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 example, a fixed beam carrying a concentrated load at mid-span has a central displacement that is one-quarter of that of a simply supported beam of the same span and carrying the same load, while the maximum bending moment is reduced by half. It follows that a smaller beam section would be required in the fixed beam case, resulting in savings in material. There are, however, disadvantages in the use of this type of beam for, as we saw in Section 13.6, the settling of a support in a fixed beam causes bending moments that are additional to those produced by the loads, a serious problem in areas prone to subsidence. Another disadvantage of statically indeterminate structures is that their analysis requires the calculation of displacements so that their cross-sectional dimensions are required at the outset. The design of such structures therefore becomes a matter of trial and error, whereas the forces in the members of a statically determinate structure are independent of member size. On the other hand, failure of, say, a member in a statically indeterminate frame would not necessarily be catastrophic since alternative load paths would be available, at least temporarily. However, the failure of a member in, say, a statically determinate truss would lead, almost certainly, to a rapid collapse.

The choice between statically determinate and statically indeterminate structures...