ANALYSIS OF TRUSSES USING SAP2000

By

Mr. Linzhong Deng and Prof. Michel Ghosn

Department of Civil Engineering

The City College of New York

 

This course demonstrated basic concepts about the equilibrium of structures and developed some principles for calculating the forces that develop within the members of a structure when the structure is subjected to external loads. There are many analytical methods available to calculate these forces in the members of a structural system. Many computer packages are also available to perform such computations. The object of this chapter is to illustrate how the program SAP2000 can be used to solve structural analysis problems.

SAP2000 is a general-purpose structural analysis program developed by Professor E. Wilson and his associates in Computers and Structures Inc. This program can be used to calculate forces and reactions in beams and trusses and to calculate the displacements. One version of the program is available for use by the students of the Department of Civil Engineering in the CE Computer Lab. This chapter demonstrates the use of SAP2000 using a simple illustrative problem. The problem chosen here is a three member steel truss subjected to two different load conditions.

 

PROBLEM STATEMENT

To demonstrate the use of SAP2000 we propose to analyze the simple three member steel truss shown in Figure 3.1 below. Members 1 and 2 have cross section areas of 10 in2. The cross section of member 3 is 20 in2. This truss has three pinned supports designated as joints 1, 2, and 3. This means that joints 1, 2 and 3 are restrained from moving horizontally and vertically but are allowed to rotate. Two loading conditions are given. The first load is a vertical force of 1000lb applied at joint 4 while the second loading condition consists of an inclined load of 1000lb at 15 degrees from the vertical. The truss is symmetric, its height is 60 in. and the base is 69.28 in.

 

 

  

     Figure 3.1 Example Truss Problem.

 

 

ANALYSIS PROCEDURE

To use a structural analysis package it is necessary to give a description of the structure being analyzed. We usually call this the preprocessing procedure. In this procedure, you need to identify all the joints and indicate how these joints are connected together. The location of the joints is determined using their coordinates in an orthogonal system of axes. After preprocessing, SAP2000 will analyze the structure you just defined. We call this procedure the Solving procedure. Finally, we reach the last procedure: Postprocessing. In this procedure, SAP2000 will display all the answers to your questions. You can print the results out, or get a graphic presentation. Following is the step by step description of the preprocessing, solving and postprocessing procedures for the three-member truss problem described in figure 3.1. Similar steps will be used for solving any other problem.

 

I. Activating SAP2000.

 

II. Preprocessing.

  • In this part, we need to set up the structure’s geometry, define material properties and section properties, assign a section to each member and define element releases. We also need to define the load cases and assign values for the loads.
  • 1. Define the units:

                From the combo (i.e. the drop down list) in the main window’s status bar (situated at the main window’s button), choose lb-in as the global units for this truss.

    2. Define the truss geometry:

     

     

    Click OK to continue. This will display 3-D and 2-D view windows with the grid lines you have already designated. The cross points of this grid will be subsequently used to define the necessary joints of our structure.

     

    3. Define material and structural section properties:

    1. Highlight the FSEC1 in the box frame name. FSEC1 means that now you will define the first set of section properties.
    2. Click the modify/show section button. This will display the window of rectangular section dialog box.
    3. In this box, choose the steel from the material combo, type in 2.5 and 4 in the section’s width and depth boxes. Click ok to close this dialog box and return to Frame sections dialog box for FSEC2. Now you will define the second set of section properties.
    4. Choose Add rectangular in the second combo box. This will display the rectangular section dialog box.
    5. In this box, choose the steel from the material combo, type in 4 and 5 in the section’s width and depth box for the second set of section properties. Click ok to close this dialog box and return to Frame sections dialog box.
    6. Click OK to accept the section properties just defined.

