HOW to ANALYZE a SIMPLY SUPPORTED BEAM for INTERNAL FORCES, REACTION

Transcription

1 HOW to ANALYZE a SIMPLY SUPPORTED BEAM for INTERNAL FORCES, REACTION FORCES and DISPLACEMENT USING RISA-2D The simply-supported beam is one of the most basic and fundamental parts of any structural design. Whether the beam stands alone or is part of a much more complicated structure, it can be analyzed either by hand or in a program like RISA-2D. While it is important to check program-calculated results, determining reaction forces and forces within the beam can be made so much faster with technological aid, increasing the speed of design output. Outside of strict design work, this program is also very useful in checking hand-calculated homework problems. Most importantly, however, learning how to analyze a simply supported beam in RISA will give you fundamental skills with the program that will later be necessary in analyzing trusses, columns, and even entire structure support systems. This tutorial will give you the tools you need in order to draw, load, and analyze a simply supported beam, but before we begin, a note on how to download the program if you do not already have access to it: RISA-2D can be purchased at risa.com for $ Free trials are available at this site, as well as free student versions valid with a student number. Before making the decision to purchase RISA-2D, be sure to check if your company (or school) will finance the purchase, as it is common for companies to allow the program to be expensed. Once the program has been downloaded (whether in a trial, student version, or official version) you are ready to begin. NOTE: The beam that will be analyzed in the instructions is shown below in a simplified version. It is important to recognize that once the basics of the programs are introduced, the type of beam to be analyzed can be altered in an almost infinite amount of ways. The different types of alterations will become clearer within the instructions. P = 40 kips L/2 L/2 L = 30 ft Material Properties: A36 Hot rolled Steel Wide Flange W8x10

2 PART A: DRAWING THE BEAM 1. First, set your joint coordinates. This is where you will set the limits and length of your beam using joint coordinates, which are also called nodes. When you open RISA, a window called Data Entry will appear on the right hand side of the screen. Click on the option labeled JOINT COORDINATES. To place node one, or N1, click on the window. To place node 2 or N2, press ENTER and set the x- and y-coordinates. Notice that N1 is located at some arbitrary origin (0,0) NOTE 1, and N2 at the coordinate (30,0), making our total length 30 ft. NOTE 2 The length of the beam may be altered by simply changing the N2 coordinate in the x component with respect to N1. NOTE 1: You may change the position of N1 to be whatever you wish, just keep in mind the effect it will have on N2 with respect to your desired length. For example, if you wish to have a total length of 30 ft., and you want N1 to have the coordinate (10,0), then N2 will have to be at the coordinate (40,0). The Y-component of the coordinate may also be changed, but be sure to keep it the same for both nodes. Typically, the origin is kept at coordinates (0,0) for simplification purposes that will become apparent later. NOTE 2: You may choose different units by selecting the Units menu located in the top left corner of the RISA window. Remember to keep in mind that if you change your units for length (from feet to meters, for example) you MUST also change your units for force, moment, etc. for your end results to make sense.

3 2. Next, draw the member. Select the Draw New Member icon from the option bar within the model view window- this will bring up the member design window. This is where you may choose the material you are working with as well as the shape. MAKE SURE that you have selected beam under the Type category, otherwise your end results may be wrong due to improper loading. For this example, we have a Wide Flange, W8x10 beam of A36 Hot Rolled steel. Once you have selected the proper settings, click Apply and draw your member by first clicking on N1 and then clicking on N2. Then press the escape key to exit member drawing. The result should be the same as shown below.

4 3. Now select supports/boundary conditions. Select the Modify Boundary Conditions icon from the option bar located in the model view window. This will bring up a window that will allow you to select what type of supports you wish. NOTE 3 First, select the support you wish to have at N1, then click APPLY (the boundary conditions window will disappear), and then click on N1. Repeat the process for N2, selecting the desired support. For this example, we have a pinned support for N1 and a roller support for N2. The end result should be similar (it may differ depending on placement of supports and length of member) to the image below. NOTE 3: By definition, a simply supported beam is supported on one side by a hinge, and on the other, a roller. It is very important that you make note of which node you have placed which support at, as it may affect your results. *This method for analysis may also be used on a beam with one free end and one fixed end, and a simply supported beam that has a small cantilever portion. THIS COMPLETES THE DRAWING PORTION OF THE INSTRUCTIONS.

