Structural Design II.pdf

APCE 114A
Study Material
Prepared By:
Rupesh Kumar
Assistant Professor
KRMU

1. Overview of R.C.C. construction
2. Cement, coarse aggregate, Water and reinforcement materials.
3. Abram‘s water-cement ratio law
4. Stress-strain curves and characteristic strengths of structural steel.
5. Properties of Cement concrete & their impact on the structural strength,
6. Introduction to Nominal mix concrete and Design Mix Concrete.
7. Characteristic compressive strength of concrete and its determination,
8. Workability of concrete, Slump test, compacting factor test;
9. Compaction and Curing of concrete,
10. Durability of concrete, Gain of strength of concrete with time, Age factor

• Reinforced Concrete Construction (R.C.C.) is a
popular building technique used for
constructing buildings, bridges, and other
structures. It is a combination of concrete and
steel reinforcement, where concrete provides
the compressive strength, while steel
reinforcement provides the tensile strength to
the structure.

• Design: The first step in R.C.C. construction is the design process. The design of the structure
is done by a structural engineer, who considers the intended use of the building, the
expected loads it will bear, and other factors such as environmental conditions.
• Formwork: Formwork is a temporary structure that is used to hold the concrete in place until
it hardens. The formwork is made of wood or metal and is designed to give the desired shape
to the concrete structure.
• Reinforcement: Steel bars, also known as rebars, are placed inside the formwork to provide
tensile strength to the structure. The rebars are placed in a particular pattern, as per the
design specifications.
• Pouring concrete: Once the reinforcement is in place, concrete is poured into the formwork.
The concrete is a mixture of cement, sand, and aggregates, and water. The mixture is poured
in layers and compacted using vibrators to remove any air voids.
• Curing: After the concrete is poured, it is left to cure for a period of time. This allows the
concrete to gain strength and harden.
• Removal of formwork: Once the concrete has cured, the formwork is removed, and the
surface of the concrete is finished as per the design requirements.
• Quality checks: The structure is checked for quality to ensure that it meets the design
specifications and is safe for use.
R.C.C. construction is a popular building technique due to its strength, durability, and flexibility. It
allows for the creation of complex designs and structures, and it is resistant to fire, weather, and
other environmental factors.

Cement, coarse aggregate, water, and reinforcement materials are all essential components of
Reinforced Concrete Construction (R.C.C.):
• Cement: Cement is a fine powder that is used to bind the concrete mixture together. It is the
primary binding agent that hardens when it reacts with water, forming a strong and durable
material.
• Coarse aggregate: Coarse aggregates are larger particles of crushed stone, gravel, or recycled
materials that are added to the concrete mixture. They provide the strength and durability to
the structure by adding mass and volume to the concrete mix.
• Water: Water is an essential component of the concrete mix, as it activates the chemical
reaction between cement and aggregates, known as hydration. It is important to maintain
the correct water to cement ratio to ensure the strength and durability of the concrete.
• Reinforcement materials: Reinforcement materials, usually in the form of steel bars, are
added to the concrete mixture to provide tensile strength to the structure. These
reinforcement bars are placed in a particular pattern as per the design specifications and are
held in place by the concrete.
Together, these components form a strong and durable material that is capable of withstanding a
variety of environmental conditions and loads. The ratio of these components and the design of
the structure must be carefully considered by a structural engineer to ensure the safety and
stability of the building or structure.

Abram's water-cement ratio law is a fundamental principle in the field of
concrete technology that relates the water-cement ratio of a concrete mix to
its strength. It was first proposed by Duff Abrams, an American civil engineer,
in 1918 and has since been widely used in the industry.
The law states that, for a given set of materials and test conditions, the
strength of the concrete is inversely proportional to the water-cement ratio.
In other words, the higher the water-cement ratio, the lower the strength of
the concrete, and vice versa.

• Stress-strain curves are graphical representations of the
behavior of a material under load. In the case of
structural steel, the stress-strain curve shows the
relationship between the stress applied to the steel and
the resulting strain. The characteristic strengths of
structural steel are also important factors in
determining its behavior under load.

