Transcript SA-I – Introduction PPT

Draft copy – Yet to modify
Introduction to
Structural Analysis
Dr. M. K. Mohan B.E, M.E, PH.D, MISTE, MISCA,
Member of Illuminati of IBC, Cambridge, England
Listed in Asia Pacific’s Who’s Who - 2016
Professor of Civil Engineering
Guru Nanak Institute of Technology
Ibrahimpatnam, Hyderabad.
INTRODUCTION TO
STRUCTURAL ANALYSIS
Structural Analysis is the analysis of a given structure subjected
to some given loads, and the idea is to predict the response of the
structure (system), thus there are some inputs referred to as
‘’stimulus’’ and some outputs referred to as ‘’response’’. The
Structural analysis is the application of Engineering Mechanics
to predict the response (interms of forces & displacements) of a
given structure (existing or proposed) which is subjected to
certain specified loads.
LOADS
(INPUTS)
RESPONSE
(OUTPUTS)
STRUCTURE (SYSTEM)
Structures can not be analyzed.
They can only be load-tested.
We analyze the “model” of a structure.
EXCITATION
RESPONSE
Loads
Vibration
Settlements
Thermal
Changes
Stresses
Strains
Displacements
Stress Resultants
Support Reactions
Structural Model
STRUCTURE
Structural Analysis is an integral
part of a structural engineering
project
CONCEPTUAL DESIGN
Architectural
Functional Plans
Final Design
Structural
System
Detailing
Connection
Design
Trial Sections
Yes
Modeling
Analysis
MODELING & ANALYSIS
Revise
Sections
Acceptable
No
Member
Design
DESIGN & DETAILING
Various Ways of Modeling Structures
(a) Real Structure
(b) Solid Model
(c) 3D Plate-Frame
(d) 3D Frame
(e) 2D Frame
“It is imperative that the model represents the real structure with an
appropriate likeness to capture the desired response. “
2D Models of Structures
(a) Beam
(b) Plane Truss
(c) Plane Frame
Modeling Loads & Supports
• Dead Load
•Live Load
• Wind Load
• Seismic Load
• Impact
• Temperature
• Roller
• Pinned
• Fixed
• Spring
• Settlements
Structural Analysis Output
• Displacements
• Axial Forces
• Shear Forces
• Bending Moments
• Stresses
BEAMS are usually horizontal members, primarily designed
to resist bending moment.
COLUMNS are generally vertical and resist axial
compressive loads.
Stonehenge, England.
One of the earliest
examples of beam and
column construction, it
was built in
approximately 2000
B.C. The picture shows
part of a 30-meter circle
of 30 upright stones,
each weighing
approximately 25 tons,
capped by a continuous
ring of 30 lintel stones,
each weighing about 7
tons. The stones were
brought 30 km from the
quarry. Transport and
construction procedures
are still a matter of
conjecture.
Temple of Olympian Zeus. Completed by the Roman Emperor Hadrian (AD 76-138)
700 years after the first columns were raised. Columns are 6 ft. 4 in. diameter, 56 ft.
high, 18 ft. centers. Architrave beam span is obviously limited by the self-weight and
tensile strength of the stone. (Athens, Greece)
Continuous Beam
14th Street Bridge over the Potomac River. Continuous riveted steel girders.
Note the absence of internal hinges and the resulting internal self-straining
forces in the girders if one of the supports should settle. (Washington, D.C.)
Cantilever Beam
U.C. parking structure 'A'.
The variable depth cantilever
slab supports its own weight,
automobile loading, and also
any impact due to an
automobile hitting the timber
wall guard. (University of
California, Berkeley)
TRUSSES consist of slender elements which
resist axial tensile or compressive forces.
Missouri River Bridge, Chamberlain. These through trusses show how complex the geometry of a
large bridge truss can become. Careful study shows X-bracing in all except the end panel. Horizontal
members in the plane of the truss at mid-height are to stiffen the verticals. (Chamberlain, So.Dakota)
Detail of pin-jointed truss connection, approach span to San
Francisco-Oakland Bay Bridge. Pin joints are used in older bridges
or situations where rotation has to be allowed for due to settlement,
or for construction purposes. (San Francisco Bay Area)
Single-story building. In a strongly seismic area, buildings have to resist
horizontal inertial forces caused by the horizontal components of
earthquake ground motions. This building has simple X-bracing in both
directions. (Larkspur, California)
Truss members as Bracing on Buildings
Merchant Exchange Building. The outside trusses of this building consist of X-braced 50-ft
square panels. The clear span between supporting columns is 100 ft, and the end of the building
(foreground) has a 50-ft overhang. (Chicago, Illinois)
ARCHES support their loads in
compression
Romans were pioneers
in the use of arches for
bridges, buildings, and
aqueducts. This bridge,
the Ponte Fabricio in
Rome, spans between
the bank of the River
Tiber and Tiber Island.
