Remember me and also my parents in your pray friends

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Assala mu alykum My Name is saqib imran and I am the
student of b.tech (civil) in sarhad univeristy of
science and technology peshawer.
I have written this notes by different websites and
some by self and prepare it for the student and also
for engineer who work on field to get some knowledge
from it.
I hope you all students may like it.
Remember me in your pray, allah bless me and all of
you friends.
If u have any confusion in this notes contact me on my
gmail id: Saqibimran43@gmail.com
or text me on 0341-7549889.
Saqib imran.

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Structural Engineering
Structural Engineering
Structure Engineering is the most major field in Civil Engineering. In this field engineers design
structures, analyze their stability by the use of softwares or manual calculations and then construct
them. In the previous five decades structural engineering has evolved to be an interesting and
important field, It includes the study of dynamics of a structure, its load capacity, design and
economy. Due to an increase in the demand of earthquake-proof buildings, the importance of
structural engineers has also come to light.
Structural engineering is a field of engineering, more appropriately, civil engineering; It deals with
the analysis and design of structures. Structural engineering is the design of structural support
systems for buildings, bridges, earthworks, and industrial structures. This branch of engineering
focuses on supporting a load safely, and relies on mathematical and Physical concepts for the
design of the supporting structures. Structural engineers can design machines, cranes, vehicles and
even other non building structures.
Structural engineering is a field of varied and complex tasks. Structural engineers combine simple
and basic structural elements to build up complex structural systems. but the main objective is
always safety, and to minimize the risk of collapse. Though aesthetics can also be a priority in
some cases. Many of the designs for concrete buildings today are specifically meant to be
earthquake and hurricane-resistant. There are also other provisions that are made for especially
important rural structures, such as design details that help to prevent against fires or bombs. This
way the structure of the building will not simply fall apart if something unexpected happens.
Months of consideration goes into the designs of these buildings. The efficient use of funds and
materials to achieve these structural goals is also a major concern.
Structure Analysis - Introduction and Background
Structure Analysis
Simple Truss Analysis
Definition:
The determination of internal actions and deformations is called Structural Analysis OR The
determination of response of the structure to loads.
The process of determination can be by:
 Structural Analysis Softwares
 Manual manipulations and calculations

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Structural Analysis consists of:
 Analysis &
 Design of a structure
In designing a structure the engineer must account for the safety, aesthetics,
serviceability and economic as well as environmental constraints.
The design is based on:
 Knowledge of Engineering materials
 Knowledge of laws of mechanics
This completes the preliminary design of a structure. Now the other part, that is Analysis of this
preliminary designed structure starts. Analysis of a structure consists of:
 Idealization of the structure
 Determination of locations of loads and their specification
 Displacements/Deformations
The obtained results are used to re-design the structure to fulfill the required building codes and
rules as well as other specifications that may be based on the specific climate, social interaction,
culture or economy of the area.
Classification of Structures
 Rods
 Beams
 Columns
 Trusses
 Cable and Arches
 Frames
 Surface Structures
Types of Loads
 Dead loads
 Live loads
 Building loads
 bridge loads
 wind loads
 earthquake loads
 soil pressure
 hydrostatic pressure
Laws of Mechanics
 Principle of superposition
 equation of equilibrium
 Determinacy and stability

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Procedure for analysis for determining joint reactions for structure composed of pin-connected
members
Free Body Diagrams
 Split the structure into members and draw a free body diagram of each member.
 All two force members should be identified
Equations of Equilibrium
 Count the total number of unknowns to make sure that an equivalent number of equilibrium
equations can be written for solution
Stability-Stable & Unstable Structures & Members
Definition
The resistance offered by a structure to undesirable movement like sliding, collapsing and over
turning etc is called stability.
 Stability depends upon the supports conditions and arrangements of members.
 Stability does not depend upon loading.
STABLE STRUCTURES
A stricter is said to be stable if it can resist the applied load without moving OR A structure is
said to be stable if it has sufficient number of reactions to resist the load without moving.
UNSTABLE STRUCTURE
A structure which has not sufficient number of reactions to resists the load without moving is
called unstable structures.
Stability of Structures
STABILITY OF TRUSS
A truss is said to be stable if it is externally and internally stable
EXTERNAL STABILITY OF TRUSS:
Externally a truss is said to be stable if
 All the reactions are not parallel to each other.
 All the reactions are not concurrent i.e. passing through same point
INTERNAL STABILITY OF TRUSS:
Internal stability of truss depends upon the arrangements of members and joints as

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* If m + r = 2j internally stable
* If m + r < 2j internally unstable
* If m + r > 2j indeterminate
Where m = number of members, J = number of joints, R = number of unknown reactions.
For complete stability the should be both internally and externally stable
Stability of Structural Members
STABILITY OF BEAMS
A beam is said to be stable if it satisfy the following conditions.
1. The number of unknown reactions must be greater or equal to available equations of
equilibrium
2. All the reactions should not be parallel to each other.
3. There should be no concurrent force system i.e. unknown reactions should not pass
through the same point or line.
STABILITY OF FRAME
A frame is said to be stable if it satisfy the following condition.
1. The number of unknown reactions must is greater to equal to available equations of
equilibrium.
Steps in Designing a Transfer Floor
What is the Loading on a Transfer Floor?
Design of reinforced concrete transfer floors, although routinely performed by structural design
engineers, is a very challenging task. The transfer floors are commonly used in multi-storey
buildings, and they are major structural elements carrying a number of floors. Normally the entire
building, 10 to 15 levels, is carried by a transfer slabs.
The major problem is the evaluation of the loading on the transfer slab, especially the columns and
walls terminating at the transfer level. When a column terminates on a transfer beam, it will carry
a smaller load since the beam supporting the column is acting as an elastic spring. The smaller the
beam depth, the smaller the axial load in the transfer column. In this case the load is distributed to
other columns which are continuous to the footing level. In an extreme case if we remove the
support below the transfer column, the axial load will be reduced to zero, i.e. the column will be
"hanging" on the floors above taking no load.

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The other challenge is considering the method of construction. In any 3D frame static analysis
we assume that the entire load is applied on the complete structure simultaneously. While in
reality the load is gradually applied on several floors as they are constructed. For instance, if we
imagine that the entire structure is propped and all the props are removed after the concrete is
fully set, the static analysis will capture the structural behavior adequately. But if the props at
each floor are removed before the floor above is constructed, the static analysis will not provide
accurate results.
On the other hand, by using the Tributary Area method we assume that the entire load is applied
on the transfer slab, ignoring the structure from above. This approach will produce the largest
possible loading at the transfer column, at the expense of loading to the continuous columns. This
approach is considered more conservative, however we may say that it is more conservative for
the mid-spans, at the transfer columns it will under-estimate the loading at another location such
as continuous columns, since the total load on the floor must remain the same.
Basically the modeling approach or design assumptions will influence the evaluation of the loading
on the transfer slab, and ultimately it will influence the entire design of the structural system.
Neither of these two approaches can be considered superior or more precise, nor more or less
conservative. Instead, we suggest that a very good understanding of the influence of the modeling
assumptions and all input parameters on the final results is essential in order to analyze and design
a transfer slab.
Strategy 1: Evaluation of the Transfer Floor Loading by Tributary Area Method
Traditionally we may evaluate the loading on the transfer floor by Tributary Area approach,
ignoring the flexibility of the transfer slabs, and its influence on the load distribution. Also, the
transfer slabs may be analyzed independently, separated from the rest of the structure and ignoring
the flexibility of the supporting columns and their influence on the bending moment in the transfer
beams and slab.

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This approach will provide no variation in the point loads on the transfer slab. In the figure above
(Fig. 2) the two point loads at the middle are identical, regardless of the supporting conditions
below.
This approach is commonly used and it is considered more conservative. Its shortcoming is that
the load distribution is uniform, ignoring the influence of the structure itself. The point loads on
the transfer slab are internal forces in the columns above and their magnitude is affected by relative
stiffness all structural elements. However, treating the transfer slab independently and ignoring the
rest of the structure is a more conservative analytical approach.
We will follow through a numerical example to illustrate the major points. If we used R/C
BUILDING software and if we set all columns on the transfer slab to have a "footing" support, we
can obtain the same results as the tributary area method. (Fig 3)

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Strategy 2: Evaluation of Transfer Loading by 3D Frame Static Analysis
We can analyze the structure using 1st order static analysis in 3D using R/C BUILDING software,
or any other frame analysis software. (Fig. 1) The point loads on the transfer slab will be different
form Tributary Area Method. In this case the reaction in the transfer column (point load on the
transfer slab) is reduced significantly, and the loading is distributed onto the surrounding columns.
(Fig 4)This is due to the fact that the transfer column is supported by a beam, which only provides
an elastic support. In this example we used a 400mm deep beam. If the beam depth is reduced to
say 300mm or 200mm the transfer column reaction will be even smaller. However, the total load
will remain the same, but it will be distributed differently.
The bending moment results in the transfer beam are shown in Fig. 5. We can observe that the
smaller point load of 348 kN will generate relatively small bending moments in the beam.
Strategy 3: "Very Stiff" Transfer Slab
We can make the transfer slab and the beams "very stiff" by assigning a different material property,
say 100 times greater modulus of elasticity. This will make the transfer floor much stiffer in
comparison to the rest of the structure and it will "enforce" an even distribution of the column
reactions. (Fig. 6)

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The introduction of a "Very Stiff" beam will have a similar effect on the reactions as the Tributary
Area method. However this will also have an effect on the bending moments in the beam. (Fig 7).
The moment magnitude will increase, and more importantly we may observe that the negative
moment at the column on the right is "lost". This is due to the elastic shortening (squashing) of the
columns below, the columns supporting the transfer slabs.
Strategy 4: "Very Stiff" Transfer Beam and Prevented Axial Shortening of
Columns Below
In addition to the "Very Stiff" beam we can introduce an increased axial stiffness of all columns,
which includes the columns below the transfer slab. In R/C BUILDING software there is a global
switch that will increase the axial stiffness of all columns by 100 or 10,000 times. In this example
we will increase the axial stiffness of the columns by 10,000 times. It is important to note that we
do not increase the columns bending stiffness, so the column below will not influence the bending
of the transfer beam.
In this case the reactions (column loads) will still be identical (Fig. 8)
In this case the bending moments will have the expected shape (Fig. 9). But the moment magnitude
has increased in comparison to the Elastic Analysis with no increased stiffness, Strategy 2. This is
expected since the load is larger and the transfer beam has increased stiffness, and therefore attracts
larger internal forces. We may say in this case the beam moments are "more conservative".
Now we can say that we have "forced" the column reactions on the transfer slabs to be uniform,
i.e. to mimic the Tributary Area method, and we have increased the bending moments in the
transfer beam, as it is working by itself, i.e. as it is analyzed as a two-span continuous beam
ignoring the rest of the structure.
The increased axial stiffness of the columns will affect the lateral stability analysis. It will provide
un-realistically smaller lateral deflections. When the axial stiffness of the columns is increased,
the model cannot be used in lateral stability assessment.