     

     

    4. Assigning member sections and frame releases:

    It is time to tell SAP2000 the size of each member and that all the members of this structure are truss members (i.e. members that do not bend but can only carry forces along their longitudinal axis). To differentiate between members that can bend (frame members) and those that do not (truss members) we need to release the ends of the members. The steps are:

     

    5. Define load cases:

     

     

    6. Assigning loads:

      

     

     

     

     

     

     

     

     

    Figure 3.2 - Division of inclined force into components

     

     

    7. Assigning restraints.

    It is very important to assign restraints to your structure. The restraints define how the structure is supported. If you assign the wrong restraints you will get wrong answers or SAP2000 will not give you any answer. To assign restraints, follow these steps:

     

     

    III  Solving.

    Now that all the information about the structure geometry, member section properties, material type and loads have been given, you can proceed to ask the computer to execute the analysis. The steps are:

     

     

     

     

    IV Post Processing.

    Post processing is an important part of any structural analysis. Depending on our objectives, we need to view different results. For large structural systems, it will be very difficult to review all the results as the amount of output will be very large. SAP2000 can reduce the size of the output by providing you with only the results you require. This possibility is available through the SAP2000 database option. The common postprocessing tasks that you normally need are: 1) Display of the deformed shapes, 2) display of member forces, 3) printing of results, 4) designing steel or concrete members… In this section we will only discuss the first three tasks of postprocessing.

    1. Display deformed shape.

    After the analysis is completed, the post processing procedure begins. SAP2000 automatically displays the deformed shape of load case 1 at first. If you want to show the deformed shape of load case 2, follow these steps:

     

     

     

     

     

    2. Display member forces.

     

    This diagram shows how the internal force in each member varies. By moving the cursor along the diagram, SAP2000 will display the actual value of the force at the point where the cursor is placed.

    3. Print results.

     

     

    3-member truss output file.

     