Built in 64 B.C. (Rome,
Italy.)
Interior of Carmel Mission.
Built in 1793 it is an interesting
design in that the walls curve
inward towards the top, and the
roof consists of a series of
inverted catenary arches built
of native sandstone quarried
from the nearby Santa Lucia
Mountains. (Carmel, California)
CABLES support their loads in tension
Manhattan Bridge. Over New York's East River, this bridge was opened in 1909. One of the first
major bridges to use steel towers. It used more flexible towers and shallower stiffening truss than
preceding bridges. (New York City)
FRAMES are often used in buildings and are
composed of beams and columns that are either
pin or fixed connected.
One story rigid frame. Both the horizontal and vertical stability of this building
depend on the concrete frame on all four sides. (Las Vegas, Nevada)
Multistory Building: First City National Bank Building, Houston,
Texas. Concrete covered steel frame multi-story building. 3 bays x
9 bays in plan. (Houston, Texas)
Space Truss Frame
Expo 86, Vancouver, Canada.
Plaza of the Nations. Triangulated
truss canopy covering the stage area
of the large open-air amphitheater.
The part of the truss system to the
right of the two support columns is
cantilevered. The part to the left is
supported on the back wall.
(Vancouver, British Columbia)
Plane Grid
Dallas Airport Terminal Building. The
ceiling structure in this building is a modern
example of a horizontal beam grid. The
columns are at every other beam intersection
point in both directions. (Dallas, Texas)
Cantilevered shell. The concrete edge beam tapers from
minimum at the unsupported end to maximum at the support
point. (San Francisco Bay Area)
SURFACE STRUCTURES, commonly referred to as thin
plates or shells, are made from material having very small
thickness compared to the other dimensions.
Public
Auditorium.
Designed to serve both
as a convention hall and
as
an
open-air
amphitheater
seating
13,600, the building has
a
retractable
dome
consisting of radial steel
ribs sheathed in stainless
steel. The dome has a
diameter of 417 ft. and a
rise
of
109
ft.
(Pittsburgh,
Pennsylvania)
FIXED-PINNED COLUMNS: Dorothy Chandler Pavilion, Los Angeles Cultural Center. The
outside of this building consists of a continuous reinforced concrete frame, the bottom of
which can be seen in this slide, and consists of tapered columns pinned at the base. As the
top of the column is built into a stiff horizontal beam, the columns are effectively fixed at the
top and pinned at the base. (Los Angeles, California)
Support Connections
PIN or HINGED SUPPORT: Main
River Bridge. Detail of the end
bearing. This rolling expansion
bearing consists of a hinge on top of
a pedestal whose base rests on a
series of rollers. This type of bearing
is not uncommon where reactions
are large. (Frankfurt, Germany)
Loads are classified into 2 parts:
 Dead loads (Self-weight; of the components of the
structure).
 Imposed loads & forces (Live, Wind, Snow, Rain,
and Temperature, Erection loads, Seismic forces &
others).
The Structural Analysis is only ascertained correct
when the following requirements were satisfied; Equilibrium Forces.
 Compatibility of Displacement.
 Force/Displacement Relations.
Therefore, In every forms of the structures, the
structural Engineer has to consider the following
structural considerations and purposes.

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Stability,
Strengths,
Stiffness,
Economy, as well as
Aesthetic aspects of the structure.
The following Softwares are available

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Orion,
STAAD III,
ANSYS,
AXIS VM,
ETABS, SAP, Etc
DIFFERENT TYPES OF SUPPORTS
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

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Roller,
Pinned,
Hinged,
Fixed,
Link,
Ball and Socket,
Rigid Support,
Spring Support.
FORCES
DIFFERENT TYPES OF STRUCTURES
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
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Frame Structure,
Truss Structure,
Shell Structure,
Arch Structure,
Suspension Structure,
Mass Structure, &
Composite Structure.
