Design for both bending and torsion

[elogesh]

Hai,

I have doubt regarding the optimal design of members for both bending and torsion.

For bending the outer fibres has high stresses as it goes away from netural layer.

For torsion, the central layer has high stresses compared to the outer layers.

How to optimize cross-section based on both bending and torsion,like thumb rules?
It doesn't mean that ,I don't know how to calculate the combined stresses?
I know,How to calculate the combined stresses and comparing with failure criteria(Von-mises for ductile and principal for brittle) for assure for reliabilty.
I heard that open section are good for bending and closed sections are good for torsion? It is true.

Thanks.

With Regards,
LOgesh.E

 

[prex]

Closed sections are also good for bending.
For torsion you prefer a round (or square) section, for bending, if as usual, there's a preferred direction of bending, you will choose a section with increased dimension in that direction.
The proportion between the two criteria depends on the relative proportion of bending load to torsion load.

prex

http://www.xcalcs.com

Online tools for structural design

 

[elogesh]

Hai prex,

Thanks for your replies,Prex. It is very useful.

for bending, if as usual, there's a preferred direction of bending, you will choose a section with increased dimension in that direction.
I understood that "The dimension of the cross-section icreased parallel to the load dirction will increase the I (moment of inertia) by cubic times and thereby the strength also.

I have one more doubt also.

If I see torsion stress diagram,the outside extreme has low stresses and netural layer has maximum stress.The bending case is obvious opposite to torsion,that is neutral layer stress is zero and outer layers stress is maximum.

But in piston-pins,they make it hollow saying that the centre portion doesn't undergo torsion,that is only in the solid piston-pin central portion is removed.But in torsional stress diagram centre has high stress. Can any one explain this?

I thought hollow piston-pin is made for some other reasons,probably for oil supply from connecting rod-piston-pin to piston for better lubrication.

Please correct me,if there is anything technically wrong.

Thanks for reading this e-mail.

With Regard,
Logesh.E

 

[prex]

You are incorrect in stating that under torsion the stress is maximum at center: it is on the contrary maximum at the points farthest from the torsional center (the geometrical center for a circular section).
Normally a hollow thin section will be used for maximum efficiency (lowest weight) in torsion: in the thickness of a hollow section the torsional stress will be substantially constant, so you don't have to worry as to where it is maximum.
Also be careful: if it is true that the inertia in bending increases with the third power of section height, this doesn't hold for the strength, that increases with the square of the height.
You should deepen your knowledge of beam section stresses if you really want to understand what you are looking for (that, by the way, is not fully clear to me)

prex

http://www.xcalcs.com

Online tools for structural design

 

[ivymike]

But in piston-pins,they make it hollow saying that the centre portion doesn't undergo torsion,that is only in the solid piston-pin central portion is removed.But in torsional stress diagram centre has high stress. Can any one explain this?

I'm not familiar with any piston pin designs that transmit substantial torque- generally the goal of the piston pin bearings is to prevent the transmission of torque through the piston pin.

The material is removed from the center of the pin to reduce weight (reciprocating mass).

The reasons you take material from the center, rather than the OD of the pin, are twofold -
1) your piston pin bearings require a certain projected area to properly carry the loads. Projected area for each bearing is (pin diameter) x (bearing length). Both dimensions have upper limits set by the physical constraints of the assembly (pin must fit within cylinder bore with clearance, etc). You don't want to reduce the diameter of the pin if you don't have to.
2) the center portion of the pin is less critical than the outside for both bending and torsion. Calculate the polar moments of area for the hollow pin, versus a solid pin with the same cross-sectional area (same weight) and compare... J is much greater for the hollow section than for the circular section.

example:
PMOI for solid circle section: pi*(D^4)/32
PMOI for hollow circle section: pi*(D^4 - d^4)/32

Hollow ---------
D = 32mm
d = 15mm
PMOI = 97974 mm^4
A = 627.5 mm^2

Solid ----------
A = 627.5 mm^2 (for same area, mass as above)
D = 28.27 mm
PMOI = 62705 mm^4

 

[ivymike]

I thought hollow piston-pin is made for some other reasons,probably for oil supply from connecting rod-piston-pin to piston for better lubrication

Just re-iterating, in case I wasn't clear above:
The material is removed from the center of the pin to reduce weight (reciprocating mass).

 

[Celebur]

As was stated by prex, torsional shear is greatest at the outer fibres. And as was stated by ivymike, piston pins are intended to rotate freely (so they don't transmit torque).

This makes me wonder if you're thinking of direct shear? There would be a direct shear in the pin at the transition between the piston and the connecting rod. It can usually be assumed to be tau=V*A. So removing material from the center does weaken shear strength of the pin, but the mass reduction is worth it if properly designed.

 

[elogesh]

Hai,

Thanks to prex,ivymike and celebur.

Sorry for the mis-conceptions.

Prex:- Thanks for correcting me.I will try to describe,the problems clearly in coming therads.

I should have seen the equations before coming to the thread.

Bending M/I=E/R=f/Y


Therfore stress,f=M*Y/I=M/Z (where Z=section modulus)

Torsion T/J=G*theta/L=f/R

Ivymike:- From your replies,I understood that hollow piston pin is primarily for reduced reciprocating mass. I hope this lower power consumption and better partial balancing of reciprocating masses.I also understood that having higher outer diameter helps to carry the load properly.Thanks to ivymike.

Regards,
elogesh