    SAP2000 v6.13 File: TRESS3M lb-in Units PAGE 1

    September 2, 1998 15:24

    J O I N T D I S P L A C E M E N T S

    JOINT LOAD UX UY UZ RX RY RZ

    1 LOAD1 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

    1 LOAD2 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

    2 LOAD1 0.0000 -6.E-5 0.0000 0.0000 0.0000 0.0000

    2 LOAD2 1.E-04 -6.E-5 0.0000 0.0000 0.0000 0.0000

    3 LOAD1 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

    3 LOAD2 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

    4 LOAD1 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

    4 LOAD2 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

    SAP2000 v6.13 File: TRESS3M lb-in Units PAGE 2

    September 2, 1998 15:24

    J O I N T R E A C T I O N S

    JOINT LOAD F1 F2 F3 M1 M2 M3

    1 LOAD1 -113.66 196.88 0.0000 0.0000 0.0000 0.0000

    1 LOAD2 -239.20 414.32 0.0000 0.0000 0.0000 0.0000

    3 LOAD1 113.66 196.88 0.0000 0.0000 0.0000 0.0000

    3 LOAD2 -19.61 -33.97 0.0000 0.0000 0.0000 0.0000

    4 LOAD1 0.00 606.23 0.0000 0.0000 0.0000 0.0000

    4 LOAD2 0.00 585.57 0.0000 0.0000 0.0000 0.0000

    SAP2000 v6.13 File: TRESS3M lb-in Units PAGE 3

    September 2, 1998 15:24

    F R A M E E L E M E N T F O R C E S

    FRAME LOAD

    LOC P V2 V3 T M2 M3

    1 LOAD1

    0.00 227.34 0.00 0.00 0.00 0.00 0.00

    17.32 227.34 0.00 0.00 0.00 0.00 0.00

    34.64 227.34 0.00 0.00 0.00 0.00 0.00

    51.96 227.34 0.00 0.00 0.00 0.00 0.00

    69.28 227.34 0.00 0.00 0.00 0.00 0.00

    1 LOAD2

    0.00 478.42 0.00 0.00 0.00 0.00 0.00

    17.32 478.42 0.00 0.00 0.00 0.00 0.00

    34.64 478.42 0.00 0.00 0.00 0.00 0.00

    51.96 478.42 0.00 0.00 0.00 0.00 0.00

    69.28 478.42 0.00 0.00 0.00 0.00 0.00

    2 LOAD1

    0.00 227.34 0.00 0.00 0.00 0.00 0.00

    17.32 227.34 0.00 0.00 0.00 0.00 0.00

    34.64 227.34 0.00 0.00 0.00 0.00 0.00

    51.96 227.34 0.00 0.00 0.00 0.00 0.00

    69.28 227.34 0.00 0.00 0.00 0.00 0.00

    2 LOAD2

    0.00 -39.23 0.00 0.00 0.00 0.00 0.00

    17.32 -39.23 0.00 0.00 0.00 0.00 0.00

    34.64 -39.23 0.00 0.00 0.00 0.00 0.00

    51.96 -39.23 0.00 0.00 0.00 0.00 0.00

    69.28 -39.23 0.00 0.00 0.00 0.00 0.00

    3 LOAD1

    0.00 606.23 0.00 0.00 0.00 0.00 0.00

    15.00 606.23 0.00 0.00 0.00 0.00 0.00

    30.00 606.23 0.00 0.00 0.00 0.00 0.00

    45.00 606.23 0.00 0.00 0.00 0.00 0.00

    60.00 606.23 0.00 0.00 0.00 0.00 0.00

    3 LOAD2

    0.00 585.58 0.00 0.00 0.00 0.00 0.00

    15.00 585.58 0.00 0.00 0.00 0.00 0.00

    30.00 585.58 0.00 0.00 0.00 0.00 0.00

    45.00 585.58 0.00 0.00 0.00 0.00 0.00

    60.00 585.58 0.00 0.00 0.00 0.00 0.00

     

     

     

    ANALYSIS OF RESULTS

    It is always important to carefully analyze the results you obtain from a computer program to make sure that they make sense. The results that we get from running the data set described in this chapter are summarized in tables 3.1, 3.2 and 3.3.

                                                    Table 3.1. Internal member forces (lb).

    Member

    Load condition 1

    Load condition 2

    1

    227.34

    -39.23

    2

    227.34

    478.42

    3

    606.23

    585.58

     

     

                                                    Table 3.2. Displacement of joint 4 (in).

    Load case

    Displacement in X

    Displacement in Y

    1

    0.0

    .627*10-4

    2

    .124*10-4

    .606*10-4

     

     

     

      Table 3.3. Reactions (lb).

     

    Load condition 1

    Load condition 2

    Joints

    X direction

    Y direction

    X direction

    Y direction

    1

    0.00

    606.23

    0.00

    585.58

    2

    113.66

    196.88

    -19.61

    -33.97

    3

    -113.66

    196.88

    -239.21

    414.33

     

     

    To check the results and to verify that no errors were committed during input data preparation or in the interpretation of the results, we will verify that overall equilibrium is maintained. This is done by verifying that the sum of the applied forces and the reactions is zero for both the x and y directions. The equilibrium equations are written as:

    In which, Fxi is the component in the x direction of the ith external force. Fyi is the component in the y direction of the ith external force. Rxi is the component in the x direction of the ith reaction. Ryi is the component in the y direction of the ith reaction. We also call the above equations the global equilibrium equations. Consider load condition 1, if we input the reactions (table 3.3) and the applied loads into equation (3.1) and (3.2), we obtain:

    å Fx = 0.0+113.67-113.67+0 = 0;

    å Fy = 606.23+19.88+196.88-1000 = 0.

     

    So, the global equilibrium is maintained because equations (3.1) and (3.2) are satisfied. This will help you determine whether the program executed the problem you have assigned and that you have entered the right data. You should always check global equilibrium every time you perform structural analysis.

     

     

    Figure 3.3. Results of forces at joint 4 for load case 2.

     

     

     The same check is also performed for load condition 2 and we find that equilibrium is also satisfied.

