instant structural analysis (isa) workshop 2015 structural analysis (isa... · getting started:...
TRANSCRIPT
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INSTANT STRUCTURAL
ANALYSIS (ISA)
WORKSHOP 2015
Paul Lam
Department of Architecture and Civil Engineering
City University of Hong Kong
7 Dec 2015
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Workshop outline
• Introduction
• Getting started:
• Beam examples
• A portal frame example
• A truss example
• A building frame example
• Semi-rigid support condition
• Various types of hinges
• Dynamic modal analysis
• Second order analysis
• Moving load analysis
• Concluding remarks
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Introduction: What is iSA?
• iSA (instant Structural Analysis) is a user-friendly 2-
dimensional structural analysis program.
• It can be used to do:
• First and second order static analysis;
• Dynamic modal analysis;
• Stability analysis;
• Moving load analysis;
• Lack-of-fit; Support settlement; Temperature loading; etc.
• It can be used for the analysis of:
• Truss
• Continuous beam
• Frame (with different types of pinned joints)
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Introduction: Assumptions
• Member axis is straight.
• Material is homogeneous, isotropic and linear elastic.
• Length of a member is large when compared to the
section dimensions, and shear deformation is neglected.
• Plane sections remain plane after deformation.
• Hook’s law is valid without any restrictions.
• All loads are assumed to act statically and do not change
the direction due to deformation.
• * Deformations are small so that equilibrium on the
undeformed structure can be assumed.
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Introduction: Element stiffness matrix
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Introduction: System stiffness matrix
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m = 0
m ≤ number of
members?
m ≤ number of
members?
Calculate the local element
stiffness matrix of the mth
member [km]l
Transform the [km]l to the
global element stiffness
matrix [km]g
Assemble the system stiffness
matrix [K]
m = m + 1
Obtain [K]YES NO
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Introduction: Solution method
• After obtaining K and Q, iSA will calculate the global
displacement vector and support reactions.
• Then obtain the local displacement vector, and calculate
the member end forces.
• Finally, calculate the axial, shear force, and bending
moment diagrams. *** All within 0.1 sec!!
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s
f
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f
D
D
KK
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Q
Q
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sfs DKDKQ 2221
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Introduction: iSA graphical user interface
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Menu bar
Tool bar
Load tree
Drawing area
Status bar
Coordinate system
x
z
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Introduction: Toolbars
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Results: axial force, shear force, and bending moment diagrams, etc.
Load: point, distributed and temperature loads, lack of fit etc.
Structure information: node and element numbers
Zoom
System (Model components): node, support, member, and hinge
General
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Getting started: A beam example
• Calculate the support reactions, the shear force and
bending moment diagrams of the cantilever beam.
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4 m4 m
10 kN/m
A
B Cx
y
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Getting started: Define nodes
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Getting started: Define elements
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Message to the users!!
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Getting started: Define support
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Warning message to the users!!
Default: pin support! The fail mechanism!
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Getting started: Define support condition
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Message to the users!!
Right mouse click at the
support to open the Support
properties window.
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Getting started: Apply loading
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The analysis is finished
instantly!!!
Defection shape!
Default: 10 kN/m
It is automatically
assigned to the
‘imposed loads’
case.
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Getting started: Result presentation
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Support reactions
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Getting started: Detail member report
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The detail report of the
selected member.
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Getting started: Another beam example
• Calculate the support reactions, shear force and
bending moment diagrams of the beam. Determine also
the deflection shape.
• Member 1: E = 200 GPa, A = 0.0150 m2, I = 2.8 104 m4
• Member 2: E = 200 GPa, A = 0.0080 m2, I = 2.2 104 m4
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4 m4 m
10 kN/m
A B Cx
y
1 2
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Getting started: Additional supports
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Release the horizontal
displacement to model
a roller support.
The analysis is finished instantly!!
But, this is not the final answer.
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Getting started: Modify member properties
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Modify the properties of
both members!
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Getting started: Member properties
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Material
Database
Cross-section
Database
Material
Properties
Cross-sectional
Properties
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Getting started: Distributed loads
• Three type of distributed loads are available in iSA. They
are summarized in the table below.
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Getting started: A portal frame example
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4 m
1 m
7 m 7 m
Nodes Supports Elements
Start a new project!!
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Getting started: Loading
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Different types of loads
The analysis will be completed right after
defining the load!
The green line shows the deflection shape.
