Guide for Using RISA3D to Calc Freq and Mode Shapes
Transcript of Guide for Using RISA3D to Calc Freq and Mode Shapes
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CE 533, Fall 2014 Guide for Using RISA3D 1 / 9
to Calculate Natural Frequencies and Mode Shapes
Example Structure. The procedure for calculating frequencies and modes shapes of a multi‐
degree of freedom (MDOF) system will be demonstrated using the following example.
3‐Story, 1‐bay x 1‐bay structure.
Plan dimensions are 30’ x 30’.
All floors
have
a 7"
‐thick
reinforced
concrete slab (f’c = 4 ksi, unit
weight = 150 pcf).
All four columns are W14x30 steel
columns, Izz = 291 in4
1. Define the material properties.
Activate the “Data Entry” menu if it’s not already visible, and click on “Materials”.
1.1. Select the “Hot Rolled” tab and “A992”. Make sure that the modulus is set to 29,000
ksi.
1.2. Select the “Concrete” tab and “Conc4000NW” (for 4000 psi normal weight concrete)
and make
sure
“Density”
= 0.150
kcf.
10'
10'
10'
v1
v2
v3
30'
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CE 533, Fall 2014 Guide for Using RISA3D 2 / 9
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2. Define the Sections.
Select “Section Sets” from the “Data Entry” menu.
2.1. Select the “Hot Rolled” tab, type in a label (e.g. “Columns”), select the W14x30 shape,
select the A992 Material, and check that the moment of inertia about the strong axis
(Izz) = 291 in4.
2.2. Select the “Concrete” tab, type in a label (e.g. “Slab”), specify a rectangular element 7
inches deep by 180” wide (half the building width).
3. Set up your drawing grid
3.1. If the Graphic Editing Toolbar is not visible, right‐click anywhere in the white part of
the screen and select it.
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3.2. Select the “Drawing Grid” icon, type in “1@30” under “X Axis” and “3@10” under “Y
Axis”.
4. Layout the structure. Select “Draw Members”, and
4.1.
Draw the
columns
after
selecting:
“Hot
Rolled”,
“Assign
a Section
Set”,
“Columns”
(make sure to select the nodes at each level to provide an intersection for the slab
floors).
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4.2. Draw the slab floors after selecting: “Concrete”, “Assign a Section Set”, “Slabs”.
4.3. Check that your model is input correctly by selecting “Plot Options”, “Members”,
“Wireframe”, and “Shape”.
5. Specify the Boundary Conditions. Since we are building a 2‐dimensional model and RISA is
3D program, the first task is to constrain the model to a single plane (the X‐Y plane). Then
we specify the boundary conditions at the support (assume fixed‐base).
5.1. To constrain the model to the X‐Y plane, select the “Modify Boundary Conditions” icon,
then select
“Fixed”
and
check
the
“Use?”
box
for
“Z
Translation”,
“X
Rotation”,
and
“Y
Rotation”. Then select the “Apply Entries to All Selected Joints”, and select “Apply”.
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5.2. To specify the support conditions, select “Reaction” and check the “Use?” box for “X
Translation”, “Y Translation”, and “Z Rotation”. The only difference between “Fixed”
and “Reaction” boundary conditions is reactions are not calculated for “Fixed”.
5.3. Check the boundary conditions by selecting ”Boundary Conditions” from the “Data
Entry” menu.
Your
boundary
conditions
should
appear
as
below.
6.
Specify
the
Loads.
RISA
is
set
up
for
structural
design
in
which
the
engineer
checks
the
structural response to multiple combinations of loads. For this example, since we are only
calculating the natural frequencies and mode shapes, we will only have one basic load case
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(self weight, others could be super‐imposed dead load, live load, seismic loads, . . .) and one
load combination (self weight times a factor of 1.0, others could be 1.2 D + 1.6 L, . . .).
6.1. Select the “Basic Load Cases” icon and the “Load Combinations” icon and arrange the
spreadsheets as shown below.
On the “Basic Load Case” spreadsheet, type a label under “BLC Description” (e.g. “self
weight”) and
type
a “‐1”
under
“Y
Gravity”
to
specify
that
the
member
self
weights
will
be applied in the negative Y direction (downward).
On the “Load Combinations” spreadsheet, type another label under “Description” (e.g.
“self weight only”) and type a “1” under “BLC” (refers to Line 1 of the BLC spreadsheet)
and type a “1” under “Factor”
6.2. Check your model by calculating the structural response to self weight only. With
Load Combination 1 selected, select the “Solve Current” icon.
Display the
deflected
shape
of
the
structure
by
selecting
the
“Plot
Options”
icon,
the
“Deflection Diagrams” tab, “Load Combination”, “Include Undeflected Shadow” and
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“Apply”. Check the indicated deformations for reasonableness (e.g. no rotation at
fixed‐base supports, small rotations at column‐to‐floor connection, etc.).
7. Calculate the Natural Frequencies and Mode Shapes.
7.1. To calculate the natural frequencies, select the “Solution” icon, “Dynamics”, and
“Solve”.
Select
“Start
Solution”
on
the
“Dynamics”
spreadsheet
that
pops
up.
The resulting frequencies are displayed to the right:
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7.2. To display the mode shape for Mode 1, select “Plot Options”, “Deflection Diagrams”,
“Mode Shape”, “Mode 1 Period .9371 Sec”, “Include Undeflected Shadow”, and
“Apply”. Display the mode shapes for the other modes using a similar procedure.
Mode 2 Mode 3
8. Adjust the RISA model to match the hand‐calculated (spreadsheet) frequencies and mode
shapes.
We made several simplifying assumptions when calculating the frequencies and mode
shapes by hand.
8.1 Make the following changes to your RISA model so that it’s frequencies match the
hand‐calculated frequencies.
On the “Boundary Conditions” menu, “Fix” the rotation about the Z‐axis at all
column‐slab joints.
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On the “Global Parameters” menu, “Solution” tab: uncheck “Shear Deformation”
On the “Materials” menu, specify a density of “0” for A992 steel.
8.2 Now compare the RISA vs. hand‐calculated frequencies and mode shapes. You can
copy the RISA mode shapes into your Excel sheet and normalize them so that the maximum
modal displacement
equals
1.0
for
each
mode.