Tutorial 1: Welded Frame - Problem Description

Transcription

1 Tutorial 1: Welded Frame - Problem Description Introduction In this first tutorial, we will analyse a simple frame: firstly as a welded frame, and secondly as a pin jointed truss. In each case, we will consider three loading situations. We will follow a standard sequence of steps commonly used in finite element modelling. 1 Define the geometry and element types; 2 Define the support conditions; 3 Define the loading conditions; 4 Define material properties and element sections; 5 Solve the model; 6 Post-process the model, to view and interpret the results. For later tutorials, the above steps may be modified slightly. Description of Geometry and Loading The geometry and loading of the frame are illustrated in Figure 1.1 below. The structure is constructed from structural steel. Three separate load cases will be considered: Load Case 1 Single vertical 10 kn force on the bottom centre frame member. Load Case 2 Single 30 kn horizontal force at roller joint. Load Case 3 Linear combination of load cases 1 and 2. Figure 1.1 Frame Geometry and Load Positions Required Results We will determine which frame members have the maximum tensile and compressive stresses under the three different load cases. We will also investigate the shear force and bending moment distribution of the bottom centre frame member.

2 Tutorial 1: Welded Frame - Creating the Model To begin modelling, start Strand7. 1 From the FILE menu select New (alternatively, press CTRL+N or click the New File button); 2 In the Model Units dialog box, click OK to accept default SI units; 3 From the FILE menu select Save As (alternatively, press CTRL+S or click the Save As button); 4 Save the model using an appropriate name like, Tutorial 1.ST7. Before you begin any finite element model, it is good practice to plan the model building procedure. This includes selecting the elements you will use to describe the physical situation being analysed, the units, and the working plane (for example the XY plane). Elements Elements available in Strand7 include beams, plates and bricks. Beam elements will be used for this tutorial since the frame members are considerably longer than they are wide or high. For the rest of this tutorial, we will refer to the frame members as beams. Units Strand7 allows you to specify the units to be used when creating the model. You can choose to work in a consistent set of units (i.e. m, N, kg, Pa) or an inconsistent set of units (i.e. ft, N, lb, MPa). The current unit settings are displayed at the bottom of the Strand7 model window. If the current settings are not appropriate for a particular model, they can easily be changed from the GLOBAL, Units, Model Units dialog box (alternatively press CTRL+U). In this tutorial, we will use metres for length, Mega-Pascals for stress (and modulus) and Kilo-Newtons for force. 1 From the GLOBAL menu select Units; 2 Under Length select m ; 3 Under Modulus/Stress select MPa ; 4 Under Force select kn ; 5 Leave the rest as default; 6 Click here to see what your dialog box should look like; 7 Click OK. Note If you normally work in the same units, you can configure your preferred system so that any new model you create uses these units. You can set the default units from the FILE, Preferences, Units tab. Working Plane The default setting in Strand7 is the XY plane. For this tutorial, we will work in the XY plane with the X-axis being the horizontal and the Y-axis the vertical.

3 Tutorial 1: Welded Frame - The Finite Element Model You are now ready to begin modelling the frame. Figure 1.2 below shows the finite element representation of the physical structure you will create. Figure 1.2 Finite Element Representation of Structure To begin this model, you will first need to create a single node. It is good practice to commence building models at the origin (i.e. coordinates 0, 0, 0). Nodes are created in the following manner. 1 From the CREATE menu select Node; 2 Ensure that the X, Y and Z text boxes are all set; 3 Enter the coordinates for the node (i.e. Node 1, X=0, Y=0, Z=0); 4 Click Apply. Referring to Figure 1.1, we see that Nodes 1 to 4 have an even spacing of two metres. In Strand7, we can create the nodes, and the beam elements that connect them, in one single step using the Extrude function. 1 From the TOOLS menu select Extrude then by Increments; 2 You should see the Extrude by Increment dialog box; 3 Under Increments in the X box enter 2; 4 Under Increments in the Y box enter 0; 5 Under Increments in the Z box enter 0; 6 In the Repeat text box, type or select 3; 7 Under Source select Leave; 8 Make sure the Keep Selection check box is cleared; 9 Select the node to extrude (i.e. Node 1); 10 Click Apply; 11 Close the dialog box. Note The selection of entities in Strand7 can be performed in a number of different ways. This is explained in detail in the Selection Overview section in the Online Help. For this tutorial, click on the node to be extruded; this will result in a colour change to indicate node selection. The Extrude tool is used to extrude the following. - nodes to form beams; - beams to form plates; and - plates to form bricks.