Stress-Strain curve of Mild steel and HYSD steel

• The characteristic strengths of structural steel vary depending on the type of steel, its
composition, and other factors such as heat treatment.
• The term characteristic strength means that value
below which not more than 5% of the test results
are expected to fall. As per IS 456:2000, the
characteristic strength of steel is equal to the
minimum yield stress or 0.2 percent proof stress.
The characteristic strengths of structural steel include the yield strength, ultimate strength, and
fracture strength. The yield strength is the stress at which the steel begins to deform
plastically, while the ultimate strength is the stress at which the steel reaches its maximum
strength before fracturing. The fracture strength is the stress at which the steel fractures.

• Mild Steel Reinforcement
Mild steel bars are also known as Fe250 because the
yield strength of this steel is 250N/mm2.
• High Yield Strength Deformed Bars (HYSD)
These are also known as HYSD bars. They have higher
percentage of carbon as compared to mild steel Their
strength is higher than of mild steel, but the yield
point is not clearly defined. E.g., Fe415, Fe500,Fe550.

TMT (Thermo mechanically Treated) Steel Bars
• Among the constituents of R.C.C., steel is the costliest, so focus has been
more on steel to make it better and better. TMT steel is new generation,
high strength steel having superior properties as compared to common
HYSD bars.
• TMT bars are manufactured by passing hot rolled steel bars through cold
water. By doing this, the outer surface of the bar becomes harder while the
inner core is still softer.
In India, Sail (Steel Authority of India Ltd.) and RINL (Rashtriya Ispat Nigam Ltd.)
are producing TMT bars. The TMT bars have following advantages:
• High yield strength
• Better weldability
• Excellent ductility
• Superior corrosion resistance.

Cement concrete is a composite material made of cement, aggregates (such as sand, gravel, or crushed stone), and
water. Here are some of the key properties of cement concrete and their impact on the structural strength:
• Compressive Strength: Compressive strength is the most important property of concrete as it measures the
maximum load that the concrete can bear without failure. The compressive strength of concrete depends on
the proportion of cement, aggregates, and water used in the mix. Higher compressive strength results in
stronger and more durable structures.
• Tensile Strength: Tensile strength is the ability of concrete to resist pulling apart or cracking. Concrete has low
tensile strength, and this property can be improved by using reinforcing materials such as steel bars (rebars) or
fibers. The presence of reinforcing materials can significantly increase the tensile strength of concrete and
improve its overall structural strength.
• Durability: Durability is the ability of concrete to resist environmental factors such as weathering, chemical
attack, and abrasion. The durability of concrete depends on the type of cement used, the quality of aggregates,
and the curing process. Durable concrete results in longer-lasting and more resilient structures.
• Workability: Workability is the ease with which concrete can be mixed, transported, placed, and compacted.
The workability of concrete depends on the water-cement ratio, the size and shape of the aggregates, and the
use of admixtures. Good workability results in better quality concrete with fewer defects and voids.
• Shrinkage: Shrinkage is the reduction in volume of concrete due to the loss of moisture. The shrinkage of
concrete can cause cracking and reduce the overall strength and durability of the structure. The use of additives
and proper curing can help to reduce shrinkage and improve the overall strength of the structure.
• Thermal Expansion: Thermal expansion is the increase in volume of concrete due to changes in temperature.
Concrete has a relatively low coefficient of thermal expansion, which means that it is less prone to cracking due
to temperature changes. However, large temperature variations can still cause significant stresses in concrete
structures.

In summary, the properties of cement concrete, such
as compressive strength, tensile strength, durability,
workability, shrinkage, and thermal expansion, have a
significant impact on the structural strength of
concrete structures. Proper mix design, use of
reinforcing materials, and appropriate curing can help
to improve these properties and ensure the long-term
durability and safety of the structures.

Nominal mix concrete and design mix concrete are two different
methods for preparing concrete mixes, with different levels of
control over the mix proportions and properties.
• Nominal Mix Concrete: Nominal mix concrete is a traditional
method for preparing concrete mixes by using nominal
proportions of ingredients without calculating their individual
quantities. The proportions are usually expressed as a ratio of
the volume of cement to the volume of aggregates. For
example, a common nominal mix for a reinforced concrete
structure may be 1:2:4 (one part cement, two parts sand, and
four parts coarse aggregates) by volume. Nominal mixes are
generally used for small-scale construction works with basic
quality requirements. For concrete grades from M5-M20 is
covered under nominal mix concrete.

