Upd

External moment A

O.I87/W0

External moment A

0.373/if0

O.I87/W0

0.373/if0

+ve B.MOncreasing curvature) (a)

Fig. 4.22 Distribution of bending moment in frame of Example 4.7.

In fact, the question of whether a structure possesses linear or non-linear characteristics arises only after the initial step of writing down expressions for the total potential or complementary energies. However, a great number of structures are linearly elastic and possess unique properties which enable solutions, in some cases, to be more easily obtained. The remainder of this chapter is devoted to these methods.

In Section 4.6 we discussed the dummy or fictitious load method of obtaining deflections of structures. For a linearly elastic structure the method may be streamlined as follows.

Consider the framework of Fig. 4.7 in which we require, say, to find the vertical deflection of the point C. Following the procedure of Section 4.6 we would place a vertical dummy load Pf at C and write down the total complementary energy of the framework, viz.

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