(Force Method - Introduction and applications) Analysis of Statically Indeterminate Beams Objectives

•Force Method - Introduction and applications
•Analysis of Statically Indeterminate Beams
Objectives

       
 In this course you will learn the following

  •Introduction to statically indeterminate structure.
  •Analysis of statically indeterminates beam using moment area and conjugate beam method.
  •To demonstrate the application of moment area and conjugate beam method through illustrative
examples.

.1 Introduction

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.

.2 Analysis of Statically Indeterminate Beams

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)).