chapter  4
16 Pages

Methods

Statically indeterminate structures are solved either by exact methods, utilizing elastic analyses, or by approximate methods, involving the use of simplifying assumptions. While there are many types of structural engineering software packages available, which are capable of solving very sophisticated structural systems, knowing some simple approximate methods to solve statically indeterminate structures is very helpful to the practicing engineer as a starting point for design or to check output from software packages. Approximate methods, which are done by hand, can often enlighten the designer’s understanding of the structural stability and force balance of a proposed structure. Solving determinant structures using principles of statics requires the system to have the

same number of unknowns as equations of statics. That is, when there are more unknowns than equations, the structure is indeterminate. A system, which has three more unknowns than equations of statics, is said to be indeterminate to the third degree. A building frame, which comprised two vertical and one horizontal member-a bent or

portal, is statically indeterminate to the third degree. Since a single portal frame is indeterminate to the third degree, a rigid frame building, which is three stories tall and three bays wide and forms a nine portal building frame, has 27 degrees of indeterminacy, thereby making rigid frame buildings highly indeterminate. For this reason, their exact method solutions are time consuming due to the number of simultaneous equations needed to be solved, and are almost always analyzed by computer. Today, even simpli‡ed approximate methods are only used on very small systems and when appropriate due to the ubiquitous computer applications which can analyze and design these systems faster than one can perform an approximate method. In order to solve indeterminate systems by an approximate method, assumptions are

made to remove the number of unknowns or the degree of indeterminacy. There are many different methods available for making approximate analyses. The methods presented here are limited to gravity and lateral force analysis of frames.