4 Depending on your screen size, not all the copied nodes may be visible in the current range of the display. If this is the case, from the VIEW menu select Redraw (alternatively, press F3 or click the Redraw button. This will re-scale the model to fit into the model window. Your model should now look like Figure 1.3 below. Figure 1.3 Nodes and Beams Created using the Extrude Tool To create the top centre beam, copy the bottom centre beam, two metres in the vertical Y-direction. 1 From the TOOLS menu select Copy then by Increment; 2 Under Increments in the X box enter 0; 3 Under Increments in the Y box enter 2; 4 Under Increments in the Z box enter 0; 5 Make sure Beam Select is On; 6 Click on the bottom centre beam; 7 Click Apply; 8 Close the dialog box. For this tutorial, it would be helpful to see the Node Numbers. You can set this option through the Entity Display dialog box 1 From the VIEW menu select Entity Display (alternatively, Right-Click the Hide Nodes button on the left toolbar); 2 Click the Node button;

5 3 Select the Node Numbers checkbox; 4 Click OK. The six nodes should now be marked with numbers from 1 to 6. The remaining beams are created in the following manner. 1 From the CREATE menu select Element; 2 You should see the Connections dialog box 3 Click on two nodes that define the endpoints of a beam (e.g. Node 1 to Node 5). The created beam is indicated by a blue line; 4 Continue selecting appropriate pairs of nodes until the frame geometry is completed; 5 Close the Connections dialog box. If you make any mistakes while connecting any of the beams, from the EDIT menu select Undo (alternatively press CTRL+Z or click the Undo button on the Strand7 toolbar). The Undo tool can be used to undo all operations in the reverse order in which they were performed. By using the Undo tool once, you will undo the last operation, by using the Undo tool twice, you will undo the last two operations and so on. It is also possible to perform multiple Undo operations using the Undo List. Once all connections have been completed, your model should look like Figure 1.4 below. Figure 1.4 Connected Beam Elements You are now ready to define the frame support conditions.

6 Tutorial 1: Welded Frame - Freedom Conditions and Restraints Now that the geometry of the frame has been defined, you need to assign some support to the model as it is currently floating in space. To give the model the correct support, you must look at the physical situation that you are modelling. Each node has 6 degrees of freedom (dof), i.e. 6 ways in which it may move. These movements are translation along the X, Y and Z axes and rotations about each of these axes. This is illustrated in Figure 1.5 below. If a support restricts movement or rotation in any of these directions, the node at that location must have its movement restricted by restraining one or more of its freedoms. Figure 1.5 Six Degrees of Freedom Freedom conditions must be considered from two aspects, Global or Default Freedom Conditions and specific Node Restraint Conditions. Global Freedom Conditions Global data includes velocities and accelerations. Freedom conditions allow fixed freedoms to be applied to all nodes and elements in the model. Other specific restraints may also be added to particular nodes. For example, if the Global DZ freedom is fixed, then every node in the model will have translational movement along the Z-axis restricted. From the GLOBAL menu select Load and Freedom Cases to specify the Global Freedom conditions. As this tutorial is a two-dimensional problem, we should set the Global Freedom condition as 2D Beam in the XY-Plane. This allows X and Y translations and Z rotations. This will prevent the model from exhibiting any out-of-plane behaviour, and ensures a faster solution by reducing the number of equations to be solved. This condition can be entered manually, or by using the Auto Set function explained below: Auto Set This function has pre-set freedom conditions for various common analysis types. To apply to a model, click the appropriate Auto Set button (in this case 2D Beam) and the appropriate check boxes will be marked. The steps below outline how to apply global freedoms to your model. 1 From the GLOBAL menu select Load and Freedom Cases; 2 Click the Freedom Cases tab; 3 Click the 2D Beam button to automatically enter the freedoms; 4 Close the dialog box;