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End Notes and Recommendations
The above example illustrates how we can "force" a structural model to behave in a certain manner
by assigning increased stiffness to selected element groups. The increase of the bending stiffness
of the transfer beam/slab by 100 times, and the axial stiffness of the column by 10,000 shows that
we can obtain similar results as the hand calculations, using Tributary Area methods and a simple
two-span beam.
We must note that this drastic increase of the stiffness of selected element groups "distorts" the
structural model, and might result in an unrealistic and unpredictable distribution on the internal
forces, and has to be used very cautiously. Our suggestion is to use middle ground. This can be
achieved by assigning a small increase of the transfer beam/slabs bending stiffness by using a
factor of 4 for the modulus of elasticity, and no axial stiffness increase of the columns. The results
are shown in Fig. 10 below.
This approach distributes the column loads on the transfer floor more evenly, but not identical as
in the Tributary Area Method. The mid-span beam moment (below the transfer column) is also
kept relatively large. This approach will probably yield safer but economical designs of the transfer
floors.
Analyzing Equilibrium and Redundancy of
Indeterminate Structures
While analyzing any indeterminate structure using any method, it is necessary that the solution
satisfy the following requirements:
I. Equilibrium of the Structure
II. Compatibility of the Structure
III. Force Displacement Requirements
I. Equilibrium of a Structure
Equilibrium of a Structure is satisfied when the actions (applied loads) and reactions hold the
structure at rest. For a finite sized structure, substructure, element or joint, the following six
equations must be satisfied:
ΣFx = 0 ΣFy = 0 ΣFz = 0
ΣMx = 0 ΣMy = 0 ΣMz = 0
Number of equations reduces to 3 for a 2D element or structure:
ΣFx = 0 ------------------------(1)
ΣFy = 0 ------------------------(2)

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ΣM = 0-------------------------(3)
These equations are known as Equations of Equilibrium. A structure in which all the
unknowns can be determined using the Equations of Equilibrium is known as Statically
Determinate Structure. While a structure in which all the unknowns cannot be determined using
these equations is known as Statically Indeterminate Structure.
II. Compatibility of a Structure
Compatibility of a Structure is satisfied when the various segments of the structure fit together
except intentional breaks or overlaps. By compatibility we mean that:
 Members initially connected together remain connected together (the distance between them may
have altered due to the deformation)
 Two initially separate points remain separate (do not overlap or move to another common point)
 Cracks or Gaps do not appear as a structure deforms
Consider the indeterminate truss. Each of the members has been elongated. Point A has movedto
a new Point A’. However, by compatibility of displacements, the elongations are such that the three
members remain connected even after deformation, which is additional information and helps in
developing an extra equation or set of equations.
In the following indeterminate propped beam; we know that at the supports A and B there is no
deflection i.e.
dA = 0 Also dB = 0
In addition slope at a point of maximum deflection is zero i.e.
dy/dx = 0
At the fixed end rotation is resisted hence i.e.
ΣA = 0
All these equations are known as compatibility equations.
Redundancy of a Structure
Any constrain in a structure when removed and do not cause instability to the structure is known
as redundant. Consider the following simply supported beam. The horizontal and vertical
reactions at a hinged support A and the only vertical reaction at the roller support B prevent both
the translation and rotation of the beam. In other words these supports are sufficient to keep the
structure stable.

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If a third support C is provided between these two, it will make the structure more stable, but its
absence is not causing any instability. Thus the vertical reaction provided by this support may
be regarded as redundant and can be removed. The structure is then known as basic released
structure or primary structure.
The choice of redundant is increased with this extra support thus if the support B is removed, the
structure is still stable. Thus any of the support B or C may be removed except the hinged one,
which if removed will cause a parallel system of reactions and thence causing the instability of a
structure.

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Examples of Redundancy/Basic Released Structures
Definition and Types of Structures

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Definition:
A combination of members connected together in such a way to serve a useful purpose is
called structure.
Types of Structure
Rigid Frame
Its is that type of structure in which the members are joined together by rigid joints e.g. welded
joints.
Truss (Pin connected joints)
A type of structure formed by members in triangular form, the resulting figure is called a truss. In
truss joints are pin connected and loads are applied at joints. No shear force & bending moment
are produced. Only axial compression and axial tension is to be determined while analyzing a truss.
Structural Members
Those members that are interconnected in such a way so as to constitute a structure are
called structural members.

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Beam
Beam is a flexure member of the structure. It is subjected to transverse loading such as vertical
loads, and gravity loads. These loads create shear and bending within the beam.
Columns
A long vertical member mostly subjected to compressive loads is called column
Strut
A compressive member of a structure is called strut.
Beam-Column
A structural member subjected to compression as well as flexure is called beam column
Grid
A network of beam intersecting each other at right angles and subjected to vertical loads is
called grid.
Cables and Arches
Cables are usually suspended at their ends and are allowed to sag. The forces are then pure tension
and are directed along the axis of the cable. Arches are similar to cables except hath they are
inverted. They carry compressive loads that are directed along the axis of the arch.
Plates and Slabs
Plates are three dimensional flat structural components usually made of metal that are often found
in floors and roofs of structures. Slabs are similar to plates except that they are usually made of
concrete.
Tunnel Engineering | Methods of Tunneling and
Hazards

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Definition
Tunnel, passage, gallery, or roadway beneath the ground or underwater. Tunnels are used for
highway traffic, railways, and subways; to transport water, sewage, oil, and gas; to divert rivers
around dam sites while the dam is being built; and for military and civil-defense purposes.
Subterranean galleries are a series of horizontal passageways on different levels, as in a mine.
Construction sites of powerhouses, blasted out of solid rock near dams, are also in the tunnel
category.
Modern Tunneling Methods
Tunneling machines, sometimes called moles, make an initial cut into rock with a cutter-head.
Individual disc-shaped cutters are set into the face of a powerful, rotating head, which may be
more than 5.5 m (18 ft) in diameter. As the machine bores through rock, conveyor belts transport
rock particles, and any other refuse away from the head. Concrete segments are erected to line
and protect the tunnel as each area is hollowed out. The segments also offer a firm surface for
the machine to grip as it continues through the rock, sometimes at rates of more than 5 m (16.4
ft) an hour.
The building of a tunnel is known as driving a tunnel and involves advancing the passageway by
blasting or boring and excavating. Tunnels through mountains or underwater are usually worked
from the two opposite ends, or faces, of the passage. In the construction of a very long tunnel,
vertical shafts may be dug at convenient intervals to excavate from more than two points. Improved

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boring and drilling machinery now allow a tunnel to be driven four or five times faster than was
possible with older techniques.
The rock drill that is driven by compressed air has helped most in reducing the time of tunnelling
in recent years. A number of these drills may be positioned on wheeled vehicles, called jumbos,
and rolled to the face of the tunnel. Many holes are then drilled concurrently in predetermined
places on the rock face. Blasting material is inserted into the holes, the area cleared, and the
explosives detonated. Broken rock is then removed and the process repeated.
Another recently developed tunneling machine is the mole, a long machine with a circular cutting
head that rotates against the face of the tunnel. Attached to the cutting head is a series of steel disc
cutters that gouge out the rock on the face as the machine rotates and is pushed forwards by
hydraulic power. Moles provide several advantages over drilling and blasting. The tunnel can be
bored to the exact size desired, with smooth walls, thus eliminating the condition called overbreak,
which results when explosives tear away too much rock. The use of moles also eliminates blasting
accidents, noise, and earth shocks. Workers are less troubled by fumes and noxious gases and can
clear away broken rock without stopping for blasting intervals. A mole can advance about 76 m
(250 ft) a day, depending on the diameter of the tunnel and the type of rock being bored.
Despite these advantages, moles have some drawbacks. They are very costly, and the cutting head
must be the same diameter as that required for the tunnel. They are useless in soft ground and mud,
which collapse as soon as the machine digs in, and, until recent years, when improved cutting
surfaces came into use, extremely hard rock quickly wore out cutting discs.
In addition to blasting and boring machines, several other methods are used to dig tunnels. The
cut-and-cover method involves digging a trench; building the concrete floor, walls, and ceiling, or
installing pre-cast tunnel sections; and then refilling the trench over the tunnel. This method is not
usually chosen for building tunnels in built-up areas in cities. In soft earth or mud, a large-diameter
pipe-like device can be driven through the ground by jacks or compressed air. Workers remove
the earth as the pipe moves forwards, its edge cutting into the earth. Underwater sunken tube
tunnels, such as the Baltimore Harbor Tunnel in the United States, have been built by fabricating
short tunnel sections in a trench in the riverbed or seafloor. Each section, after sinking, is attached
by oversized bolts to the previously sunk section in line. Heavy, thick concrete walls prevent the
tunnel from floating.
Another method of underwater tunnel construction uses a caisson, or watertight chamber, made of
wood, concrete, or steel. The caisson acts as a shell for the building of a foundation. The choice of
one of three types of caissons, the box caisson, the open caisson, or the pneumatic caisson, depends
on the consistency of the earth and the circumstances of construction. Difficult conditions
generally require the use of the pneumatic caisson, in which compressed air is used to force water
out of the working chamber.
Hazards of Tunnel Construction
New tunneling techniques have not eliminated all the hazards of tunnel digging. Water, sometimes
as much as 72,000 liters (about 19,000 gal) a minute, can pour into tunnels not yet lined with

