Page 101 - Aircraft Stuctures for Engineering Student

4.7 Solution of statically indeterminate systems 85

From B to C

giving

From C to D

so that
dM dM
= i(L - z)
-=$(L-z), -
dPB,f apt,,
Substituting these values in Eqs (iv) and (v) and remembering that PB,f = Pc,f = 0 we
have, from Eq. (iv)

from which
1 19wL4
A-
B - 24 576EI
Similarly
5wL4
A,=-
384EI
The fictitious load method of determining deflections may be streamlined for
linearly elastic systems and is then termed the unit loud method; this we shall discuss
later in the chapter.

In a statically determinate structure the internal forces are determined uniquely by
simple statical equilibrium considerations. This is not the case for a statically indeter-
minate system in which, as we have already noted, an infinite number of internal force
or stress distributions may be found to satisfy the conditions of equilibrium. The true
force system is, as we demonstrated in Section 4.5, the one satisfying the conditions of
compatibility of displacement of the elastic structure or, alternatively, that for which
the total complementary energy has a stationary value. We shall apply the principle to