7 The global freedom conditions are now set. Next, we will enter the node restraint conditions to simulate the supports of the frame. Node Restraint Conditions As you can see from Figure 1.1, the frame has two supports, one at each end of the structure. The left side is a simple support and the right side is a roller support. Simple Support The only movement that is allowed for a two-dimensional simple support is rotation about the Z-axis. This means that at the left-hand support (i.e. at Node 1) the frame cannot move. It may only rotate about the Z-axis. Roller Support A two dimensional roller support allows one translational movement and one rotational. On your model, this condition exists at Node 4, where we allow X translation and Z rotation. Assigning Restraints To begin assigning restraints to your model, select ATTRIBUTES, Node, Restraint. A dialog box appears that contains inputs for each of the six degrees of freedom: three translations (DX, DY and DZ) and three rotations (RX, RY and RZ). For each restraint, you can either fix the movement (set the check box), or leave it free to move (clear the check box). The following steps outline how to set the simply supported condition at Node 1 and the roller support condition at Node 4. (See the note at the end of this section for details of numerical entries). 1 From the ATTRIBUTES menu select Nodes then Restraint; 2 Select the appropriate check boxes so they appear identical to Figure 1.6 below; 3 Select Node 1; 4 Click Apply; 5 To apply the roller support to Node 4, clear the Translational X check box; 6 Select Node 4; 7 Click Apply; 8 Close the dialog box. Figure 1.6 Node Attributes Dialog Box for Node 1 The restraint condition you have set for the node is shown graphically. Figure 1.7 below illustrates the graphical representation used by Strand7 to display the restraint condition for the case when all 6 degrees of freedom are fixed (ie. no translation or rotation is permitted). For each freedom that is fixed, a graphic label is added to the node. The graphic label is always drawn parallel to the axis

8 system, so that if you rotate the view, the graphic label also rotates. Figure 1.7 Graphical Representation of a Fixed Restraint Note Adjacent to each check box on the Node Attributes dialog box is a text box that accepts numerical values (default value is zero). By entering a non zero value, you can enforce a node to move by a specified amount. For this tutorial, we leave the values as zero since we want to enforce a zero displacement for the degrees of freedom that are fixed.

9 Tutorial 1: Welded Frame - Applying Forces In Strand7, there are various methods of applying loads to a model. These include point forces, pressure loading, and dynamic effects to name a few. In addition, Strand7 allows as many as 32,000 independent load cases to be applied. This is useful in situations where you want to analyse a model under a variety of independent loading situations. The current load case is displayed via a drop down list, at the top of the Strand7 model window. You can change the current load case at any time by selecting from this list. As explained in the problem description, three different loading situations will be applied to the model, using different load cases. To add a new load case to the model: 1 From the GLOBAL menu select Load and Freedom Cases; 2 The Load Cases tab should be selected by default; 3 Click New Case; 4 A new load case with a default name will be created (i.e. Load Case 2 ); 5 Close the dialog box. Note The name of the load case can always be modified by double clicking the load case label or clicking the Edit Load Case Name button. You now have two load cases with which to apply the loads. The third load case is a combination case which does not need to be defined now. This will be defined at the post processing stage. For this tutorial, the loading will be applied using point forces. From Figure 1.1, you can see that Load Case 1 has a single 10 kn force applied in the negative Y-direction on the bottom centre beam. Load Case 2 has a single 30 kn force applied in the positive X-direction at Node 4. Load Case 3 is a linear combination of load cases 1 and 2. The load on the bottom centre beam (Load Case 1) can be applied in the following manner. 1 Ensure the current load case is Load Case 1; 2 From the ATTRIBUTES menu select Beam, Point Force, Global; 3 The Beam Attributes dialog appears as shown in Figure 1.8 below; 4 Under Global Point Force in the Y box enter 10; 5 Under Global Point Force in the a box enter 0.5; 6 Select the bottom centre beam; 7 Click Apply; 8 Close the dialog box.

10 Figure 1.8 Beam Attributes Global Point Force Dialog Box Before applying the 30 kn force for Load Case 2, change the current load case to Load Case 2, by selecting it from the drop down list. Since a node exists at the location of the force for Load Case 2, the 30 kn force can be applied as a node force. 1 From the ATTRIBUTES menu select Node, Force; 2 Under Force in the X box enter 30; 3 Select Node 4; 4 Click Apply; 5 Close the dialog box. Your model should now look like Figures 1.9a and 1.9b below for Load Case 1 and 2 respectively. (Ensure that you have the display node and element attributes On)

11 Figure 1.9a - Load Case 1

12 Figure 1.9b - Load Case 2 Strand7 allows the user to view a number of load cases at the same time. To view Load Cases 1 and 2 together, use the Multi View display function. 1 From the VIEW menu select Multi View; 2 In the X Views box, type or select 2; 3 Click OK. You can see that Strand7 displays Load Case 1 in the left window and Load Case 2 in the right

13 window. For the remainder of the tutorial, we will work in single view mode, so reset the screen back to One View. 1 From the VIEW menu select Multi View; 2 Click One View; 3 Click OK. You have now defined the model geometry, restraint conditions (supports) and loading. All that is required to completely define the problem is for the beams to be given material and cross sectional properties.