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Getting started: Results presentation
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Getting started: Member report
• For each
member, a detail
report on the
internal member
forces and
displacements at
different locations
on the member is
available.
• Users can
change the
subdivision
points.
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Getting started: Element & system K
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Contribution of the each
element in the system
stiffness matrix
Local and global element
stiffness matrices
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Getting started: A truss example
• Calculate the support reactions and axial force diagram
of the truss. Determine also the deflection shape.
• All member: E = 210 GPa, A = 0.0150 m2
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10 kN 10 kN10 kN
3 m 3 m 3 m 3 m
3 m
2 m
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Getting started: Structure generator
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Getting started: Truss shape/configuration
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Getting started: Define truss location
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Modelling completed!!
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Getting started: Loading
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Getting started: Modify member properties
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Right mouse click at one of
the selected members!!
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Getting started: Axial force diagram
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Getting started: A building frame example
• Construct the axial force, shear force, and bending moment diagrams of the building frame.
• Determine also the top draft.
• Given: • All columns are:
UC 356 368 202
• All beams are:
UB 406 178 74
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6 s
tori
es @
3.5
m4
m
6 m 6 m
50 kN
15 kN/m
30 kN
30 kN
50 kN
30 kN
30 kN
30 kN
15 kN/m
15 kN/m
15 kN/m
15 kN/m
15 kN/m
15 kN/m
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Getting started: Structure generator
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Getting started: Delete members
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Select the unwanted
members
Delete the selected
members
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Getting started: Change first story height
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Select all nodes at
the ground floor.
Right mouse click
to open the ‘Move
selected nodes’
window.
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Getting started: Apply vertical load
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Select all beams and
apply the load on one
of them.
Change the default
load magnitude from
10 to 15 kN/m.
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Getting started: Apply horizontal load
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Change the default load
from 10 kN vertical to the
desired magnitudes and
directions.
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Getting started: Result presentation
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Getting started: Define grid size
• Model components, such as element and support, must
be added AFTER the definition of nodes.
• In general, Nodes can ONLY be added to the grid points
in the drawing area.
• In order to put nodes at the desired positions, one may
need to re-define the grid spacing in the drawing area.
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Getting started: Load on node or member
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Getting started: Display information
• One can switch on/off the display of:
• Loads
• Node number
• Element number
• Material properties
• Geometrical properties (e.g., length of member)
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Semi-rigid connection
• A semi-rigid connection can be modeled by a rotational
(torsional) spring with stiffness equal to that of the actual
connection.
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m
x
y
bb ee
11,dq22 ,dq
33,dq
44 ,dq
L
Infinitesimal
Rotational springs
mbb ee
1q2q
3q
4q1q
2q
1q2q
3q
4q3q
4q
The equilibrium
of the springs:
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Semi-rigid connection
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bk ek
2d
2d
11 dd
33 dd
4d
4dDisplaced position
Initial position
mbb ee
L
Infinitesimal
11 dd
33 dd
222 ddkq b
444 ddkq e
bk
qdd 2
22
ek
qdd 4
44
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Support conditions
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Allow users to model supports
as different types of springs.
Allow users to rotate
the support.
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Hands-on: Semi-rigid support
• Model a 4m by 6 m steel frame (using default section) and
apply a horizontal load of 10kN at the top left connection
of the frame. Show the bending moment diagram.
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• Change one of the
supports to semi-rigid by
inserting a rotational
spring of 100000kNm/rad,
and observe the changes.
• Change the rotational
stiffness to 1000kNm/rad,
and observe the changes.
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Various types of hinges
• There are three types of hinges in iSA. They are:
• Full hinge: all members are connected to this joint as a
pin connection.
• Half hinge: this allows users to define pin joints at the
end of individual members.
• Pinjointed hinge: this allows users to model the
situation when two members are hinged at the middle.
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Select
Node
Support
MemberMember polygon
Full hinge
Pinjointed hinge
Half hinge
Split member
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Hands-on: Hinges in iSA
• Consider a 4 m by 4 m steel frame under a horizontal load
at the top left connection.
• Record the horizontal displacement.
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Hands-on: Half hinge
• Install two brace members to the steel frame (using
default member).
• Record the horizontal displacement.
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Hands-on: Pinjointed hinge
• Install a pinjointed hinge at the middle of the two braces to
further reduce the horizontal displacement of the system.
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Hands-on: Continuous beam analysis
• Use iSA to model a continuous beam with four spans (4m,
6m, 4m, 6m).
• Apply various design actions onto the beam to consider
the most unfavorable conditions.
