INTRODUCTION TO STRUCTURAL ANALYSIS INTRODUCTION TO STRUCTURAL ANALYSIS USING COMPUTERSUSING COMPUTERS

Tamer B. SabrahTamer B. SabrahPh.D. Candidate - Civil Engineering Dept. Faculty of Engineering & Applied Science 1

Session 1: Introduction (ENG 6705)

SESSION 1 OUTLINE

1. Structural Analysis Using Computers2. Brief on Finite Element Method

3. Introduction to S-Frame 4. Overview of Modeling Environment 5. Example: 2D Model Continuous Beam

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WHAT’S REQUIRED FROM STRUCTURAL ANALYSIS ?

Shear ForcesShear Forces

Normal ForcesNormal Forces

Bending MomentsBending Moments

RotationsRotations

DeflectionsDeflections

DisplacementsDisplacements

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•• Select MaterialSelect Material

•• Design Sections/membersDesign Sections/members……..•• Check stability/serviceabilityCheck stability/serviceability

TorsionTorsion

Statically DeterminateStatically Determinate Statically InStatically In--DeterminateDeterminate

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Q: After your graduation; assume Q: After your graduation; assume -- for some reason for some reason -- that that your boss ask you to work in a special project to reyour boss ask you to work in a special project to re--analyze, and reanalyze, and re--design the Eiffel Tower in Paris!design the Eiffel Tower in Paris!

•• How much time you will take to do that?! How much time you will take to do that?! What is the degree of indeterminacy?!What is the degree of indeterminacy?!

•• How much effort is needed to calculate How much effort is needed to calculate BMD, NFD, SFD, deflections, rotations, etc.?BMD, NFD, SFD, deflections, rotations, etc.?

•• Do you think that Do you think that EiffelEiffel did an efficient did an efficient analysis and design in the 19th century?analysis and design in the 19th century?

•• Assuming you Assuming you ““succeededsucceeded”” to do that and to do that and he told you that the loads on the tower will be he told you that the loads on the tower will be higher that he gave to you in the beginning?!! higher that he gave to you in the beginning?!! What you are going to do ?!!!!!!!!What you are going to do ?!!!!!!!!

STRUCTURAL ANALYSIS USING COMPUTERS?

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““ACCURATE ANALYSISACCURATE ANALYSIS””

SAVE TIMESAVE TIME

SAVE EFFORTSAVE EFFORT

CAN REANALYSIS ANY TIME AND FOR UNLIMITED NUMBERCAN REANALYSIS ANY TIME AND FOR UNLIMITED NUMBER

CAN DO MORE COMPLEX STRUCTURESCAN DO MORE COMPLEX STRUCTURES

CAN ANALYZE FOR INFINITE NUMBER OF LOADING CASES CAN ANALYZE FOR INFINITE NUMBER OF LOADING CASES AND COMBINATIONSAND COMBINATIONS

ANALYSIS CAN BE LINEAR, NONLINEAR, STATIC AND/OR ANALYSIS CAN BE LINEAR, NONLINEAR, STATIC AND/OR DYNAMIC.DYNAMIC.

Structural Analysis Using Computers (Theories)

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• Structural analysis using computers are

mainly based on so many theories. The most

popular is the Finite Element Method.

• The F.E. method is based on one of two

general approaches: force (flexibility) method,

and/or the displacement (stiffness) method.

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Structural Analysis Using Computers(History)

• The F.E. method has become a practical one for solving engineering problems only in the past 40 years (parallel to the development of modern high speed computers).

• The modern development of the F.E. method began in the 1940s in the field of structural engineering by Hrennikoff (1941), McHenry

(1943), and R. Courant (1943), and then followed by so many others.

• The F.E. method is a numerical method for solving problems of engineering and mathematical physics.

• Simply, the F.E. method is based on dividing the structures into smaller elements (pieces/ elements) and solve for each element individually. Then, assemble the solutions together for the whole structures.

• The F.E. analysis utilize matrices calculations. And it’s based on the laws of equilibrium, strain compatibility and idealization of the materials stress-strain relations. 8

WhatWhat’’s F.E. Method?s F.E. Method?

Computer Programs

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• There are so many programs in the market, such as SAP, SAFE, ALGOR, COSMOS, STAAD, S-FRAME, STARDYNE, and other general-purpose programs such as ANSYS, ABAQUS.

• The selection of the software will depend on the resources, structure type, complexity, computer capacity,etc.