14 Tutorial 1: Welded Frame - Property Input To define the beam properties, from the PROPERTY menu select Beam. You should now see the Beam Element Property dialog box with the default title 1: Beam Property. Edit the property name to a more descriptive title such as Welded Beams. This dialog box is used for entering and editing the properties of the beam elements. There are several methods of entering beam properties. They can be entered by hand, chosen from a selection of standard sections, or read from a library of materials and sections. For this tutorial, we will use the materials and sections libraries. 1 From the PROPERTY menu select Beam; 2 Under Type click Beam; 3 Click the Geometry tab, and click Library; 4 Select BHP Universal Beams Collection; 5 Select BHP: Universal Beam 150UB18.0 Section; 6 Ensure Import Material is set; 7 Click OK; 8 Click Close. Note I11, I22, J and A are automatically calculated when the dimensions of the standard cross-section are defined. They can be accessed by selecting the Section tab in the Beam Element Property dialog box. The beam properties are now defined. To give a more realistic look to the model, you can render and shade the beam cross-section by configuring the beam element display characteristics. Before doing so, turn the node numbers off and change the viewing angle. 1 From the VIEW menu select Angles (alternatively press F12); 2 In the Angle X box, type or select 20; 3 In the Angle Y box, type or select 35; 4 In the Angle Z box, type or select 0; 5 Click here to see what your Viewing Angles dialog box should look like; 6 Click OK; 7 From the VIEW menu select Entity Display; 8 Click the Node tab; 9 Turn off the node numbers by clearing the appropriate check box; 10 Click the Beam tab; 11 Under Display Mode click Solid; 12 Select the Light Shade check box; 13 Click OK; Your model should look like Figure 1.10 below.

15 Figure 1.10 Rendered and Shaded Model There is now sufficient information to define the problem. You can now solve the model.

16 Tutorial 1: Welded Frame - Solving the Model To solve the model, from the SOLVER menu select Linear Static. The Linear Static Analysis dialog box will appear with a number of options for the solver. For now just use the default values. (See the Online Help for a detailed explanation of the solver options). After starting the Linear Static Solver, a series of messages will be printed on the screen, such as element assembly, matrix reduction, back substitution and summation of forces. These provide information on the current stage of the solution. When the solution is complete, Strand7 will give you information such as CPU time taken, date and time the solution was completed and the solution time. 1 From the SOLVER menu select Linear Static; 2 Click Solve; 3 Wait until the solver has completed; It is good practice before you close the solver panel, to review the text relating to the solution to ensure that no errors have occurred. The log file (as it is called) may also be opened using the RESULTS, View Results Log File command.

17 Tutorial 1: Welded Frame - Post Processing Post-processing is a term that describes reviewing and interpreting the results of a finite element analysis. In Strand7, the post processor allows you to view the results in many ways, such as contour plots, which use colour contours to represent particular results (eg. stresses, displacements, strains etc.), graphs, animations, deformed plots and data listings. All of the post processing in Strand7 is performed via the RESULTS menu. Since the Strand7 post processor is really the same program as the pre processor, many of the functions are the same for both modes of operation. Opening the Result File Before you can post-process a model, you need to the retrieve the corresponding results file for the particular model and solution type. 1 From the RESULTS menu select Open Results File; 2 Select the file Tutorial 1.LSA and click Open; 3 You are now in the post-processing environment. Note Strand7 stores all of its output data in a single file. For Linear Static analysis, this is the *.LSA file. The *.LSA file has the same file name as the model file (for example, if the model file is Tutorial 1.ST7, the linear static results file is Tutorial 1.LSA). For advanced users there is the option to save results files with different names from the input file. This is controlled in the Solver dialog box under the Files tab. Checking the Results Log File It is a good idea to check the results log file, which contains a list of all the solver messages generated during the solution procedure. From the RESULTS menu select View Results Log file, and open Tutorial 1.LSL. Search through the file and inspect any warning or error messages. Also, it is a good idea to check the summation of loads to ensure the correct loads have been applied to the frame. Displacement Scale Function It is important to inspect the deformed shape of the structure to ensure that the model is exhibiting the correct behaviour, taking into consideration the forces and restraints that have been applied. To see a deflected display of the frame, you must set the displacement scale to a non-zero value. To adjust the scale, 1 From the RESULTS menu select Displacement Scale (alternatively, click the Displacement Scale button); 2 The Displacement Scale dialog box has two Scale Type options, Percent Scale and Absolute Scale. Absolute Scale If you set the scale type to Absolute Scale, and set the value to 1.0 in the edit box, the displacements will be drawn at the same scale as the model. If the value is set to 10.0, then the magnitude of deflection will be scaled up 10 times. Percent Scale In most applications, the displacements are orders of magnitude smaller than the dimensions of the structure, and it is easier to set the scale in a relative manner. For example, if you set the scale type to Percent Scale and set the value to 15.0, the displacements will be scaled such that the largest displacement appears as 15% of the size of the largest dimension of the structure. The largest dimension is taken to be the longest distance between nodes along the X, Y, or Z-axes. 1 Close the Displacement Scale dialog box; 2 Set the viewing angle back to the XY-Plane (Hint: press F12);

