Cosmas Tzavelis

Professor of Civil Engineering

CE321 Structural Analysis I

Vibration Theory 

Strain-Gage instrumentation

Transverse vibration of beams


Course:            CE 321:– Structural Engineering I

Credits:           4.5 credits in 6 contact hours (3 lecture hours and 3 laboratory hours)

Instructor:       Prof. Cosmas Tzavelis, Ph.D., P.E.


Textbook:       Hibbeler, R.C.  Structural Analysis, 10th Ed. Pearson Prentice Hall, New Jersey.

Course Description:

Discussion of materials, loads, and forms of structures. Analysis of determinate structures. Displacements of structures and their importance in applications. Experimental aspects of materials behavior in structural applications. Emphasis is placed on basic experimental techniques, design of experiments, selection and use of appropriate instrumentation, and interpretation of results.

Prerequisites:  ESC201: Mechanics of Materials

Designation:   Required Course

Student Outcomes:

This course address the following Civil Engineering student outcomes: (a), (b), (c), (e), (g), (i), (j), (k), and (l) (see below for a definition).

Lecture Topics:                      

Week 1:          Types of Structures and Loads and Introduction to Autodesk Robot Structural Analysis Professional

Week 2:          Analysis of Statically Determinate Structures

Week 3:          Analysis of Statically Determinate Trusses

Week 4:          Internal Loadings Developed in Structural Members

Week 5:          Internal Loadings Developed in Structural Members

Week 6:          Cables and Arches     

Week 7:          Approximate Analysis of Statically Indeterminate Structures

Week 8:          Midterm Exam

Week 9:          Influence Lines for Statically Determinate Structures

Week 10:        Influence Lines for Statically Determinate Structures

Week 11:        Deflections

Week 12:        Deflections with the Moment Area Method

Week 13:        Deflections Using Energy Methods

Week 14:        Deflections Using Energy Methods

Week 15:        Final Exam

Laboratory Topics:

Week 1:          Introduction to Materials and Structures and Laboratory

Week 2:          Tensile Testing of Aluminum Rod

Week 3:          Buckling Testing of Aluminum Column

Week 4:          Mixing and Casting of Standard Concrete Cylinder

Week 5:          Vibrational Testing of Aluminum Bar

Week 6:          Strain Gage Installation

Week 7:          Flexural Testing of Aluminum Beam

Week 8:          Compressive Testing of Standard Concrete Cylinder

Week 9:          Preliminary Design of Scale Model Bridge

Week 10:        Final Design of Scale Model Bridge

Week 11:        Begin Fabrication of Scale Model Bridge

Week 12:        Continue Fabrication of Scale Model Bridge

Week 13:        Finish Fabrication of Scale Model Bridge

Week 14:        Load Testing of Scale Model Bridge

Week 15:        Bridge Project Report

Grading Breakdown:

                        Homework                                          10%

                        Lab Reports                                        10%

                        Midterm Exam                                    20%

                        Final Exam                                         45%

                        Bridge Project Report                         15%

                        Total                                                   100%





How to write a Technical Paper (by ASCE),--Editors/Journals/General-Journal-Information/Parts-of-a-Journal-Article/,--Editors/Books/General-Book-Information/Author-s-Guide--Writing-Style/

 The following publications can provide useful guidance in preparing your Technical report

  • For guidance on the mechanics of written communication, consult the current edition of The Chicago Manual of Style (University of Chicago Press).
  • For spelling and word usage, ASCE follows the current editions of Merriam-Webster’s Collegiate Dictionary and Webster’s International Dictionary, Unabridged.
  • For rules of grammar and usage, refer to Words into Type (Prentice-Hall) or New York Public Library Writer’s Guide to Style and Usage (HarperCollins).
  • For guidance on engineering terms, refer to McGraw-Hill Dictionary of Scientific and Technical Terms, Wiley Dictionary of Civil Engineering and Construction, or Means Illustrated Construction Dictionary.
  • For assistance in the presentation of mathematics, refer to Mathematics into Type (American Mathematical Society).
  • For assistance with the use of SI (metric) units, refer to IEEE/ASTM SI-10, Standard for Use of the International System of Units (SI): The Modern Metric System (this standard replaces the former ASTM E-380 and ANSI/IEEE Std 268-1992) or to Metric Units in Engineering: Going SI (ASCE Press).