THE GENERAL MAIN STEPS IN ANY THE GENERAL MAIN STEPS IN ANY COMPUTER ANALYSIS SOFTWARECOMPUTER ANALYSIS SOFTWARE

1.Building model geometry (member geometry, nodes, meshing, …etc).

2.Define supports (constraints/restraints..)3.Defining member properties, sections.4.Assigning loads (load cases, combinations..)5.Defining analysis type, printouts in the out-put

results.6.Defining design requirements.7.Plotting of deformed geometry/ stresses…etc.8.Check and view results 10

1 2 3 4

1. DiscretizationDivide the structure into number of nodes and elements (truss/beam elements, shell elements, solid elements).

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1 2 3

1

2 4

5

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2

3

4

• Nodes should be defined at supports locations, concentrated loads, any discontinuity in loads, sections.

• Beam elements are connecting between nodes (numbers > one)

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BASIC TECHNICAL POINTSBASIC TECHNICAL POINTS

2 3 4

2. CoordinatesGlobal Coordinate System

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1 2 3

1

2 3

4

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2

3

4

• Each Node should has unique

certain coordinates related to the

global coordinate system (x, y, z)

• Also, loads should be defined

relative to the coordinate system.

X

Y

Z

1

(0,0,0) (5,0,0)

(0,6,0)(5,6,0)

(0,0,0) (5,0,0) (12,0,0)(18,0,0)

BASIC TECHNICAL POINTSBASIC TECHNICAL POINTS

SS--FRAMEFRAME

An interactive structural analysis programAn interactive structural analysis program

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Session 1: S -Frame

www.sframe.com

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Structural Office Programs

Advanced structural analysis with integrated RC and steelwork design.

P-Frame 2D structural analysis

S-Frame 3D structural analysis

S-Steel: Steel design

B-Sect: Concrete beam section design

C-Sect t : Concrete column section design

W-Sect t: Concrete wall section design

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Overview of Modeling Procedure

1. General Modeling Environmental Settings

Open Structure Dialog

Project Description Dialog

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Click Input Units …

Make the settings require and then click OK to return to the Project Description Dialog.

Similarly, the Result Units.

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Model Generation Options Dialog

You use this dialog

to tell the S-Frame

whether you want to

create a blank

model, or use

various wizards to

create generic model

types.

Select and then click

OK.

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S-Frame WindowsIf you cascade the windows your screen should look like this

GeometryGeometryLoadsLoadsGraphical ResultsGraphical Results

Numerical ResultsNumerical Results

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Geometry Window

Aerial Window

Status Line

Views and Grids ToolbarData Bar

Geometry Tools toolbox

Edit toolbar

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S-Frame Example 1ANALYSIS OF CONTINUOUS BEAM

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5 m 6 m 4 m

1.5 kN/m3.0 kN/m

6.0 kN/m

(0,0) (5,0) (11,0) (15,0)

There are so many ways to build the geometry of this beam, one of them is to create the joints (nodes) first and then connect in between.

Joint tool

1. Enter the nodes (node by node) according to their coordinates

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Data Bar

2. Now, we have created the four main nodes defining the supports of the beam.

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3. If you want to see the nodes numbers

Click on View/Geometric Labels.

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Here you go !Here you go !

4. Connect in between joints by members (beam elements).

Click on the Member definition tool then you can use the mouse (double click) on each joint and then connect it to the next.

Or use the data bar (and enter the joints numbers)

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X

Y

ZHinged ( pinned )

Fixed in X-dir.

Fixed in Y-dir. Fixed in Y-dir.

DEGREES OF FREEDOM (2D)DEGREES OF FREEDOM (2D)

Fixed in Y-dir.

Fixed in X-dir.

Fixed from rotation about Z-dir.

Roller

Fixed

BASIC TECHNICAL POINTSBASIC TECHNICAL POINTS

D.o.F. = 1

D.o.F. = 0

D.o.F. = 2

5. Assign the restraints (supports)Click on the Support Tool.Degrees of freedom ( 1= free , 0 = fix)for example: 0,1,1 = restrained only in the x-direction.0,0,1 = restrained in x- and y-directions

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Change the Degrees of freedom according to the support type, and then double click on the joints.

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6. Select sections dimension

Click on Section Properties Tool

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Data Base:

Steel Section Properties

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Custom Sections

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Note: If you created only one section it will be defined to all members.

