Question:
I am a little embarrassed to ask a basic question about
material stress to this group however after looking over the
sci.materials threads you seem to be a friendly bunch so here goes...
My text books give direct stress as the" ratio of a applied load to
the initial
cross-sectional area" of a material. Ok fine. thus e= f/A however, I
want to know why this information is useful! If a load on a given
cross section is increased the formula will give a simple result that
would be the same for all materials (assuming that the initial cross
section does not change).
So to ask a direct question,
Is my explanation and assumption above correct and if so why is the
stress formula useful?
I would apprectiate any other illumination on the subject of stress
and strain in material. If this subject has already been covered in
depth please direct me to the thread.
Answer:
That's correct. If cross section doesn't change given load creates same
stress, no matter what material is being used. This formula is useful,
because you can tell how much material deflects uder load (under the same
stress deflection depend of material's type), and whether stress exceeds
material's strength.
It is useful in estimating the EFFECT of the load on the material.
Suppose someone is pushing against your belley with a force of 50 pounds
applied with a flat hand with a surface area of about 20 square inches.
The stress at the hand-skin contact is 50 pounds/20 square inches or
about 2.5 pounds per square inch (PSI). Your skin will easily withstand
this small stress. The fracturing stress of skin being several hundred to
a few thousand pounds per square inch.
Suppose the same person exhanges his hand for a knife with a fine point,
but still applies the same 50 pounds of force. The area of knife/skin
contact is very small, say 0.005 square inches. So the contact stress on
the skin is 50 pounds / .005 square inches or about 10,000 pounds per
square inch (PSI).
Your skin will rupture under 10,000 PSI and you will die.
So, you see, it has a practical value in estimating the degree to which
force is concentrated within a piece of material, and the tendency of the
material to break, and possibly kill you, is expressed in terms of this
concentration.... and in terms of the concentration needed to cause
breakage or yielding or....... These are called material properties and
are measured in the lab by putting forces on specimens of different sizes
and seeing what happens and recording the results.
So, we are monitoring the initial cross section to see how much it
changes under load? then using the changed cross sectional area (ie a
different value)in the formula if it changes? This has been the
confusing part for me; the phrasing "initial cross-sectional area"
implies (to me) that this value can not change in the formula.
It depends of what kind of research you do on a material specimen.
Most common is (for metallic materials):
1. You place a specimen (with round, square or flat cross section) in a
machine that tries to tear it (sometimes squeeze, as I said it depends).
2. The meachine registrates what load is being applied and what deflection
(perpendicular to cross section) accompanies that particular load. Load is
increased till the specimen breakes.
3. Because metals are not compressible (specimen's volume is constant), the
sepcimen's cross section area reduces as load increases (these changes are
not registered by the machine).
4. Dividing maximum load by "initial cross section area" gives tensile
material strength. Reduced cross section is not taken under consideration in
calculation because of couple reasons:
- specimen doesn't thin uniformly (even ones made of the same material -
caused by chemical/structural composition flucuations and all kind of
impurities)
- calculated strength is smaller than real one, so you've got kind of
"factor of safety".
You are right, "initial cross-sectional area" cannot change in the formula.
You can evaluate real strength of the specimen, by measuring cross section
where crack/breakage occured. It all depends what do you want to know about
material or what standards you have to conform.
