##### From Structural and Stress Analysis, Second Edition

## 16.4 STATICALLY INDETERMINATE BEAMS

Beams are statically indeterminate generally because of their support systems. In this category are propped cantilevers, fixed beams and continuous beams. A propped can tilever and some fixed beams were analysed in Section 13.6 using either the principle of superposition or moment-area methods. We shall now apply the methods described in Chapter 15 to some examples of statically indeterminate beams.

Calculate the support reaction at B in the propped cantilever shown in Fig. 16.14.

Figure 16.14: Propped cantilever of Ex. 16.5

In this example it is unnecessary to employ the procedures described in Section 16.2 to calculate the degree of statical indeterminacy since this is obvious by inspection. Thus the removal of the vertical support at B would result in a statically determinate cantilever beam so that we deduce that the degree of statical indeterminacy is 1. Furthermore, it is immaterial whether we use the principle of virtual work or complementary energy in the solution since, for linearly elastic systems, they result in the same equations (see Chapter 15). First, we shall adopt the complementary energy approach.

The total complementary energy, *C*, of the beam is given, from Eq. (i) of Ex. 15.8, by

in which ? _{B} is the vertical displacement of the cantilever at B (in this case ? _{B} = 0 since the beam is supported at B).

From the principle of the stationary value of the total complementary energy we have

which, by comparison with Eq. (iii)...

##### Products & Services

##### Topics of Interest

16.5 STATICALLY INDETERMINATE TRUSSES A truss may be internally and/or externally statically indeterminate. For a truss that is externally statically indeterminate, the support reactions may be found...

OVERVIEW The majority of the structural problems we have encountered so far have involved structures in which the support reactions and the internal force systems are statically determinate. These...

Overview Many structural problems are statically determinate, i.e., the support reactions and internal force systems may be found using simple statics where the number of unknowns is equal to the...

16.1 FLEXIBILITY AND STIFFNESS METHODS In Section 4.4 we briefly discussed the statical indeterminacy of trusses and established a condition, not always applicable, for a truss to be stable and...

OVERVIEW Statically indeterminate structures occur more frequently in practice than those that are statically determinate and are generally more economical in that they are stiffer and stronger. For...