Page 109 - Aircraft Stuctures for Engineering Student

4.7 Solution of statically indeterminate systems 93

from which

Hence the forces in each member of the framework. The deflection A of the load P or
any point on the framework may be obtained by the method of Section 4.6. For
example, the stationary value of the total complementary energy of Eq. (i) gives A, i.e.

Although braced beams are still found in modern light aircraft in the form of
braced wing structures a much more common structural component is the ring
frame. The role of this particular component is discussed in detail in Chapter 7; it
is therefore suflicient for the moment to say that ring frames form the basic shape
of semi-monocoque fuselages reacting shear loads from the fuselage skins, point
loads from wing spar attachments and distributed loads from floor beams. Usually
a ring is two-dimensional supporting loads applied in its own plane. Our analysis is
limited to the two-dimensional case.
A two-dimensional ring has redundancies of direct load, bending moment and
shear at any section, as shown in Fig. 4.17. However, in some special cases of loading
the number of redundancies may be reduced. For example, on a plane of symmetry
the shear loads and sometimes the normal or direct loads are zero, while on a
plane of antisymmetry the direct loads and bending moments are zero. Let us consider
the simple case of a doubly symmetrical ring shown in Fig. 4.18(a). At a section in the
vertical plane of symmetry the internal shear and direct loads vanish, leaving one
redundancy, the bending moment MA (Fig. 4.180)). Note that in the horizontal
plane of symmetry the internal shears are zero but the direct loads have a value

el

Fig. 4.17 Internal force system in a two-dimensional ring.