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TRANSCRIPT
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STRUCTURAL ANALYSIS
Instructor: Muhammad Haroon
Assistant Professor,
Civil Engineering Department,
Wah Engineering College,
University of Wah Wah Cantt
Course Code: CE-302
Credit hours: 3+1
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INTRODUCTION
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Reference Books
Structural Analysis by R.C. Hibbeler
Pentice Hall
Indeterminate Structural Analysis by Chu Kia Wang
McGraw Hill
Analysis of Structures by West, H.H.
John Wiley and Sons
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Class Decorum
The person who will not be serious will be treated accordingly
Late comers will not be allowed
Mobile phones are must to be kept silent
Class participation is encouraged
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Course Grading
4 Quizzes 7.5%
4-6 Assignments 7.5%
Mid Term Exam 15%
Final Exam 37.5%
Practicals 15%
Project 7.5%
Viva 10%
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What is a Structure?
A structure is a system of connected parts used to support a load.
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Elements/Parts of a Structure
Some of common elements from which structures are composed are
as follows:
Tie Rods / Struts
Structural members subjected to a tensile force are often referred to
as tie rods or bracing struts.
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Beams
Beams are usually straight horizontal members used primarily to
carry vertical loads.
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Tapered Beams
When the cross-section varies the beam is referred to as tapered or
haunched.
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Built-up Sections
Beam cross-sections may also be built-up by adding plates to their
top and bottom. Such sections are known as built-up sections.
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Plate Girder
When the span and loads are very large, cross-sections are fabricated
by using a large plate for the web and welding or bolting plates to its
ends for flanges, known as plate girder.
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Columns
Members that are generally vertical and resist axial compressive
loads are referred to as columns.
Occasionally, columns are subjected to both an axial load and a
bending moment. These members are referred to as beam-columns.
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Column Beam column
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Types of Structures
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Frames
Frames are normally used in buildings.
They are composed of beams and columns connected by pinned or
fixed ends.
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Trusses
Trusses are composed of slender straight members connected at their
ends by hinged connections in a triangular fashion. The members are
either in uniform tension or compression.
When the span of a structure is large, and depth is not an important
criterion for design, a truss may be selected.
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10/9/2013
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http://upload.wikimedia.org/wikipedia/commons/5/5c/Grammene-vierendeelbridge_20030618.jpg
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Cables and Arches
For Long span distances, cables and arches can be used.
Cables are usually flexible and carry their loads in tension.
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Arch supports their loads in compression.
Arches are frequently used in bridge structures, dome roofs, and for
openings in masonry walls.
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Triangular Arch Round Arch Segmental Arch
Rampant Round
Arch Lancet Arch Shoulder Flat
Arch Three-Foiled
Cusped Arch
Equilateral
Pointed Arch
http://upload.wikimedia.org/wikipedia/commons/a/a0/Treledsb%C3%A5ge.pnghttp://upload.wikimedia.org/wikipedia/commons/4/4a/Rundb%C3%A5ge.pnghttp://upload.wikimedia.org/wikipedia/commons/b/b1/Segmentb%C3%A5ge.pnghttp://upload.wikimedia.org/wikipedia/commons/1/1f/Stigande_b%C3%A5ge.pnghttp://upload.wikimedia.org/wikipedia/commons/0/0e/Lansettb%C3%A5ge.pnghttp://upload.wikimedia.org/wikipedia/commons/1/16/Skulderb%C3%A5ge.pnghttp://upload.wikimedia.org/wikipedia/commons/7/79/Trepassb%C3%A5ge.pnghttp://upload.wikimedia.org/wikipedia/commons/e/e9/Spetsb%C3%A5ge.png
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Horseshoe Arch Three-centered
Arch
Elliptical Arch
Inflexed Arch Ogee Arch Reverse Ogee
Arch Tudor Arch
Parabolic Arch
http://upload.wikimedia.org/wikipedia/commons/1/1d/H%C3%A4stskob%C3%A5ge.pnghttp://upload.wikimedia.org/wikipedia/commons/4/45/Korgb%C3%A5ge.pnghttp://upload.wikimedia.org/wikipedia/commons/2/22/Ellipsb%C3%A5ge.pnghttp://upload.wikimedia.org/wikipedia/commons/d/d0/Draperib%C3%A5ge.pnghttp://upload.wikimedia.org/wikipedia/commons/b/b7/K%C3%B6lb%C3%A5ge.pnghttp://upload.wikimedia.org/wikipedia/commons/2/2d/Karnisb%C3%A5ge.pnghttp://upload.wikimedia.org/wikipedia/commons/9/92/Tudorb%C3%A5ge.pnghttp://upload.wikimedia.org/wikipedia/commons/5/5e/Parabelb%C3%A5ge.png
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Surface/shell Structures
These are made from materials having a very small thickness
compared to its other dimensions.
