Paper ID #16445

Enhancement of a Finite Element Analysis Course for Structural Engineer-ing

Dr. Shahnam Navaee, Georgia Southern University

Dr. Navaee is currently a Full Professor in the Civil Engineering and Construction Management Depart-ment in the Allen E. Paulson College of Engineering and Information Technology at Georgia SouthernUniversity. Dr. Navaee received his B.S. and M.S. degrees in Civil Engineering from Louisiana StateUniversity in 1980 and 1983, and his Ph.D. degree from the Department of Civil Engineering at ClemsonUniversity in 1989.

Dr. Junsuk Kang, Georgia Southern University

Dr. Junsuk Kang earned his Ph.D. degree in Structural Engineering in the Department of Civil Engineer-ing at Auburn University, AL, USA in 2007. He obtained his master’s degree in Structural Engineeringfrom Korea University, South Korea, in 2000 and his Bachelor’s degree was in Civil and EnvironmentalEngineering from Korea University, South Korea, in 1998. Prior to entering PhD study, Dr. Kang workedas a Senior Civil Engineer in Hong Kong site and Seoul Headquarter of Hyundai Engineering and Con-struction Co., Ltd. during 2000- 2002. After his PhD study, he had taken many projects supported byALDOT and Air Force Research Laboratory as a research associate at Auburn University during 2007– 2011. Dr. Junsuk Kang has taught Structures courses in the Department of Civil Engineering andConstruction Management at Georgia Southern University as an assistant professor since 2012.

c©American Society for Engineering Education, 2016

Enhancement of a Finite Element Analysis

Course for Structural Engineering

Abstract

In this paper the enhancement of an introductory Finite Element course in the newly established

Civil Engineering and Construction Management Department at Georgia Southern University is

discussed. Typically in an Introductory Finite Element course offered in many engineering schools,

a simple less elaborate FE package is used to deliver the course concepts. In the newly developed

course discussed in the paper, a state-of-the-art commercial software package is planned to be

utilized to further enhance the marketability of the students upon graduation. Along with this choice

comes the challenge of developing suitable tutorials and examples to familiarize the students with

various important tools and special features of this sophisticate package in the minimum amount of

time possible. The submitted paper explores one possible strategy to accomplish this task. This

course is designed for exploring the civil engineering applications focusing specifically on analysis

of structural components, rather than solving problems related to other fields such as fluid mechanics

or heat transfer. The planned projects in the course explore strategies in analyzing a variety of

structural members such as trusses, beams, frames, as well as other solid continuums. The course is

expected to complement other structural engineering related courses delivered in the curriculum

such as Structural Analysis and Advanced Structural Analysis. Solutions of problems obtained in

this course using the FE package can be compared and contrasted against the results from other

classical methods discussed in these courses. Some of these methods include: Slope-Deflection

Method, Moment Distribution Method, and Matrix Stiffness Method. These comparisons further

enhance the knowledge of the students in area of structures and provide them with new perspectives.

Several prepared example problems for the course are included in the paper to further illustrate the

value of the project. Each of these examples is selected for a unique purpose, covering specific

topics, and illustrating important principles. Collection of the prepared course examples such as the

ones included in this paper will provide the students with the strong foundation in the areas of

analysis of structures, preparing them well for their future studies and for pursuing rewarding

professional careers.

I. Introduction

In this educational project instructional modules and examples are created for analyzing various

structural members using the Abaqus software, a well-known Finite Element Analysis (FEA)

package used in many research institutions and prestigious engineering schools in the United States

and around the world. Even though a number of electronic tutorial files accompany this

comprehensive software packages, these files in their presented format are not suited for direct

utilization in a course. In the current project, the investigator has prepared an easier and more

practical guide for students to be able to use this sophisticated simulation package. The instructional

modules and examples created in this project are developed to complement the CENG 5336

(Introduction to Finite Elements) course, a technical elective in the Civil Engineering program at

Georgia Southern University. This course that has never been taught previously in the CE program.

These modules provide an overview of some of the most powerful features of this package and aid

in introducing the users to various Abaqus special components and commands. Each example is

selected to demonstrate the utility of a particular feature of the software in accomplishing a new task,

a task which was not required in the previous examples. Developed tutorials essentially provide the

details related to performing the following listed activities using the order indicated.