LIST OF EQUILIBRIUM EQUATIONS
DETERMINACY AND INDETERMINACY OF A
STRUCTURE
TECHNIQUES USED IN ANALYSING
STRUCTURE
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Macaulay’s Method
Moment Area Method
Conjugate Beam Method
Virtual Work Method
Unit load Method
Influence line theory
The Three Moment Equation (Clapeyron’s Theorem)
Stiffness & Flexibility Method
Slope Deflection Method
Moment Distribution Method
MACAULAY’S METHOD
This is a method suggested by W. H. Macaulay to relate the
stiffness, radius of curvature, deflection and the bending
moments in a beam by integration methods. Beam Deflections
using successive integration;
Consider an infinitely small
Section, dx, of the above loaded
beam;
MOMENT AREA METHOD
 This is a method suitable for calculating slope &
deflection at selected points on a beam.
 It is also effective for calculating the deflections of beams
with various cross sections.
 The simplest way to evaluate the fixed-end moments, etc,
will often be by the use of the Moment area method.
There are two theorems associated with the moment area
methods:
First Moment Area Theorem:
“The difference in slope between two points on a beam is
equal to the area of the M/EI diagram between the two
points.”
Second Moment Area Theorem:
“The moment about a point A of the M/EI diagram between
points A and B will give the deflection of point A relative to the
tangent at point B.”
First Moment Area Theorem
Second Moment Area
Theorem
Some of the most famous
structures of the world.
The Colosseum
Rome, Italy
The Colosseum or Coliseum also
known
as
the
Flavian
Amphitheatre is an oval shaped
amphitheatre in the centre of the
city
of
Rome,
Italy.
Built
of concrete and sand, it is the
largest amphitheatre ever built.
Construction began under the
emperor Vespasian in AD 72, and
was completed in AD 80 under his
successor and heir Titus. Further
modifications were made during the
reign of Domitian (81–96).
The Colosseum could hold, it is
estimated, between 50,000 and
80,000 spectators, having an
average
audience
of
some
65,000;
it
was
used
for
gladiatorial contests and public
spectacles such as mock sea
battles, animal hunts, executions,
re-enactments of famous battles,
and dramas based on Classical
mythology.
The Great Wall of China
China
The Great Wall of China is a
series of fortifications made of
stone, brick, tamped earth,
wood, and other materials,
generally built along an east-towest line across the historical
northern borders of China to
protect
the
Chinese
states and empires against the
raids and invasions of the
various nomadic groups of
the Eurasian Steppe. Several
walls were being built as early
as the 7th century BCE; these,
later joined together and made
bigger and stronger, are now
collectively referred to as the
Great Wall.
The Great Pyramid of Giza
Cairo, Egypt
The Great Pyramid of Giza is
the oldest and largest of the
three pyramids in the Giza
pyramid complex bordering
what is now El Giza, Egypt. It is
the oldest of the seven wonders
of the ancient world and the
only one to remain largely intact.
Initially at 146.5 metres (481
feet), the Great Pyramid was the
tallest man made structure in
the world for more than 3,800
years
Donghai Bridge, China
Donghai Bridge is a Chinese
bridge counted among the
longest cross-sea bridges in the
world. It was completed on
December 10, 2005. It has a
total length of 32.5 kilometres
(20.2
mi)
and
connects
mainland Shanghai‘s Pudong
New Area with the offshore
Yangshan
Deep-Water
Port in Zhejiang's Shengsi
County. Most of the bridge is a
low-level viaduct. There are
also cable-stayed sections to
allow for the passage of large
ships, the largest with a span of
420 metres (1,380 ft). Donghai
Bridge is part of the S2 Hulu
Expressway. The bridge has a
long and narrow speedway and
does not allow vehicles that do
not
meet
the
weight
requirements.
Incheon Bridge
New Songdo City, Korea
The Incheon Bridge is a
reinforced concrete bridge in
South Korea constructed and
opened in October 2009. The
Incheon Bridge is South Korea's
longest spanning cable-stayed
bridge connecting Yeongjong
Island
and
the
mainland
of Incheon. In comparison, the
Incheon Bridge is the world's
seventh longest cable-stayed
bridge as of October 2010. The
main purpose of the bridge is to
provide
direct
access
between Songdo and Incheon
International Airport, reducing
travel time between them by up
to one hour.
Tower Bridge
London, England
Tower Bridge (built 1886–1894) is
a
combined
bascule
and
suspension bridge in London. The
bridge
crosses
the
River
Thames close to the Tower of
London and has become an iconic
symbol of London. It is the only one
of the Trust's bridges not to
connect the City of London directly
to the Southwark bank, as its
northern landfall is in the Tower
Hamlets.