• Design Mix Concrete: Design mix concrete, on the
other hand, is a more precise method for preparing
concrete mixes, where the mix proportions are
calculated based on the desired strength and
properties of the concrete. In design mix, the
proportions of cement, aggregates, water, and other
additives are calculated based on laboratory tests and
statistical analysis of the properties of the materials to
ensure the required strength and workability of the
concrete. Design mixes are usually used for large-scale
construction works and for projects with specific
quality requirements. For concrete grades above M20
is covered under Design mix concrete.

• The characteristic compressive strength of concrete
is the strength value below which, not more than
5% of the test results are expected to fall. It is an
important property of concrete that is used to
assess its overall strength and durability. The
characteristic strength is often used in design
calculations to ensure that the concrete is strong
enough to support the intended load.

• The determination of the characteristic compressive
strength of concrete is typically done by conducting
compressive strength tests on concrete cubes
(15x15x15cm) or cylinders (15x30cm). The cubes or
cylinders are made in accordance with standard
procedures and are cured under controlled
conditions. After the curing period, the cubes or
cylinders are subjected to a compressive load using
a compression testing machine.

• The compressive strength test involves applying a
compressive load to the specimen until it fails. The
load is applied gradually, and the deformation of
the specimen is measured. The maximum load that
the specimen can withstand before failure is
recorded as the compressive strength of the
concrete. Several specimens are tested, and the
average strength value is calculated. The
characteristic strength is then determined by
applying statistical analysis to the test results.

• Workability of concrete refers to its ability to be easily mixed,
placed, and compacted without segregation or bleeding. It is
an important property of concrete as it affects its ease of use,
strength, and durability. Two common methods used to
assess the workability of concrete are the slump test and the
compacting factor test.
1. Slump Test: The slump test is a simple and widely used
method for measuring the workability of concrete. It involves
filling a standard slump cone with freshly mixed concrete and
then lifting the cone slowly to allow the concrete to spread out.
The difference between the original height of the cone and the
height of the concrete after the cone has been removed is
measured and recorded. The measurement of the slump is an
indication of the consistency and workability of the concrete.

2. Compacting Factor Test: The compacting factor test
is another method used to measure the workability of
concrete. It involves compacting a standard amount
of concrete in a standard manner in a metal cone and
measuring the volume of the concrete after
compaction. The ratio of the volume of the
compacted concrete to the original volume is known
as the compacting factor. The compacting factor is an
indication of the workability of the concrete, with
higher values indicating better workability.

Both the slump test and compacting factor test are
commonly used to determine the workability of
concrete in the field and in the laboratory. The test
results are used to adjust the mix proportions of the
concrete to achieve the desired workability and
strength.

Compaction and curing are both critical steps in the
production of strong and durable concrete structures.
Adequate compaction helps to remove air voids, while proper
curing helps to ensure that the concrete reaches its maximum
strength and durability potential.
• Compaction: The process of compacting concrete involves
removing any voids or air pockets in the concrete mixture
by using mechanical vibration, tamping or rolling. This
process ensures that the concrete is dense and has a
minimum amount of voids. Compaction can be done using
hand tools, vibrators, or other mechanical devices.
Adequate compaction helps to improve the strength and
durability of the concrete by reducing the number of voids
and improving its overall homogeneity.

• Curing: The process of curing concrete involves
maintaining the concrete in a moist and
temperature-controlled environment to ensure
that it hydrates and hardens properly. This
process is important to ensure that the concrete
reaches its maximum strength and durability
potential. The curing period can last for several
days or even weeks depending on the type of
cement and the environmental conditions. Proper
curing helps to prevent shrinkage, cracking and
improves the durability and strength of the
concrete.