(1) Creating a part

(2) Creating a material

(3) Defining and assigning section properties

(4) Assembling the model

(5) Creating an analysis step

(6) Requesting data output

(7) Applying boundary conditions

(8) Applying loads

(9) Meshing the model

(10) Creating an analysis job

(11) Checking the model

(l2) Running an analysis job

(13) Post processing.

Even though the analysis of any structural member using Abaqus mainly involves undertaking the

above listed tasks, the intricacies involved in each of these steps can significantly be different

depending on the special type of problem analyzed and the analysis method selected. Tutorial

examples developed in this project cover the analysis of structural members such as (1) trusses, (2)

beams, (3) frames, and (4) solid continuum elements. The project will continue so that other

examples can be developed for investigating more complicated problems such as those involving

non-linear structures and structures subjected to dynamic loads.

The following two factors can be perceived as possible drawbacks in utilization of this sophisticated

tool in a FE course; (a) the cost of the package, and (b) the steep learning curve associated with the

software. Each one of these issues has been addressed in the project. It should be noted that even

though the commercial cost for purchasing this package is relatively high, the Dassault Systems

offers substantially discounted educational licenses of the full version of the software for classroom

use. Additionally, the student version of Abaqus can be downloaded free of charge from the

Dassault Systems website. The free student version of the software is the essentially the full

commercial version, limited to handling models containing up to one thousand nodes. It is deemed

that this number of nodes is sufficient enough for the purpose of modeling a variety of structural

components in an introductory finite element course. The student can download this free version on

their personal computers and use it as they wish to master their expertise. The second possible

drawback associated with the steep learning curve of the software has been addressed by creating a

series of tutorials in the course as further discussed in more details in the remaining sections of the

paper.

In this course the students are instructed to construct and analyze a variety models for structures

such as trusses, beams, frames, and various other solid continuums. Some of these structures are

taken from well-known textbooks such as the one listed in the reference section of the paper1-8.

Several of these textbooks are currently adopted for use in the Civil Engineering program at the

authors’ institution.

The Finite Element solutions for several of the examples used in the course are provided in the paper

to better illustrate the scope of the project. In performing the special tasks needed for each selected

sample problem, a series of steps have to be followed in succession in order to yield the correct

solution. In most cases, these steps involve selection of various options in specific menus,

submenus, and dialog boxes of the software interface. Remembering and following these steps

without a having a properly prepared guide can be a difficult and confusing task. For the sample

problems such as the ones presented in this paper, a step-by-step guide is prepared to outline the

needed procedures. In preparing these guides, screenshots of various important stages of the

procedures are included to clearly outline the sequence of required steps. The prepared guides will

be of outmost importance in completing the assigned exercises. A sample four-page tutorial guide

developed for a frame example is included at the end of section IV in Figure 11. This guide outlines

the key steps and the specific procedures needed in analyzing the discussed frame.

Once the students are familiarized with the special features of this comprehensive software tool

using the provided tutorial examples, they are assigned to develop the solutions for other more

complicated problems using their newly acquired skills. Solving these new problems will provide an

excellent opportunity for students to test their understanding, gain further experience, and further

enhance their competencies in utilizing this tool. Utilization of Abaqus in this course in the manner

described will prepare the students for pursuing rewarding professional and academic careers.

II. Truss Analysis

The first type of structure the students are assigned to analyze in the course is a simple truss such as

the one presented in Figure 1. By completing this exercise the students learn how to perform the

thirteen essential operations involved in the finite element analysis of a part utilizing Abaqus. These

operations were listed in the previous section of the paper. The tools used for initiating each of the

thirteen tasks can be seen on the left hand-side of the screen shown in Figure 1. In addition to

experimenting with these tools, in this exercise the students specifically learn how to create various

cross sectional profiles and assign them to different truss members, and additionally learn how to

generate a tabular report of the computed results. In this problem, students are instructed to use a 2-

noded linear 2-D truss element (“T2D2 Element”) when meshing the model. A screenshot of the

report showing the computed values of the reaction forces at the roller and pin supports, nodal

displacements at the joints, as well as the axial stresses in the truss members is provided in Figure 2.

