The Direct Stiffness Method For Linear Static Analysis

Go from beginner to pro in using The Direct Stiffness method for linear static analysis of structural systems.

What you'll learn

Stiffness Matrix for 2D Truss

Stiffness Matrix for 2D Frames

Stiffness Matrix for 3D Truss

Deflection Calculation using Stiffness Matrices

Support reaction calculation using stiffness matrices

Truss member force calculation using stiffness matrices

What can be calculated by hand using the direct stiffness method

Where and how the direct stiffness method can be used easily without the help of Computer Programing

Requirements

Basic knowledge of Matrices

Basic Structural Analysis concepts like Equation of statics, Support types and reactions, load patterns.

Description

The only course you will need to learn the direct stiffness method for Beam, 2D Frame, 2D Truss, and 3D Truss linear static analysis.This course aims to introduce and push your understanding further to the direct stiffness method for linear static analysis so that you are ready to go to the next step, which is making your own computer programs to do structural analysis. The course also shows you when and how you can do complex analysis in just a few minutes instead of hours without the help of software and/or programs using hand calculations.In this course, you will learn about these techniques and how and when you can bypass some of the common use and rules to do quick hand calculation checks or to do the entire thing by hand without having to write a piece of computer code.Understanding how structures behave and analyzing complex structures is crucial for competent engineers. This requires knowledge of structural analysis theory and hand-analysis techniques, which form the foundation for intuitive understanding.However, most engineers now rely on structural analysis software for large-scale analyses due to its speed and efficiency. Modern software commonly uses matrix analysis methods like the direct stiffness method to facilitate faster and more complex analyses.the course is divided into 5 sections where you will learn: 3D Truss analysis by hand without any software or programing languageThe essential formulation behind the direct stiffness method.The sign conventions used in the direct stiffness method and even the Finite Element Method.Structural analysis methods and the direct stiffness method.The key stiffness formula for Finite Element Analysis.Formulation of the local and global stiffness matrix of 2D Truss.Transformation of the stiffness matrix Formulation of the local and global stiffness matrix of 2D Frame.Formulation of stiffness matrix using equilibrium of joints.Observation of structures for a quick analysis using the very long procedure of the FEA without the need for computer programs or software packages.This course will prepare you for the next courses where you will learn the direct stiffness method for non-linear static analysis.and use of computer programing languages such as Python in the field of Civil Engineering. The course also has Example and practice problems to make you understand all the concepts to the fullest and also to challenge yourself.

Overview

Section 1: Introduction

Lecture 1 Introduction to the Course

Lecture 2 Introduction

Section 2: Essential Formulations and sign conventions for the course

Lecture 3 Stiffness

Lecture 4 Joint Displacement & Forces

Section 3: 2D Truss

Lecture 5 Stiffness MATRIX for Truss Members in the Local Axis System

Lecture 6 Transformation of Stiffness Matrix from Local to Global Axis

Lecture 7 Transformation of Stiffness Matrix from Local to Global Axis Part-2

Lecture 8 Using Global Matrix to get local stiffness matrix

Lecture 9 Assembly of Stiffness Matrix and Load Vector of a 2D Truss (P-1)

Lecture 10 Assembly of Stiffness Matrix and Load Vector of a 2D Truss (P-2)

Lecture 11 Stiffness Formulation using Equilibrium of Joints

Lecture 12 Zero Force Members a Short Note

Lecture 13 Practice Problem

Lecture 14 What can easily be done by hand

Section 4: 2D Frame

Lecture 15 Stiffness Matrix for 2D Frame

Lecture 16 Transformation of Stiffness Matrix from local to global

Lecture 17 Example Problem

Lecture 18 Example problem neglecting axial deformation

Lecture 19 Practice Problem Using Matrix

Lecture 20 Practice Problem 2

Lecture 21 Understanding Joint load vector use

Lecture 22 Equation method for 2D Frame

Lecture 23 Equation method Practice problem 1

Lecture 24 Equation method Practice Problem 2

Section 5: 3D Truss

Lecture 25 3D Truss Zero Force Members

Lecture 26 Stiffness Matrix for 3D Truss P-1

Lecture 27 Stiffness Matrix for 3D Truss P-2

Lecture 28 Determining the length of a member in 3D Space

Lecture 29 Example Problem-Zero Force Members

Lecture 30 Example problem-Determining K for a single member

Lecture 31 Example Problem- Formulating Matrix

Section 6: Bonus

Lecture 32 Bonus

Civil Engineers,Engineering Students,students and Civil Engineering professionals who've studied the Direct Stiffness Method but got lost along the way