Active versus Passive Voice

Wherever possible, use active verbs that demonstrate what is being done and who is doing it.

Instead of: The bridge was built by James Eads.

Use: James Eads built the bridge.

Instead of: Six possible causes of failure were identified in the forensic investigation.

Use: The forensic investigation identified six possible causes of failure.

Direct versus Indirect Statements

Direct statements are clear, concise, and do not wear on your reader. Indirect statements are those that begin with phrases such as “it should be noted that…” or “it is common that….” Other types of indirect statements may begin with “to be” statements such as “there are” or “it was”.

Instead of: It should be noted that the flow was interrupted by a surge…

Use: A surge interrupted the flow…

Instead of: It is common that the steel rebars are weakened by oxidation…

Use: Oxidation commonly weakens steel rebars…

Instead of: There are many reasons that concrete may fail…

Use: Concrete may fail for many reasons…

Instead of: There are three kinds of bolt that can be used in these circumstances…

Use: Three kinds of bolt can be used in these circumstances.

Use of “I” and “We”

While the use of first-person pronouns (I, we, my, our) should be sparing in technical material, the use of “I” and “we” is preferable to awkward constructions such as “the authors” or “this researcher.”

  • If you are the sole author, use “I” to indicate your actions or opinions.
  • If you are working with coauthors, use “we” to refer to your collective actions or opinions. Use last names to refer to the actions or opinions of individual coauthors.
  • If you use “we” to refer to yourself and your coauthors, avoid the use of “we” in other contexts, such as referring to other people or humankind in general.

Inclusive Language

Writing without bias may feel stiff or unnatural at first, but usually results in greater precision and consideration for your readers. Therefore, avoid language that arbitrarily assigns roles or characteristics or excludes people on the basis of gender; racial, ethnic, or religious background; physical or mental capabilities; sexual orientation; or other sorts of stereotypes.

  • Avoid using man or men to refer to groups containing both sexes. Substitute words and phrases such as humankind, humanity, people, employees, workers, workforce, staff, and staff hours.
  • Avoid the use of masculine pronouns to refer to both sexes. Use plural pronouns, a locution that carries no bias, imperative verb forms, or second-person pronouns.

Instead of: When an engineer begins to design an overpass, he should consider…

Try: When engineers begin to design overpasses, they should consider…

Or: When beginning to design an overpass, an engineer should consider…

Instead of: A manager should not assume that his staff will alert him to potential problems.

Try: As a manager, do not assume that staff will alert you to potential problems.

Or: As a manager, you should not assume that your staff will alert you to potential problems.

Acronyms and Abbreviations

An abbreviation is a shortening form of a word or phrase, such as “Jan.” for “January”, “U.S.” for “United States,” and “ASCE” for “American Society of Civil Engineers.” An acronym is formed when the abbreviation forms a pronounceable word, such as “NATO” for “North Atlantic Treaty Organization” or “AASHTO” for "American Association of State Highway and Transportation Officials."

  • Abbreviations and acronyms in text must be spelled out the first time that they appear in each chapter or paper, with the shortened form appearing immediately in parentheses. Thereafter, the shortened form should be used throughout the chapter.
  • Several very common abbreviations (U.S. and U.K. as adjectives; DNA and PVC for nouns) do not need to be spelled out on first usage.
  • Basic units of measure do not need to be spelled out on first usage. These include: ft, in., lb (customary) and m, mm, kg (SI).

SI versus Customary Units

ASCE publications use Système Internationale (SI) units, the most widely and officially recognized system of metric units, as the primary system of weights, dimensions, and other physical measures. For more information about SI units, visit the Web sites of the U.S. Metric Association (USMA), Inc. or the National Institute of Standards and Technology (NIST) or consult the book, Metric Units in Engineering: Going SI.

All ASCE publications use SI units in text, figures, and tables. Customary (also known as English or imperial) units may be included in parentheses, if the author chooses.

One exception is recognized for ASCE Press titles. Case studies, examples, and problem sets can become difficult to use when both systems of units are presented. Therefore, it is acceptable to alternate metric and customary units in cases, examples, or problems.

Figures, Tables, and Other Supporting Materials

Elements such as figures, tables, and boxes containing lists or case studies are included to support or augment what appears in the text.

