Elastic Bending Angle Calculation

[parthanml]

Hi Guys, as i understand the basic rule of math to calculate angle subtended by an arc is to divide the arc length by radius. This rule is extensively used in calculating Hot and cold bending angles for a given arc length. I was given a similar calculation for elastic bend angles by one of my colleague. However in this case of calculating elastic bending angle, he has divided the arc length by two times the radius instead of simple calculation of arc length by radius. I am puzzled by this calculation as why he used two times radius instead of one. is there anything i am missing in this ?

 

[robyengIT]

PS : it depends which angle you consider (phi or phi/2)

 

[parthanml]

Thanks for the response.
However, i am still struggling to understand the division by 2R here

 

[robyengIT]

the formula is clear enough :

 

[parthanml]

If i put the my values in the highlighted formulae above

b = 30m
r = R

ψ = 30/R (radians), why r is taken as 2R instead of R

 

[robyengIT]

calculation check :
1 - R=163 m that is circumference C = 2 x 3.14 x 163 = 1024.16 m
2 - 30 m is 1024.16/30 = 34.139 times (34.139 x 30 = 1024.16)
3 - 360° / 34.139 = 10.545 °

Conclusion : division by 2 is wrong !
PS : you can check with CAD

 

[parthanml]

Thanks Roby, this is what i am also thinking.
Only doubt remaining is if i am ignorant to any additional consideration in elastic bending.

 

[3DDave]

Aren't there spring-back formulas? That's the only part that makes sense if elastic bending is considered.

 

[robyengIT]

3DDave : I don't think this is the case (30 m bend, 163 m radius ??)

 

[3DDave]

If the bend is elastic then the part straightens completely when the load is removed. Formulas that deal with spring back for small bends show the bend result is half the angle/twice the radius of the applied bend radius.

 

[parthanml]

I think 3DDave has a point there. However in this particular case, does that mean irrespective of the bend angle that you select (whether it is by R or 2R) there will be further spring back ?. Or does this mean if you have already selected 2R and selected angle accordingly, there is no further spring back?

 

[3DDave]

I think you should ask the person who supplied the formula what it was intended to do.

 

[saplanti]

When the pipe bends elastically it creates a longitudinal stress. Pipe will face this additional stress in addition to the operational stresses. There might be a limitation for this reason. The best is to talk to the person who limited the radius.