18 3 From the RESULTS menu select Displacement Scale; 4 Click 10%; 5 Click OK. Note When you open the results file, it automatically defaults to Load Case 1. To access the other load cases, simply select them from the load case drop down list. The deformed plots should look like those shown in Figures 1.11a and 1.11b below. Figure 1.11a Deflected Display for Load Case 1

19 Figure 1.11b Deflected Display for Load Case 2 Combining Load Cases Earlier in this tutorial, it was explained that there are three loading conditions. These consist of two independent loadings (load cases 1 and 2) as well as a linear combination of these to produce Load Case 3. Strand7 allows you to create a linear combination of primary load cases. This can be done either before or after you have run the Linear Static Solver and have obtained results for the primary load cases. Since Load Case 3 is a combination of Load Cases 1 and 2, you can use the load case combination function of Strand7 to create the third load case. This procedure is explained below: 1 Close the results by selecting RESULTS, Close Results File; 2 From the RESULTS menu select Linear Load Case Combinations; 3 Click Add; 4 Rename Combination Case to Load Case 3 and enter a factor of 1 for both Load Case 1 and Load Case 2; 5 Click OK. To view the results of the newly created Load Case 3, you need to re-open the results file. There is no need to Solve the model again before opening the results file. You can use the Multi View function to view the results of the three load cases simultaneously. This will speed up the comparisons between the respective load cases, and will help to identify the differences between the different loading situations.

20 1 Re-open the results file; 2 Click Yes when asked if you wish to calculate the combination cases; 3 From the VIEW menu select Multi View; 4 In the X Views box, type or select 3; 5 Click OK. Your display should be like Figure 1.11c. Figure 1.11c Deflected Display for all 3 Load Case 3 Bending Moment/Shear Force Diagrams For this tutorial, we are interested in Plane 2 Bending Moment and Plane 2 Shear Force. These are the bending moments and shear forces acting on Plane 2 of the beam. Plane 2 is the plane in which the beam s principal 2 axis lies. 1 Switch back to One View; 2 From the RESULTS menu select Results Settings (alternatively, click the Results Settings button); 3 Under Draw As select Diagram; 4 Under Quantity select Force/Moment; 5 Under Diagrams select Plane 2 Shear Force and Plane 2 Bending Moment; 6 Click OK;

21 Switch to Multi View to show the Plane 2 Shear Force and Plane 2 Bending Moment diagrams for the three load cases. Note that you do not need to view both the bending and shear results at the same time (as explained above). You can view them independently, or in combination with other entities such as axial force, torque etc. Once you have examined the diagrams, you can turn them off by selecting VIEW, Result Settings and under Draw As select None. The Peek Function The Peek function allows you to extract a variety of specific results from a finite element solution. You can access individual properties of nodes, beams, plates and bricks. The best method of becoming familiar with the Peek function is to simply experiment. As an example, consider the case where you want to investigate the shear force and bending moment distribution of the bottom centre beam (for Load Case 1). 1 Switch back to One View; 2 Set Displacement Scale to zero; 3 Ensure the current load case is Load Case 1; 4 From the RESULTS menu select Peek (alternatively, click the Peek button); 5 Click the Beam button; 6 Under Quantity select Plane 2; 7 Select the bottom centre beam; 8 The Shear Force and Bending Moment distribution for the beam will appear in the dialog box; 9 If you wanted to show the Bending Moment (or Shear Force) distribution on the actual model itself, set the 3D check box underneath the Bending Moment (or Shear Force) diagram (highlighted by the red ellipse shown in Figure 1.12 below); 10 Press F3 to refresh the screen. Your screen should look like Figure 1.12 below.

