Full resolution (JPEG) - On this page / på denna sida - Strength of Materials - To calculate deflection in beams under different modes of support and load - To find suitable size of beam for a given limit of deflection
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STRENGTH OF MATERIALS. 263
Solution
:
43
X 2000 X 0.0000288 X 1.7
S = X
s
74 — 5*
256 X 2000 X 0.0000288 X 1.7 X %
1776
^ = 0.0085 inch.
In this example, 1.7 is used as a multiplier because the
beam is round, and $£ because the load is distributed evenly
throughout the length of the span.
Example.
A fly wheel weighing 800 pounds is carried on the free end
of a 3-inch shaft, 1 foot from the bearing. How much will the
shaft deflect?
This is the same as a round beam loaded at one end and
fastened at the other; therefore, constant c is multiplied by
16 X 1.7.
Solution
:
o Z3 P 1.7 c X 16
S 1 X 800 X 1.7 X 0.0000156 X 16
34
.5 = 0.0042 inch.
FIG. 37
Previous calculations for breaking load and also for
deflection are based upon a dead load slowly applied and not
exposed to jar and vibrations. If the load is applied suddenly
it will have greater effect toward breaking the beam than if
applied slowly. For instance, imagine a load having its whole
weight hanging on a rope, like Fig. 37, just touching the beam
but not actually resting upon it.
If that rope was cut off suddenly
this load would produce twice as
much effect toward breaking the
beam and would cause twice as
much deflection as if it was loaded
on gradually. A railroad train
running over a bridge will, for the
same reason, strain the bridge
more when running fast than it
would if running slow.
To Find a Suitable Size of Beam for a Given Limit of
Deflection.
For a square beam supported under both ends and loaded
at the center, use the formula
:
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