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Theory of Structures-II Engr. Shahzad Saleem Assistant Professor Department of Civil Engineering University of Engineering & Technology, Taxila 10/19/2022 1 Theory of Structures-II
Theory of Structures-II
Engr. Shahzad SaleemAssistant Professor
Department of Civil EngineeringUniversity of Engineering & Technology,
Taxila
10/19/2022 1Theory of Structures-II
INTRODUCTION
Course Name: Theory of Structures – IICourse ID: 301Books: “Structural Analysis” by R. C. Hibbeler
“Structural Analysis” by Aslam Kassimali
Instructor: Engr. Shahzad [email protected]
Reference Books:•Any Book on Structural Analysis10/19/2022 2Theory of Structures-II
What is Engineering?The science concerned with putting scientific knowledge to practical uses, divided into different branches, as Civil, Mechanical, etc.
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OR
The planning, designing, construction, or management of machinery, roads, bridges, buildings, etc.
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Who is an Engineer?A person skilled or occupied in some branch of engineering.
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What is Civil Engineering?The branch of engineering dealing with the design and construction of highways, bridges, buildings, tunnels, waterworks, etc.
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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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Parts of a StructureSome of common elements from which structures are composed are as follows:
Tension Members
Structural members subjected to a tensile force are often referred to as tension members such as tie rods or bracing elements.
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Beams
Beams are usually straight horizontal members used primarily to carry vertical loads.
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Beams
When the cross-section varies the beam is referred to as tapered or haunched.
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Beams
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.10/19/2022 16Theory of Structures-II
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Column Beam column
Types of StructuresTrusses
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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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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Frames
Frames are normally used in buildings.
They are composed of beams and columns connected by pinned or fixed ends.
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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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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 Codes10/19/2022 32Theory of Structures-II
The ultimate responsibility for the design lies with the structural engineer.
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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?The prediction of the performance of a structure under prescribed loads and/or other external effects.The performance characteristics are:
• Stresses i.e. axial force, shear force and bending moment
• Deflections• Support Reactions
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What is Structural Design?Knowing the expected loads and span lengths of the members, finding the required material properties and cross-sectional dimensions is called Design of Structure.
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Principle of SuperpositionThe total displacement or internal loading (stress) at a point in a structure subjected to several external loadings can be determined by adding together the displacements or internal loadings (stress) caused by each of the external loads acting separately.
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Equations of EquilibriumThe structure or its member is in equilibrium when it maintains a balance of force and moment.
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0 0 00 0 0
zyx
zyx
MMMFFF
Equations of EquilibriumThe 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
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0 0 0
MFF
y
x
Internal LoadingsIn 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.
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VN
M V
N
M
DeterminacyWhen 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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DeterminacyFor a coplanar structure there are at most three equilibrium equations for each part.
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 10/19/2022 45Theory of Structures-II
StabilityA 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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Stabilityr < 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
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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For example, reinforced concrete buildings are almost always statically indeterminate.
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Advantages of SIS– Smaller Stresses– Greater Stiffness– Redundancies
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P
P
8maxPLM
4maxPLM
Advantages of SIS– Smaller Stresses– Greater Stiffness– Redundancies
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w
EIwL384
4
max
w
EIwL
3845 4
max
Advantages of SIS– Smaller Stresses– Greater Stiffness– Redundancies
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Statically determinate beam
Internal hinge
Statically unstable
Advantages of SIS– Smaller Stresses– Greater Stiffness– Redundancies
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Statically indeterminate beam
Statically stable
Disadvantages of SIS– Stress due to Support Settlement
– Stress due to Temperature Changes and Fabrication Errors
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Internal hinge
Statically determinate beam
Disadvantages of SIS– Stress due to Support Settlement
– Stress due to Temperature Changes and Fabrication Errors
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Statically indeterminate beam
Disadvantages of SIS– Stress due to Support Settlement
– Stress due to Temperature Changes and Fabrication Errors
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Statically determinate beam
Disadvantages of SIS– Stress due to Support Settlement
– Stress due to Temperature Changes and Fabrication Errors
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Statically indeterminate beam
Thank You
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Thank Y
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