• Durability of concrete refers to its ability to withstand environmental exposure, aging,
and other forms of degradation without significant loss of performance. Concrete
durability is affected by several factors, including the quality of materials used, the
curing process, the degree of compaction, and the environmental exposure of the
structure. Properly designed and constructed concrete structures can have a service life
of up to 100 years or more.
• Gain of strength of concrete with time: The strength of concrete typically increases
with time, as the cement continues to hydrate and harden. This process is called gain of
strength, and it occurs over a period of several weeks to several months depending on
the type of cement and the environmental conditions. The rate of strength gain varies
depending on factors such as the cement content, water-cement ratio, curing
conditions, and age of the concrete.
• The age factor is an important consideration when determining the strength and
durability of concrete. The strength of concrete increases with age, and its durability is
influenced by the age of the concrete at the time of exposure to environmental factors.
The age of concrete can affect its resistance to chemical attack, freeze-thaw cycles, and
other forms of degradation. The age factor is also important when assessing the long-
term durability of concrete structures, as older structures may be more vulnerable to
environmental exposure and degradation.

1. Theory of R.C.C.
2. Advantages of RCC
3. Assumptions in the theory of RCC – Hooke‘s law
4. Distribution of stress in Steel & concrete – Modulus of Elasticity
5. Equivalent area of composite section
6. Theory of bending of RCC beams – Elastic theory & Ultimate load theory
7. Limit state method
8. Stress Strain diagram & Neutral axis & its position
9. Lever arm
10. Classification of RCC section
11. Balanced or economical
12. Over & under reinforced sections
13. Moment of resistance

Reinforced concrete (RCC) has several advantages over other construction materials, including:
• Strength and durability: RCC is a strong and durable material that can withstand heavy loads
and resist weathering, erosion, and other forms of deterioration. It has a long service life
and requires minimal maintenance.
• Versatility: RCC can be used to construct a wide range of structures, including buildings,
bridges, dams, and other infrastructure. It can be moulded into various shapes and sizes to
meet the design requirements.
• Fire resistance: RCC has excellent fire resistance properties due to the slow rate at which it
conducts heat. This makes it a suitable material for building fire-resistant structures.
• Cost-effectiveness: RCC is a cost-effective material due to the abundance of its constituent
materials (cement, sand, and aggregates). It also has a low maintenance cost, making it a
cost-effective choice for long-term construction projects.
• Sustainability: RCC is a sustainable material that can be recycled and reused. It also has a
low carbon footprint compared to other construction materials.
• Resistance to earthquakes: RCC structures have high resistance to earthquakes and seismic
activity due to their ability to absorb and dissipate energy.
In summary, RCC is a versatile, strong, and durable material that is cost-effective, fire-resistant,
and sustainable. It is an excellent choice for a wide range of construction projects, including
large-scale infrastructure projects.

The theory of RCC is based on several assumptions,
including the use of Hooke's law. Hooke's law states
that the strain in a material is proportional to the
stress applied to it, as long as the material remains
within its elastic range. In the context of RCC, this
means that the steel reinforcement and concrete
behave elastically when subjected to loads that do
not exceed their respective yield strengths.

The theory of reinforced concrete (RCC) is based on several assumptions, including:
• Homogeneous material: RCC is assumed to be a homogeneous material with uniform properties
throughout its volume. In reality, concrete is a composite material that contains aggregates of varying
sizes and compositions, which can affect its properties.
• Elastic behavior: RCC is assumed to behave elastically under normal service loads, meaning that it can
be deformed and return to its original shape without undergoing any permanent deformation. This
assumption is generally valid as long as the loads do not exceed the elastic limit of the material.
• Linear behavior: RCC is assumed to exhibit linear behavior under loading, meaning that the relationship
between stress and strain is linear. This assumption is valid within the elastic range of the material.
• Plane sections remain plane: It is assumed that plane sections of the RCC member remain plane after
bending. This assumption is valid as long as the material is not subjected to excessive loading or large
deflections.
• Neglect of cracking: In the analysis of RCC, it is often assumed that the concrete is uncracked. However,
in reality, cracking can occur due to various factors such as shrinkage, temperature changes, and
overloading.
• Perfect bond: It is assumed that there is perfect bond between the steel reinforcement and the
surrounding concrete. However, in reality, there can be slip between the steel and concrete, which can
affect the behavior of the RCC member.

Despite these simplifications and assumptions, the theory of RCC has
proven to be an effective tool for designing and analysing reinforced
concrete structures. Engineers use appropriate safety factors to ensure
that the assumptions made in the theory do not compromise the safety
and integrity of the structure.