The student will have an opportunity to compare the values obtained from their FE analysis to the

results from other methods of analysis such as the Virtual Work Method or Castigliano’s Method.

The students were exposed to these methods in the Structural Analysis courses they have previously

taken.

III. Beam Analysis

The procedure for analyzing a beam utilizing Abaqus is next discussed in the course. One sample

exercise assigned to the students is presented in Figure 3. In this exercise, a statically indeterminate

continuous beam subjected to several loads is analyzed. In addition to providing the students with

additional expertise in modeling a structural member, the students are further instructed about the

techniques in Abaqus by which a variety of loads can be applied to the structures in various

combinations and load cases. In this problem, a 2-noded linear beam element in a plane (“B21

Element”) is used in modeling the beam. This exercise also outlines a method by which the

distribution of the internal reactions along the length of the beam can be plotted. One sample plot

showing the moment distribution for the beam is provided in Figure 4. Similar to the previous case,

the FE analysis results for this problem can be compared against the calculated values obtained using

other methods of analysis such as the Slope-Deflection Method or Moment Distribution Method.

IV. Frame Analysis

The third type of exercise included in the course involves the analysis of a frame utilizing Abaqus.

Two sample two-dimensional frame examples that could be assigned to the students are provided in

Figures 5 and 8. As stated previously, each assigned exercise in the course is selected to teach the

students about a new feature of the package, a feature that was not explored in the previous

exercises. For example, when analyzing the frame presented in Figure 5, students learn how to

apply an inclined distributed load and also place a roller support on an inclined surface. Each of

these specific operations requires following a set of steps. Moreover in this exercise, the students

learn how to cut a member to obtain the internal reactions at the cut surface. One sample cut has

been presented in Figure 6. In this exercise the students additionally become more familiarized with

specific techniques for preparing tabular reports. A sample report showing the computed values of

the support reactions as well as the displacements and rotations of the nodes on the frame has been

presented in Figure 7. These results are based on utilizing a “B21 Element” and correspond to the

case where E = 200 GPa and ν = 0.32. As stated in the Introduction section, a four-page tutorial

developed for the frame example shown in Figure 5, is included at the end of this section in Figure

11. This guide outlines the key steps and the specific procedures needed in analyzing the discussed

frame. As in the previous examples, the students can be asked to compare the results from their FE

analysis against the values obtained utilizing other classical methods of analysis discussed in the

Structural Analysis courses.

A sample three-dimensional multi-story frame such as the one presented in Figure 9 is also intended

to be used as an additional exercise to further enhance the students’ competencies in analyzing a full

range of structures . The specific cross sectional profiles of structural members can be inputted in

Abaqus utilizing dialog boxes such as the ones depicted in Figure 10. In addition to discovering

more about the analysis of three-dimensional structures, in this exercise the students also learn more

details related to displaying a variety of results such as the ones presented in Figure 9. Included in

Figure 9 is the deflected shape of the frame, along with the Von Mises stress contours produced in

the frame members. The results displayed in Figure 9 correspond to the case when a three-

dimensional 2-noded beam element (“B31 Element”) is used to mesh the part.

In the discussed course, the students further have the opportunity to verify the accuracy of their

results obtained using Abaqus to the output generated from other structural engineering software

packages such as SAP2000. Verification of these results will provide the students with additional

confidence in their ability to properly and effectively utilize Abaqus.

Figure 1. Determinate Truss Subjected to Concentrated Loads Applied at Joints

Figure 2. Report Tabulating the Reactions at the Truss Supports, Displacement at Joints, and

Axial Stress in Members

6 k

2 in2

3 in2 3 in2

2 in2

3 in2

4 ft

A

4 ft

6 k

4 ft

2 in2

C

B

Model Tree/Results Tree

providing all essential

tools needed for creating

and analyzing a part.