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concrete or plastic sealers. The water, which must be pumped out continuously, inconveniences
workers, causes tunnel roofs and walls to collapse, damages equipment, and causes delays in
digging. In recent tunnel projects, attempts have been made to freeze the tunnel area before blasting
or digging to prevent flooding before the walls can be sealed and lined. With the exception of some
water and sewer tunnels, in which water seepage is not a problem, most tunnels are lined
permanently with wood, concrete, or steel, or a combination of the three.
Dust from blasting is another serious hazard, causing illness among workers and delay in
digging. A machine that sprays a fine curtain of water to settle the dust following a blast has
recently been used. Despite extensive safety precautions, accidents in tunneling are common,
such as a blasting accident in Japan in 1960, which killed 22 workers.
Famous Tunnels of the World
Chesapeake Bay features a piece of construction that may startle unprepared travelers. The 28.2-
km (17.5-mi) crossing between Norfolk and Cape Charles, Virginia, begins as a bridge, but
disappears into the water midway. A combination structure, the Chesapeake Bay Bridge-Tunnel
combines two bridges with two tunnels that pass under major shipping channels.
Chesapeake Bay Bridge and Tunnel District
1. Seikan Tunnel,in Japan, which links the islands of Honshu and Hokkaido across the
Tsugaru Strait, 53.8 km (33.4 mi); the world's longest rail tunnel.
2. Channel Tunnel, the 3-bore railway tunnel beneath the English Channel from Calais to
Dover, 50 km (31 mi); the world's longest underwater rail and road tunnel and Europe's
largest ever civil engineering project.
3. Mont Cenis (1871), through the Alps between France and Italy, 13.7 km (8.5 mi) long;
the first rail tunnel built; first use of compressed-air drills.
4. Simplon (1922), railway tunnel through the Alps between Switzerland and Italy, 19.8 km
(12.3 mi) long; the world's deepest tunnel.
5. An immense road-header machine drills out clay during the construction of the Channel
Tunnel, which runs for 50.4 km (around 31 mi) beneath the English Channel and became
operational in May 1994. Completed at a cost of £10 billion, it was the largest construction
project ever undertaken in Europe.
6. Yerba (1936), through Yerba Buena Island, San Francisco Bay, California, 165 m (540
ft) long, 23 m (76 ft) wide, and 15 m (50 ft) high; the world's largest-diameter bore
tunnel, carrying two decks for traffic.
7. Delaware Aqueduct (1944), in New York State, 137 km (85 mi) long; starts at Roundout
Reservoir in the Catskill Mountains and ends at Hillview Reservoir, Yonkers; the world's
longest tunnel.
8. Mont Blanc (1965), highway tunnel through the Alps between Chamonix, France, and
Courmayeur, Italy, 11.6 km (7.25 mi) long.
9. Snowy Mountains Scheme (1972), in Australia, a complex of tunnels totalling about 145
km (90 mi), linking reservoirs and powerhouses; among the complex, Eucumbene-Snowy
(1965), 23.5 km (14.6 mi) long.

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10. Fréjus Tunnel (1980), through the Fréjus Pass in the Alps, 12.8 km (8 mi) between
France and Italy.
11. Laerdal Tunnel (2000), in Norway, 24.5 km (15.2 mi), the longest road tunnel in the
world. Previously, the St Gotthard Pass Tunnel (1980), in Switzerland, 16.9 km (10.5
mi), had been the longest.
Functions of Slab and Design of Slab
A flat piece of concrete, put on the walls or columns of a structure. It serves as a walking surface
but may also serve as a load bearing member, as in slab homes.
Functions of Concrete
1. Provide a flat surface
2. To support load
3. Sound, heat and fire insulator
4. Act as a divider (privacy) for the occupants
5. Upper slab became the ceiling for the storey below
6. Space between slab and ceiling can be used to place building facilities
Design Considerations in Slab:
1. Locate position of wall to maximize the structural stiffness for lateral loads
2. Facilitates the rigidity to be located to the center of building
3. Its necessary to check the slab deflection for all load cases both for short and long term
basis. In general, under full service load, Deflection (d) < L/250 or 40 mm whichever is
smaller.
4. Its preferable to perform crack width calculations based on spacing of reinforcement.
5. Good detailing of reinforcement will Restrict the crack width to within acceptable
tolerances as specified in the codes and Reduce future maintenance cost of the building

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6. Take care of punching shear i.e use more steel or thickness of concrete where there is
chance of punching shear in the concrete slab. To increase shear capacity at the edges of
walls and columns embed shear studs or stirrup cages in the slab.
7. Check for lateral stability
Methods of Design of Slab
1. The finite element analysis
2. The simplified method
3. The equivalent frame method
Methods of Simple Truss Analysis
 A truss structure is composed of slender members joined together at their end points
 Members are commonly wooden struts or metal bars
 Joint connections are formed by bolting or welding the ends of the members to a common
plate (gusset plate) or by simply passing a large bolt or pin through each of the members
 Planar trusses lie in a single plane (often seen supporting roofs and bridges), 2-D analysis
of forces appropriate
1. Truss Analysis Method of joints
 If a truss is in equilibrium, then each of its joints must also be in equilibrium
 The method of joints consists of satisfying the equilibrium conditions for the forces exerted
“on the pin” at each joint of the truss
 Truss members are all straight two-force members lying in the same plane
 The force system acting at each pin is coplanar and concurrent (intersecting)
 Rotational or moment equilibrium is automatically satisfied at the joint, only need to satisfy
∑ Fx = 0, ∑ Fy = 0
 Draw the free-body diagram of a joint having at least one known force and at most two
unknown forces (may need to first determine external reactions at the truss supports)
 Establish the sense of the unknown forces
 Always assume the unknown member forces acting on the joint’s free-body diagram to be
in tension (pulling on the “pin”)
 Assume what is believed to be the correct sense of an unknown member force
 In both cases a negative value indicates that the sense chosen must be reversed
 Orient the x and y axes such that the forces can be easily resolved into their x and y
components
 Apply ∑ Fx = 0 and ∑ Fy = 0 and solve for the unknown member forces and verify their
correct sense
 Continue to analyze each of the other joints, choosing ones having at most two unknowns
and at least one known force
 Members in compression “push” on the joint and members in tension “pull” on the joint
 Mechanics of Materials and building codes are used to size the members once the forces
are known

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Zero-force members
 Truss analysis using the method of joints is greatly simplified if one is able to determine
those members which support no loading (zero-force members)
 These zero-force members are used to increase stability of the truss during construction
and to provide support if the applied loading is changed
 If only two members form a truss joint and no external load or support reaction is applied
to the joint, the members must be zero-force members
 If three members form a truss for which two of the members are collinear, the third member
is a zero-force member provided no external force or support reaction is applied.
2. Method of sections for trusses
 Based on the principle that if a body is in equilibrium, then any part of the body is also in
equilibrium
Procedure for analysis
 Section or “cut” the truss through the members where the forces are to be determined
 Before isolating the appropriate section, it may be necessary to determine the truss’s
external reactions (then 3 equations equations of equilibrium can be used to solve for
unknown member forces in the section)
 Draw the free-body diagram of that part of the sectioned truss that has the least number of
forces acting on it
 Establish the sense of the unknown member forces
 Apply 3 equations of equilibrium trying to avoid equations that need to be solved
simultaneously
 Moments should be summed about a point that lies at the intersection of the lines of action
of two unknown forces
 If two unknown forces are parallel – sum forces perpendicular to the direction of these
unknowns
Frames and Machines
 Structures are often composed of pin-connected multi force members
 Frames are generally stationary and are used to support loads
 Machines contain moving parts and are designed to transmit and alter the effect of forces
 Can apply the equations of equilibrium to each member of the frame or machine to
determine the forces acting at the joints and supports (assuming the frame or machine is
properly constrained and contains no more supports or members than are necessary to
prevent collapse)
 Construct applicable free-body diagrams
 Draw an outline of the shape
 Show all forces or couple moments that act on the part
 Indicate dimensions needed for determining moments
 Identify all two force members in the structure

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 All loadings are applied at the joint
 Members are joined together by smooth pins
 Members have two equal but opposite forces acting at their points of application
 The line of action of the forces are along the axis of the members
 Forces common to any two contacting members act with equal magnitudes but opposite
sense on the respective members
 Apply the equations of equilibrium
Simply Supported UDL Beam Formulas and
Equations
 Below are the Beam Formulas and their respective SFD's and BMD's
A simply supported beam is the most simple arrangement of the structure. The beam is supported
at each end, and the load is distributed along its length. A simply supported beam cannot have
any translational displacements at its support points, but no restriction is placed on rotations at
the supports.
Fig:1 Formulas for Design of Simply Supported Beam having Uniformly Distributed Load are
shown at the right

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Fig:2 Shear Force & Bending Moment Diagram for Uniformly Distributed Load on Simply
Supported Beam
Figure 1

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Figure 2
Fig:3 Formulas for Design of Simply Supported Beam having Uniformly Distributed Load at its
mid span
Fig:4 SFD and BMD for Simply Supported at midspan UDL carrying Beam

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Figure 3

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Figure 4
Fig:5 Shear Force and Bending Moment Diagram for Simply Supported Uniformly distributed
Load at left support
Fig:6 Formulas for finding moments and reactions at different sections of a Simply Supported
beam having UDL at right support

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Figure 5

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Figure 6
Fig:7 SFD and BMD for UDL at both ends
Fig:8 Formulas for analysis of beam having SFD and BMD at both ends

