# Stress or deflection which is important

1. Aug 7, 2006

### chandran

I want to know in mechanics of materials what is the real objective of finding the deflections at various points in structures
like

1)deflection in the end of an axially loaded bar

2)vertical deflection along the beam length

3)beam slope along the beam length

5)torsion bar twist about the torsion bar axis.

I believe stress is a major criteria rather than deflection because it determines the failure. Then why should we care about deflection at all? Particularly in beam
bending is the slope a major criteria?

2. Aug 7, 2006

### Clausius2

We care about strain because strain is relationed to stress through Hooke's law, and an external deformation caused by a load generates an internal stress state that leads to plastification in some ultra stressed zones. Plastification is usually the criterion used for the breakdown of a structure (i.e. Von Mises criterion).

3. Aug 7, 2006

### FredGarvin

One major thing to realize as well is that stress is a calculated value. You do not directly measure stress. I'm sure you can probably envision a circumstance where one would need to know the things you aer asking about. The only one I really have never come across is the calculation of the slope. Usually the slope is used as a boundary condition for solving DEs.

I can tell you, in my line of work, we deal with 1, 2 and 5 (as you labeled it) on an regular basis with the behaviors of engine shafts.

4. Aug 7, 2006

### Q_Goest

Deflection and stress are both important in engineering on a case by case basis. How much a bridge deflects (ie: a beam in bending) is obviously a very important consideration - not just stress.

If you were designing any kind of spring mechanism for example, you'd be very interested in deflection since your system would depend on deflection and spring constant. Even deflection (or stretch) in bolts is sometimes important as it determines what kind of cyclic stresses the bolt undergoes (for fatigue considerations).

You can determine the stress in something due to loads, or you can find the stress in something due to strain. Both are equally valid, and both are used.

5. Aug 7, 2006

### Astronuc

Staff Emeritus
In a structure one cares about 1) geometric stability and 2) structural integrity, i.e. the structure should not fail.

With regard to point 1, if a bridge where designed to deflect several inches a vehicle pass over it, the driver would feel it.

In a dynamic system, too much deflection would cause 'wear and tear' on the structure.

As others have mentioned, there is a constitutive relationship between stress and strain. Most, if not all, mechanical systems are designed to be used in the elastic region, i.e. the local maximum stress is sufficiently below the local yield stress in order to prevent any local permanent deformation (of which one consequence could be and undesirable redistribution of stress or enhanced stress concentration (and enhanced strain) elsewhere in the structure).

There is also a difference between mechanical and thermal strain.

And - deformation is measurable, stress is not.

6. Aug 7, 2006

### Clausius2

Hey guys, this is not the area of my expertise, but I barely remember when I studied Photoelasticity that this technique measured directly stress contours by means of the change of the refraction index (stress refringence). Is that right? Actually I remember I did a lab exercise with a beam deflection.

http://scienceworld.wolfram.com/physics/StressRefringence.html

7. Aug 7, 2006

### FredGarvin

I don't know on that one. I think I'll leave that one to Perennial. In a standard setting, I don't know if that kind of equipment would be available in the field.

8. Aug 7, 2006

### Clausius2

I do know it is used in superficial testing. For instance, for a piece of fuselage one needs to cover it with a birrefringent layer of material. When the whole is stressed/strained one illuminates the piece and look at it through special lens-filters. The light comes into the birrefringent layer and gets its refraction index changed according to the stress field applied, and then it comes out to the lens. You can see bands corresponding to isocontours of stress of different colours, which can be interpreted looking at tables. It's a nice method.

Other methods such as strain gauges clearly only measure deformation.

9. Aug 9, 2006

### PerennialII

I suppose the good old photoelasticity is as close to directly measuring stress as anything (yeah, refractive index varying with the direction of polarization and light axis of propagation - optical anisotropy referred to as birefringence ). Even with photoelasticity people quarrel about what they are actually measuring (stress or strain), which is understandable since birefringence is induced by stress and deformation. And it's pretty difficult to separate the two when looking at the mechanism as a whole.

Other than that, think the tougher criterion to supersede is that photoelasticity actually has the word "elasticity" in there for a reason. I know it has been used for example in studying viscoelastic material behavior and people have studied/verified whether the stress optic coefficient they're using is applicable in such cases, but in any case there is at least a 'mild' assumption of the underlying constitutive equation (and hence, both stresses and strains)(which may not be even 'that mild' at all if working with deformation resulting in something dissipative, not unusual in the case of cracks etc. singularity like situations).

Other optical methods are a bit more straightforward in this respect, since methods such as laser holography, Moire interferometry, electronic speckle pattern interferometry arrive at stresses by first characterizing the deformation (in 3D generally, like the common modern uses of ESPI, and since use 'speckles' don't have to coat the pieces/structures with anything).

10. Aug 9, 2006

### Astronuc

Staff Emeritus
I did think if photoelasticity, but I'm on the side that understands that it is strain being measured. The question would come down to what affects the optical properties, atomic/molecular displacement, or force. If it is energy, that would have to be strain energy (or strain energy density), or integral of stress & strain, which in the elastic region is proportional to E*e2, where e is strain.

For a given photoelastic material, I can't imagine that the constitutive is the same as the material on which it is placed, e.g. apply a photoelastic layer on aluminum, high strength steel and tungsten. All three metals have greatly different strengths, but the photoelastic material must have the same strength properties regardless of the metal on which it is applied.

I think it would be safe to say that strain is much easier to measure than stress.

11. Aug 9, 2006

### PerennialII

No argument there

Yeah, I've tough time separating some part of the whole system and pointing it as the cause. Always safe to say "everything affects everything" :tongue2: .

The latter is why don't like the methods where have to coat the material with a photoelastic layer (why for example have had problems with limitations of some when studying behavior of cracks [both resolution and arising from the property mismatch]). ESPI seems to be able to produce similar (or better ... I'd say so) resolution and requires little or none (usually) surface preparation ....... just turn the thing on, start loading the specimen, and you'll see the result on your PC screen while it develops ("experimental finite element analysis with animation" ).

12. Aug 9, 2006

### Pyrrhus

Well in typical rigid frames buildings in reinforced concrete, we mostly deal with 2. Also we deal with 5 from time to time, like on beams that support balconies. Seldomly, we might consider 1 depending on the type of structure.