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Structural Analysis of Statically Indeterminate beams using Slope Deflection method.

Introduction

Structural analysis is the computation of the effects of loads on physical structures and their components. Structures that undergo this type of analysis must be able to carry loads, some of which include bridges, buildings, ships, and aircraft (Kassimali, 2010). According to (Chang, 2015) Structural analysis is the part of structural engineering that deals with determining the analytical behavior of structures.  The structural analysis utilizes the concept of materials science, applied mechanics, and applied mathematics to determine the accelerations, deformations, internal forces, stability, stresses, and support reactions of a structure. The result gotten from the analysis is used to establish the fitness of a structure before it can be used, also sometimes it is augmented by physical tests. In simple terms, structural analysis is a tool used to find out how a structure or a structural member behaves when subjected to load (Williams, 2009). Therefore, Structural analysis is a vital aspect of the design of structures in engineering.

In the construction of engineering structures, structural analysis is succeeded by structural design, that is after the components of the structures have been verified to be fit during structural analysis, then the structure’s design process can begin.  Parameters used for the structural design are gotten from structural analysis. They are shear force, bending moment, axial force, deflection, displacement, and torsion. To determine these parameters, various methods are used. Bending moment is a principal parameter used for structural design, hence, the calculations of the geometry and materials of a structure are dependent on the bending moment (Sharma, Jain, and Jain, 2017).

In the analysis of beams, beams could either be statically determinate or statically indeterminate. Statically determinate structures can be resolved by the simple equilibrium of forces. This is because the structure is usually simple, with not more than three unknowns and redundancies to be determined in the structure, either forces or moment. Conversely, statically indeterminate structures have to be analyzed by other exceptional methods because beams are continuous, have many redundancies, and are complex to resolve using simple equilibrium of forces. Several methods could be used to analyze statically indeterminate structures. They include the force method, displacement method, and approximate method (McCormac and Nelson, 1997). For determining the bending moment of structures methods like slope deflection method, moment area method, moment distribution method, stiffness matrix method, and flexibility matrix method are used. For this study, the slope deflection method would be employed due to its simplicity and easiness to work. 

The slope deflection method is a structural analysis method used for the analysis of beams and frames. It is one of the various methods that are utilized to analyze beams and frames. It was first introduced in 1914 by George A. Maney. This method was extensively used for more than a decade until the development of the moment distribution method. In the book "The Theory and Practice of Modern Framed Structures" by Johnson J.B., Bryan C.W., and Turneaure F.E., it was asserted that the slope deflection method was first developed by Professor Otto Mohr in His book "Evaluation of Trusses with Rigid Node Connections". The method was later improved separately by Professor G.A. Maney (Maney, 1915). Python is an interpreted high-level general-purpose programming language (Kuhlman, 2012). It was selected for this study because of its simplicity and ease to use.

Problem Statement

The major problem faced in structural analysis is the time involved in carrying out analysis manually. Although there have been applications developed to carry out this analysis, some of them are inaccurate, complicated, expensive, and difficult to use.  The importance of time and structural analysis cannot be over-emphasized in engineering especially in construction projects both to ensure safety and economy. This has spurred this work to develop a program that can help students and engineers analyze beams in a quicker, more accurate, and efficient method.

Aim and Objectives

This study aims to create a computer program that can accurately, quickly, and successfully analyze a statically indeterminate beam.

The objectives of the research work are;

  • Objective 1: To theoretically analyze several statically indeterminate beams with different support and loading conditions using the Slope Deflection method (SLD).
  • Objective 2: To write a successful computer program using Python to solve problems in objective 1 above
  • Objective 3: To determine the efficiency of the program by solving several examples with the code and comparing with answers gotten manually.

Research Questions

The identified research questions for this project are provided below:

  • What are statically indeterminate beams?
  • Why and how is the Slope Deflection method (SLD) used to analyze statically indeterminate beams?
  • Why and how is Python used for the computer program?
  • What is the efficiency of the program written with Python?