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Figure 7

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Figure 8
Fig:9 Collection of Formulas for analyzing a simply supported beam having Uniformly Varying
Load along its whole length
Fig:10 Shear force diagram and Bending Moment Diagram for simply supported Beam having
UVL along its span

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Figure 9

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Figure 10

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Fig:11 SFD and BMD for simply supported beam having UVL from the midspan to both ends
Fig:12 Formulas for calculating Moments and reactions on simply supported beam having UVL
from the midspan to both ends
Figure 11

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Figure 12
Structural Design Criteria for Coastal Structures
Coastal structures are the structures that are constructed near to the coastal areas for different
purposes. Different types of coastal structures are constructed under different circumstances but
the criteria to be used for the selection and design of specific type of coastal structure must be
authentic and comply with the standards. There are a various set of criteria that need to be
considered in the selection and design of coastal structures.
 Structural stability criteria
 Functional performance criteria
These two areas are of primary concern for selection and evaluation of coastal structures.
Structural stability criteria are usually associated with extreme environmental conditions, which
may cause severe damage to, or failure of a coastal structure. These stability criteria are,
therefore, related to episodic events in the environmental (severe storms, hurricanes,
earthquakes) and are often evaluated on the basis of risk of encounter probabilities. A simple
method for evaluating the likelihood of encountering an extreme environmental event is to
calculate the encounter probability (Ep) as:
Ep =1-(1-1/TR)
where TR = the return period
L = the design life of the structure (see Borgman, 1963)

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Typical Example of Coastal Structure
The greatest limitation to structural stability criteria selection is the need for a long-term data
base on critical environmental variables sufficient enough to determine reasonable return periods
for extreme events.
For example coastal wave data for U.S. coasts is geographically sparse and in most locations
where it exists the period of collection is in the order of 10 years. Since most coastal structures
have a design life well in excess of 10 years, stability criteria selection often relies on
extrapolation of time limited data or statistical modeling of environmental processes.
Functional performance criteria are generally related to the desired effects of a coastal structure.
These criteria are usually provided as specifications for design such as the maximum acceptable
wave height inside a harbor breakwater system or minimum number of years for the protective
lifetime of a beach nourishment fill project. Functional performance criteria are most often
subject to compromise because of initial costs. The U.S. Army Shore Protection Manual (1984)
provides a complete discussion of coastal structures, their use, design and limitation. A P-C
based support system entitled Automated Coastal Engineering System (ACES) is also available
through the USAE Waterways Experiment Station, Coastal and Hydraulics Laboratory,
Vicksburg, MS 39180-6199.
Types of Coastal Structures
Following are the few types of Coastal structures

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 Sea walls and groynes
 Culverts and storm water pipes
 Cables
 Boat ramps and launch access
 Fencelines and posts
 Wharves and jetties
 Buildings and Maimai
 Bridges, causeways and fords
 Dump sites and derelict structures
 Marine farms
Environmental Impacts of Coastal Structures
The placement of engineered structures on or near the coastline must be contemplated with
extreme care. In general, alteration of the natural coastline comes with an associated
environmental penalty. Hard (structures made of stone, steel, concrete, etc.) or soft (beach
nourishment, sediment filled bags, etc.) engineering structures can alter many physical properties
of the beach to often induce undesired effects. These alterations of natural processes can take the
form of increased reflectivity to incident waves,
These coastal engineering structures increase in scope and complexity, moving down the page.
Anticipated regions of shoreline sediment accretion and erosion are also indicated for each type
of structure. A significant body of recent research has indicated that these regions of structural
impact along the shoreline extend between five and ten times the length of the structure. Hence,
for a structure protruding from the undisturbed shoreline a distance of 100 m, the anticipated
region of impact should be expected to extend from 500 to 1000 m either side of the structure.
The field of coastal engineering is far from a mature science. This is a time of rapid and
significant advances in our understanding of the physical processes, which control the response
of the near shore region to wind, waves and water level changes. Furthermore, advances in the
design, implementation and in predicting the response of coastal structures and fortifications are
made almost daily. Hence, it is nearly impossible to provide a comprehensive review of the most
current material.
Retrofitting Techniques for Existing Damaged
Buildings

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(Special Emphasis on FRP)
Techniques for Strengthening
Prevailing Techniques for Strengthening
Primary aim of strengthening a structure is to increase its load bearing capacity with respect to its
previous condition. Only those aspects related to flexure are discussed here. Established techniques
which have been in use successfully for a number of years are recognized as follows:
1. Over Slabbing
2. Sprayed Concrete with Additional Reinforcement
3. Steel Plate bonding
4. External Prestressing
Over Slabbing:
In this technique, a plain or reinforced concrete slab is overlaid on top of the existing slabs or
beams to increase the section dimension in order to increase flexural strength. To ensure the
composite action between the two, dowels or shear studs may be installed. This method in
particular may be advantageous when the member needing strengthening possesses
reinforcement near or equal to balanced steel. However, as the flexural strength of a reinforced
concrete member is usually limited by the capacity of the reinforcement rather than by the
capacity of the concrete, over-slabbing may therefore, be of no significant value. Any strength
increase may be offset by the increase in dead load.
"DRITSOS ET AL" has concluded that the chances of interface failure are increased when the
existing beam is over-reinforced and the depth of the overlay is too deep. This observation
further limits the scope of its use. Apart from disruption to use of the structure, extensive surface
preparation is required.
Sprayed Concrete With Additional Reinforcement
Sprayed concrete is a mixture of cement, aggregates and water which is projected into place at
high velocity from nozzle. Many names have been associated with sprayed concrete including
spray concrete, shotcrete and gunite. In the USA the "American Concrete Institute" described
shotcrete as "mortar or concrete conveyed through a hose and pneumatically projected at high
velocity onto a surface". In the UK Gunite is referred to "sprayed concrete where the aggregate
size is less than 10mm, and where the size of aggregate exceeds 10mm, it is termed as shotcrete".
Strengthening of beams deficient in flexure is accompanied by addition of reinforcing steel in the
tensile zone. The method is, therefore, sometimes referred to as tensile overlay. The method
essentially requires removal of concrete cover, cutting recesses if necessary to accommodate
additional bars, either by providing sufficient anchorage length in the concrete, or by steel plates
and bolts with anchoring yokes. Once the whole system is in place concrete is sprayed to the
desired thickness. It is essential to have a satisfactory bond between existing and new concretes
as the evaluation of new concrete section is based on the same principles as those of normal
reinforced concrete. Apart from the capability of the joint to transfer shear stresses without

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relative movement, differences in creep and shrinkage properties of old and new concrete need
careful evaluation. It is reported that most shotcrete durability failures do not involve failures of
the material itself, but generally there is a peeling off sound shotcrete because of bond failure.
The Department of Transport suggested the use of sprayed concrete where the reinforcement is
not too congested.
This method involves extensive surface preparation, and disruption to use of the structure is
inevitable with this technique. Full advantage of the additional reinforcement can only be taken
if the cross-section has sufficient capacity to incorporate additional reinforcement without
becoming an over-reinforced section.
Steel Plate Bonding
This method of strengthening which materialized with the development of epoxy resin is about
39 years old and is now used in almost all parts of the world. In this method of enhancing
flexural capacity, mild steel plates are bonded to the soffit of the beam by an epoxy adhesive.
There is practically no increase in depth of member or in its dead weight. The method is
versatile, flexible, economical and expedient. The behavior of resulting composite system largely
depends on the inter-layer bond between concrete and plate. The thickness of the plate needs
special attention on relatively thick plates can initiate horizontal cracking and plate separation.
With increase width, there is a risk of defects in adhesive, and with increasing thickness of the
adhesive; the slip between the reinforcing element and concrete becomes greater. Anchor plates
are needed where the width-thickness ratio of the plate is less than 50:1 due to production of high
stresses near the ends of the plates leading to premature failure. The technique cannot be used
where the member shows any sign of reinforcement corrosion.
External PreStressing
External Pre-stressing is defined as pre-stress produced by cables which are placed outside the
structure over a great part their length and which, except at the deviators and at anchorage zones
has no relation the shape of the concrete structure.
The advantages over plate bonding technique include:
1. Less susceptibility to weather conditions during repair
2. Elimination of surface preparation
3. Easy installation
4. Use on any structural material
5. Use on structures contaminated on chlorides.
6. Strengthening with external unbounded pre-stressed tendons is now a widely used method;
however, its use has been restricted in the developing world because of its sophistication, skill
required and lack of experience in designing, handling and application.

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Newer Techniques for Strengthening
Newer techniques are sometimes derived through already existing techniques and sometimes
advances in different aspects of newer material pave the way for introduction of newer techniques.
Two such techniques which have shown some promise of their future development are:
Externally Bonded FRP Composites
Ferrocement
Fiber Composite Plate & Tendons
Recent developments in the field of plastics and composites have resulted in the manufacturing
of high strength fiber reinforced plastics (FRP), with strength and fatigue properties higher than
those of steel. The fiber could be glass fiber, aramid fiber or carbon fiber.
If two dissimilar materials which have to have composite action are to be used structurally, it is
necessary for designer to have a thorough understanding of the mechanical and service material
properties of the components, the method of joining, the composite action and failure mechanism
and overall structural analysis of these systems.
Glass, aramid and carbon fiber composites may be considered for strengthening applications
with particular regard to plate bonding. A comparison of the important characteristics of an FRP
produced from these fiber types is shown in "Table 6.1", in which the fiber fraction volume is
typically around 65% and the fibers are unidirectional aligned.
Methods
Two primary methods are used to attach FRP composite materials to concrete structures (and to
masonry, timber, and even metallic structures) for "retrofitting" purposes.
One method employs per-manufactured rigid FRP strips (approximately 4 in. (100 mm) wide and
in. (1.6 mm) thick) that are adhesively bonded to the surface of the structural member.
The other method, known as "hand lay up", consists of in situ forming of the FRP composite on
the surface of the structural member using flexible dry fiber fabrics or sheets of width
approximately 6 to 60 in. (150 to 1500 mm) and liquid polymers.
In recent years a new variant of the pre-manufactured strip method called Near Surface
Mounting (NSM) has been developed (Refer Figure 6.1). In this method, a thin, narrow FRP
strip (3 by 18 mm) or small-diameter round FRP bar (6 mm) is inserted and then bonded
adhesively into a machined groove at the surface of the concrete member. (Refer Figure 6.2)
FRP retrofitting has been used with bridge and building structures to strengthen static and quasi-
static loads (such as increases in dead or live load in a bridge or building structure), and for
dynamic loads (such as strengthening for improved seismic or blast response in a bridge or
building structure). FRP composites have been used successfully for flexural strengthening of