• In an RCC member subjected to bending, the stress distribution is generally
assumed to be linear across the cross-section, with the maximum tensile stress
occurring at the bottom of the beam, and the maximum compressive stress
occurring at the top of the beam. This is known as the "neutral axis," which is a line
that runs through the cross-section where there is zero stress. The distribution of
stress is governed by the flexural equation, which relates the stress to the moment
of the applied load.
• In the steel reinforcement, the stress distribution is assumed to be uniform along
the length of the bar. However, the actual distribution of stress can be affected by
the bond between the steel and concrete. The bond between the steel
reinforcement and the surrounding concrete is essential to ensure that the forces
are transferred between the two materials. The bond strength depends on several
factors, including the surface area of the bar, the surface texture of the bar, and the
quality of the surrounding concrete.

Stress-Strain Curve for Concrete

Stress-Strain Curve for RCC beam

• The equivalent area of a composite section is a concept
used in the design and analysis of reinforced concrete
(RCC) members that are reinforced with steel bars. It is
used to simplify the calculation of the stresses and
strains in the section and to determine the ultimate
capacity of the section.
• The equivalent area is the area of an imaginary cross-
section that has the same bending moment capacity as
the actual composite section. The equivalent area
takes into account the contribution of both the steel
reinforcement and the surrounding concrete. The steel
reinforcement is assumed to carry all the tensile stress,
while the concrete carries the compressive stress.

• To determine the equivalent area, the steel reinforcement
area is added to the area of the concrete section that is
above the neutral axis. The concrete below the neutral axis
is ignored, as it is assumed to be in compression and does
not contribute to the bending moment capacity of the
section. The equivalent area is then used to calculate the
stresses and strains in the section using the flexural
equation.
• The concept of the equivalent area is particularly useful in
the design of composite sections with complex geometries
or irregular shapes. By using the equivalent area, the
section can be simplified into a rectangular or circular
shape, which makes the analysis and design process much
easier.

The bending of reinforced concrete (RCC) beams can be analyzed using two
different theories: elastic theory and ultimate load theory.
• Elastic Theory:
The elastic theory assumes that the materials in the beam behave elastically,
which means that they deform proportionally to the stress applied. According
to this theory, the stress-strain relationship of both the steel reinforcement
and the concrete are linear. This theory is valid as long as the stresses in the
beam do not exceed the elastic limit of the materials.
The flexural equation, which is the basic equation used to analyze RCC beams,
is derived from the elastic theory. The equation relates the bending moment,
the section modulus, and the maximum tensile and compressive stresses in
the beam. The maximum tensile and compressive stresses occur at the
extreme fibers of the beam, and their values depend on the distance of the
fiber from the neutral axis.

• Ultimate Load Theory:
The ultimate load theory assumes that the beam fails when the
stresses in the beam reach their ultimate values. According to this
theory, the concrete in the compression zone of the beam fails by
crushing, while the steel reinforcement in the tension zone fails by
yielding. The ultimate load theory is used to predict the ultimate
strength of the beam, which is the maximum load that the beam can
support before it fails.
The ultimate load theory takes into account the non-linear behavior of
both the concrete and steel reinforcement. The concrete in the
compression zone is assumed to have a parabolic stress-strain curve,
while the steel reinforcement in the tension zone is assumed to have a
non-linear stress-strain curve that includes yielding.

• In practice, the elastic theory is used for the
design of RCC beams, while the ultimate load
theory is used to verify that the beam can
support the design loads without failing.
Design codes specify safety factors that must
be applied to the maximum stresses
calculated using the elastic theory to ensure
that the beam can withstand the loads during
its entire life span.

• The limit state method is a modern approach to
the design of reinforced concrete (RCC) structures
that has replaced the older working stress
method. The method is based on the concept of
limiting states, which are conditions that a
structure should not exceed in order to ensure
safety and serviceability.
• The limit state method is based on two types of
limit states: ultimate limit state (ULS) and
serviceability limit state (SLS).

