Ansys Lab3 on Beam

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5003 Lab#3: ANSYS Analysis of a Beam page 1

Engineering 5003 - Ship Structures I

Lab#3

ANSYS Analysis of a BeamBy 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 = 5×10-6 m4

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);




> 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 willanalyze 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 DetailsView 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.




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.




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 M ove Dimensions.




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.




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 2nd

beam using line pressure of 5 N/mm. Right click on the static structural and choose line

pressure.




4) Choose the 2nd

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.




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 tool. The moments are identical to the

Maple solution.

The Shear force results are also just as expected :




The deflection is too:




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 MomentDiagram 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.




These are just like the Maple results. Using the Beam Tool, we can plot the bending stresses. The max

bending stress is 6.2669e5 pa., exactly equal to our estimate. Horray!!




Analyze the beam for stresses

Now we will analyze the same beam using a 3D solid model. We need to see the bending and shearstress 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 modelling1) 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).




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.




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 0.




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.




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




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 justslightly 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.




Self Study Exercise: Student: ____________________

Exercise 3: Work in groups of 2 or alone (but have each student hand in this page). Make 2 models ofthe 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 theresults and identify potential concerns.

Items Beam model Solid model

Mid-span deflection

Max. bending stress (MPa)

Max. shear stress (MPa)

Comments

2.0 m 200 mm

300 mm

50 mm

50 mm

P = ? MPa

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Ansys Lab3 on Beam