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• Assigning Loads– Change to the LOADS window

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Define Load Case (dead load for example)

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• Assigning Loads– Assign uniform load in the Y-global. (-ve direction of Y)

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• S-Frame Finite Element Solver Window

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• In the Graphical Results Window:– Ex.: Bending Moment Diagrams

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• In the Graphical Results Window:– Ex.: Shear Forces Diagrams

Support ReactionsSupport Reactions

Questions ?Questions ?

Thank you...Thank you...

This presentation can be downloaded from the following link :www.engr.mun.ca/~sabrah/

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SS--FRAMEFRAME

An interactive structural analysis programAn interactive structural analysis program

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Session 2: Introduction to S -Frame

Tamer B. SabrahTamer B. SabrahPh.D. Candidate - Civil Engineering Dept. Faculty of Engineering & Applied Science

SESSION 2 OUTLINE

1. Revise some concepts from session 12. Concept of discretization (meshing) 3. Example 2: 2D Frame Analysis

- Exercise (2-3 mins).- Review geometry modeling.- Assigning loads.- View Results

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1. Review of Some Concepts1. Review of Some Concepts

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Structural Analysis Using Computers (Theories)

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• Structural analysis using computers are

mainly based on so many theories. The most

popular is the Finite Element Method.

Force (Flexibility) method Displacement (Stiffness) method

Finite Element Method

Laws of Equilibrium

Laws of Strain Computability

Relations define the stress-strain response of the materials

MATRICES MATHEMATICS

THE GENERAL MAIN STEPS IN ANY THE GENERAL MAIN STEPS IN ANY COMPUTER ANALYSIS SOFTWARECOMPUTER ANALYSIS SOFTWARE

1.Building model geometry (member geometry, nodes, meshing, …etc).

2.Define supports (constraints/restraints..)3.Defining member properties, sections.4.Assigning loads (load cases, combinations..)5.Defining analysis type, printouts in the out-put

results.6.Defining design requirements.7.Plotting of deformed geometry/ stresses…etc.8.Check and view results 46

2 3 4

2. CoordinatesCoordinatesGlobal Coordinate System

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1 2 3

1

2 3

4

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2

3

4

• Each Node should has unique

certain coordinates related to the

global coordinate system (x, y, z)

• Also, loads should be defined

relative to the coordinate system.

X

Y

Z

1

(0,0,0) (5,0,0)

(0,6,0)(5,6,0)

(0,0,0) (5,0,0) (12,0,0)(18,0,0)

BASIC TECHNICAL POINTSBASIC TECHNICAL POINTS

X

Y

ZHinged ( pinned )

Fixed in X-dir.

Fixed in Y-dir. Fixed in Y-dir.

3. DEGREES OF FREEDOM (2D)3. DEGREES OF FREEDOM (2D)In the 2D plane we have 3 D.o.F. in totalIn the 2D plane we have 3 D.o.F. in total

Fixed in Y-dir.

Fixed in X-dir.

Fixed from rotation about Z-dir.

Roller

Fixed

D.o.F. = 1

D.o.F. = 0

D.o.F. = 2

BASIC TECHNICAL POINTSBASIC TECHNICAL POINTS

2. Concept of Discretization 2. Concept of Discretization (Meshing)(Meshing)

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1 2 3 4

1. DiscretizationDiscretizationDivide the structure into number of nodes and elements (truss/beam elements, shell elements, solid elements).

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1 2 3

1

2 4

5

51

2

3

4

• Nodes should be defined at supports’ locations, concentrated loads, any discontinuity in loads, sections.

• Beam elements are connecting between nodes (numbers > one)

33

BASIC TECHNICAL POINTSBASIC TECHNICAL POINTS

• Each Node should has unique certain coordinates related to the global coordinate system (x, y, z).

• For instances, nodes are required at locations of:

1. Concentrated loads.

2. Discontinuity in loads.

3. Abrupt changes in sections geometry.

4. Abrupt changes in materials properties.

5. Other natural subdivisions at corners.

• The software calculates the displacements ONLY at the nodes. This means that without enough number of nodes, we will not be able to get the deflection values.

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MESHING CONCEPTMESHING CONCEPT

• In any structure it should be divided into nodes (loosely speaking: main nodes/mesh nodes!)

• At each node there are certain numbers of degrees of freedom. As the number of nodes within the structure increases, the number of degrees of freedom increases. This enhances the accuracy of the solution.

• A computer facilitates the solution for large number of degrees-of-freedom. However, as the number of nodes becomes very large, the model will become slow for being solved in a reasonable time.

• So, optimizing the meshing step needs to be wisely done.