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concrete beams and slabs, shear strengthening of concrete beams, and axial strengthening and
ductility enhancement of concrete columns.
Advantages
All structural problems have more than one technical solution, and final selection will ultimately
rest upon an economic evaluation of the alternatives. Enlightened clients will ensure that this
evaluation includes of the total cost that will be incurred during the minimum initial cost. The
potential advantages of FRP composites plate bonding are as follows:
Strength of Plates: FRP composites plates may be designed with components to meet a
particular purpose and may comprise varying proportions to different fibers. The ultimate
strength of the plates can be varied, but for strengthening schemes the ultimate strength of the
plates is likely to be at least three times the ultimate strength of steel for the same cross-sectional
area.
Weight of Plates: The density of FRP composite plates is only 20% of the density of steel. Thus
composite plates may be less than 10% of the steel weight with same ultimate strength. Apart
from transport costs, biggest saving arising from this is during installation. Composite plates do
not require extensive jacking and support system to move and hold in place. The adhesive alone
will support the plate until curing has taken place. In contrast, fixing of steel plates constitutes a
significant proportion of the works costs.
Versatile Design of Systems: Composite plates are of unlimited length, may be fixed in layers to
suit in two directions may be accommodated by varying the adhesive thickness.
Reduced Mechanical Fixing: Composite plates are much thinner than steel plates of equivalent
capacity. This reduces peeling effects at the ends of the plates and thus reduces the likelihood of
a need for end fixing. The overall depth of the strengthening scheme is reduced, increasing head-
room and improving appearance.
Durability of Strengthening System: There is the possibility of corrosion on the bonded face of
steel plates, particularly if the concrete to which they are fixed is cracked or chloride
contaminated. This could reduce the long term bond. Composite plates do not suffer from such
deterioration.
Improved Fire Resistance: Composite plates are a low conductor of heat when compared to
steel, thus reducing the effect fire has on the underlying adhesives. The itself chars rather than
burns and the system thus remain effective for a much longer period than steel plate bonding.
Maintenance of Strengthening System: Steel plates require maintenance and painting and
access costs as well as the works costs. Composites plates will not require such maintenance,
reducing the whole life cost of this system.
Ability to Pre Stress: The ability to pre-stress composites opens up a whole new range of
applications for plate bonding. The plate bonding may be used to replace lost pre-stress and shear

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capacity of the section be increased by the longitudinal stresses induced. Formation of cracks be
inhibited and the serviceability of the structure enhanced. Strengthening of materials such as cast
iron also becomes more practicable.
Disadvantages
Cost of Plates: Fiber reinforced composite plates are more expensive than steel plates of the
equivalent load capacity.
Mechanical Damage: FRP composite plates are more susceptible to damage than steel plates
and could be damaged by determined attack, such as with an axe. Fortunately, if damage should
occur to expose FRP composite plate, such as by a high load, repairs can be undertaken much
more easily then with a steel plate. A steel plate may be dislodged, or bond broken over a large
area, which would damage bolt fixing and necessitate complete removal and replacement.
However, with FRP composite plate bonding the damage is more likely to be a localized, as the
plate is thinner and more flexible. With FRP composite, the plate may be cut the top with an
appropriate lap.
FERROCEMENT
Ferro cement is said to be the first form of reinforced concrete. Ferro cement is the type of
reinforced concrete which uses wire mesh rather than heavy rods and bars as the primary part of
its metal reinforcement, and uses sand and cement mortar rather than a mixture of cement, sand
and gravel as the primary part of its concrete mixture. Cement and sand mortar having a ratio of
1:2 is impregnated in the mesh reinforcement either by hand or by shotcrete to produce almost a
fabric of steel packed and coated with mortar.
Although there are many obstacles to the greater use of ductility is attracting researchers to
exploit its potential. Ferro cement have no apparent advantage over any other type of reinforced
concrete either in direct tension or flexure, but it has a high level of control over cracking
provided by the close spacing and specific surface area of the wire reinforcing mesh.
Waliuddin and Rafeeqi through an experimental study have indicated a possibility of confining
concrete with Ferro cement to enhance the capacity of columns and to strengthen other concrete
structures. Remualdi showed that Ferrocement has the ability to retain its structural integrity
through relatively large strains, has excellent crack control and remarkable ductility, which
makes it a choice for use as a strengthening material. All these studies have shown that the
strengthened beams have shown superior crack control, enhanced flexural strength and enhanced
ductility.
Characteristics Carbon Aramid E-glass
Tensile strength Very good Very good Very good
Compressive strength Very good Inadequate Good
Stiffness Very good Good Adequate
Long term behavior Very good Good Adequate
Fatigue behavior Excellent Good Adequate

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Bulk density Good Excellent Adequate
Alkaline resistance Very good Good Inadequate
Cost Adequate Adequate Very good
Definition and Types of Retaining Walls
Definition
A retaining wall is a structure that retains (holds back) any material (usually earth) and prevents it
from sliding or eroding away. It is designed so that to resist the material pressure of the material
that it is holding back.
Types of Retaining Walls
An earth retaining structure can be considered to have the following types:
1. Gravity Walls
o Reinforced Gravity Walls

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2.
1. Concrete Cantilever retaining wall
2. Counter-fort / Buttressed retaining wall
3. Precast concrete retaining wall
4. Prestressed retaining wall
2. Brick
3. Brick Masonry retaining wall
4. Stone
5. Reinforced Soil Walls
o Reinforced Soil
o Soil Nailing
6. Hybrid System
o Anchored Earth
o Tailed Gabion
o Tailed Concrete Block
o Miscellaneous
Gravity Retaining Walls
It is that type of retaining wall that relies on their huge weight to retain the material behind it and
achieve stability against failures. Gravity Retaining Wall can be constructed from concrete, stone
or even brick masonry. Gravity retaining walls are much thicker in section. Geometry of these
walls also help them to maintain the stability. Mass concrete walls are suitable for retained
heights of up to 3 m. The cross section shape of the wall is affected by stability, the use of space
in front of the wall, the required wall appearance and the method of construction.
Reinforced Retaining Walls
Reinforced concrete and reinforced masonry walls on spread foundations are gravity structures in
which the stability against overturning is provided by the weight of the wall and reinforcement
bars in the wall. The following are the main types of wall:
Concrete Cantilever retaining wall
A cantilever retaining wall is one that consists of a wall which is connected to foundation. A
cantilever wall holds back a significant amount of soil, so it must be well engineered. They are
the most common type used as retaining walls. Cantilever wall rest on a slab foundation. This
slab foundation is also loaded by back-fill and thus the weight of the back-fill and surcharge also
stabilizes the wall against overturning and sliding.
Counter-fort / Buttressed retaining wall
Counterfort walls are cantilever walls strengthened with counter forts monolithic with the back
of the wall slab and base slab. The counter-forts act as tension stiffeners and connect the wall
slab and the base to reduce the bending and shearing stresses. To reduce the bending moments in
vertical walls of great height, counterforts are used, spaced at distances from each other equal to

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or slightly larger than one-half of the height Counter forts are used for high walls with heights
greater than 8 to 12 m.
Precast concrete retaining wall
Prestressed retaining wall
Reinforced Soil Retaining Walls
Mechanically stabilized earth walls are those structures which are made using steel
or GeoTextiles soil reinforcements which are placed in layers within a controlled granular fill.
Reinforced soils can also be used as retaining walls, if they are built as:
1. As an integral part of the design
2. As an alternative to the use of reinforced concrete or other solutions on the grounds of economy
or as a result of the ground conditions
3. To act as temporary works
4. As remedial or improvement works to an existing configuration.
This category covers walls which use soil, reinforced with reinforcing bars, to provide a stable
earth retaining system and includes reinforced soil and soil nailing.
Soil Nailing
Constructing a soil nailed wall involves reinforcing the soil as work progresses in the area being
excavated by the introduction of bars which essentially work in tension, called Passive Bars.
These are usually parallel to one another and slightly inclined downward. These bars can also
work partially in bending and in shear. The skin friction between the soil and the nails puts the
nails in tension.