• Calculate the design moment envelop.
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Hands-on: Truss analysis
• Calculate the support reactions and internal member
forces of the truss.
• Given: E = 200 GPa and A = 0.0077 m2
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6 m
5 m5 m 5 m 5 m
15kN15kN
15kN
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Hands-on: Rigid frame analysis
• Given:
• E = 210 GPa for all members.
• Columns: UC 305 x 305 x 283
• Beams: UB 686 x 254 170
• Plot the axis force, shear force,
bending moment diagrams
under:
• Vertical load ONLY
• Horizontal load ONLY
• Combine vertical and horizontal load
• [Demonstrate temperature load,
support settlement and lack of fit]
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3 m
4 m
6 m
20 kN
10 kN
3 kN/m
3 kN/m
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Hands-on: Temperature load
• Two types of
temperature loads are
available in iSA.
• The constant
temperature across the
depth of a section, and
• Linear varying
temperature along the
depth of a section.
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Hands-on: Lack of fit & support movement
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Dynamic modal analysis
• Consider the undamped free vibration of an N-DOF
system, the equation of motion:
• where M and K are the system mass and stiffness
matrices of the structure. Assuming a solution form of:
• The natural frequencies and mode shapes of the
structural system can be calculated by solving the
eigenvalue problem.
iSA Workshop 2015, University of Queensland, Brisbane, Australia 58
0KXXM
tsinφX
0φMK 2
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Dynamic modal analysis
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Second order analysis
• is the nodal displacement due to sway induced by loads
in the frame and imperfection.
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P
F
H
P
F
1
P
F
1 2
FH FH+P1 FH+P1+P2
(a) (b) (c)
…
(a) (b) (c)
P
F
H
P
F
1
P
F
1 2
FH FH+P1 FH+P1+P2
(a) (b) (c)
…
P
F
H
P
F
1
P
F
1 2
FH FH+P1 FH+P1+P2
(a) (b) (c)
…
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Second order analysis
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ww
P
8
2wL
ww
P
11
2
8P
wL
ww
P
221
2
8 PP
wL
(a)
(b)
(c)
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Second order analysis: Formulation
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x
x
w
yy + y
M
M + M
V + V
V
P
P
A
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Second order analysis: Formulation
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0 yF 0 xwVVV wx
V
0x wdx
dVWhen .......................(1)
0 AM
02
2
yPx
wxVVMMM
0 yPxVMNeglecting higher order terms
DM
Dx-P
Dy
Dx=V
When dM
dx-Pdy
dx=V ..................(2) 0x
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Second order analysis: Formulation
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EI
M
dx
yd
2
2
2
2
dx
ydEIM
Vdx
dyP
dx
ydEI
3
3
wdx
ydP
dx
ydEI
2
2
4
4
EI
w
dx
yd
EI
P
dx
yd
2
2
4
4
…………………..(3)
…………………..(3a) With (2)
With (1)
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Second order analysis: iSA solution
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Calculate the first order
displacement vector {u}I
Determine the axial forces
N(n) using {u}I
Assemble the second order
stiffness matrix [K]II
Calculate the second order
displacement vector {u}II
Determine the axial forces
N(n) using {u}II
n = 1
n = n + 1
nN
nNnN 1
nN
nNnN 1YES
NO
Calculate member forces
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Hands-on: Second order analysis
• Given: • All columns are UC 15215230
• All beams are UB 17810219
• Use iSA to model the frame together with the two vertical loads.
• Apply a horizontal load of 1 kN at the top left corner of the frame and carry out second order analysis. What happened?
• Increase the vertical loads to 550kN. What happened?
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4 m
3 m
5 m
400 kN400 kN
1 kN
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Moving load analysis
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Hands-on: Vehicle load on bridge
• Given:
• The I & A of the bridge desk are 2.13 107 cm4 and 4.00 104 cm2.
• The I & A of the columns are 1.80 107 cm4 and 2.25 104 cm2.
• Plot the bending moment and displacement envelopes for
a point load of 10 kN moving on the bridge deck.
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16 m 22 m 22 m 16 m
10 m 10 m12 m
A B C D E
FG
H
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Concluding remarks
• Various features of iSA in 2D truss, beam and
frame analysis were demonstrated.
• Through a series of hands-on exercises,
participants should be able to use iSA in:
• Structural analysis of 2D structures
• Modeling semi-rigid supports
• Dynamic modal analysis
• Second order analysis
• Moving load analysis
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