Page 280 - Boiler_Operators_Handbook,_Second_Edition

Strength of Materials 265

than compression because it goes across the coupon at when you stand on them but they hold you up. Just like
an angle. Since most metals would swell (increasing the the rubber band the material length changes when force
cross-sectional area and strength of the coupon) when is applied to it. The bottom layers get longer and the top
their yield point is reached, the test is not run past the layers get shorter to compensate for the applied force
yield point. The slope of the curve is usually the same of your weight. Since the layer at the middle neither
for metals under tensile stress so the compressive stress- shortens or lengthens it doesn’t do anything to counter
strain diagram matches the tensile stress-strain diagram the applied force. The stress in the material increases
in the proportional range. from zero at the center to maximum at the extreme outer
Shear stress, as it’s name implies, is resistance to fibers (engineer’s word for edge) and that’s why all the
being cut and is considered primarily for fabrication steel beams we see are made in the form of the letter I,
activities where the material is cut by shears. Unlike by putting most of the material at the outer layer (where
tensile and compressive stress, where the force is ap- the maximum stress is) we get the strongest beam.
plied through the cross-sectional area in tensile stress it Now that you know about the actual measured
is applied parallel to the cross-sectional area. It’s seldom strength of the material we can talk about “allowable”
a consideration in boiler design. Mainly because you’re or “design” stress. For everything boiler and pressure
not allowed to make a riveted boiler anymore. If you run vessel related those values are listed in the ASME Code
into a situation that requires knowledge of shear stress in Section II which is called “Material Specifications.”
you should be able to understand its function from the Section II is broken down into three parts. Part A is for
previous discussion. ferrous (engineer’s and scientist’s word for iron) metals,
Bending stress is not a special kind of stress, it’s a Part B is for non-ferrous metals (like brass and copper),
function of compressive, tensile and shear strength. To and Part C is for welding materials (welding rod). Those
describe how it relates I use an example that you can sections define the quality of a material and how it must
reproduce yourself. Take several pieces of 1 by 4 (that’s be made and tested.
lumber which is really about 3/4 of an inch thick by For the most part the Section II contents is identical
3-1/2 inches wide) and stack them up on the floor be- to the material specifications prepared by ASTM (The
tween two bricks and stand on them. The result is some- American Society of Testing and Materials) and differs
thing like that shown in Figure 9-3 because the layers of primarily in the certification requirements. A boiler or
lumber can’t support your weight. Note, however, that pressure vessel manufacturer has to buy material that is
the lumber ends are not flush like they were when you certified by the manufacturer to conform to the specifi-
laid them out. Gluing all the layers of lumber together cations in Section II.
(or even securing them to each other with several nails Part D is called “Properties” and it lists the allow-
or screws) prevents the equivalent of shearing stress able stress for each of the metals described in the three
from occurring in the material and they will support other parts. If you were to look at Part D you would
your weight when you stand on them. The force of your discover that the ASME has different values for allow-
weight is countered by tension on the bottom layers of able stress depending on the use of the material and the
the material and compression on the top layers with maximum or minimum operating temperature. Allow-
shear stress applied to the individual layers. able stresses vary for use as boilers (BPVC Sections I and
Once you’ve glued (or fastened) the layers to- IV) and pressure vessels.
gether you might not notice that they still bend a little To relate to that yield strength determined by
testing a coupon you could look at the minimum yield
values for a material in the applicable Part (A, B, or
C) and the allowable stress in Part D. Since you really
don’t want to pay ASME’s price for those books it’s not
recommended. I can tell you that what you would find
for ferrous metals, the allowable stress is one fifth to one
fourth the yield. That means the boiler is constructed
of metal that should not fail (by deforming) until the
pressure is four or five times higher than the maximum
allowable pressure. It’s a safety factor of 4 or 5 and it’s
one thing that helps protect you from injury due to a
Figure 9-3. Layered board sample of bending stresses material failure.