D E

A-36 Steel

E = 29,000 ksi, ν = 0.32

3 in2

Figure 3. Continuous Beam Subjected to a Concentrated and a Distributed Load

Figure 4. Sample Plot Showing the Distribution of the Moment along the Beam

A C B

12 k 2 k/ft

24 ft 4 ft 4 ft

A-36 Steel

E = 29,000 ksi, ν = 0.32

Figure 5. 2D Frame with an Inclined Roller Support Subjected to an Inclined Distributed Load

Figure 6. A free Body Diagram of the Cut Frame Showing the Resultant Internal Force and

Moment at the Cut Section

4 m 2 m

C A

B

50 kN/m

1.5 m

Computed internal resultant

force and moment at the

cut section.

Computed resultant

reaction at the pin

support.

A-36 Steel

E = 200 GPa, ν = 0.32

Figure 7. Generated Tabular Report Showing the Reaction Forces at the Frame Supports and the

Displacements and Rotations of Nodes

Figure 8. Example of a 2D Frame Containing Various Cross Section Profiles

6 k

650 in4

3 k/ft

800 in4

8 ft 8 ft 12 ft

A D

B

15 ft 200 in4 400 in4

E

C

A-36 Steel

E = 29,000 ksi, ν = 0.32

Figure 9. Sample 3D Frame Subjected to Four Distributed Loads

(a) (b)

Figure 10. Dialog box in Abaqus for Specifying the

Cross Sectional Profiles of Members

1 k/ft

2 k/ft

2 k/ft

20 ft 20 ft

20 ft

20 ft

W 8

x3

1

W 18x35

W 8

x3

1

W 18x35

1 k/ft

A-36 Steel

E = 29,000 ksi, ν = 0.32

Figure 11(a). Sample Tutorial Guide Prepared for the Frame_1 Exercise (Page 1 of 4)

CENG 5336 - Introduction to Finite Elements

ABAQUS Tutorial Guide: Frame_1 Exercise (Page 1 of 4)

In this tutorial a guide for obtaining the support reactions and displacement of the frame joints are outlined. The

modulus of elasticity and the Poisson’s Ratio of the frame members are respectively: E = 200 GPa and = 0.32.

Cross-Section Frame

Steps:

1. Create Model: In the Model Tree, double-click the Parts container to open the Create Part dialog box.

Name the part Frame_1 and for the Modeling Space, Type and Base Feature Shape, respectively use: 2D

Planar, Deformable, and Wire. For the Approximate size you can use 10. Click Continue. Sketch the frame

shown above as instructed in the previous tutorials. Click Done.

2. Create Material: In the Model Tree, double-click the Materials container and create a new material. In the

Edit Material dialog box, name the material Steel. Click on Mechanical > Elasticity> Elastic, and enter the

values of Young’s Modulus and Poisson’s Ratio indicated above. Click OK.

3. Create Profile: On the menu bar of the Materials module, select Profile > Create and further select the

Rectangular shape for the cross-section and click Continue. Enter the dimensions of the cross section as

specified above (a = 0.050 m, b = 0.250 m) in the Edit Profile dialog box and click OK.

4. Create Beam Section Orientation: On the menu bar of the Materials module, select Assign > Beam Section

Orientation and select the entire frame by drawing a box around it and click Done. Press the Enter key on the

keyboard to accept the default setting. Once this done, you will see the local axial & transverse coordinate axes

generated on each member of the frame. Click OK and Done. Note that this step is needed for applying the

inclined load on the frame at a later time.

5. Create a Section: In the Model Tree, double-click the Sections container to open the Create Section dialog

box. In this box, select both Beam and Beam options for the Category and Type. Click Continue and OK.

6. Assign the Section to the Frame: On the Model Tree, expand the branch for part named Frame_1 by first

clicking on the “+” symbol to expand the Parts container and subsequently clicking on the “+” symbol again to

expand Frame_1. Double-Click the Section Assignments, select the entire frame by drawing a box around it.

Subsequently, click Done and OK.

7. Define the Frame Assembly: In the Model Tree, expand the Assembly container and double-click the

Instances. In the Create Instances dialog box, select the Frame_1 and click OK.