22 Figure 1.12 Using Peek to extract beam results Contour Plots Contour plots offer an added dimension to a graphical image using colours or shading patterns to represent the variation of the selected quantity. Presenting results in this manner gives an overall picture of the distribution of quantities such as stress, temperature and displacement. Contour plots are commonly used with plate and brick elements, however they still provide an effective method for quickly extracting results for beam elements. Since we are interested in finding the maximum compressive and tensile axial stresses, it would be useful to plot a contour plot of the stress distribution within the frame. 1 From the RESULTS menu select Result Settings; 2 Under Draw as select Contour; 3 Under Quantity select Stress; 4 Under Stress Quantity select Axial; 5 Click OK. Note When you are in Single View mode and you have displayed a contour plot, the contour settings will remain when you switch to the other load cases. When you click OK, the screen will be redrawn and you will see a stress/colour legend ranging from purple to blue with a +/- scale next to it. The convention is for tensile stress to be positive and compressive stress to be negative. The legend has the positive number at the purple end of the scale, and the negative at the blue end. Thus, the most highly stressed region is shaded either blue or purple. By inspecting the beam colours in the display, you can easily see which beams are in tension, which are in compression and how stressed they are. Since for this tutorial we are interested in the highest levels of tensile and compressive axial stresses; look at the values at the top and bottom of the Axial Stress legend. They are automatically scaled to show the maximum levels of the selected components of stress (i.e. axial stress in this case). You will find that the beams with the highest and lowest values of stress are indicated in square brackets on the legend adjacent to the maximum and minimum values. You should find your results are: Load Case Max. Axial Stress (MPa) [Beam] Min Axial Stress (MPa) [Beam] [2] [9] [1] [8] [2] [9] As with the Peek function, the best way to get a feel for the contour function is to simply experiment.

23 Tutorial 1: Pin Jointed Frame - Truss Elements As explained in the tutorial introduction, the frame is to be analysed by considering the beams as pin-jointed. To do this, you need to make a few modifications to the welded frame model. It is much easier to modify the file from the Welded Joint analysis instead of beginning from scratch. 1 Open the file for the welded frame (if not open already); 2 Make sure the results are closed; 3 From the FILE menu select Save As; 4 Enter a new file name (e.g. Tutorial 1b.ST7) 5 Click Save. You can now begin to modify the beam element properties, so that the beams behave as though they are pin-jointed. Truss Elements The beams in a pin-jointed truss are not subjected to bending loads since moments cannot be transmitted through a pin joint. To eliminate the ability of the beams to transmit bending moments, we change the element Type from Beam to Truss within the Beam Element Property dialog box. This will ensure that the elements transmit axial forces only. However, the element that has a mid-span load does develop a bending moment internally which tends to zero at the ends. 1 From the PROPERTY menu select Beam; 2 Under Type select Truss; 3 Close the dialog box. The pin-jointed model is now ready to be solved. 1 From the SOLVERS menu select Linear Static; 2 Click Solve; 3 Close the solver panel.

24 Tutorial 1: Pin Jointed Frame - Post Processing Once your solution has completed, you can examine the results in the same manner as for the welded frame. First you need to open the results file by selecting RESULTS, Open Results File. Since this model was created from the Welded model, the Axial Stress may be showing. We shall turn this off for now (Hint: RESULTS, Results Settings, Draw as, None). Set the Displacement Scale to 10%. You may notice that all the beams in the deformed plot are now straight as shown in Figure 1.13 below. This indicates that the beams are carrying no bending moments. To check this: 1 From the RESULTS menu select Peek; 2 Click on the Beam button; 3 Under Quantity select End Force; 4 Click on any of the truss elements; 5 You will notice that all the moment values (i.e. M1, M2, M3, MX, MY, MZ) are zero; 6 Check this for the three load cases. Figure 1.13 Deformed Plot of Pin Jointed Model (Combined Case) Thus, as expected, the truss elements only transmit axial forces. To view the values of the Axial

25 Stresses: 1 From the RESULTS menu select Results Settings; 2 Under Draw as select Contour; 3 Under Quantity select Stress; 4 Under Stress Quantity Select Axial; 5 Click OK. Find the maximum tensile and compressive stresses as you did in the Welded Joint case. You should have the following results: Load Case Max. Axial Stress (MPa) [Beam] Min Axial Stress (MPa) [Beam] [1] [5] [1] [6] [1] [5]