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Hybrid Systems
The type of retaining walls that use both factors that is their mass and reinforcement for stability
are called Hybrid or Composite retaining wall systems.
Anchored Earth walls
Any wall which uses facing units tied to rods or strips which have their ends anchored into the
ground is an anchored earth wall. The anchors are like abutments. The cables used for tieing are
commonly high strength, prestressed steel tendons. To aid anchorage, the ends of the strips are
formed into a shape designed to bind the strip at the point into the soil.
Tailed Gabion
Gabions are cages, cylinders, or boxes filled with earth or sand that are used in civil engineering,
road-building, and military application and many others. OR Gabion elements fitted to geogrid
'tails' extending into supported soil. For erosion control caged rip-rap are used. For dams or
foundation building, metal structures are used.
Sheet Pile Walls
Steel sheet pile walls are constructed by driving steel sheets into a slope or excavation upto the
required depth. Their most common use is within temporary deep excavations. They are
considered to be most economical where retention of higher earth pressures of soft soils is
required. It cannot resist very high pressure.
Reinforcement Detailing in Concrete Structures

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Detailing is as important as design since proper detailing of engineering designs is an essential link
in the planning and engineering process as some of the most devastating connections. ACI
Reinforcement location in non prismatic beam. ACI reinforcement detailing in cantilever beam.
ACI Reinforcement location in non prismatic beam
 A design engineer's responsibility should include assuring the structural safety of the
design, details, checking shop drawing.
 Detailing is as important as design since proper detailing of engineering designs is an
essential link in the planning and engineering process as some of the most devastating
collapses in history have been caused by defective connections or DETAILING. There are
many examples explained in the book "DESIGN AND CONSTRUCTION FAILURES"
by Dov Kaminetzky.
 Detailing is very important not only for the proper execution of the structures but for the
safety of the structures.
 Detailing is necessary not only for the steel structures but also for the RCC members as it
is the translation of all the mathematical expression's and equation's results.
 For the RCC members for most commonly used for buildings we can divide the detailing
for

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o slabs-with or without openings.(rectangular,circular,non-rectangular-pyramid
slab,triangular etc)
o balcony slab, loft slab, corner slab etc
o beams- with or without openings.(shallow & deep beams)
o columns. (rectangular, l-shape, t-shape, circular, octagonal, cross shape etc)
Foundations
 Detailing for gravity loads is different from the lateral loads specially for the SEISMIC
FORCES.
 Apart from the detailing for the above there is a different detailing required for the
rehabilitation and strengthening of damaged structures.
 We will now dwell on the DETAILING OF MEMBERS FOR THE GRAVITY AND
SOME DETAILINGS according to the code
 AS PER IS CODE IS 13920 AND IS 4326 AS REQUIRED FOR SEISMIC FORCES.
Do's & Do Not's for Reinforcement detailing:
Do's General:
1. Prepare drawings properly & accurately if possible label each bar and show its shape for
clarity.
2. Cross section of retaining wall which collapsed immediately after placing of soil backfill
because ¼" rather than 1-1/4" diameter were used. Error occurred because Correct rebar
dia. was covered by a dimension line.
3. Prepare bar-bending schedule , if necessary.
4. Indicate proper cover-clear cover, nominal cover or effective cover to reinforcement.
5. Decide detailed location of opening/hole and supply adequate details for reinforcements
around the openings.
6. Use commonly available size of bars and spirals. For a single structural member the number
of different sizes of bars shall be kept minimum.
7. The grade of the steel shall be clearly stated in the drawing.
8. Deformed bars need not have hooks at their ends.
9. Show enlarged details at corners, intersections of walls, beams and column joint and at
similar situations.
10. Congestion of bars should be avoided at points where members intersect and make certain
that all rein. Can be properly placed.
11. In the case of bundled bars, lapped splice of bundled bars shall be made by splicing one
bar at a time; such individual splices within the bundle shall be staggered.
12. Make sure that hooked and bent up bars can be placed and have adequate concrete
protection.
Indicate all expansion, construction and contraction joints on plans and provide details for such
joints. The location of construction joints shall be at the point of minimum shear approximately at
mid or near the mid points. It shall be formed vertically and not in a sloped manner.
DO'S - BEAMS & SLABS:
1. Where splices are provided in bars, they shall be , as far as possible, away from the sections
of maximum stresses and shall be staggered.

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2. Were the depth of beams exceeds 750 mm in case of beams without torsion and 450mm
with torsion provide face rein. as per IS456-2000.
3. Deflection in slabs/beams may be reduced by providing compression reinforcement.
4. Only closed stirrups shall be used for transverse rein. For members subjected to torsion and
for members likely to be subjected to reversal of stresses as in Seismic forces.
5. To accommodate bottom bars, it is good practice to make secondary beams shallower than
main beams, at least by 50mm.
Do's - COLUMNS
1. A reinforced column shall have at least six bars of longitudinal reinforcement for using in
transverse helical reinforcement.-for CIRCULAR sections.
2. A min four bars one at each corner of the column in the case of rectangular sections.
3. Keep outer dimensions of column constant, as far as possible , for reuse of forms.
4. Preferably avoid use of 2 grades of vertical bars in the same element.
DO NOT'S - GENERAL
1. Reinforcement shall not extend across an expansion joint and the break between the
sections shall be complete.
2. Flexural reinforcement preferably shall not be terminated in a tension zone.
3. Bars larger than 36mm dia. Shall not be bundled.
4. Lap splices shall be not be used for bars larger than 36mm dia. Except where welded.
5. Where dowels are provided, their diameter shall not exceed the diameter of the column
bars by more than 3mm.
6. Where bent up bars are provided, their contribution towards shear resistance shall not be
more than 50% of the total shear to be resisted.
7. USE OF SINGEL BENT UP BARS(CRANKED) ARE NOt ALLOWED IN THE CASE
OF EARTHQUAKE RESISTANCE STRUCTURES.
DETAILING OF SLABS WITHOUT ANY CUT OR OPENINGS
 The building plan DX-3 shows the slabs in different levels for the purpose of eliminating
the inflow of rainwater into the room from the open terrace and also the sunken slab for
toilet in first floor.
 The building plan DX-A3 is one in which the client asked the architect to provide opening
all round.
 Different shapes of slabs used in the buildings Minimum and max. reinforcement % in
beams, slabs and columns as per code provisions should be followed.
SLABS
1. It is better to provide a max spacing of 200 mm(8") for main bars and 250mm(10") in order
to control the crack width and spacing.
2. A min. of 0.24% shall be used for the roof slabs since it is subjected to higher temperature.
Variations than the floor slabs. This is required to take care of temperature differences.
3. It is advisable to not to use 6mm bars as main bars as this size available in the local market
is of inferior not only with respect to size but also the quality since like TATA and SAIL
are not producing this size of bar.
BEAMS
ACI reinforcement detailing in cantilever beam:

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1. A min. of 0.2% is to be provided for the compression bars in order to take care of the
deflection.
2. The stirrups shall be min. size of 8mm in the case of lateral load resistance
3. The hooks shall be bent to 135 degree.
Bonded Concrete Slab Post Tensioning
This can be defined as the method of applying compression force on concrete after it has been
poured and cured.
Introduction to Post tensioning and benefits of post tensioning in concrete slab
Post-tensioning is a method of reinforcing (strengthening) concrete or other materials with high-
strength steel strands rebars, typically referred to as tendons. It has the following benefits as
compared to unbonded post tensioning.
Bonded post-tensioned concrete is the descriptive term for a method of applying compression
after pouring concrete and the curing process (in situ). The concrete is cast around plastic, steel

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or aluminum curved duct, to follow the area where otherwise tension would occur in the concrete
element.
A set of tendons are fished through the duct and the concrete is poured. Once the concrete has
hardened, the tendons are tensioned by hydraulic jacks that react against the concrete member
itself. When the tendons have stretched sufficiently, according to the design specifications (see
Hooke's law), they are wedged in position and maintain tension after the jacks are removed,
transferring pressure to the concrete.
The duct is then grouted to protect the tendons from corrosion. This method is commonly used to
create monolithic slabs for house construction in locations where expansive soils (such as adobe
clay) create problems for the typical perimeter foundation. All stresses from seasonal expansion
and contraction of the underlying soil are taken into the entire tensioned slab, which supports the
building without significant flexure. Post-tensioning is also used in the construction of various
bridges; both after concrete is cured after support by falsework and by the assembly of
prefabricated sections, as in the segmental bridge.
The advantages of this system over un-bonded post-tensioning are:
1. Large reduction in traditional reinforcement requirements as tendons cannot de-stress in
accidents.
2. Tendons can be easily 'weaved' allowing a more efficient design approach.
3. Higher ultimate strength due to bond generated between the strand and concrete.
4. No long term issues with maintaining the integrity of the anchor/dead end.
Advantages of Post-tensioning
1. Allows longer clear spans, thinner slabs
2. Lower overall building height for the same floor-to-floor height.
3. Allows a high degree of flexibility in the column layout, span lengths and ramp
configurations
4. The use of traditional reinforcement requirement can be reduced as tendons cannot de-
stress in accidents.
5. Increases the ultimate strength due to strong bond between the strand and concrete.
6. Significant savings in costs can be achieved by post tensioning in concrete slabs because
of:
1. Reduced cracking and deflections
2. Reduced storey height
3. Better Water tightness
Placement of Tendons
 Positioning and fixing of casting and block-outs to the edge formwork or construction
joint form work
 The support bars shall be prepared in advance.
 Lay tendons according to tendon layout in accordance with the drawings.
 Fix tendons to correct profiles with support bars and chairs and the tendons are made
with provisions for grouting using grout using grout vents and grout hoses
 Prepare installation report for every installation as per the enclosed format.
 Tolerance of tendon profiles is recommended as follows:

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o vertical: + 5 mm (at lowest and highest points)
o Horizontal: + 100 mm
Types of Supports for Loads
Roller Supports
Roller supports are free to rotate and translate along the surface upon which the roller rests. The
surface may be horizontal, vertical or slopped at any angle. Roller supports are commonly
located at one end of long bridges in the form of bearing pads. This support allows bridge
structure to expand and contract with temperature changes and without this expansion the forces
can fracture the supports at the banks. This support cannot provide resistance to lateral forces.
Roller support is also used in frame cranes in heavy industries as shown in figure, the support
can move towards left, right and rotate by resisting vertical loads thus a heavy load can be shifted
from one place to another horizontally.

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Hinge Supports
The hinge support is capable of resisting forces acting in any direction of the plane. This support
does not provide any resistance to rotation. The horizontal and vertical component of reaction
can be determined using equation of equilibrium. Hinge support may also be used in three hinged
arched bridges at the banks supports while at the center internal hinge is introduced. It is also
used in doors to produce only rotation in a door. Hinge support reduces sensitivity to earthquake.

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FIXED SUPPORT
Fixed support can resist vertical and horizontal forces as well as moment since they restrain both
rotation and translation. They are also known as rigid support For the stability of a structure there
should be one fixed support. A flagpole at concrete base is common example of fixed support In
RCC structures the steel reinforcement of a beam is embedded in a column to produce a fixed
support as shown in above image. Similarly all the riveted and welded joints in steel structure are
the examples of fixed supports Riveted connection are not very much common now a days due to
the introduction of bolted joints.