Deliverables

The deliverables of this project are a project report, a complete Python code of the Slope Deflection method (SLD), and results of solved examples of statically indeterminate beams. The code would be written in line with how the Slope Deflection method (SLD) is applied manually and for several supports and loading conditions. Results from the code and those derived manually would be compared to find the accuracy and efficiency of the program.

Relevance

This project focuses on developing a computer program using Python to write code for solving statically indeterminate beams adopting the Slope Deflection method (SLD). Basically, it shows the application of the knowledge and skill of coding in solving structural analysis problems.

Methodology

This project focuses on secondary research, and programming. They are discussed below:

Secondary Research

The secondary research in this project will utilize a systematic approach (Johnson et al., 2016) to review the works of literature. The steps involved in the systematic review of the literature are provided below:

  • Step 1: Identify the research questions that can be used for the project.
  • Step 2: Identify the keywords that should be used to research the works of literature.
  • Step 3: Extract the journals and books that are appropriate for this project.
  • Step 4: Write the literature review chapter.

Programming

Programming or coding is the main aspect of this work. It would be carried out in stages, and as such described below;

  • Stage 1: Getting a computer and Python programming language installed on it.
  • Stage 2: Laying out the scope of the program i.e., how the code would be written and what the code would be able to do.
  • Stage 3: Step by step implementation of functionalities into the code.
  • Stage 4: Gradually increase the capability of the program.
  • Stage 5: Getting and documenting the results of each program operation.
  • Stage 6: Finishing the code
  • Stage 7: Result testing, analysis, evaluation, and optimization.

Evaluation

The risk assessment conducted for this project is provided in the table below:

Table 1:  Risk assessment

Risk

Impact

Mitigation Plan

Inability to meet the deadline

High

Get an extension from the supervisor in due time

Inability to get required process inputs

Low

Refer to research institutes and skilled professionals for help

Inability to properly develop the program

High

Refer to programming guide and professionals for help

Insufficient data

Low

Refer to journals and textbooks for help

Schedule

Table 2: Project Plan

Task Name

Start Date

End Date

Duration (Days)

Initial Research

15/01/2022

29/01/2022

14

Proposal

29/01/2022

06/02/2022

21

Secondary Research

06/02/2022

18/03/2022

40

Introduction Chapter

18/03/2022

23/03/2022

5

Literature Review Chapter

23/03/2022

20/04/2022

24

Methodology Chapter

20/04/2022

02/05/2022

12

Writing the code

02/05/2022

02/08/2022

90

Presentation 1

02/08/2022

10/08/2022

8

Testing and optimizing the code

10/08/2022

10/09/2022

30

Evaluation and comparison of Results

10/09/2022

17/09/2022

7

Discussion Chapter

17/09/2022

27/09/2022

10

Evaluation Chapter

27/09/2022

02/10/2022

5

Conclusion Chapter

02/10/2022

04/10/2022

2

Abstract and Report compilation

04/10/2022

06/10/2022

2

Report Proofreading

06/10/2022

16/10/2022

10

Presentation 2

16/10/2022

26/10/2022

10

 

References

Chang Kuang-Hua (2015), Chapter 7 - Structural Analysis, Academic Press, Pages 325-390, ISBN 9780123820389, https://doi.org/10.1016/B978-0-12-382038-9.00007-7

Johnson, D., Deterding, S., Kuhn, K.A., Staneva, A., Stoyanov, S., and Hides, L., 2016. Gamification for health and wellbeing: A systematic review of the literature. Internet interventions, 6, pp.89-106.

Kassimali, Aslam, 2010. Structural Analysis. 2nd ed. Cengage Learning.

Maney, George A. (1915). "Studies in Engineering". Minneapolis: University of Minnesota.

McCormac, J. and Nelson, J., 1997. Structural Analysis (Engineering). Addison Wesley.

Sharma, R., Jain, A. and Jain, V., 2017. Analysis of a continuous beam by using different structural analysis methods. International Research Journal of Engineering and Technology (IRJET), 04(09), pp.1281-1283.

Williams, Alan, 2009. Structural Analysis in Theory and Practice.

 

Last updated: Jan 13, 2022 12:34 PM

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