250 mm

50 mm

Figure 11(b). Sample Tutorial Guide Prepared for the Frame_1 Exercise (Page 2 of 4)

CENG 5336 - Introduction to Finite Elements

ABAQUS Tutorial Guide: Frame_1 Exercise (Page 2 of 4)

8. Create an Analysis Step: In the Model Tree, double-click the Steps container. In the appeared Create Step

dialog box, enter a name for the Step. You can use Load Step as the step name. Subsequently in this box,

select Linear Perturbation as the Procedure type, and further select Static, Linear perturbation as the

specific option from the provided list. Click Continue and on the appeared Edit Step dialog box enter the

following description for the load Step: Inclined Load Applied on the Frame. Click OK to finalize this

step.

9. Request Data Output: In the Model Tree, right-click the mouse on the Field Output Requests container, and

select Manager from the appeared list to open the Field Output Requests Manager dialog box. In this box,

select the cell labeled “Created” if not already selected, and click the Edit button on the right side of the dialog

box. In the Edit Field Output Request box, you can view the list of variables that are selected by default to be

written to the output database (.odb file). This list can be modified as desired. In this exercise, in addition to

the variables already selected as defaults, we also toggle on the SF check box to also output the section forces

and moments (this task can be done by first expanding the Forces/Reactions and subsequently selecting the SF

option). By choosing this option, we will be able to shows the internal reactions graphically at any cut section

and also print these results in the tabular format. Click OK and Dismiss to finalize this step. Save your file at

this point. Remember that it is always a good idea to save your file periodically in the middle of the process to

be on the safe side.

10. Create Boundary Conditions: To assign a pin at point A (shown on the frame diagram), in the Model Tree,

double-click the BCs container to open the Create Boundary Condition dialog box. In this box, name the

boundary condition Pin, select Initial as the Step (from the drop down menu), choose Displacement/Rotation

option from the Types for Selected Step list, and click Continue. Next, in the viewport, select point A and

click Done. On the appeared Edit Boundary Condition dialog box, toggle on U1 and U2 check boxes to

constrain the translational motions in the global x and y directions. Click OK.

Procedure for Creating a Boundary Condition on an Inclined Member:

To place a roller at the inclined edge of the frame at pint B, perform the following steps:

(a) As outlined previously for the pin support, double-click the BCs container to open the Create

Boundary Condition dialog box. In this box, name the boundary condition Roller, select Initial as

the Step (from the drop down menu, if not already selected), choose Displacement/Rotation option

from the Types for Selected Step list, and click Continue. Next, in the viewport, select point B

(shown on the frame diagram) and click Done.

(b) On the appeared Edit Boundary Condition dialog box, click the Create Datum CSYS icon and

on the appeared Create Datum CSYS dialog box, accept the default name of Datum csys-2, and

select Rectangular as the Coordinates System Type. Click Continue.

(c) Click successively on points C and B (located on the inclined member of the frame) to respectively

define an origin and a point on the positive x-axis. This is needed to define a rotated local coordinate

system. Click the button in the Prompt area at the bottom of the Viewport to finalize

this procedure. On the appeared Create Datum CSYS, click Cancel since we do not want to create

another new Datum csys (Datum csys-3).

(d) On the appeared Edit Boundary Condition dialog box, click the Edit icon , click on the

button in the Prompt area at the bottom right-hand side of the Viewport, select Datum

csys-2 from the Datum CSYS List dialog box, and click OK.

Figure 11(c). Sample Tutorial Guide Prepared for the Frame_1 Exercise (Page 3 of 4)

CENG 5336 - Introduction to Finite Elements

ABAQUS Tutorial Guide: Frame_1 Exercise (Page 3 of 4)

(e) In the Edit Boundary Condition Dialog Box, toggle on the U2 check box to constrain the motion in

the direction perpendicular to the inclined member of the frame. Click OK. Now you should see the

constraint placed on the node in the correct direction.

11. Apply Load: In the Model Tree, double-click the Loads container to open the Create Load dialog box. In

this box, (a) name the load Distributed; (b) from the list of steps, select the Load Step; (c) in the Category

list, accept Mechanical as the default option; (d) in the Types for Selected Step list, select Pressure, and click

Continue, (e) select the surface for the load by clicking on the edge of the inclined member (member BC) and

click Done, (f) the direction of the load can be specified by clicking on either or button,

depending on how the load is applied. For this exercise, select the Magenta button, (g) enter the magnitude of

the distributed load (50 kN/m) in the appeared Edit Load dialog box, and click OK.