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PINNED SUPPORTS
A pinned support is same as hinged support. It can resist both vertical and horizontal forces but
not a moment. It allows the structural member to rotate, but not to translate in any direction.
Many connections are assumed to be pinned connections even though they might resist a small
amount of moment in reality. It is also true that a pinned connection could allow rotation in only
one direction; providing resistance to rotation in any other direction. In human body knee is the
best example of hinged support as it allows rotation in only one direction and resists lateral
movements. Ideal pinned and fixed supports are rarely found in practice, but beams supported on
walls or simply connected to other steel beams are regarded as pinned. The distribution of
moments and shear forces is influenced by the support condition.

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INTERNAL HINGE
Interior hinges are often used to join flexural members at points other than supports. For example
in above fig two halves of an arch is joined with the help of internal hinge.
In some cases it is intentionally introduced so that excess load breaks this weak zone rather than
damaging other structural elements as shown in above image.
Frame Structures - Types of Frame Structures
Frame structures are the structures having the combination of beam, column and slab to resist the
lateral and gravity loads. These structures are usually used to overcome the large moments
developing due to the applied loading.

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Types of frame structures
Frames structures can be differentiated into:
1. Rigid frame structure
Which are further subdivided into:
 Pin ended
 Fixed ended
2. Braced frame structure
Which is further subdivided into:
 Gabled frames
 Portal frames
Rigid Structural Frame
The word rigid means ability to resist the deformation. Rigid frame structures can be defined as
the structures in which beams & columns are made monolithically and act collectively to resist
the moments which are generating due to applied load.

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Rigid frame structures provide more stability. This type of frame structures resists the shear,
moment and torsion more effectively than any other type of frame structures. That's why this
frame system is used in world's most astonishing building Burj Al-Arab.
Braced Structural Frames
In this frame system, bracing are usually provided between beams and columns to increase their
resistance against the lateral forces and side ways forces due to applied load. Bracing is usually
done by placing the diagonal members between the beams and columns.
This frame system provides more efficient resistance against the earthquake and wind forces.
This frame system is more effective than rigid frame system
Pin Ended Rigid Structural Frames
A pinned ended rigid frame system usually has pins as their support conditions. This frame system
is considered to be non rigid if its support conditions are removed.

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Fix Ended Rigid Frame Structure:
In this type of rigid frame systems end conditions are usually fixed.
Gabeled Structural Frame:
Gabled frame structures usually have the peak at their top. These frames systems are in use
where there are possibilities of heavy rain and snow.
Portal Structural Frame
Portal structural frames usually look like a door. This frame system is very much in use for
construction of industrial and commercial buildings
Load path in Frame Structure:
It is a path through which the load of a frame structure is transmitted to the foundations. In frame
structures, usually the load path is:

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Load first transfers from slab to beams then to from beam to columns, then from columns
it transfers to the foundation.
Advantages of Frame Structures
1. One of the best advantages of frame structures is their ease in construction. it is very east to teach
the labor at the construction site.
2. Frame structures can be constructed rapidly.
3. Economy is also very important factor in the design of building systems. Frame structures have
economical designs.
Disadvantages of Frames:
In frames structures, span lengths are usually restricted to 40 ft when normal reinforced concrete.
Other wise spans greater than that, can cause lateral deflections.
Comparison of Frame structures with Normal Load bearing Traditional High Rise
Building
Selection of frame structures for the high rise building is due to their versatility and advantages
over the normal traditional load bearing structures. These include the following:
Actually the performance of load bearing structures is usually dependent on the mass of
structures. To fulfill this requirement of load bearing structures, there is the need of increase in
volume of structural elements (walls, slab). This increase in volume of the structural elements
leads toward the construction of thick wall. Due to such a type of construction, labor and
construction cost increases. in construction of thick wall there will be the need of great attention,
which will further reduce the speed of construction.
If we make the contrast of load bearing structures with the framed structures, framed structures
appear to be more flexible, economical and can carry the heavy loads. Frame structures can be

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rehabilitated at any time. Different services can be provided in frame structures. Thus the frame
structures are flexible in use.
Bending Moment - Definition and Calculation
Definition
It is the internal resistance to rotation.
OR
Bending moment at a point or at a section is the algebraic sum of Moments caused by forces
action to the left or right of that point or section. Mathematically it can be written as
'''Moment = Σ ML = Σ MR'''
Moment can not be find out directly however it can be find out by using many practical and
theoretical methods such as:
1. Double integration method
2. Conjugate beam method
3. Area moment method
Bending Moment at any section
Bending moment at any section is the sum of all moments to the left or right of that section.
Positive bending moment
Bending which produces compression in upper (outer) fibers and tension in lower fibers.
Negative bending moment
Bending which produces compression in lower (inner) fibers and tension in upper fibers.

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Analysis of Statically Indeterminate Beams by
Force Method
1. Analysis of Indeterminate Structures by Force Method - An Overview
2. Introduction
3. Method of Consistent Deformation
4. Indeterminate Beams
5. Indeterminate Beams with Multiple Degree of Indeterminacy
6. Truss Structures
7. Temperature Changes & Fabrication Errors
2. Introduction
While analyzing indeterminate structures, it is necessary to satisfy (force) equilibrium,
(displacement) compatibility and force-displacement relationships
a. Force equilibrium is satisfied when the reactive forces hold the structure in stable
equilibrium, as the structure is subjected to external loads
b. Displacement compatibility is satisfied when the various segments of the structure fit
together without intentional breaks, or overlaps

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Force-displacement requirements depend on the manner the material of the structure responds to
the applied loads, which can be linear/nonlinear/viscous and elastic/inelastic; for our study the
behavior is assumed to be linear and elastic
Two methods are available to analyze indeterminate structures, depending on whether we satisfy
force equilibrium or displacement compatibility conditions. They are: Force
method and Displacement Method
Force Method satisfies displacement compatibility and force-displacement relationships; it treats
the forces as unknowns - Two methods which we will be studying are Method of Consistent
Deformation and (Iterative Method of) Moment Distribution
Displacement Method satisfies force equilibrium and force-displacement relationships; it treats
the displacements as unknowns - Two available methods are Slope Deflection Method and
Stiffness (Matrix) method
3. Solution Procedure:
i. Make the structure determinate, by releasing the extra forces constraining the structure in
space
ii. Determine the displacements (or rotations) at the locations of released (constraining) forces
iii. Apply the released (constraining) forces back on the structure (To standardize the
procedure, only a unit load of the constraining force is applied in the +ve direction) to
produce the same deformation(s) on the structure as in (ii)
iv. Sum up the deformations and equate them to zero at the position(s) of the released
(constraining) forces, and calculate the unknown restraining forces
Types of Problems to be dealt:
1. Indeterminate beams;
2. Indeterminate trusses; and
3. Influence lines for indeterminate structures
4.1 Propped Cantilever - Redundant vertical reaction released
i. Propped Cantilever: The structure is indeterminate to the first degree; hence has one unknown in
the problem.
ii. In order to solve the problem, release the extra constraint and make the beam a determinate
structure. This can be achieved in two different ways, viz.,
iii. By removing the vertical support at B, and making the beam a cantilever beam (which is a
determinate beam); or
iv.

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a. The governing compatibility equation at B is
b. By releasing the moment constraint at A, and making the structure a simply supported
beam (which is once again, a determinate beam).
Overview of Method of Consistent Deformation
To recapitulate on what we have done earlier, Structure with single degree of indeterminacy:
(a) Remove the redundant to make the structure determinate (primary structure)
(b) Apply unit force on the structure, in the direction of the redundant, and find the displacement
Δ B0 + fBB x RB = 0
5. Indeterminate beam with Multiple Degrees of Indetermincay
(a) Make the structure determinate (by releasing the supports at B, C and D) and determine the
deflections at B, C and D in the direction of removed redundant, viz.,Δ BO, Δ CO and Δ DO
(b) Apply unit loads at B, C and D, in a sequential manner and determine deformations at B, C and
D, respectively.
(c ) Establish compatibility conditions at B, C and D
Δ BO + fBBRB + fBCRC + fBDRD = 0
Δ CO + fCBRB + fCCRC + fCDRD = 0
Δ DO + fDBRB + fDCRC + fDDRD = 0

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Compatibility conditions at B, C and D give the following equations:
Δ BO + fBBRB + fBCRC + fBDRD = Δ B
Δ CO + fCBRB + fCCRC + fCDRD = Δ C
Δ DO + fDBRB + fDCRC + fDDRD = Δ D
6. Truss Structures
(a) Remove the redundant member (say AB) and make the structure a primary determinate
structure
The condition for stability and indeterminacy is:
r + m > = < 2j
Since, m = 6, r = 3, j = 4, (r + m =) 3 + 6 > (2j =) 2 x 4 or 9 > 8 Δ i = 1
(b) Find deformation Δ ABO along AB:
Δ ABO =Δ (F0uABL)/AE
F0 = Force in member of the primary structure due to applied load
uAB= Forces in members due to unit force applied along AB
(c) Determine deformation along AB due to unit load applied along AB:
(d) Apply compatibility condition along AB:
ΔABO+fAB,ABFAB=0
Hence determine FAB
(e) Determine the individual member forces in a particular member CE by
FCE = FCE0 + uCE FAB
where FCE0 = force in CE due to applied loads on primary structure (=F0), and uCE = force in
CE due to unit force applied along AB (= uAB)
7. Temperature changes affect the internal forces in a structure
Similarly fabrication errors also affect the internal forces in a structure

