introduction - university of nebraska–lincoln. introduction.pdf · advanced structural analysis...

Advanced Structural Analysis

Introduction Notes prepared by: R.L. Wood of 15

Introduction

Lesson Objectives:

1) Outline what this course will entail.

2) Describe how matrix methods relate to structural analysis.

3) Identify classical methods that are utilized within the matrix analysis technique:

a. Slope Deflection Method

b. Moment Distribution Method

4) Classify various types of structures that will be examined and recognize their modeling

techniques.

Background Reading:

1) Read ___________________________________________________________________

Course Objectives:

1) In this course, what is the simple objective?

a. Expand on the knowledge introduced in CIVE 341 (or similar).

2) This includes the follow precursor methods to matrix analysis of:

a. __________________________________________________________________

b. __________________________________________________________________

c. __________________________________________________________________

d. __________________________________________________________________

__________________________________________________________________

3) In this course, let’s start with a review of:

a. Moment Area and Slope Deflection

b. Moment Distribution

c. Matrix Math or Linear Algebra



Why Focus on Matrix Methods:

1) Matrix mathematical based methods are the core method used within ________________

____________________________________________.

2) Due to the advancement in computer hardware and efficiency, the potential for ________

___________________________________ exist.

a. Generally, are very user friendly.

b. Programs with a graphical user interface allows nearly

_______________________________________________.

3) Examples of analysis software include:

a. __________________________________________________________________

b. __________________________________________________________________

c. __________________________________________________________________

d. __________________________________________________________________

e. __________________________________________________________________

f. __________________________________________________________________

Importance to Understanding the Formulation of Structural Analysis:

1) Does one need to learn the formulation behind the structural analysis process? _________

a. Read and review two handouts online.

2) It is critical to understand the ____________________________ behind the solution.

3) Examples:

a. What is a ______________________________________________? And how is

this formed?

b. Local versus global coordinate systems.

c. Matrix ___________________________________________________________.

d. Matrix condensation/substructuring which assists greatly in both _____________

and ________________________________.

4) A computer is only as _______________________________.



Matrix Structural Analysis Overview:

1) As stated previously, matrix analysis is an extension of the previous course: CIVE 341.

2) Basically to elaborate on the formulation of structural analysis:

a. What is a general definition of structural analysis? _______________________

__________________________________________________________________

b. Focus here for the matrix techniques is placed on the analysis of ______________

_____________________________________, which are comprised of ________

______________________________________.

3) Let’s reiterate once again, if computers are able to perform structural analysis why should

one learn the methods:

a. Computers will only perform the analysis that is based on ___________________

__________________________.

i. What does that include? ________________________________________

b. Understand the significance of the computer ______________________________

i. Analysis is _______________________?

ii. Does is make _____________________?

Matrix Analysis History:

1) The classical methods where introduced before the introduction of computers. These

include:

a. 1864 – Maxwell – Method of Consistent Deformations _____________________.

b. 1873 – Green – Moment Area Theorems/Method _________________________.

c. 1915 – Maney – Slope Deflection Method _______________________________.

d. 1932 – Cross – Moment Distribution Method ____________________________.

2) Then in the 1940’s computers were introduced. The timeline for more sophisticated

methods include:

a. 1947 – Levy – Matrix Flexibility Approach

b. 1954 – Lindsey – Matrix Stiffness Method.

c. 1956 – Direct Stiffness Method: _______________________________________.

i. Which also includes __________________________________________.



d. Mid 1950’s until today – further advancement and computation in matrix/finite

element approaches.

e.

Classical Versus Matrix Methods:

1) Classical methods typically include:

a. Method of Consistent Deformations

b. Moment Area Method

c. Slope-Deflection Method

d. Moment Distribution Method

2) Classic methods are typically designed to examine specific structures.

a. As a result, certain ____________________________ are made to perform the

analyses.

b. For example: ignore ________________________________________________.

c. Simply by neglecting _______________________________________________.

3) Matrix methods on the other hand are developed for an ___________________________

approach.

a. Methods are typically _________________________________ allowing for

programming ease.

b. General in nature, therefore can be referred to as __________________________.

i. Applicable to ________________________________________________.

4) Are classical methods still needed? ________________

a. Why?

i. Understand _________________________________________________.

ii. Quick ______________________________________________________.

iii. Approximate ________________________________________________.



Matrix Methods vs Finite Element:

1) Finite Element Method (FEM) is an extension of matrix.

a. The ability exists to examine more than just _____________________________,

such as ______________________ and ______________________.

2) Matrix methods are generally developed in the following way:

a. Exact solution from ____________________________________________ are

used to obtain the member force-displacement relationships.

3) Finite element methods, on the other hand, still utilize force-displacement relationships

that are derived from assumed _______________________________________________

using __________________________________________________________________.