    Another verification is performed by checking the equilibrium at joint 4. If we have more than one joint, like the example in the next chapter, we may need to check several internal joints. The internal forces obtained from SAP2000 for load condition 1 are shown in table 3.1. Figure 3.2 shows the internal and external forces under load case 2. Equilibrium is maintained when the sum of the member forces at joint 4 as shown in Figure 3.2 is equal to zero in both x and y directions. The first step in the process is to determine the angle q between the vertical direction and the line of action of each force. Since this is a truss, the line of action of each force is the same as the longitudinal axis of the member. In this example, member 1-4 is vertical and therefore its angle is equal to zero. Member 2-4 and 3-4 are inclined. Their angle of inclination is found using the equations:

                                            tan q = 34.64/60=0.577

                                q = arctan(0.577)=30 degrees.

    The equilibrium equations become:

                                 å Fx = 227.34 * sin(30)-227.34 * sin(30)=0.0

                                        å Fy = 606.23 + 227.34 * cos(30) +227.34 * con(30)-1000=0.0

    So, the equilibrium is also maintained. Through the above checking procedure, we verify that the results we obtained from SAP2000 are correct for load case 2. You can do the same check for load case 1.

     

    SUMMARY

    SAP2000 is a powerful tool for analyzing civil engineering structures. This chapter demonstrated the use of SAP2000 for performing static analysis of trusses. The program is also capable of analyzing frames, plates and shells for static as well dynamic loads. In the next chapter, you will be required to use SAP2000 to perform the analysis of an example truss bridge. The Appendix gives a brief summary of the steps required to perform a structural analysis for structures. Save the appendix for future use in Civil Engineering courses.

     

     

     

     

    APPENDIX

    STRUCTURAL ANALYSIS WITH SAP2000

    By Mr. Linzhong Deng and Prof. Michel Ghosn

    Department of Civil Engineering

    The City College of New York

    CUNY

     

    SAP2000 is a general purpose finite element program which performs the static or dynamic, linear or nonlinear analysis of structural systems. It is also a powerful design tool to design structures following AASHTO specifications, ACI and AISC building codes. These features, and many more make SAP2000 the state-of-the-art in structural analysis program.

    The SAP2000 graphic user interface (GUI) is used to model, analyze, design, and display the structure geometry, properties and analysis results. The analysis procedure can be divided into three parts:

    1. Preprocessing.
    2. Solving.
    3. Postprocessing

     

     

    Part I. Preprocessing.

    In preprocessing, the following information is needed by SAP2000.

    1. Choosing the units for this project.
    2. Setting up geometry.
    3. Defining material and member section properties.
    4. Assigning member section properties and element releases.
    5. Defining load cases.
    6. Assigning load magnitudes.
    7. Assigning restraints.

     

    I.   Choosing units.

  • From the combo (i.e. the drop down list) in the main window’s status bar, choose the units for this project.
  • II. Setting up structure’s geometry.

    There are two ways to set up the structure’s geometry: The first is from the SAP2000’s templates. The other is by creating a completely new model.

    When creating from a template, follow these steps:

    1. From File menu, choose New Model from Template… This will display the Model Template dialog box.
    2. In this dialog box:

                 a. Click on the template which most closely resembles the structure you want to analyze. This will display

                      the template dialog box.

                  b. In this dialog box, choose the appropriate parameters.

                  c. Click OK button.

    The screen will refresh and display 3-D and 2-D views of the model in vertically tiled adjoining windows. You can activate the one you plan to work in by clicking the window’s title. You can any one of the two windows if you wish.

    When creating from a new model, follow these steps:

    1. From the File menu, choose the New Model… This will display the window of coordinate system definition.
    2. In the window of coordinate system definition, enter the appropriate grid information. The cross points of the grid will define the necessary joints of your structure. This will display the 3-D and 2-D view window with grid.
    3. 3-D and 2-D views of the model are displayed in vertically tiled adjoining windows. You can close the 3-D windows if you wish. Active the 2-D view by click the x-y button in toolbox or by clicking any point inside the 2-D window.
    4. From draw menu, choose "Draw From Element". This will change your mouse point from " " to " " in the area of 2-D view.
    5. Draw your structure in the grid based on the grid spacings defined in step 2. Click your left mouse button to define the joints. Every joint needs one click. SAP2000 will connect the joints automatically. Double click the left mouse button to stop the action of connection. When you draw something wrong, click the " " inside the floating toolbox situated in the lower part of your screen. Then click the members which need to be deleted. Then from the edit menu, choose "delete". To see the modified structure, from the display menu, choose the show undeformed shape.

