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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
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
iSA Workshop 2015, University of Queensland, Brisbane, Australia 2
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)
iSA Workshop 2015, University of Queensland, Brisbane, Australia 3
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.
iSA Workshop 2015, University of Queensland, Brisbane, Australia 4
Introduction: Element stiffness matrix
41
2
3
5
6
' ',ix ixq d
' ',iy iyq d
' ',iz izq d
' ',jx jxq d
' ',jz jzq d
' ',jy jyq d
3 2 3 2' '
'
2 2'
'
'
'3 2 3 2
2 2
0 0 0 0
12 6 12 60 0
6 4 6 20 0
0 0 0 0
12 6 12 60 0
6 2 6 40 0
ix ix
iy
iz
jx
jy
jz
EA EA
L L
EI EI EI EIq d
L L L Lq dEI EI EI EIq L LL L
q EA EA
L Lq
EI EI EI EIq
L L L L
EI EI EI EI
L LL L
'
'
'
'
'
iy
iz
jx
jy
jz
d
d
d
d
iSA Workshop 2015, University of Queensland, Brisbane, Australia 5
Introduction: System stiffness matrix
iSA Workshop 2015, University of Queensland, Brisbane, Australia 6
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
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!!
iSA Workshop 2015, University of Queensland, Brisbane, Australia 7
s
f
s
f
D
D
KK
KK
Q
Q
2221
1211
sfs DKDKQ 2221
sff DKQKD 12
1
11
Introduction: iSA graphical user interface
iSA Workshop 2015, University of Queensland, Brisbane, Australia 8
Menu bar
Tool bar
Load tree
Drawing area
Status bar
Coordinate system
x
z
Introduction: Toolbars
iSA Workshop 2015, University of Queensland, Brisbane, Australia 9
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
Getting started: A beam example
• Calculate the support reactions, the shear force and
bending moment diagrams of the cantilever beam.
iSA Workshop 2015, University of Queensland, Brisbane, Australia 10
4 m4 m
10 kN/m
A
B Cx
y
Getting started: Define nodes
iSA Workshop 2015, University of Queensland, Brisbane, Australia 11
Getting started: Define elements
iSA Workshop 2015, University of Queensland, Brisbane, Australia 12
Message to the users!!
Getting started: Define support
iSA Workshop 2015, University of Queensland, Brisbane, Australia 13
Warning message to the users!!
Default: pin support! The fail mechanism!
Getting started: Define support condition
iSA Workshop 2015, University of Queensland, Brisbane, Australia 14
Message to the users!!
Right mouse click at the
support to open the Support
properties window.
Getting started: Apply loading
iSA Workshop 2015, University of Queensland, Brisbane, Australia 15
The analysis is finished
instantly!!!
Defection shape!
Default: 10 kN/m
It is automatically
assigned to the
‘imposed loads’
case.
Getting started: Result presentation
iSA Workshop 2015, University of Queensland, Brisbane, Australia 16
Support reactions
Getting started: Detail member report
iSA Workshop 2015, University of Queensland, Brisbane, Australia 17
The detail report of the
selected member.
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
iSA Workshop 2015, University of Queensland, Brisbane, Australia 18
4 m4 m
10 kN/m
A B Cx
y
1 2
Getting started: Additional supports
iSA Workshop 2015, University of Queensland, Brisbane, Australia 19
Release the horizontal
displacement to model
a roller support.
The analysis is finished instantly!!
But, this is not the final answer.
Getting started: Modify member properties
iSA Workshop 2015, University of Queensland, Brisbane, Australia 20
Modify the properties of
both members!
Getting started: Member properties
iSA Workshop 2015, University of Queensland, Brisbane, Australia 21
Material
Database
Cross-section
Database
Material
Properties
Cross-sectional
Properties
Getting started: Distributed loads
• Three type of distributed loads are available in iSA. They
are summarized in the table below.
iSA Workshop 2015, University of Queensland, Brisbane, Australia 22
Getting started: A portal frame example
iSA Workshop 2015, University of Queensland, Brisbane, Australia 23
4 m
1 m
7 m 7 m
Nodes Supports Elements
Start a new project!!
Getting started: Loading
iSA Workshop 2015, University of Queensland, Brisbane, Australia 24
Different types of loads
The analysis will be completed right after
defining the load!
The green line shows the deflection shape.
Getting started: Results presentation
iSA Workshop 2015, University of Queensland, Brisbane, Australia 25
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.
iSA Workshop 2015, University of Queensland, Brisbane, Australia 26
Getting started: Element & system K
iSA Workshop 2015, University of Queensland, Brisbane, Australia 27
Contribution of the each
element in the system
stiffness matrix
Local and global element
stiffness matrices
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
iSA Workshop 2015, University of Queensland, Brisbane, Australia 28
10 kN 10 kN10 kN
3 m 3 m 3 m 3 m
3 m
2 m
Getting started: Structure generator
iSA Workshop 2015, University of Queensland, Brisbane, Australia 29
Getting started: Truss shape/configuration
iSA Workshop 2015, University of Queensland, Brisbane, Australia 30
Getting started: Define truss location
iSA Workshop 2015, University of Queensland, Brisbane, Australia 31
Modelling completed!!