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MESHING CONCEPTMESHING CONCEPT

Number of elements

Dis

plac

emen

t

Exact solution

Compatible displacement formulation

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So, Reasonable Number of Nodes and Elements

are Required

S-Frame Example 1 (From Session 1)ANALYSIS OF CONTINUOUS BEAM

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5 m 6 m 4 m

1.5 kN/m3.0 kN/m

6.0 kN/m

(0,0) (5,0) (11,0) (15,0)

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S-Frame Subdividing Option

The average beam spans varied from 4 m to 6 m

so, dividing each span into 10 elements is reasonable.

The element length is ~ 0.50 m.

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Deformed Shape After Meshing

Deformed Shape Before Meshing

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Note that we have now more numbers of sections the shear calculated on.

so, dividing each span into finite elements give us the opportunity to have more accurate results.

2. Example 2: 2. Example 2: 2D Frame Analysis2D Frame Analysis

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5 m

8 m 8 m

7 m5 m 6 m

4 m3 m 3 m

3 kN/m1 kN/m

5 kN/m4 kN/m

4 m

4 m

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1 m 3 m

10 kN

EXERCISEEXERCISE : DEFINE THE REQUIRED MAIN NODES FOR THIS FRAME USING THE PRINCIPLES OF DISCRETIZATION (MESHING)

1 m

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Review of Modeling Procedure

General Modeling Environmental Settings

Open Structure Dialog

Project Description Dialog

62

Click Input Units …

Make the settings require and then click OK to return to the Project Description Dialog.

Similarly, the Result Units.

63

Model Generation Options Dialog

You use this dialog

to tell the S-Frame

whether you want to

create a blank

model, or use

various wizards to

create generic model

types.

Select and then click

OK.

64

Geometry Window

Aerial Window

Status Line

Views and Grids ToolbarData Bar

Geometry Tools toolbox

Edit toolbar

65

There are so many ways to build the geometry of this beam, one of them is to create the joints (nodes) first and then connect in between.

1. Enter the nodes (node by node) according to their coordinates.

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2. There is an option in the S-Frame called (Grids). You create a grid

and define nodes at the intersections of this grid, and then connect in

between.

3. Draw the frame in AutoCAD. Save the file as ( . DXF) file type.

From inside the S-Frame Import that file.

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Using whatever option, we can create the main elements as shown below.

While, activating the Member Definition Tool, double click on the member. The left menu will open. Divide the member at mid point.

And at % distance.

Here, we only defined the required essential nodes

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DEFINE THE INTERMEDIATE HINGEDEFINE THE INTERMEDIATE HINGE

Using Release tool , we can create the intermediate hinge at the end of the member

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DEFINE THE SUPPORTSDEFINE THE SUPPORTS

Click on Section Properties Tool

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DEFINE THE SECTIONSDEFINE THE SECTIONS

Custom Sections

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Note: If you created only one section it will be defined to all members.

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• Assigning Loads– Change to the LOADS window

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DEFINE THE LOADSDEFINE THE LOADS

Define Load Cases (Dead load and Live Load)Define Load Cases (Dead load and Live Load)

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DEFINE THE LOAD COMBINATIONSDEFINE THE LOAD COMBINATIONS

Assume we have a load combination

1.25 X D.L. + 1.4 X L.L

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DEFINE THE UNIFORM LOAD AT THE MID SPANDEFINE THE UNIFORM LOAD AT THE MID SPAN

Refer to Session 1

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Refer to Session 1

DEFINE THE UNIFORM LOAD AT THE MID SPANDEFINE THE UNIFORM LOAD AT THE MID SPAN

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DEFINE THE TRAPEZOID LOAD AT THE FIRST SPANDEFINE THE TRAPEZOID LOAD AT THE FIRST SPANPart 1: Triangular load

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Part 2: Uniform load

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Part 3: Triangular load

Typically we can define the triangular load at the end spanTypically we can define the triangular load at the end span

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DEFINE THE CONCENTRATED LOAD ON THE COLUMNDEFINE THE CONCENTRATED LOAD ON THE COLUMN

Note this load is the L.L.

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SELECT THE ANALYSIS TYPESELECT THE ANALYSIS TYPE

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• S-Frame Finite Element Solver Window

• In the Graphical Results Window: Dead Load

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Dead Load

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• In the Graphical Results Window:

Ultimate Load

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• In the Graphical Results Window:

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NUMERICAL RESULTS MENU

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• Displacements

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• Reactions

Any Questions ?Any Questions ?

Thank you...Thank you...

This presentation can be downloaded from the following link :www.engr.mun.ca/~sabrah/

91