The bridge consists of two bridge
towers tied together at the upper
level by two horizontal walkways,
designed
to
withstand
the
horizontal tension forces exerted
by the suspended sections of the
bridge on the landward sides of the
towers. The vertical components of
the forces in the suspended
sections and the vertical reactions
of the two walkways are carried by
the two robust towers. The bascule
pivots and operating machinery are
housed in the base of each tower.
Banpo Bridge
Seoul, South Korea
The
Banpo
Bridge
is
a
major bridge in downtown Seoul over
the Han River, South Korea,
connecting
the
Seocho
and
Yongsan districts. The bridge is on top
of Jamsu Bridge, forming the upper
half of a double-deck bridge; it is the
first double deck bridge built in South
Korea. During periods of high rainfall,
the Jamsu Bridge is designed to
submerge as the water level of the
river rises, as the lower deck lies close
to the waterline. The bridge was built
as a girder bridge and was completed
in 1982.
The Moonlight Rainbow Fountain is
the world's longest bridge fountain that
set a Guinness World Record with
nearly 10,000 LED nozzles that run
along both sides that is 1,140m long,
shooting out 190 tons of water per
minute. Installed in September 2009
on the Banpo Bridge, the water is
pumped directly from the river itself
and continuously recycled. The bridge
has 38 water pumps and 380 nozzles
on either side, which draw 190 tons of
water per minute from the river 20
meters below the deck, and shoots as
far as 43 meters horizontally.
The Falkirk Wheel
Scotland
The Falkirk Wheel is a
rotating boat lift in Scotland,
connecting the Forth and Clyde
Canal with the Union Canal.
The lift, named after the nearby
town of Falkirk in central
Scotland, opened in 2002. It
reconnects the two canals for
the first time since the 1930s as
part
of
the
Millennium
Link project.
The wheel raises boats by 24
metres (79 ft), but the Union
Canal is still 11 metres (36 ft)
higher than the aqueduct which
meets the wheel. Boats must
also pass through a pair
of locks between the top of the
wheel and the Union Canal.
The Falkirk Wheel is the only
rotating boat lift of its kind in the
world, and one of two working
boat lifts in the United
Kingdom, the other being
the Anderton boat lift.
Petronas Towers
Kuala Lumpur, Malaysia
The Petronas Towers, also known
as the Petronas Twin Towers,
are twin skyscrapers in Kuala
Lumpur, Malaysia. According to the
Council on Tall Buildings and Urban
Habitat (CTBUH)'s official definition
and ranking, they were the tallest
buildings in the world from 1998 to
2004 and remain the tallest twin
towers in the world. The buildings
are a landmark of Kuala Lumpur,
along with nearby Kuala Lumpur
Tower.
The 88-floor towers are constructed
largely of reinforced concrete, with
a steel and glass façade. Because
of the depth of the bedrock, the
buildings were built on the world's
deepest foundations. 104 concrete
piles, ranging from 60 to 114
metres (197 to 374 ft) deep, were
bored into the ground. The
concrete
raft
foundation,
comprising 13,200 cubic metres
(470,000 cu ft) of concrete was
continuously poured through a
period of 54 hours for each tower.
The raft is 4.6 metres (15 ft) thick,
weighs 32,500 tonnes (35,800
tons) and held the world record for
the largest concrete pour until
2007.
HABITAT67 - A residential housing
complex Montreal, Canada
Habitat 67, or simply Habitat, is
a model community and housing
complex in Montreal, Canada.
1967. It is located at 2600
Avenue Pierre-Dupuy on the
Marc-Drouin Quay next to the
Saint Lawrence River. Habitat 67
is
widely
considered
an
architectural landmark and one of
the most recognizable and
significant buildings in both
Montreal and Canada.
The Tajmahal, India
The Taj Mahal
more
often for Crown of Palaces
is
an
ivory-white
marble mausoleum on the
south
bank
of
the
Yamuna river in the Indian
city of Agra. It was
commissioned in 1632 by
the Mughal emperor, Shah
Jaha to house the tomb of
his favorite wife, Mumtaz
Mahal. The tomb is the
centrepiece of a 42-acre
complex, which includes
a mosque and a guest
house, and is set in formal
gardens bounded on three
sides by a crenellated wall.
