Lab#3 ANSYS Analysis of a Beam By Claude Daley 2012

Transcription

1 Engineering Ship Structures I Lab#3 ANSYS Analysis of a Beam By Claude Daley 2012 INTRODUCTION A 10.0 m long rectangular beam carries a patch load of 5 N/m (excluding its own weight) as shown below. Draw the shear force, bending moment diagram and calculate the shear and normal stresses at mid span and near the support of the beam. What is the maximum deflection of the beam? E = 200 GPa I = m 4 Step 1: Solve the problem by hand. This problem was solved in three different ways in the notes. The Maple results are reproduced below for reference; > plot(v,x=0..l,title=`shear`, color=blue); > plot(m,x=0..l,title=`bending Moment`, color=blue); > plot(th,x=0..l,title=`beam Slope`, color=blue); 5003 Lab#3: ANSYS Analysis of a Beam page 1

2 > plot(yy,x=0..l,title=`beam Deflection`, color=blue); > evalf(subs(x=0,m));evalf(subs(x=l,m));evalf(subs(x=l,yy)); Max Stress = 62.67x(.1/2)/5e-6 = 6.27e5 Pa Step 2: Analyze the beam using workbench. In this step, we will first draw the shear force, bending moment, and deflected shape. Then we will analyze this beam for different stresses in bending. 1) Open Workbench and save the project as Tutorial 3. Drag Static structural project icon to project schematic window as shown below: Step 3: CAD modeling 1) Double click Geometry to create CAD model and choose meter for units. 2) Generate 4 points at (0,0,0), (2,0,0), (6,0,0) and (10,0,0) using the point tool. In the Details View at the lower left, under Definition, select Manual Input and enter (0,0,0) for X, Y, and Z coordinate respectively for first point and (2,0,0), (6,0,0) and (10,0,0) for the other points Lab#3: ANSYS Analysis of a Beam page 2

3 3) Click Concept in the menu bar to draw a line from points. For the first line, choose the first two points by holding the Ctrl key and selecting the first two points. Then click apply for Point Segments and generate the line. This will create a line body. Repeat for each pair of points to create 3 lines Lab#3: ANSYS Analysis of a Beam page 3

4 4) Draw the cross-section. To do this, click Concept again and choose Rectangle from Cross-Section, dimension it to.06 for B and 0.1 for H in Details View. The rectangle named Rect1 is created as shown below. To adjust the dimension position, right click on the window and choose Move Dimensions Lab#3: ANSYS Analysis of a Beam page 4

5 5) Now we have to assign the cross-section to this line body. Click on line body. In Details View, beside Cross Section and choose rectangle (Rect1) that was just created from the. 6) Align the cross section with the line body. Select the line body from the Tree and right click mouse. Click on and leave the cross section alignment default. To bring the cross section in desired orientation, use 90 for rotation and choose yes for orientation as shown below Lab#3: ANSYS Analysis of a Beam page 5

6 Step 4: Open Model and create Finite Element model 1) Double click on the model in ANSYS window and it will open the Mechanical window. We need to mesh the beam and apply loads and support. For mesh, use the default element size and generate by right clicking on the mesh icon and select Generate Mesh. 2) To apply the fixed support, right click on the static structural and go to insert and choose Fixed Support. Click on left end of the beam and apply button for geometry. On the other end you need to apply a guided support. This can be done with a support called Remote Displacement. 3) Load the 2 nd beam using line pressure of 5 N/mm. Right click on the static structural and choose line pressure Lab#3: ANSYS Analysis of a Beam page 6

7 4) Choose the 2 nd line for geometry and apply. From definition, choose defined by Components and write -5 for Y Component (downward load). 5) Plot the Moment Shear and Deflection of the beam. To do this, right click on the Solution, and select Insert > Beam Results > Bending Moment and Insert > Beam Results > Shear Force. Also select Insert > Deformation > Total Lab#3: ANSYS Analysis of a Beam page 7

8 The bending moment results are shown below. The undeformed beam is shown in light grey, by using the Show Undeformed Model option of the contour display button. The two end moments can be found by using the Maple solution. tool. The moments are identical to the The Shear force results are also just as expected : 5003 Lab#3: ANSYS Analysis of a Beam page 8