Getting started: Loading
iSA Workshop 2015, University of Queensland, Brisbane, Australia 32
Getting started: Modify member properties
iSA Workshop 2015, University of Queensland, Brisbane, Australia 33
Right mouse click at one of
the selected members!!
Getting started: Axial force diagram
iSA Workshop 2015, University of Queensland, Brisbane, Australia 34
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
iSA Workshop 2015, University of Queensland, Brisbane, Australia 35
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
Getting started: Structure generator
iSA Workshop 2015, University of Queensland, Brisbane, Australia 36
Getting started: Delete members
iSA Workshop 2015, University of Queensland, Brisbane, Australia 37
Select the unwanted
members
Delete the selected
members
Getting started: Change first story height
iSA Workshop 2015, University of Queensland, Brisbane, Australia 38
Select all nodes at
the ground floor.
Right mouse click
to open the ‘Move
selected nodes’
window.
Getting started: Apply vertical load
iSA Workshop 2015, University of Queensland, Brisbane, Australia 39
Select all beams and
apply the load on one
of them.
Change the default
load magnitude from
10 to 15 kN/m.
Getting started: Apply horizontal load
iSA Workshop 2015, University of Queensland, Brisbane, Australia 40
Change the default load
from 10 kN vertical to the
desired magnitudes and
directions.
Getting started: Result presentation
iSA Workshop 2015, University of Queensland, Brisbane, Australia 41
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.
iSA Workshop 2015, University of Queensland, Brisbane, Australia 42
Getting started: Load on node or member
iSA Workshop 2015, University of Queensland, Brisbane, Australia 43
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)
iSA Workshop 2015, University of Queensland, Brisbane, Australia 44
Semi-rigid connection
• A semi-rigid connection can be modeled by a rotational
(torsional) spring with stiffness equal to that of the actual
connection.
iSA Workshop 2015, University of Queensland, Brisbane, Australia 45
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:
Semi-rigid connection
iSA Workshop 2015, University of Queensland, Brisbane, Australia 46
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
Support conditions
iSA Workshop 2015, University of Queensland, Brisbane, Australia 47
Allow users to model supports
as different types of springs.
Allow users to rotate
the support.
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.
iSA Workshop 2015, University of Queensland, Brisbane, Australia 48
• 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.
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.
iSA Workshop 2015, University of Queensland, Brisbane, Australia 49
Select
Node
Support
MemberMember polygon
Full hinge
Pinjointed hinge
Half hinge
Split member
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.
iSA Workshop 2015, University of Queensland, Brisbane, Australia 50
Hands-on: Half hinge
• Install two brace members to the steel frame (using
default member).
• Record the horizontal displacement.
iSA Workshop 2015, University of Queensland, Brisbane, Australia 51
Hands-on: Pinjointed hinge
• Install a pinjointed hinge at the middle of the two braces to
further reduce the horizontal displacement of the system.
iSA Workshop 2015, University of Queensland, Brisbane, Australia 52
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.
iSA Workshop 2015, University of Queensland, Brisbane, Australia 53
Hands-on: Truss analysis
• Calculate the support reactions and internal member
forces of the truss.
• Given: E = 200 GPa and A = 0.0077 m2
iSA Workshop 2015, University of Queensland, Brisbane, Australia 54
6 m
5 m5 m 5 m 5 m
15kN15kN
15kN
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]
iSA Workshop 2015, University of Queensland, Brisbane, Australia 55
3 m
4 m
6 m
20 kN
10 kN
3 kN/m
3 kN/m
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.
iSA Workshop 2015, University of Queensland, Brisbane, Australia 56
Hands-on: Lack of fit & support movement
iSA Workshop 2015, University of Queensland, Brisbane, Australia 57
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
Dynamic modal analysis
iSA Workshop 2015, University of Queensland, Brisbane, Australia 59
Second order analysis
• is the nodal displacement due to sway induced by loads
in the frame and imperfection.
iSA Workshop 2015, University of Queensland, Brisbane, Australia 60
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)
…
Second order analysis
iSA Workshop 2015, University of Queensland, Brisbane, Australia 61
ww
P
8
2wL
ww
P
11
2
8P
wL
ww
P
221
2
8 PP
wL
(a)
(b)
(c)
Second order analysis: Formulation
iSA Workshop 2015, University of Queensland, Brisbane, Australia 62
x
x
w
yy + y
M
M + M
V + V
V
P
P
A
Second order analysis: Formulation
iSA Workshop 2015, University of Queensland, Brisbane, Australia 63
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
Second order analysis: Formulation
iSA Workshop 2015, University of Queensland, Brisbane, Australia 64
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)
Second order analysis: iSA solution
iSA Workshop 2015, University of Queensland, Brisbane, Australia 65
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
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?
iSA Workshop 2015, University of Queensland, Brisbane, Australia 66
4 m
3 m
5 m
400 kN400 kN
1 kN
Moving load analysis
iSA Workshop 2015, University of Queensland, Brisbane, Australia 67
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.
iSA Workshop 2015, University of Queensland, Brisbane, Australia 68
16 m 22 m 22 m 16 m
10 m 10 m12 m
A B C D E
FG
H
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
iSA Workshop 2015, University of Queensland, Brisbane, Australia 69
iSA Workshop 2015, University of Queensland, Brisbane, Australia 70