12. Select an Element Type: In the Model Tree, expand the Frame_1 model under the Parts container and

double-click Mesh item. On the menu bar of the Mesh module, select Mesh > Element Type and drag the

mouse to select the entire frame to be assigned an element type. Click on Done. In the appeared Element

Type dialog box; select Standard as the Element Library, Linear as the Geometric Order, and Beam as the

Family of elements. Note that a brief description of the element type selected appears at the bottom of the

dialog box. In this example, we have selected the element type: “B21: A 2-node linear beam in a plane”. Click

OK and Done successively.

13. Seed and Mesh the Model: At this stage, we have to first seed the edge of the part instance and then mesh the

part instance. To seed the model, on the menu bar of the Mesh module select Seed > Edges, drag the mouse to

select the entire frame to be assigned seeds. Click Done. In the appeared Local Seeds dialog box, select

By Number as the Method, and choose the number of elements desired on each edge. For this exercise, choose

10 elements on each edge. Click OK and Done successively. From the menu bar of the Mesh model, select

Mesh > Region and drag the mouse to select the entire frame to be meshed. Click Done.

14. Create an Analysis Job: In the Model Tree, double-click the Jobs container to open the Create Job dialog

box. In this box, name the job Frame_1_Job and click Continue. In the appeared Edit Job dialog box, use

Frame_1 Analysis as the Description for the job, and click OK.

15. Run Analysis: In the Model Tree, click on the “+” symbol to expand the Jobs container, right-click on

Frame_1_Job, select Submit from the appeared menu, and click OK. Once the job is submitted, the status of

the job will be indicated next to the job name. If there are not any errors, the status will change from

Submitted to Running, and finally to Completed. Wait till the job is completed to proceed with the

remaining steps.

16. Graphical Post-processing: Once the job has been successfully run, the Visualization module of Abaqus/CAE

allows you to graphically view the results and generate the tabular data in the form desired. Details regarding

various graphical post-processing procedures were covered in an earlier tutorial and therefore not included in

this particular guide. The only specific procedure provided in this tutorial is related to the creation of a View

Cut at a section of the structure, a feature that was not discussed in the previous tutorials.

Procedure for Creating a View Cut:

(a) In the Model Tree, right-click on Frame_1_Job, and select Results from the appeared menu to enter

the Visualization module.

(b) On the menu bar of Visualization module, select Tools > View Cut > Create as illustrated on the

first screenshot provided on the next page.

Figure 11(d). Sample Tutorial Guide Prepared for the Frame_1 Exercise (Page 4 of 4)

CENG 5336 - Introduction to Finite Elements

ABAQUS Tutorial Guide: Frame_1 Exercise (Page 4 of 4)

(c) On the appeared Create Cut dialog box, you have the option of choosing a name for your cut. For

this exercise, accept the default name Cut-4 and click OK.

(d) Again on the menu bar of Visualization module, select Tools > View Cut > Manager.

(e) In the View Cut Manger dialog box, toggle on the check box under the icon in the Model

columns (as shown on the second screenshot provided below) to display the resultant force and

moment along the View Cut. Additionally note that by dragging the Position slider available at the

bottom of the View Cut Manger dialog box, you are also able to translate or rotate the Plane View

Cut.

(a)

(b)

Snapshots of Abaqus Screen Showing Several Stages of Creating a View Cut

17. Generate Data Report: To generate the tabular data report for this problem, proceed with the following steps.

Note that the first outlined step is only necessary in case you have decided to skip the graphical post-processing

procedure discussed above. (a) In the Model Tree, right-click on Frame_1_Job and select Results from the

appeared menu to enter the Visualization module, (b) On the menu bar of this module, select Report > Field

Output, (c) From the Variable tabbed page of Report Field Output, select Unique Nodal as the Output

Variables Position, and toggle on: RF1, RF2, RM3, U1, U2, and UR3 to print the reactions forces and

displacements at the frame nodes, (d) Click on the Setup tabbed page of the Report Field Output, toggle off

the “Append to File” check box, and click OK. The tabular report of the requested data will now be written by

default into the abaqus.rpt file located in the Temp folder of your computer’s C drive. This file can be

viewed using the Notepad text editor.

