Design and Stress Analysis of Extraterrestrial ... - The Black Vault

In order to find the relationship between the coefficient of
rigidity and unit load, let us examine a beam on two supports loaded
by force P and moment M (Fig. 3.70) Under the effect of the force
and the moment the beam at point 1 will be deflected by quantity y
and turned by angle a-.
If we use a "method of deformation," we can express the force
and the moment in terms of, deformations:
P=CIIY+C 1 2 a1; M=c 2 1Y1+C2 (3. 117)
where cl, c 1 2 , c21' and c 22 are the i 1 tidity coefficients.
Fig. 3.70. Determining the rela- I
tionship between the coefficients
of rigidity and unit load.
From the system of equ.tions. (3.117) we find the value of
deflection y and the angle of turn a:
P~ C12L
Af = I= - P-- -- M
I
C21 C22I
~1C
C22 IC22
C21 M 21 P+ C11 M
JCH C12C1K2--C1 1C2-C2
cnc --c• ( 3.118)
On the other hand, if we use the "method of forces, we can
express the deflection y and angle turn a in terms of force P and
moment M:
f 363