These structures are difficult to analyze, due to three dimensional
geometry of their surface.
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Loads
The loads on a structures are determined after finding the structural
dimensions.
The loads define the type of structure to be constructed.
Once the structural form has been decided, the actual design begins.
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Types of Loads
Dead Loads
Live Loads
Bridge Loads
Wind Loads
Earthquake Loads
Hydrostatic and Soil Pressure
Other Natural Loads
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What is Structural Analysis?
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What is Structural Design?
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The design of structure starts with those elements
which are subjected first to the primary loads.
For example, first the slabs are designed then beams,
then columns and then footing.
Loads are specified in:
General Building Codes
Design Codes
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IMPORTANT!
The ultimate responsibility for the design lies with the structural
engineer.
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Equations of Equilibrium
The structure or its member is in equilibrium when it maintains a
balance of force and moment.
0 0 0
0 0 0
zyx
zyx
MMM
FFF
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Equations of Equilibrium
The principal load-carrying portions of most structures lie in a single
plane, and since the loads are also coplanar, the above requirements
for equilibrium reduces to
0
0
0
M
F
F
y
x
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Internal Loadings
In general, the internal loadings acting at the cut section of the
member will consist of a normal force N, shear force V, and bending
moment M.
V
N
M V
N
M
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Determinacy
When all the forces in a structure can be determined from the
equilibrium equations, the structure is referred to as statically
determinate.
When the unknown forces in a structure are more than the available
equilibrium equations, that structure is known as statically
indeterminate.
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Determinacy
If there is a total of n parts and r force and moment reaction
components, we have
r = 3n statically determinate
r > 3n statically indeterminate
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Stability
A structure will be geometrically unstable (it will move slightly or
collapse) if
there are fewer reactive forces than equations of equilibrium or
there are enough reactions and instability will occur if the lines of
action of reactive forces intersect at a common point or are parallel to
one another.
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Stability
r < 3n unstable
r 3n unstable if member reactions are concurrent or parallel
or some of the components form a collapsible mechanism
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Statically Indeterminate Structures (SIS)
When the unknown forces in a structure are more than the available
equilibrium equations, that structure is known as statically
indeterminate.
Most of the structures designed today are statically indeterminate.
This indeterminacy may be due to the added supports or members, or
by the general form of the structure.
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Advantages of SIS
Smaller Stresses
Greater Stiffness
Redundancies
P
P
8max
PLM
4max
PLM
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49
w
EI
wL
384
4
max
w
EI
wL
384
5 4
max
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Advantages of SIS
Smaller Stresses
Greater Stiffness
Redundancies
Statically determinate beam
Internal hinge
Statically unstable
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Advantages of SIS
Smaller Stresses
Greater Stiffness
Redundancies
Statically indeterminate beam
Internal hinge
Statically stable
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Disadvantages of SIS
Stress due to Support Settlement
Stress due to Temperature Changes and Fabrication Errors
Statically indeterminate beam
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Disadvantages of SIS
Stress due to Support Settlement
Stress due to Temperature Changes and Fabrication Errors
Statically determinate beam
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Disadvantages of SIS
Stress due to Support Settlement
Stress due to Temperature Changes and Fabrication Errors
Statically indeterminate beam
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METHODS OF
ANALYSIS
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TYPES OF METHODS There are two type of methods for Statically
Indeterminate Structures
Displacement Method:
Slope Deflection Method
Moment Distribution Method
Force Method:
Method of least work (Unit load method)
Method of consistent deformation
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FEM VALUES CHART