Glasgow Science Centre
Glasgow, Scotland
Glasgow Science Centre is
a visitor attraction located in
the
Clyde
Waterfront
Regeneration area on the
south bank of the River
Clyde in Glasgow, Scotland
opened on 5 June 2001. It is
one of Britain's most popular
places to visit. It is a purposebuilt
science
centre composed of three
principal buildings which are
the Science Mall, Glasgow
Tower and an IMAX cinema.
Sears Tower
Chicago, Illinois
The Willis Tower, built and still
commonly referred to as Sears
Tower, is a 108-story, 1,451foot
(442 m) skyscraper in Chicago,
Illinois, United States. At
completion
in
1973,
it
surpassed the World Trade
Center towers in New York to
become the tallest building in
the world, a title it held for
nearly 25 years. The Willis
Tower is the second-tallest
building
in
the
United
States and the 14th-tallest in
the world. More than one
million
people
visit
its
observation deck each year,
making it one of Chicago's
most
popular
tourist
destinations. The structure was
renamed in 2009 by the Willis
Group as part of its lease on a
portion of the tower's space.
Rungrado May Day Stadium
Pyongyang
The Rungrado 1st of May
Stadium is a multi-purpose
stadium in Pyongyang, North
Korea, completed on May 1,
1989. It is currently the largest
stadium in the world, with a
capacity of 150,000, and
occupies 20.7 hectares (51
acres).
Its scalloped roof features
16 arches arranged in a ring,
and it is said to resemble a
magnolia blossom. It is not to
be confused with the nearby
50,000 capacity Kim Il-sung
Stadium.
It hosts events on a main pitch
sprawling
across
over
22,500 m² (242,200 ft²). Its
total floor space is over
207,000 m² (2.2 million ft²)
across eight stories, and the
lobes of its roof peak at more
than 60 m (197 ft) from the
ground.
Milwaukee Art Museum
Milwaukee, USA
The Milwaukee Art Museum is
an art museum in Milwaukee,
Wisconsin.
Its
collection
contains more than 30,000
works of art. It is one of the
largest museums in the USA.
The Quadracci Pavilion contains
a movable, wing-like brise
soleil that opens up for a
wingspan of 217 feet (66 m)
during the day, folding over the
tall, arched structure at night or
during inclement weather. The
pavilion
received
the
2004 Outstanding Structure
Award from the International
Association for Bridge and
Structural Engineering. This
iconic building, often referred to
as "the Calatrava," is used in the
museum logo.
Atomium
Brussels, Belgium
The Atomium is a building
in
Brussels
originally
constructed for Expo 58, the
1958 Brussels World's Fair. It
is 102 m (335 ft) tall. Its nine
18 m (59 ft) diameter stainless
steel
clad
spheres
are
connected so that the whole
forms the shape of a unit cell of
an iron crystal magnified 165
billion times. The name is a
combination of atom and
aluminium. It is a museum.
Tubes of 3 m (9.8 ft) diameter
connect the spheres along the
12 edges of the cube and all
eight vertices to the centre.
They enclose stairs, escalators
and a lift (in the central, vertical
tube) to allow access to the five
habitable
spheres
which
contain exhibit halls and other
public spaces. The top sphere
includes a restaurant which has
a
panoramicview
of
Brussels. CNN named it
Europe's
most
bizarre
[2]
building.
Burj Dubai, Dubai
Burj Khalifa
known
as Burj Dubai before its
inauguration,
is
a
supertall skyscraper in D
ubai,
United
Arab
Emirates. It is the tallest
structure in the world,
standing at 829.8 m
(2,722 ft).
The Y-shaped plan is
designed for residential
and hotel usage. A
buttressed core structural
system is used to support
the height of the building,
and the cladding system
is designed to withstand
Dubai's
summer
temperatures. A total of
57 elevators and 8
escalators are installed
with a capacity of 12 to
14 passengers per cabin
Dynamic Tower, Dubai
(still under construction)
The Dynamic Tower (also
known
as
Dynamic
Architecture Building or the Da
Vinci Tower) is a proposed 420metre (1,378 ft), 80-floor moving
skyscraper,
designed
by
architect David Fisher.
Similar
to
the
Suite
Vollard completed in 2001 in
Brazil, each floor is designed
to rotate independently, resulting
in a changing shape of the tower.
Each floor is designed to rotate a
maximum of 6 metres (20 ft) per
minute, or one full rotation in 90
minutes.
It was proposed as the world's
first prefabricated skyscraper
with 40 factory-built modules for
each floor
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