To understand, learn and apply DSM effectively, a modular approach
in learning is proposed. Each module is like a building block which is
put in place one after the other until the whole coverage of the course is
completed. This blog presents modules of online resources that can
be accessed by civil and structural engineers for learning matrix analysis of
structures.
MODULE 1A - MATRIX ALGEBRA - You need to review matrix algebra to be able to apply the direct stiffness method. The YouTube Channel on Matrix Algebra for Engineers by Prof. Jeffrey Chasnov (HKUST) has a complete set of videos. Khan Academy has also a collection of videos about matrix algebra. The most important matrix operations that you need to learn are addition, subtraction, multiplication, transposition and inversion. Go to these YouTube channels - explore, navigate and learn.
MODULE 1B - USING MS EXCEL FOR MATRIX OPERATIONS - MS Excel has commands for performing matrix operations. MS Excel is a very useful tool for the course since the application of the DSM will result to matrices of large sizes which is not practical to be solved manually. Hence, MS Excel is an ideal supportive tool for matrix operations. Using MS Excel, the derived elements of the structural stiffness matrices can be easily inputted and appropriate matrix operations can be easily performed.
MODULE 2 - STRUCTURAL ANALYSIS CONCEPTS - It is important to review basic concepts on structural analysis to understand the direct stiffness method. The YouTube channel for Dr. Structure has a collection of videos on structural analysis. One important concept that you need to understand is on Stability and Determinacy of Structures. There are more videos on basic concepts like truss analysis, beam analysis (shear and moment diagrams) and analysis of plane frames for deflections and more.
MODULE 3 - ANALYSIS OF PLANE TRUSSES - The direct stiffness method has a common algorithm that can be applied to any type of structure but the elements of the matrices depends on the type of structure being analyzed. What you need to know are the stiffness matrix for each type of structural element. Let us start with the truss element where each node has two degrees-of-freedom (DOF) - the horizontal and vertical displacements. You need to learn how to transform the DOFs and matrices from local axes (x-y) to global axes (X-Y) before you can apply the DSM to the analysis of trusses. The YouTube channel of The Efficient Civil Engineer by Dr. S. El-Gamal has video of two parts on Truss Analysis using DSM. A problem in the textbook by Hibbeler is solved. Dr. Structure has also videos on Matrix Displacement Method for Indeterminate Trusses.
MODULE 4- ANALYSIS OF BEAMS - The next element that you must understand is a beam element. Each node of a beam element has also two DOFs but these DOFs corresponds to the vertical displacement and rotation. You need to review the type of loadings applied to beams - concentrated load, uniform load, couple, etc - since these loadings have to be converted into equivalent nodal forces so that the DSM can be implemented. The YouTube channel of DCBA Online has a collection of videos on the direct stiffness method. Dr. Structure has also videos on Matrix Displacement Method for Indeterminate Beams. Explore navigate and learn.
MODULE 5- ANALYSIS OF PLANE FRAMES - For a plane frame, each node has three DOFs which consist of the horizontal displacement, vertical displacement and rotation. The stiffness matrix of a plane frame element is actually a combination of a truss and beam element. Watch and learn from the videos from DCBA Online and Dr. Structure.
MODULE 6- DSM APPLICATIONS ON PLANE FRAMES
Dr. Structure has two interesting videos on application of the direct stiffness method on two types of framed structures.
(a) Analysis of a Tea House Frame
(b) Frame Analysis under Wind Load (Airplane Hangar)
MODULE 7- MASTAN2
Now that you have learned the use of DSM to various types of structures and applied the procedure using MS Excel, you can verify your results using a structural analysis software. You can use MASTAN2 - a free software!
MASTAN2 is an interactive structural analysis program that provides preprocessing, analysis, and post processing capabilities that can be adopted in the course. MASTAN2's linear and nonlinear analysis routines are based on the theoretical and numerical formulations presented in the textbook Matrix Structural Analysis, 2nd Edition, by McGuire, Gallagher, and Ziemian.
Download the software and tutorial at http://www.mastan2.com/