5 PART B: LOADING THE BEAM Now that a stable, determinable beam has been created, we can begin to load the beam. For the example beam, we see that only one point load has been applied at the location L/2 with a magnitude of P = 40 kips in the downward direction. 1. Place point load. Begin by selecting the Point loads for Selected Members icon in the Model View window. This will bring up another window that will allow you to choose the direction NOTE 4, magnitude, and location NOTE 5 of the vertical load. After inputting the desired information, and after making sure Basic Load Case 1 is selected (this is explained in Part C), and that Apply Load by Clicking Members option is selected, press APPLY (The window will disappear.) Click on the beam to apply the load. NOTE 6 The end result should resemble the figure shown below. NOTE 4: It is important to be specific when detailing the magnitude of the load. If you want to have the load applied perpendicularly to the beam (in the y direction), then you must also specify whether you want the load applied pushing down or up on the beam. Having the magnitude be positive will result in a load being applied in the positive y-direction (up) while having it be negative will result in the load being applied in the negative y- direction (down). NOTE 5: When it comes to the location when the load is in the y-direction, location is referring specifically to the x- coordinate. So since we want the load applied at L/2, we calculate 30/2 = 15ft so the load is applied at (15,0). IMPORTANT: If you did not elect to have your beam start at (0,0), you will need to take this into account. Remembering our example from NOTE 1 where we chose to have our beam start at (10,0), in order to have the load applied at L/2, we would have to add 10 to our calculated number- so we would input the location as 25. This is why the origin is more commonly used than another coordinate for N1- it makes human error less likely and keeps the problem simpler. NOTE 6: The program can be finicky when it comes to applying load, if you do not see the load, continue clicking on different sections of the beam. Since you specified in the Points Loads for Selected Members section where on the beam you wanted the load applied, it doesn t matter where on the beam you click. THIS COMPLETES THE LOADING PORTION OF THE INSTRUCTIONS.

6 PART C: ANALYZING THE BEAM Now that our beam has been loaded, we can now analyze the beam for shear, moment, and reaction forces, and displacement. 1. Create the load case. In Part B, we selected Basic Load Case 1 (BLC1) while setting up our point load, now we must create that load case. First select the icon that represents Load Combinations to bring up the window. The only sections you need to fill in are the Description (which is at your discretion), BLC (which is 1) and the Factor (which is also 1) NOTE 7. After this is completed, the Load Combinations window can be exited. NOTE 7: For the purposes of this exercise, the other BLC and FACTOR sections may be ignored. Be sure that the solve box is checked as well. 2. Solve the load case. To solve for the reaction forces, shear forces, moments, and displacement, select the Solution Choices located directly to the right of the Load Combinations Icon. Select SINGLE LOAD COMBINATIONS, and make sure that your Load is chosen (it will go by whatever you called it in the description from Part C Step 1). Then press SOLVE. There will be no discernable difference with the beam- how to display the solutions will be discussed in Part C Step 3.

7 3. Display Solutions. In order to display the results of the analysis, select the Set Options for Current View icon located in the top left corner of the RISA-2D window. a. To Display Shear and Moment Diagrams. Select the Members tab and look to the right under the section labeled Member Results. Select Shear in the drop down menu and click OK. This will display the shear diagram. To display the Moment diagram, repeat the process but select Moment in the drop down menu. The results for the shear and moment diagrams should look like the figures below: Shear Diagram Moment Diagram

8 b. To Display Reaction Forces. Select the Joints Tab and look at the section labeled Show the Reactions on the right-hand side. Check the boxes for x-direction and y-direction and also the box labeled Include the Magnitude. Then Press OK. The results should look like the figure shown below.

9 c. To Display Displacement. Select the Deflection Diagrams tab and then select the option Load Combination. Since we only have one Load case, it is automatically selected and we do not have to specify the load case. Ignore the Animation options, and select a desired magnification factor. NOTE 8 After this is done, click OK. The results should look like the figure shown below. NOTE 8: For most simply supported beams, a magnification factor of 1 is sufficient, but as the stiffness of the designed beam increases or as the structures get more complicated, a higher magnification factor may be necessary to see the deflected shape. THIS CONCLUDES THE INSTRUCTIONS.