178
Chapter 3
tains stability. Constraint 3 will be ignored but definitely checked at the
end.
The modulus, E, and the density, 7, are related [3.13] from vibration
E/y the specific stiffness
E
--= 105 × 106 in
(3.127
for most common structural members. This could introduce another vanable to solve for, but, what does one do when the solved value for E does
not exist in any known material. The best method is to introduce the known
discrete values of E and 7 for common materials.
The relationship for E and G [3.21] is
E
E
G
(3.128)
2(1 - v) 2.6
Now substitute E=30x 106 psi and 7=0.283 lb/in 3 into Eqs. (3.119)(3.123) and (3.128). Note: If a known spring material is used more precise
numbers are available. The equation for solution are
Spring weight, go
Wspring
= 1.77814 Rtl = A RtL
(3.129)
Constraint 1 fr
[- L -]1/2
15.9254 x 10-3|~|
< 1
BILl ’/2L-I~-~ <1
(3.130)
Constraint 2 fe
_3 [- L3 -]1/2
5.37663 × 10 /~-~| --< 1
I_ /
(3.131)
Constraint 4 acre
600 (~)
(3.132)
1