9 The deflection is too: 5003 Lab#3: ANSYS Analysis of a Beam page 9

10 6) Next we want to draw the shear force and moment diagrams. For this, we need to define the path for these diagrams. Select the beam (all 3 lines) for path, right click on the Solution in the Tree menu and choose insert -> beam results -> shear moment diagram. This will add the Total Shear Moment Diagram below the solution information. 7) Change the Total Shear-Moment Diagram to Direction Shear moment diagram (VZ-MY-UZ). The reason to choose VZ-MY-UZ is that the ANSYS Z-axis is same as the DesignModeler Y-axis as shown below. This will also give us negative and positive moments (vs just magnitude) Step 5: Solve the problem. 1)by selecting the Directional-shear-moment diagram we see the results Lab#3: ANSYS Analysis of a Beam page 10

11 These are just like the Maple results. Using the Beam Tool, we can plot the bending stresses. The max bending stress is e5 pa., exactly equal to our estimate. Horray!! 5003 Lab#3: ANSYS Analysis of a Beam page 11

12 Analyze the beam for stresses Now we will analyze the same beam using a 3D solid model. We need to see the bending and shear stress through the cross section at the end of the beam. We will model the beam in three parts as before. Let us see how we can do this. Step 1: CAD modelling 1) Choose XY Plane and sketch a rectangle of.06 m wide and.01 m high. Extrude the shape 10m to get the basic solid bar. 2) Now we need to tell Ansys to create a face where the load can be applied. Click on icon for new plane and chose From Face. Select the top of the beam and hit Apply. Now sketch a rectangle over the beam. Add dimensions for the distance from the end of the beam to the rectangle (2m) and for the length of the rectangle (4m) Lab#3: ANSYS Analysis of a Beam page 12

13 3) Extrude the rectangle through the beam with the option Imprint Faces. By Doing this we have created a separate surface on which to apply the load. Step 2) Open Model and Create the Finite Element model 1) Return to the ANSYS Window, and click Model. 2) The Mechanical window shows one solid. We need to mesh the beam and apply loads and support. Under mesh, insert a body sizing option and set the mesh size to 0.015m Lab#3: ANSYS Analysis of a Beam page 13

14 The mesh should look like: 3) To apply support, right click on the static structural and go to insert and choose Fixed Support for one end face. Click on other end face of the beam and apply a Remote Displacement. Set the Y component to Free, and all others to Lab#3: ANSYS Analysis of a Beam page 14

15 4) Load the beam. Select pressure from the static structural and choose top middle face of the beam. Click apply for geometry and write 83.3 for magnitude (w = 5 N/m, width of beam =.06 m, so pressure = 5/0.06 = 83.3 Pa). Hit solve to get results. 5) Output To get the deflection, right-click on Solution and select Deformation: Total Deformation Lab#3: ANSYS Analysis of a Beam page 15

16 We see the deformation pattern we would expect and we see that the total deformation is.0006m The same as the Maple and beam element models. OK 5003 Lab#3: ANSYS Analysis of a Beam page 16

17 b) The normal stress (in the Z direction which is along the beam) should be similar to the estimated bending stress of 6.27e5 Pa. The peak stresses at the very end of the beam are 8.5e5 (35% high) but just slightly in from the end the normal stress is 6.1e5 Pa. (3% low). This illustrates the false stress concentration around the fixed support that we saw in the first lab. Overall the deflection and bending stresses agree very well, as one would hope Lab#3: ANSYS Analysis of a Beam page 17

18 Self Study Exercise: Student: Exercise 3: Work in groups of 2 or alone (but have each student hand in this page). Make 2 models of the fixed-pinned T-section steel frame shown below (with beam and solid elements). Find the pressure that needs to be applied on a 200mm x 200mm central load patch to cause yielding. Comment on the results and identify potential concerns. 50 mm 300 mm 50 mm 2.0 m P =? MPa 200 mm Items Beam model Solid model Mid-span deflection Max. bending stress (MPa) Max. shear stress (MPa) Comments 5003 Lab#3: ANSYS Analysis of a Beam page 18