Another theoretical situation for you to help me deal with

[DBCox]

Ok everyone,

I am been running this situation through my head and am having trouble with it. Lets say I have two beams, say sqaure tubes of the same dimensions (length and everything), but different material. One is A36 and the other is heat treated 4140. Both have the same modulus of elasticity, but the 4140 is obviously higher strength.

Loading and Support:
Both have the same load applied, both are simply supported on each end by supports spaced the same on each beam.

I want to know the deflection at the center. Deflection is based on load, section modulus, and modulus of elasticity; all of which are common for both materials. It would seem both would deflect the same amount.

That part I am OK with. What seems odd is in my experience, the lower strength materials have the ability to bend more than the higher strength materials before fracture (generally speaking). Well, the common links between deflection and stress in the part are the section modulus and load (thus moment). With that in mind, deflection can be directly related to stress in the part (as deflection increases, so does stress). With that mind set, it would seem that the 4140 could bend significantly more than the A36 before fracture, but that contradicts what I have seen in past experience.

So, what am I missing?

 

[CoryPad]

PLASTICITY!

Elastic modulus and second moment of area are the important parameters for elastic deflection. However, elastic deformation of steels is tiny compared to the plastic deformation capacity. Quenched and tempered 4140 will have higher strength, but lower plastic strain capacity, than A36. In deflection limited designs (like your hypothetical one), the A36 material will plastically strain more than the 4140 material.

Regards,

Cory

Please see FAQ731-376 for tips on how to make the best use of Eng-Tips Fora.

 

[DBCox]

Cory,

Thanks for the info. To clarify, the deflections (assuming elastic deformation limit is not exceeded) will be the same. However, the elastic limit of the 4140 is larger than that of the A36, BUT, the plastic 4140 range is smaller. So, what will happen is the A36 can bend more without fracture, but will remain deformed. The 4140 will not necessarily be able to bend as far without fracture, BUT, it can bend more than the A36 and still return to its origional shape (elastic deformation)

Am I understanding you correctly?

Also, am I remembering correctly that the deformation equations are valid only for elastic deformation?

Thanks!

 

[eromlignod]

The "strength" of a material is simply the point at which it fails, either by yielding or breaking. It is basically independent of its stiffness.

A high-strength steel beam and a low-strength steel beam will deflect the same amount under the same load, since their elastic moduli are the same. But as you continue to add load, the lower-strength beam will eventually break while the stronger beam will continue to deflect.

Don
Kansas City

 

[rb1957]

look out cozzone plastic bending analysis.

the more ductile material will strain more than the less ductile material, so you'll see bigger deflections.

Cozzone connects the ultimate strain with the ultimate stress, so your two materials are tradin off one property against the other.

 

[CoryPad]

blakrapter,

Yes, you are understanding me correctly. Yes, the standard beam equations are for elastic deformation.

rb1957 has provided a good tip regarding plastic analysis. Also, "plastic hinge" is sometimes used.

Regards,

Cory

Please see FAQ731-376 for tips on how to make the best use of Eng-Tips Fora.

 

[DBCox]

Thanks for the info everyone. As for the Cozzone and Plastic Hinge methods, are they more accurate than the standard deflection equation used in most statics books (in the elastic range only of course)?

Or, are they supposed to be used if the elastic range of the material is exceeded for an accurate analysis? If more accurate regardless of plastic or elastic deformation, how "wrong" is the basic analysis that uses only the modulus of elasticity as a material property?

Thanks!

 

[rb1957]

yes, i think to your 2nd thought ...
cozzone is used to account for plastic stresses ...
it calculates a maximum moment that the section can absorb by going plastic.

 

[plasgears]

The behavior of a structure until failure will reflect the area under the s-s curve. A material with modest strength but high elongation will exhibit great capacity to absorb overload before fracture or collapse.

For example, in a plastic worm gear set, a flexible worm like nylon 6 will absorb more punishing stall overloads than acetal without failure. This is very different from the metal gear set model.