     

    III. Define material and structural section properties.

    In this step, we are going to define all the material types and all section properties which are present in this structure. This requires the following steps:

    1. From the define menu, choose material… This will display the window of define material.
    2. If your material is standard steel or concrete, you can click modify/show material button and use the library supplied properties. Click button OK to accept appropriate properties. Otherwise click the button add new material to define a new material’s properties, or the button modify/show material to change the library’s data according to your material’s properties.
    3. From the define menu, choose Frame sections… This will display the Frame sections dialog box.
    4. In this dialog box, you can define a new section type, import a section’s geometry from the SAP2000’s library, or modify a section’s geometry from the default values. Suppose you have two rectangular sections, you need the following steps to define these sections.

     

    IV. Assigning member section properties.

    There are three selection methods used by SAP2000 to assign member properties, support restraints, loads... For clarity and convenience, these three selection methods are summoned here. The first is to click the members one by one after you click on the pointer tool button (" ") on the floating toolbox. The second way is to drag a rectangular box after you click on the pointer tool button on the floating toolbox. All of the objects inside this rectangular will be selected simultaneously. The third way is to draw a straight line after you click the "Sect intersecting line select mode" button on the floating toolbox. All the objects intersecting the line you draw will be simultaneously selected.

    You need the following steps to assign member section properties:

     

    V. Defining load cases.

    Now, it is time to give SAP2000 the applied load’s information. The steps are:

     

    In the following section of assigning joint load cases, you must assign a numerical volume and the location of each joint loads for every load cases.

     

    VI. Assigning loads.

    For simplicity, we just talk about assigning joint loads. If you wish to apply a distributed load on a member, you can refer to SAP2000 manual for detail. To assign joint loads execute the following steps:

    Repeat these steps until you finish every load case’s load assignment.

     

    VII. Assigning restraints.

    It is very important to assign restraints to your structure. Otherwise your structure will become unstable or it becomes a free body and it cannot be solved by SAP2000. Applying joint restraints requires the following steps:

     

    PART II. Solving

    In this part, SAP2000 will assemble and solve the global matrix. The following steps are needed:

    1. From the Analysis menu, select Set Option… This will display the Analysis Option dialog box.
    2. In this dialog box, check the available DOF. If you are analyzing a plane truss, check UX and UY, leave the UZ, RX, RY and RZ blank.
    3. Click OK to accept what you choose.
    4. From the analysis menu, select Run. This will display the Save Model File As dialog box.
    5. In this dialog box, save the model under a filename. No extension is necessary.
    6. Click the OK button, the analysis will begin. A top window is opened in which the various phases of analysis process are progressively reported. When the analysis is complete, the screen will display the message "ANALYSIS COMPLETE".
    7. Click OK button in the top window to close it.

     

     

    PART III. Postprocessing.

    The main options in postprocessing are:

    1. Displaying the deformed shape.
    2. Displaying the member forces.
    3. Printing the results.
    4. Designing the structural members and checking the safety of a design.
    5. Modifying the structure.

    For simplicity, we just discuss the three fundamental options: displaying the deformed shape, displaying the member forces and printing results here.

    1. Displaying the deformed shape.

    After the analysis is complete, SAP2000 automatically displays the deformed shape of the model for the default load case, LOAD1, in the active display window. We can now display the deformed shape for another load case in one of the two view windows.

    2. Displaying the member forces.

    3. Printing the results.

    You can also get the detailed results in another way. When we analyze a structure, by default, SAP2000 will create three output files: filename.out, filename.log and filename.EKO. The output file filename.out stores the output of your analysis. The output file filename.EKO stores the input information for this structure. The output file filename.log take all of the running information. These files are text files. You can print these files using computer operating system. For example, we can print these files from Notepad. The steps are: