Lectures on Advanced Structural Analysis I

Following are course content on Advanced Structural Analysis I

Course Intructor: Prof. Dr. Shahzad Rahman

Course Outline


Lecture 1: Overview of Bernoulli-Euler Beam Theory, Theory of Torsion, Static Indeterminancy, Kinematic Indeterminancy

Lecture 2: Slope-Deflection Method

Lecture 3: Virtual Work Principles

Lecture 4: Moment Distribution Method

Lecture 5: Modifications in Moment Distribution Method

Lecture 6: Moment Distribution Method – Frame with Side Sway

Lecture 7: Compatibility Method of Analysis

Lecture 8: Matrix Analysis of Structures

Lecture 9: Matrix Analysis / Stiffness Method

Lecture 10: Matrix Analysis / Stiffness Method Contd.

Lecture 11: Matrix Analysis / Stiffness Method – Static Condensation

Lecture 12: Approximate Analysis

Lecture 13: Matrix Analysis – Member Releases


Introduction to SAP2000


Assignment 1: Slope and Deflection of Beam

Assignment 2: Displacements in Truss

Assignment 3: Solving Beam using Moment Distribution Method

Solution of Assignments


Mid Term Exam Paper

Solution of Mid Term Paper

Final Term Exam Paper and Solution

Lectures on Introduction to Bridge Engineering

Following is the course content for Introduction to Bridge Engineering

Course Intructor: Prof. Dr. Shahzad Rahman

Course Outline

Introductionary Videos on Bridge

  1. Anchor Block
  2. Brooklyn Bridge
  3. Golden Gate Bridge
  4. History of Bridge Engineering
  5. Introduction to Bridge Engineering
  6. Stone Arch Action
  7. Tacoma Narrow Bridge
  8. Truss Action


Lecture 1: Historical Overview and Introduction

Lecture 1A: Planning of Bridges

Lecture 1A Updated

Lecture 2: Loads, Design Procedures, ASD and LRFD Philosophy

Lecture 2 Updated

Lecture 3: Grillage Method of Superstructure Analysis

Lecture 3 Updated

Lecture 4: Concrete Bridges

Lecture 4B: Concrete Deck Example

Lecture 5: Prestressed Girder Bridge

Lecture 6: Abutments

Lecture 7: Abutments Contd.

Lecture 8: Bearings

Lecture 9A: SAP2000 Bridge Lab Exercise video

Lecture 9B: SAP2000 Bridge pdf files

Lecture 9C: Camtesia player for lab exercise videos

Lecture 9: Bridge Engineering Spreadsheets

The official videos of bridge modeler can be downloaded from SAP2000 Official Videos.


Assignment 3: Slab-Girder Bridge


Mid Term Exam Paper

Final Term Exam Paper

Lectures on Introduction to Finite Element Analysis

Following are course content for Introduction to Finite Element Analysis –  FEA.

Course Intructor: Prof. Dr. Shahzad Rahman

Introduction to FEA

Very Informative lectures on FEA are also available on Youtube.


Course Outline

Lecture 1: Overview of Finite Element Method – FEM, Historical Background and its Application

Lecture 2: Method of Weighted Residual, Least Square, Collocation, and Galerkin

Lecture 3: General derivation of Finite Element Equilibrium Equations

Lecture 4: Development of Stiffness Matrix for a Beam Element

Lecture 5: Some rules governing relationship between Global and Local Coordinates

Lecture 6: Comments on Numerical Integration

Lecture 7: Error and Convergence in FEM


Assignment 1: Bar Element Problem

Assignment 2: Beam Problem

Assignment 3: Thick walled cylinder Problem

Solution of Assignments

Note: Solution of Assignment 1 is in Lecture 2. There is excellent solution of axial bar problem using FE and comparing with Exact Solution plot along with matlab code in here.

Solution of Assignment 2

Solution of Assignment 3


Midterm Exam Paper

Final Term Paper

Solver based on Direct Stiffness Method

DSM-SOLVER is based on Direct Stiffness Method.  Direct Stiffness Method is implementation of Finite Element Method. It is available in two flavors. One is octave/matlab while other is scilab script and distributed under GNU/GPL v2.0 license.

GNU Octave is free clone of matlab. It is fully compatible with matlab.

Scilab is an open source, cross-platform numerical computational package and a high-level, numerically oriented programming language. Scilab is alternative to matlab.

You can download the source-code of DSM-OCTAVE-SOLVER or  DSM-SCILAB-SOLVER. To understand how this script works,  read the document provided along with the source files. Consider the following example:

scilab dsm example
Example Problem

The above example can be solved in one of the two scripts explained as under:

For Octave/Matlab example, first define some input variables as:


To run the program, you need to update the directory to src folder, then, write following:

Note that truss2d has same code as that of frame 2d. You can get pretty accurate result for trusses by considering it as frame.


For SCILAB example, the input matrices and command for making var01.bin as provided in the preproc.sce file are:

To run the program, you need to update the directory to src folder, then, write following: