flexibility method of structural analysis examples

Flexibility Method of Structural Analysis: Examples and Applications

The flexibility method of structural analysis is a powerful tool used to solve complex engineering problems, particularly in the field of civil engineering. This method involves using equations of static equilibrium to determine the reactions at supports or joints in a structure. In this article, we will explore some examples and applications of the flexibility method.

Example 1: Fixed Beam with Uniform Distributed Load

Consider a fixed beam AB of constant flexural rigidity, as shown in Fig. 1.3. The beam is subjected to a uniform distributed load w per unit length and a moment M = wL^2 kN.m at the free end A. To find the reactions R3 and R4 at the supports B and C, respectively, we can use the flexibility method.

Using the equations of static equilibrium, we can write:

R3 = 0.771 KN m

Substituting the value of E and I in the above equation, we get:

R4 = ?0.755 KN m

Flexibility Matrix

The flexibility matrix is a square matrix that relates the displacements at supports or joints to the reactions. In this case, the flexibility matrix can be written as:

'flexibility matrix'

where a11 and a12 are the coefficients of the flexibility matrix.

Moment-Area Method

In the moment-area method, we use the concept of virtual work to calculate the deflections of the released structure at B and C. By applying moments about point A, we can find the reactions R1 and R2 at supports B and C, respectively.

Primary Structure with Given Loading

Consider a primary structure with a given loading, as shown in Fig. 2. The primary structure is a cantilever beam AC, which is statically indeterminate to second degree. By selecting two reactions, vise, at B (R1) and C (R2), we can find the reactions R3 and R4 at supports B and C, respectively.

In conclusion, the flexibility method of structural analysis is a powerful tool used to solve complex engineering problems. This method involves using equations of static equilibrium to determine the reactions at supports or joints in a structure. By applying this method to various examples, we can find the reactions and deflections of structures subjected to different types of loads.

References

1. Textbook on Structural Analysis

2. Journal of Civil Engineering

Flexibility method of structural analysis examples