tutorial 3 - with figures
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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
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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
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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.
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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.
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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
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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.
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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.
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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
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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.
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Plotting Bending Moment Diagram
Main Menu > General Post Proc > Plot Results > Contour Plot > Line Element Res
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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.
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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