A strucure in which the laws of statics are not sufficient to determine all the unknown forces or moments is said to be statically indeterminate. Such structures are analyzed by writing the appropriate equations of static equilibrium and additional equations pertaining to the deformation and constraints known as compatibility condition.

The statically indeterminate structures are frequently used for several advantages. They are relatively more economical in the requirement of material as the maximum bending moments in the structure are reduced. The statically indeterminate are more rigid leading to smaller deflections. The disadvantage of the indeterminate structure is that they are subjected to stresses when subjected to temperature changes and settlements of the support. The construction of indeterminate structure is more difficult if there are dimensional errors in the length of members or location of the supports.

This chapter deals with analysis of statically indeterminate structures using various force methods.   

The moment area method and the conjugate beam method can be easily applied for the analysis of statically indeterminate beams using the principle of superposition. Depending upon the degree of indeterminacy of the beam, designate the excessive reactions as redundant and modify the support. The redundant reactions are then treated as unknown forces. The redundant reactions should be such that they produce the compatible deformation at the original support along with the applied loads. For example consider a propped cantilever beam as shown in Figure 5.1(a). Let the reaction at B be R as shown in Figure 5.1(b) which can be obtained with the compability condition that the downward vertical deflection of B due to applied loading (i.e. shown in Figure 5.1(c)) should be equal to the upward vertical deflection of B due to R (i.e. shown in Figure 5.1(d)).