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234 STRENGTH OF MATERIALS.
lfoot.
1
25 lbs. Fig. 2.
1
n ...
\m&> r-\ y&m*
100 lbs.
LA
100 lbs.
Fig. 3.
L
50 lbs.
other. This may be understood by
referring to Fig. 2, as when the beam
is one foot long and loaded with
100 pounds in the middle, each half
of the beam supports only 50 pounds,
and this 50 pounds acts only upon an
arm y
2 foot long, consequently it
exerts no more force toward break-
ing this beam than the 25 pounds
would upon the end of the other
beam one foot long.
A beam twice as wide as another and of the same length,
thickness, and material, will carry twice the load, because the
wide beam could, of course, be split into two equal beams ;
consequently it must, as a whole ,
beam, have twice the strength of \~ i*
2 {eet—\
another one of the same material
but of only half the width.
A beam twice as long as another
will break under half the load. This
is seen by referring to Fig. 3, be-
cause 50 pounds on an arm two feet
long will balance 100 pounds on an arm one foot long.
A beam twice as thick as another, of the same material,
length and width, will carry four times the load. ( See Fig. 4).
Suppose the weight a is act-
ing on the arm b, tending to swing
it around the center c, and this
action being counteracted by the
weights g and k, also by the
arrows e and f. If the weights
is taking hold twice as far from
the center as the weighty it will
offer twice the resistance against
swinging the beam that g will
;
and exactly the same with the
arrows/" and e. Consider the line c b as the neutral fiber, the
arrows e and f as representing the fibers resisting crushing,
and the weigh ts^- and h as representing the fibers resisting tensile
stress. It will be understood that if the fibers are twice as far
above or below the neutral fiber they are in a position to orTer
twice the resistance to the breaking action of the load ; but a
beam of twice the thickness has not only its average fiber twice
as far from the neutral point, but it has also twice the area or
twice as many fibers, consequently the result must be that it
can resist four times the load.
Fig. 4.
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