Tutorial 3 - With Figures

8/8/2019 Tutorial 3 - With Figures

1/14

Tutorial 3 1/14

ANSYS - Structural Analysis/FEA2D Continuous Beam with Distributed Load

Problem: For a steel continuous beam with distributed loads as shown below, calculate

the load factor if the moment capacity of the cross section is limited to Mmax = zFy,

where, = 0.9. The beam is made of steel with Youngs modulus of 200 GPa, Poisson

ratio 0.30 and the allowable stress (Fy) 350 MPa. The beam has a box cross-section

(HSS 356x250x16) (Figure 2) with plastic section modulus (z) 1910103

mm3. (not the

same as elastic section modulus).

Figure 1: Continuous Beam

Figure 2: Beam cross-section

254 mm

356 mm

14.29 mm

200 kN/m150 kN/m

7.0 m 2.1 m7.0 m

50 kN

50 kN/m

3.0 m

A B C DE


2/14

Tutorial 3 2/14

Step 1: Start up & Initial Set up

Set preferences and unit.

Step 2: Specify Element types and Material Properties

Use BEAM3 element.

Step 3: Specify Sections

Main Menu > Preprocessor > section > beam > common sections.

We can define the cross section from this window.

Choose sub-type of the beam to be a box cross-section and select Offset to: Centroid. This

defines the reference axis of the beam.

ClickPreview to see the data summary.

Now look at the values ofIyy andIzz. In this figure, y-axis is in the horizontal direction and

z-axis is in the vertical direction.

y

z


3/14


4/14

Tutorial 3 4/14

To create point E,

Main Menu > Preprocessor > Operate > Booleans > Divide > Lines w/ Options.

Pick the line to be divided by clicking on L1. Click Ok.

Enter NDIV = 2 and RATIO = 3/7. Click OK.


5/14

Tutorial 3 5/14

Step 5: Meshing

Main Menu> Preprocessor> Meshing> Mesh Attributes> Default Attribs

Click OK.

Main Menu > Preprocessor > Meshing > Mesh Tool

There will be a Mesh Tool window pop up.

In the third section Size Controls >Lines, clickSet. Select Pick All.

Another window pops up.

Here, you can either define the element edge length or number of element divisions.

Enter the element edge length to be 0.1. ClickOK.


6/14

Tutorial 3 6/14

In general, the size of element will influence the accuracy of the solution. Smaller size of

elements (or more numbers of elements) gives more accurate results but requires more time

to obtain the solutions.

However, for this beam problem, only 3 elements are needed (AB, BC and CD) to obtain the

exact solution. In the example, we use more numbers of element in order to obtain a smooth

bending moment diagram.

In the Mesh Tool pop up (fourth section), Mesh: Lines. ClickMesh. Select Pick All

To see node and element numbering, use: Plot Ctrls >Numbering>Node Numbers and Plot

Ctrls >Numbering >Element/Attr Numbering

Choose Plot > Elements to see the elements and the nodes


7/14

Tutorial 3 7/14

Step 6: Specify Boundary Conditions & Loading

Main Menu > Preprocessor > Loads > Define Loads > Apply > Structural > Displacement >

On Keypoint

Now select Keypoint 1, select UX, UY.

Set UX, UY as 0. Click Apply.

Next, constrain UY of Keypoint 2 and 3.

Apply Loading:

Main Menu > Preprocessor > Loads > Define Loads > Apply > Structural >Force/Moment >

On Keypoint

Now select Keypoint 5.

Select FY and enter-50000 as the Force value.


8/14

Tutorial 3 8/14

Apply distributed load

Main Menu> Preprocessor> Loads> Define Loads> Apply> Structural> Pressure> On Beams

Now select all elements between point A and B by click on Box and drag a box to cover all

the elements.

Click OK.

For uniform distributed load, enter VALI = 200e3 kN/m

Note that, the positive value indicates the direction of pressure acting inward the beam

surface.


9/14

Tutorial 3 9/14


10/14

Tutorial 3 10/14

Similarly, distributed loads on beam BC and CD can be added.

Step 7: Solve

Main Menu > Solution > Solve > Current LS

Click OK in the Solve Current Load Step pop up window.

Step 8: Post Processing

Plot Deformed Shape

Main Menu > General Postproc > Plot Results > Contour Plot> Nodal SolutionSelect DOF solution> UY

In Items to be plotted, select Deformed+Undeformed

Click OK


11/14

Tutorial 3 11/14

Create Element Table

Main Menu > General Post Proc > Element Table > Define Table

Click Add.

In the next window select By Sequence number, in the right window select SMISC and enter

SMISC, 6 at the bottom text box. (MMOMZ = Member moment at node i1)

Click Apply.

Then add SMISC, 12 (MMOMZ = Member moment at node j1)

Then add LS, 2,5 (SBYT = Bending stress on the element +Y side of the beam1)

Then add LS, 3,6 (SBYB = Bending stress on the element -Y side of the beam1)

Click OK

Click Close

1See BEAM3 - Table 3.2 (Element Output Definitions) for description of each option.


12/14

Tutorial 3 12/14

Plotting Bending Moment Diagram

Main Menu > General Post Proc > Plot Results > Contour Plot > Line Element Res


13/14

Tutorial 3 13/14

Similarly, you can plot the stresses at the top (or bottom) fibers of the beam by selecting LS2

(or LS3) from the list

List Stress Values

Main Menu > General Post Proc > Element Table > List Element Table >

Select LS2 and LS3

Click OK

You will be able to see the bending stress values of each element in +Y and Y direction and

the maximum stresses.


14/14

Tutorial 3 14/14

Calculate Load Factor

Mmax = )m10101910()Pa10350(9.03936

= 601650 mN

In this problem, the maximum moment is 979907 mN

Load factor = 601650/979907 = 0.614

Documents

Tutorial 3 - With Figures