Matrix Approaches:

1) Matrix approaches can be developed into two classifications:

a. ___________________________________________

b. ___________________________________________

2) Which of these methods is predominately taught?

a. ____________________________ as it is most applicable to computer programs.

Matrix Approaches - Flexibility Method:

1) The flexibility method is also known as force/compatability approach.

2) This is a generalization of the method of _______________________________________

_________________________________________________________ in a matrix form.

3) In this approach, the primary unknowns are ____________________________________.

4) The structure is solved using ________________________________________________

to find the ____________________________________.

5) Once the redundants are known, use _____________________ and force-displacement

relationships to compute the ________________.



Matrix Approaches - Stiffness Method:

1) The stiffness method is also known as displacement/equilibrium approach.

2) This originated from the ___________________________________________________.

3) In this approach, the primary unknowns are ____________________________________

for the Direct Stiffness Method.

4) The structure is solved using ________________________________________________

to find the ____________________________________.

5) Once the deformatinos are known, use _________________________ and force-

displacement relationships to find the _________________________________________.

Types of Framed Structures:

1) In this course, the focus is on “framed structures” (straight members).

2) All “framed” members are long, straight members.

3) Six general types of framed structures exist:

a. _______________________________________________

b. _______________________________________________

c. _______________________________________________

d. _______________________________________________

e. _______________________________________________

f. _______________________________________________

4) These will be explained and illustrated in the PowerPoint.



Structural Idealization/Discretization and Modeling Techniques:

1) Simplifications within structural analysis of a complicated structure is done by ________

___________________________________________ that have a negligible effect on the

_______________________________________________________________________.

2) In such an approach, it is critical to represent the possible characteristics of interest as __

__________________________________________________________.

a. Thereby creating an analytical model.

3) How does one create an effective ____________________________________________?

a. Rely on experience and background to understand the:

i. ____________________________________________________________

ii. ____________________________________________________________

iii. ____________________________________________________________

4) Within matrix analysis, the structure is modeled as an assembly of straight members (also

known as ______________________________) that are connected to joints (also known

as _________________).

5) Within the matrix analysis and finite element method (FEM), two components exist:

a. _______________________________________________________: portion of

the structure for which the force-displacement relationships are valid.

b. _______________________________________________: component of

__________________________________________ size to which the member

ends are connected.

6) What are the supports?

a. _______________________________________________________ the structure.

i. Fixed - _____________________________________

ii. Pinned - _____________________________________

iii. Roller - _____________________________________

7) How is the model constructed?

a. Most computer programs represent the models using line diagrams or also known

as a __________________________________.

b. Members are represented by lines through the ____________________________.



i. As a result, there are no dimensions or sizes associated with the

______________________, other than the length.

8) Nomenclature:

a. Joints are illustrated as:

i. Rigid with a point, such as:

ii. Hinged or released with a circle, such as:

b. Components are labeled as

i. Members with the number in a ______________________:

ii. Nodes with numbers in a ___________________________:

c. Support conditions and applied loads are applied to the diagram. Examples

include:

i. Truss structure:



ii. Frame structure:

Review of Fundamental Relationships:

1) Equilibrium: _____________________________________________________________

2) Compatibility: ___________________________________________________________

3) Constitutive: _____________________________________________________________

Equilibrium:

1) A structure is in equilibrium if when initially at rest, it stays at rest when subjected to a

system of __________________________________________.

2) Equations in two-dimensions include:

3) Equations in three-dimensions include:



Compatibility:

1) Relates the deformation of structures such that the components (____________________,

____________________ and _____________________________) fit together without

_____________ or _____________________.

2) This ensures that the deformed shape is _________________________ (exception when

a _________________________ is present) and consistent with support conditions.

3) Compatibility equations are used to relate _____________________________________

________________________ to __________________________________________ or

______________________________________________________.

a. It is critical such that the member end displacements are equal to the

_________________________________________ as connected.

Constitutive Relationships:

1) Also known as _______________________________________ or force-displacement

relationships.

a. Recall that equilibrium relates to forces (and moments), while compatibility

relates to deformation/displacement

2) For framed structures, _____________________________________________________

___________________________________ are used to estimate the forces and

deformations at member ends.

a. Then member force-displacement relationships are then used to provide the

structural force-displacement relationship; where the link of equilibrium and

compatibility is applied to the structure.



Computer Programs Available for Matrix/Finite Element Analysis:

1) A number of programs are available to perform these desired analysis where various

levels of sophistication are possible.

a. Two-dimensional frames up to ___________________________________

2) Common to these programs is the architecture:

a. Preprocessor: ______________________________________________________

_________________________________________________________________.

b. Analysis Engine: ___________________________________________________.

c. Postprocessor: _____________________________________________________.

3) All of these programs utilize matrix operations/mathematics to formulate a solution.

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