Tools used for creating and

managing a View Cut.

Toggle on the check box

shown to place the internal

reactions along the View.

Cut.

Position slider used for

translating or rotating the

Plane View Cut.

V. Continuum Member Analysis

Once the students have been familiarized with the essential features of Abaqus for analyzing

structural members such as the ones presented in the previous sections, they are next instructed to

utilize this package to perform a FE analysis for investigating the behavior of continuum members

using several other planned exercises. Two sample exercises are included in this section to further

illustrate.

Lever Arm Example

In the presented exercise a lever arm containing two small cylindrical holes is subjected to two

concentered load at one end and is supported by a fixed hexagonal shaped prism inclusion at the

other end. The inclusion has a different material property than the lever arm. A generated three-

dimensional model for this problem is provided in Figure 13. Included in this figure are the

material specifications for each of the two material types used. To create the three-dimensional

model of the problem, students are first coached to develop a two-dimensional sketch that they can

later extrude. The sketching and modifying tools in Abaqus along with the two-dimensional sketch

of the lever arm can be seen in Figure 12. Using these tools, any combination of geometric shapes

can be created, modified, dimensioned, and further edited. Introduction of students to these tools

enables the students to generate the model for most any structural component they may encounter.

Once the three-dimensional model is created, the students are further instructed to partition the

model using several portioning techniques and tools available in Abaqus. This partitioning provides

a guide for effective meshing of the model. The specific partitions created for this problem can be

seen in Figure 13.

The procedure for meshing of a part including topics related to various meshing techniques, and

selecting appropriate element shapes, element types, and seed numbers are explored in detail at this

stage of the exercise, so that students fully understand this essential stage in the FE analysis of a

part. A 10-noded quadratic tetrahedron element (“C3D10 Element”) is used in this exercise for the

main and the sub part. Figure 14 shows the meshing used along with the Von Mises stress contours

for each of the two parts of the model.

Figure 12. 2D Sketch of the Part Created for Construction of the 3D Model

Sketching toolbox in

Abaqus containing a

variety of tools for

creating, modifying,

dimensioning, and

further editing of the

parts in a model.

Figure 13. Screenshot of the Created Abaqus Model showing the Partitions Used for the Lever

Arm and the Inclusion

Figure 14. Von Mises Stress Contours for the Separated Parts of the Model

A-36 Steel

(E = 29,000 ksi, ν = 0.32)

Stainless 304 Steel (E = 29,000 ksi, ν = 0.27)

Partitions created for meshing the

model using various partitioning tools

in Abaqus.

100 N

100 N

100 N

100 N

A special powerful feature of Abaqus allows the users to be able to cut a model with the planar,

cylindrical, or spherical cut surface to reveal and examine the stress distribution in the interior of a

part. Once this surface cut has been generated, it can also easily be translated along specified

directions to conveniently allow the user to inspect the stress distribution at any desired location on

the part. In a case where a planar cut has been used, the students can also rotate this plane surface

cut around specified axes, if necessary.

Another useful feature in Abaqus allows the users to create a “free body cut” to compute the

resultant force and moment at the any cut surface on the continuum member. One such free body

cut is shown in Figure 15 for the discussed model. This cut is generated by cutting the lever arm by

a plane perpendicular to the axis of the lever arm.

Once the full set of results for the created model is successfully generated, students are further

instructed on how to create a tabular report of the variables needed for any subset of the model, in

the format desired.

Figure 15. A Free Body Cut Generated by a Planar Cut Perpendicular to Axis of the Lever Arm

Computed internal

resultant force and

moment at the cut

planar surface.

Bolted Connection Example

In this exercise a three-dimensional FE model of a bolted joint for a full-scale two-story aluminum

frame is developed and discussed. The frame assembly shown in Figure 16 is constructed in the

Structures laboratory in the Civil Engineering and Construction Management Department at Georgia

Southern University.