  • For books, each element should be numbered consecutively with the chapter number and an Arabic numeral: Fig. 9-1, Fig. 9-2, Fig. 9-3 …; Table 7-1, Table 7-2 …; Box 10-1, Box 10-2 …. For journal articles and conference proceedings volumes, which do not have chapter numbers, the chapter number is left out: Fig. 1, Fig. 2, Fig. 3....
  • If a figure or table has parts, a capital or lowercase letter is used to identify the parts: Fig. 9-1A, Fig. 9-1B…; Fig. 1(a), Fig. 1(b)…
  • In books, do not use subheading numbers for figures and tables. This practice is awkward and confuses readers.
  • Every element must be discussed in text, with a reference to the element and its number. The first reference to a figure, table, or box is the call-out. The call-outs must be worded consistently throughout your manuscript. Spell out “Table” and abbreviate “Fig.” For example: "The results of the stress tests (Fig. 1) clearly demonstrate…" and "Table 6-2 presents a range of planning options along with…".
  • When your manuscript is typeset, the element will be placed on the page on which it is called out—or as soon as possible thereafter.
  • Tables and figures must be numbered in the order in which they are discussed in text so that call-outs also appear in numerical order. In other words, Table 3 must be called out in text before Table 4.





Instructions on how to use the ROBOT Structural Analysis software by Autodesk

Goto to register as a student and download free AutoDesk software.

Open Robot

Select a Project type using the large icons. Click on Building Design (for a 3-D building), Truss 2D Design (for 2-D Trusses), etc.

In the model area, click the House Cube (on the upper right) and then the Front view to show the ZX plane. Or Click the View menu and then Projection Zx

Define a Grid to draw your model by clicking the View menu, Grid, Grid Step Definition. While there, define your Grid step Dx and Dy and click Apply.

If you have a statically indeterminate structure, you need to define some x-sections . Click on Geometry, Properties, Sections and on the Section window click the top left white icon, which defines a New Section. In the New Section window, click on the Standard Tab (top left) or  Parametric etc and define your new Section. Make you have the correct material in the Section Type at the bottom right (Steel, Timber, etc).

Click the Geometry menu and then Bars. Click the … next to Section, to change the x-Section.    If you have set the grid correctly, you should now click on the grid points and define the Beginning and End point of each Bar.

Note the Green field on the Bars menu that defines the current point. If you make a mistake you can click the bar and Delete.

If you do not like the coordinates of a Node you can click on it and change them via the Object Inspector window (on the left of your screen. See Geometry and expand Coordinates.

Click the Geometry menu and then Supports to define your supports.  If Roller does not exist, click on the top left of the Supports window (white page icon) to add a New Support Definition. (Fixed directions should be clicked for UZ only if you define a Roller)

Click on a Node to define the support

Click on the Loads menu to define Load types. Click Add to add the default Dead Load and then click on Nature, Live, Add, to define the Live Load Case. Close

Make sure that the correct Load Case is displayed on a small white field on the top of your screen.

Click the Loads menu again, and Load Definition. Make sure that the correct Case No is shown! If not Close the Load Definition window and select the correct Load Case from the small white field on the top of your screen. While in the correct Load Definition window, click Node and the Left most icon to see a Nodal Force window where you can define your X force and your Z force on the node (Z is UP positive!). Click Add and then click on the node where you want the load to be applied. For another Load click on the Load Definition and repeat the procedure. If you want to delete a Load use the X button on the Load Definition window. If you do not see any of the Loads you applied try clicking the yellow buttons on the bottom of you screen


To run the Analysis just click the Analysis menu and then Calculations. You may see nothing on the screen, but on the bottom of your screen you should see a Green dot with Result (FEM) available.


Click the Results menu, Diagrams for Bars, and Click on Fx Force, Apply, to see the Axial load diagram. Click Normalize if the diagram is too large and in the Diagrams window, scroll to the right and select Parameters (click labels or text and then Apply) in order to see values on your diagram.

You  can also click on Stresses to see a table of Axial Stresses. These stresses should be less than the allowable for a correct design. You can try optimizing your design by assigning different x-sections to bars, until most stresses are close to allowable. A safe structure is when ALL stresses are less than the allowable.