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(i) Subject the primary structure to temperature changes and fabrication errors. - Find the
deformations in the redundant direction
Reintroduce the removed members back and make the deformation compatible
Analysis & Design Report for Store & Generator
Room
It is a frame structure single storey unit & includes areas for various purposes, such as
transformer generator space. Ultimate Strength Design (USD) or Load and Resistance Factors
Design (LRFD) method is used for structural design of all the components. The concrete used for
all structural members should have a minimum 28 days cylinder crushing strength of 3,000 Psi.
Introduction to the Project
It is a frame structure single storey unit & includes areas for various purposes, such as
transformer , generator space etc.
Design Specifications & Design Methods
ACI (American Concrete Institute) is the governing code for design of the structure.
Design Methods
Ultimate Strength Design (USD) or Load and Resistance Factors Design (LRFD) method is used
for structural design of all the components. USD method is based on load and resistance factors,
which make it economical and deterministic as compared to the Allowable Stress Design (ASD)
method. Sizes of the footings are designed using the allowable bearing capacity with an
appropriate factor of safety (FOS).
Loads on the Structures
The structures are subjected to some or all of the following load types:
1. Self weight of the structure
2. Dead Load of the floor finishing, walls etc.
3. Floor live loads
4. Earthquake loads
Design Criterion & Parameters
Parameters used in analysis and design are:

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Load Factors and Load Combination
The structures are investigated for the following load combinations with appropriate load factors
for different types of loads.
1. Service Load Combination U = 1.0 D + 1.0 L
2. Ultimate Load Combination U = 1.2 D + 1.6 L
3. Earthquake Load Combination U = 0.75 x (1.2 D + 1.6 L + 1.87 E) And U = 0.9 D ± 1.43 E
4. Earth pressure Load Combination U = 1.2 D + 1.6 L + 1.5 H And U = 0.9 D ± 1.7 H
Where,
D = Dead loads including self-weight of the structure, Weight of floor finishing, walls and
backfill soil.
L = Floor Live Loads
E = Earthquake loads
H = Horizontal earth pressures
Resistance Factors
1. Flexure and tension in reinforced concrete, = 0.90
2. Shear and torsion in normal density concrete,= 0.85
3. Axial compression with spirals, = 0.75
4. Axial compression with spirals, = 0.70
5. Bearing on concrete, = 0.70
Material Properties
The concrete used for all structural members should have a minimum 28 days cylinder crushing
strength of 3,000 Psi. The reinforcement steel used in the structural members should be deformed
bars having minimum yield strength of 40,000 Psi conforming to ASTM standards A615.
Structural Analysis Method/Software used
For structural analysis & designing, three-dimensional analysis software ETABS & SAFE were
used & cross checked using ACI design Guidelines. These softwares are based on the Finite
Element Method of Structural Analysis.
Elements used in Three Dimensional Structural Models:
1. Shell elements with the capabilities of resisting plate bending and membrane force (in
plane actions) are used for modeling of slabs and concrete wall panels
2. Thick Plate Shell Elements are used for modeling of the elements where through-
thickness shear deformations are important/possible, like pile caps and footings.
3. Frame elements are used for modeling girders/beams, columns, etc.

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Procedure Adopted for Calculation of Earthquake Loads
Equivalent static lateral force procedure of UBC is adopted for the project. Based on the Seismic
Zoning map of Pakistan, Peshawar & related areas fall in the minor seismic zone (zone 2b)
The lateral force procedure of UBC is given below:
Design Base Shear (1630.2.1)
Where,
R= Response modification factor
I= Occupancy importance factor
T= Fundamental period of the structure
W= Total service dead load plus applicable portion of live load
Cv= Earthquake coefficient depending on seismic zone
The total design base shear, need not to exceed:
V = 2.5 Ca x l x W / R
The total design base shear shall not be less than:
V = 0.11 Ca x l x w
T = Ca (hn)3/4
Alternatively T= 0.1 N (For moment resisting frames with no. of stories less than 12)
where, N= number of stories
Vertical Distribution of Forces:
V = F + Σ (F)
Ft = 0.07 T V
Ft = (V - Ft) wshs / Σ w x h

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Ft need not exceed 0.25 V and may be considered as zero where T is 0.7 Seconds or less. The
remaining portion of the base shear shall be distributed over the height of the structure, including
level, n, according to the above mentioned formulae:
The data for finding base shear is:
S.No Seismic Load Factors Values:
(Based on seismic zoning)
1. Z = 0.2
2. Cv = 0.4
3. Ca = 0.28
4. I = 1
5. Ct = 0.03
6. R = 5.5
Design Equations for Concrete Structure
Following design equations of the Ultimate Strength Design method are adopted for various
structural components:
Slabs and Foundation
Design equations for flexural design of the slabs are:
Mu = As fy (d-a/2)
a = As fy / 0.85 x fc' x b
Beams
Design equations for flexural design of beams and stiffeners are:
Mu = As fy (d-a/2)
a = Asfy /0.85 x fc' x b
In case of doubly reinforced beams, T-beams and L-Beams these equations are modified
accordingly.
Design equations for shear design of normal beams are:

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Design equations for shear design of deep beams are:
Columns
Two methods are generally used for design of the bi-axially loaded columns i.e. the Load
Contour Method and Reciprocal Load Method. Also the Concrete Design Module of SAP2000
automatically accounts for slenderness ratios of the connecting elements, lateral bracing (sway
conditions), and relative stiffness of the columns.
Design Summary
Loads Calculation for building
Live Load on slabs of Ground floor (not used for single storey building) 60 PSF
Live Load on roof 40 PSF
Design of SLAB
Type of slab = two way slab
Total depth of the slab = 5 in.
Preliminary effective depth of the slab = 4 in.
Maximum bending moment in short direction = 21 k-in
Maximum bending moment in long direction = 17 k-in
Steel reinforcement in short direction = # 4 @ 8" c/c (As = 0.29 in2
)
Steel reinforcement in long direction = # 4 @ 8" c/c
Minimum allowed required steel reinforcement area/unit width = 0.002 x b x d = 0.002 x 12 x 4
= 0.096 in2
.

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Max. Allowed Steel Reinforcement / unit width for the slab section =0.0206 x b x d= 0.0206 x
12 x 4 = .98 in2
This reinforcement steel is sufficient against the applied bending moments. This reinforcement
steel is not less than the minimum requirements nor greater than the maximum allowable.
Summary of Design for Beams:
Design of Beam 1
Total depth of the beam, = 17 in.
Preliminary effective depth of the beam = 14.5 in.
Web width of the beam = 12 in.
Minimum required steel reinforcement = 0.005 x b x d = 0.005 x 12 x 14.5 = 0.87 in2
.
Max. Allowed Steel Reinforcement for the Rectangular beam section =0.0206 x b x d= 0.0206 x
12 x 14.5 = 3.58 in2
.
Main Steel provided = 3 # 5 bars
Shear Reinforcement Steel = #3 bars @ 7 in c/c at ends & centre of the beam.
This reinforcement steel is sufficient against the applied bending moments. This reinforcement
steel is not less than the minimum requirements nor greater than the maximum allowable.
Design of Beam 2
Total depth of the beam, = 17 in.
Preliminary effective depth of the beam = 14.5 in.
Web width of the beam = 12 in.
Minimum required steel reinforcement = 0.005 x b x d = 0.005 x 12 x 14.5 = 0.87 in2
.
Max. Allowed Steel Reinforcement for the Rectangular beam section =0.0206 x b x d= 0.0206 x
12 x 14.5 = 3.58 in2
.
Main Steel provided = 3 # 5 bars
Shear Reinforcement Steel = #3 bars @ 7 in c/c at ends & centre of the beam.
This reinforcement steel is sufficient against the applied bending moments. This reinforcement
steel is not less than the minimum requirements nor greater than the maximum allowable.

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Design of Beam 3
Total depth of the beam, = 17 in.
Preliminary effective depth of the beam = 14.5 in.
Web width of the beam = 12 in.
Minimum required steel reinforcement = 0.005 x b x d = 0.005 x 12 x 14.5 = 0.87 in2
.
Max. Allowed Steel Reinforcement for the Rectangular beam section =0.0206 x b x d= 0.0206 x
12 x 14.5 = 3.58 in2
.
Main Steel provided = 5 # 5 bars
Shear Reinforcement Steel = #3 bars @ 7 in c/c at ends & centre of the beam.
This reinforcement steel is sufficient against the applied bending moments. This reinforcement
steel is not less than the minimum requirements nor greater than the maximum allowable.
Design of column C1 & F1
Size of column = 12" x 12"
Max. Reinforcement steel allowed= 0.08 x 144 = 11.52 in2
Min. reinforcement steel allowed= 0.01 x 144 = 1.44 in2
Steel provided = 8 # 5 bars
Stirrups provided = # 3 @ 6"c/c
Size of concrete footing = 4' x 4'
Concrete depth of footing = 12 in
To avoid any chances of differential settlement & non-structural cracks strip footing of 4' width
is provided.
Steel provided along short direction = # 4@ 9" c/c
Steel provided along long direction = # 3@ 9" c/c
Approximate Analysis of Indeterminate
Structures

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1. Conventional design process is normally based on the ‘local’ structural elements (column,
beam, floor slabs, wall, etc.)
2. But theoretical and experimental studies have shown that structural systems cannot be
considered to be a simple collection of individual elements
3. The responses of the structure is often more than the ‘sum’ of the responses of individual
elements since structural integrity ensures that the elements work together, producing
global responses through the complex interaction of its elements
4. Hence ‘local’ and ‘global’ approaches are necessary for proper design
5. Global analysis carried out on two levels:
a. A ‘numerically exact’ analysis using finite element method or another
mathematical procedure, in which each of the element of the system is described
by a mathematical equation and joined together at various points (or along edges)
by proper boundary or continuity conditions (MATHEMATICA) - This procedure
is quit complex and may have in-built data errors
b. The second procedure is a simplified or approximated procedure, which reduces
the complex structural system to a much simpler system that could be handled
easily by simple calculations; this will be the subject of our study in this set of
lectures
6. Approximate global structural analysis of a complex structure will contain:
a. Reduction of the complex system into an equivalent simple system to carry out
i. Stability analysis
ii. Frequency analysis
iii. Elementary structural analysis - this will form the basis of our study in these
lectures
7. A model - which is a determinate structure - must be developed for analysis
8. Results obtained from this approximated model compares favorably with the correct results
9. This study makes the transition from determinate to indeterminate structural analysis
10. Preliminary design of all structures is based on this approximate analysis
11. Structures considered include: Indeterminate Trusses, Portals and Trussed Frames, Multi-
story frames