(a) (b)

Figure 16. Two Story Aluminum Frame under Investigation: (a) Entire Structure,

and (b) Shear-Moment Connection at 6B1-6B2 Location

The FE model for one of the connection of the frame depicted in Figure 16(b) is provided in Figure

18. This model was constructed using the details obtained from the shop drawing of this particular

connection provided in Fig. 17. Figure 18(a) shows the beam and loading conditions, while Figures

18(b) and 18(C) respectively show the generated mesh and the corresponding Von-Mises stress

contours. In producing the FE model of this connection, various connecting parts consisting of two

I-beam girders, four gusset plates, and thirty bolts & nuts were created and assembled to accurately

describe the details of the bolted connection.

Figure 17. Shop Drawing of Bolt Connection Depicted in Figure 16(b)

Analyzed Bolted Connection

Material properties of various components of the analyzed connection are provided in Table 1.

Similar to the previous exercise a 10-noded tetrahedron element (“C3D10 Element”) is used in this

study for all girders, plates, bolts, and nuts. Von-Mises stress contours for the bolt and nut

assemblies are provided in Figure 19 along with a truncated section of the produced report showing

the numerical values of some the computed stresses.

(b) (c)

(a)

Figure 18. Devloped Finite Element Model: (a) Load and Boundary Conditions, (b) Generated

Mesh, and (c) Von Mises Stress Contours

Table 1. Material Properties for the Bolted Connection

Components Material Elastic Modulus (psi) Poisson’s Ratio

Girders & Plates Aluminum 10 (106) 0.33

Bolts & Nuts A-36 Steel 29 (106) 0.32

Once the students are fully familiarized with the more advanced features of Abaqus related to

analyzing connected and assembled parts using the example such as the one presented above, they

will be assigned to develop the FE solution for various other connections used in the discussed

frame. Calculated FE analysis results can be compared against the theoretical values obtained using

the AISC design codes. The assigned exercises offer the following two main advantages: (a) they

enhance the competencies of students in properly applying the finite element tools and techniques in

analyzing continuum members, and (b) they elevate the students’ understanding of the behavior of

structural connections under loads covered in other courses such as the Structural Steel Design. To

make the discussed course more challenging, the students can additionally be assigned to perform

the FE analysis to determine the response of the frame connections subjected to a variety of

dynamically applied loads.

Fixed Fixed

L/4 L/2 L/4

100 psi 100 psi W 5 x 5 1/4

L = 36.5 in.

Fixed Ends

100 psi.

(b)

(a)`

(c)

Figure 19. (a) Von Mises Stress Contours for the Entire Bolt-Nut Assemblies, (b) Sample Element

Designations for a Bolt-Nut Assembly, and (c) Sample Report Showing the Von Mises Stress

Results

(In-between results omitted)

Bolt Head Elements

Nut Elements

Element 39862

Element 41393 Element 41417

Element 39801

VI. Summary & Conclusion

In the presented paper a procedure for delivering a finite element analysis course in a civil

engineering program using Abaqus is outlined and discussed. The newly designed course guides the

students to effectively utilize various powerful features of this comprehensive package to analyze a

variety of structural components using a series of easy-to-follow tutorials. Some of the special

procedures included in these tutorial guides may not even be known to more experienced Abaqus

users. As previously stated, the electronic documentation files that accompany the software, even

though well-prepared, are not suitable for use in a course in the form presented.

After mastering the essential finite element tools and techniques through performing the discussed

tutorial exercises, the students are assigned additional more complicated problems to further enhance

their knowledge, expertise, and competencies in using this powerful tool. Since the newly designed

course has not yet been delivered, no assessment data is provided in the paper. Once the course is

offered, the collected assessment results will be used to further tweak and enhance the course.

Introducing the students to the powerful features of this comprehensive package will provide them

with the foundation and expertise they need to be able to pursue high level research in an academic

or professional setting. This perhaps is one of the most significant outcomes of the proposed

project. At the authors’ institution, this tool can specifically be utilized for preparing students to

conduct undergraduate research, or graduate research in the Master of Science in Applied

Engineering (MSAE) program.

The authors hope to be able expand this project further and possibly develop more advanced tutorial

examples for other advanced topics such as analysis of nonlinear problems and dynamic analysis of

structures. These new guides can be incorporated in more advanced courses such as Advanced

Finite Elements and Structural Dynamics.

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