate the beam as shown in the bottom part of the image?

 

[jh0]

In beams shear usually has to be taken into account when two opposite forces are close. In my opinion this is not the case, at least if the lengths of the beam at both sides are similar. To be sure it is best to make the calculations with the actual forces, dimensions and materials, but I'd say the shear stresses will be small compared to the flexural stress at the section with higher bending moment.
As the bending moment at the supports is the same, it is OK to consider just the separated beams, as we know the forces at the tips and we also know the highest bending moment has to be at either support. But if we had to calculate the deflection of course we should consider the problem as it is: a single beam with two supports and two loads, calculate the forces at the supports and so on.

 

[wahaj]

Thankyou for answering. I was thinking it would be ok to ignore shear but I just wanted someone elses opinion on the matter.
You said that to do deflections I would have to analyze the beam as a whole. But what if I only wanted to find the deflection for the ends of the beam where the forces are applied. Would it still be alright to split the beam into two sections?

 

[jh0]

No, it wouldn't. In order to evaluate the deflection the beam has to be considered as a whole. Think about the angle of the beam at the supports. In the original problem the beam will cross the supports at an angle (albeit small), but if we consider a cantilever beam the angle at the fixed end is supposed to be zero.
You can see http://www.me.berkeley.edu/~lwlin/me128/BeamDeflection.pdf.
You can save yourself all the differential equations and look for formulas for each specific case. This seems a nice resource:
http://www.engineersedge.com/beam_calc_menu.shtml
Your original case is at:
http://www.engineersedge.com/beam_bending/beam_bending4.htm
The cantilevered beam with one load at the end is at:
http://www.engineersedge.com/beam_bending/beam_bending9.htm

 

[wahaj]

Sorry about the late reply I got caught up in something. Thank you for helping me out. The links you gave solved my problem