• Limit State of collapse :
The Limit State of collapse is the condition at which the
structure can no longer support the load safely and
collapses. The limit state design approach involves
calculating the maximum load that a structure can
withstand without collapsing. The ultimate load that can
be supported by the structure is calculated based on the
strength of the materials used in the structure, such as
the strength of the concrete and steel reinforcement. The
design is carried out using partial safety factors, which
provide a level of safety against uncertainties in the
material properties and design loads.

• Serviceability Limit State (SLS):
The SLS is the condition at which the structure no longer
provides the desired level of serviceability, such as
excessive deflection, cracking, or vibration. The limit state
design approach involves ensuring that the structure does
not exceed the allowable serviceability limits. The design
is carried out based on the deflection and cracking limits
specified in the design codes. The deflection and cracking
limits are usually based on the comfort and safety of the
occupants of the structure.

• In summary, the limit state method is a modern
approach to the design of RCC structures that
considers both the Limit State of collapse and the
serviceability limit state. The method involves
calculating the maximum load that a structure
can withstand without collapsing and ensuring
that the structure does not exceed the allowable
serviceability limits. The design is carried out
using partial safety factors that provide a level of
safety against uncertainties in the material
properties and design loads.

• In reinforced concrete (RCC) design, the lever arm is a measure of the
distance between the centroid of the compressive force and the centroid of
the tensile force in a cross-sectional area of a structural element, such as a
beam or column.
• The lever arm is used to determine the moment of resistance of the
section, which is the maximum bending moment that the section can resist
before it reaches its ultimate limit state. The moment of resistance is
calculated as the product of the lever arm and the compressive force in the
section. The lever arm is typically measured in the direction of the applied
moment and is denoted by the symbol "z".
• The lever arm is an important parameter in RCC design because it affects
the strength and stability of the section. A longer lever arm indicates a
greater moment of resistance and a more stable section. The lever arm is
affected by the shape and size of the cross-sectional area, the position of
the reinforcement, and the distribution of the compressive and tensile
forces in the section.

Under-reinforced, over-reinforced, and balanced sections are different types of reinforced
concrete (RCC) sections that can be classified based on the relative amounts of reinforcement
and concrete in the section.
• Under-reinforced section: An under-reinforced section is a section in which the amount of
steel reinforcement provided is not sufficient to resist the ultimate tensile stress developed
in the concrete. In such a section, the concrete will crack and fail in tension before the steel
reinforcement reaches its yield stress. Under-reinforced sections are commonly used for
flexural members such as beams and slabs where ductility is required.
• Over-reinforced section: An over-reinforced section is a section in which the amount of steel
reinforcement provided is greater than the amount required to resist the ultimate tensile
stress developed in the concrete. In such a section, the steel reinforcement will reach its
yield stress before the concrete fails in tension. Over-reinforced sections are generally not
preferred because of their brittle behavior, especially in seismic regions.
• Balanced section: A balanced section is a section in which the amount of steel
reinforcement provided is just enough to resist the ultimate tensile stress developed in the
concrete. In such a section, both the concrete and the steel reinforcement reach their
ultimate strengths at the same time, resulting in a ductile behavior. Balanced sections are
preferred for most design situations as they provide good strength and ductility
characteristics.

• The moment of resistance of a reinforced concrete section is the bending moment that the
section can resist without reaching its limiting condition of tensile failure in the concrete or
yielding of the reinforcement. It is a measure of the strength of the section to resist bending
and is an important design parameter in RCC design.
• The moment of resistance of a section is dependent on the properties of the material used,
such as the compressive strength of concrete and yield strength of steel, as well as the
geometry of the section, such as the depth and width of the beam, the amount and location
of reinforcement, and the effective depth of the section.
• The moment of resistance of a section can be calculated using the following formula:
M.R. = 0.87 fy Ast (d - 0.42x)
where M.R. is the moment of resistance, fy is the yield strength of steel, Ast is the area of
reinforcement, d is the effective depth of the section, and x is the depth of the neutral axis.
• The neutral axis is the line that separates the compression zone from the tension zone of the
section. The depth of the neutral axis is dependent on the moment and the properties of the
section, and is calculated by equating the moments of the compressive and tensile forces
acting on the section.

1. Shear stresses in Beams
2. Design for shear
3. Bond stress & development length
4. Design of Singly Reinforced Beams

Structural Design II.pdf

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Structural Design II.pdf