What are some helpful resources for calculating stress and strain in beams?

[Michaelcarson11]

Homework Statement

I have been asked to make a presentation about a material for my AS coursework. I have chosen to talk about titanium and its use in sport. The only problem is, we have to do some sort of calculation which involves elastic modulus/ hardness/ tensile strength etc. I was thinking of doing a calculation about the force that a titanium grille on a cricket helmet needs to withstand. Has anybody got any better suggestions or can help me with my proposed calculation?

Homework Equations

The Attempt at a Solution

 

[andrevdh]

It is also used in golf clubs.

 

[berkeman]

Compare and contrast the stress/strain behavior of titanium versus (fill in other common metals here like steel, aluminum, etc.)


EDIT -- Oh, and include the density numbers for each in your table. Without the density numbers, the other numbers wouldn't mean much. Quiz question -- why?

 

[PerennialII]

golf clubs might be easier to calculate. Although since you're comparing materials you could simplify the grille to be a beam under bending or something like. You get nice illustrative differences between materials when working with "specific" properties (or relative), modulus/density etc. which you can then interpret with respect to performance in your particular application.

 

[AlephZero]

golf clubs might be easier to calculate. Although since you're comparing materials you could simplify the grille to be a beam under bending or something like.

The structure of a cricket mask is made up of CURVED beams not straight ones. In fact they behave much more more like an arch (of a bridge etc) that "a (straight) beam under bending".

I don't think you will have studied how to do the correct calculations on the of stress, stiffness, etc on the mask. Even if you do know the theory the calcs are very hard to do "by hand". The practical way to do it would be to make a computer model using Finite Element Analysis software, but that is Univ. level stuff not AS level I think.

I would suggest you go for the golf club. That is basically a beam with a mass on the end, and know you how to analyse it correctly. For example you could find the stiffness of a "real" titanium club, then see what thickness of the shaft and what mass it would have, to get the same stiffness with different materials like steel, aluminium, wood, etc.

 

[andrevdh]

Titanium is valuable because of its high strength to density ratio. Which means that objects made out of this material are both lightweight and strong, which makes it easy to carry around. It also has a relatively low modulus of elasticity. I seem to recall that it is used in the head of the club (the strike area?). What materials are used in the shaft is a production secret.

 

[Michaelcarson11]

The golf club idea sounds excellent but can anybody help to do the calculation?

Any help is greatly appreciated

 

[AlephZero]

Another use for titanium in sport ... don't forget about the medical applications for patching up injured sportsmen and -women (plates and screws to repair broken bones, replacing damage joints, etc)

 

[PerennialII]

The golf club idea sounds excellent but can anybody help to do the calculation?

Any help is greatly appreciated

How familiar are you with bending of beams? One online source which looks about ok :

http://efunda.com/formulae/solid_mechanics/beams/theory.cfm

 

[Michaelcarson11]

Can anybody give me the equations the equations for displacement and maximum surface stress in a beam fixed at both ends and the load in the centre?

 

[AlephZero]

Can anybody give me the equations the equations for displacement and maximum surface stress in a beam fixed at both ends and the load in the centre?

The classic reference book for this sort of question is the book "Formulas for Stress and Strain" by Roark and Young (probably owned by 99.999% of "real engineers", and called just "Roark")

It appears to be available online here: http://www.roarksformulas.com/ (with free registration)

Or try http://www.engineersedge.com/beam_calc_menu.shtml