PRINCIPLE OF
REINFORCED/PRESTRESSED
CONCRETE DESIGN
INTRODUCTION
1.1 CONCRETE, REINFORCED CONCRETE,
PRESTRESSED CONCRETE.
• Concrete is a mixture of cement, sand and
aggregate, which are bound chemically by
the addition of water.
• Concrete can be given any shape, with
any practical dimensions, without any
joints.
• Concrete has a very good compressive
strength, concrete -like stone- is a weak
material as far as tensile forces are
concerned. Since the flexural and shear
resistance of a material is directly related
to its tensile strength; concrete is not a
suitable material for the loading conditions
that generate flexure and shear.
• Weakness of concrete in tension can be
overcome by reinforcing it with steel bars
in the tensile regions.
• Steel bars placed in their positions before the
concrete is poured can have a very good bond
with concrete, both mechanically and chemically
after the hardening of concrete.
• This means that the reinforcing bars become an
integral part of the material. This new
combination of two materials is called “
Reinforced Concrete ”.
• Because of the bond the deformation of both
concrete and steel i.e. strains and in surrounding
concrete are the same. What’s more, the
coefficients
of
thermal
expansion
and
contraction of steel and concrete are luckily the
same.
• Concrete cracks even under the normal
loads. The cracks may be invisible, hence
the term “ hairline cracks”.
P1
A
P2
SECTION A-A
n.a
A
Reinforcement
FIG. 1.1
Fig.1.1 shows a reinforced concrete beam under the action of bending
moments.
• One important result of the cracking is that, the
tensile zone of the beam can no more contribute
to the resistance of the beam. This part of the
beam is there simply ignored during the design
process. Resisting forces in a beam section after
the cracking is shown in Fig.1.2.
c
z
FIG. 1.2
• On the other hand, if a beam is compressed
before any lateral exterior load is applied,
superposition of flexure stresses and initial
compressive stresses will yield either totally
compressive stress on the whole concrete
section or very small tensile stress at a small
area. These are shown in Fig. 1.3.
comp.
comp.
comp.
Mex
Nin
+
Bending
initial
compression stresses
FIG. 1.3
=
or
Tension
• The initial compression applied to the
beam should be fixed in a way that it
would last through the life span of the
beam.
• This process is called “pre-stressed
concrete” and during the pre-stressing
process, steel wires or strands are used.
1.2. HISTORY OF REINFORCED CONCRETE
• First known reinforced concrete product is not a
building but a boat, which was demonstrated in
1855 Paris World Exhibition. Later, reinforced
concrete was used for manufacturing flowerpots.
• In 1855 Fraucois Coiguet used reinforced
concrete for the first time in a building.
• In 1861 Coiguet wrote a book and explained the
use of the reinforced concrete.
• In 1861 Coiguet wrote a book and
explained the use of the reinforced
concrete.
• First theory of reinforced concrete was
published in 1886 by Koennen.
• Hennebique explained the monolithic
behavior of the reinforced concrete in
1892 and he exhibited his works in 1900
Paris World Exhibition.
1.3. LOADS
• In a building certain parts are essentially
structural members. They form the skeleton of
the building and are known as the “structural
system” of the building. The purpose of the
structural system is to make the building strong
and safe, that is all kinds loads acting on the
building must be carried and transferred to the
ground safely by this system. Other parts of the
building such as walls, floor fill, plaster etc. do
not take a load-carrying role in the system even
if they are fixed to the structural elements.
Structures must be designed so that they will not
fail or deform excessively under load. Engineers
must anticipate probable loads a structure must
carry. Structures be able to carry all the loads
that may act on throughout its economical life.
The design loads specified by the codes are
satisfactory in general. However, depending on
the nature of the structure, an engineer may
refer to experiments etc. and increase the
minimum loads specified by the code.
• Typical loads acting on structures are:
– Dead Loads
– Live Loads
– Construction Loads (settlement in supports,
lack of it of element temperature changes
etc).
– Wind Loads
– Earthquake Loads
– etc.
• Dead Loads
The load associated with the weight of the
structure and its permanent components (floors,
ceiling, ducts etc.) is called the dead load. Dead
loads can not be calculated exactly before the
design since the dimensions of the members are
not known at the beginning. Therefore, initially
magnitude of the dead load is estimated for
preliminary design and after sizing of the
members it is calculated more accurately.
• Distribution of Dead Load to Framed Floor
Systems
Floor systems consist of a reinforced
concrete slab supported on a rectangular
grid of beams and load of the slab is
carried by these beams. The distribution of
load to a floor beam depends on the
geometric configuration of the beams
forming the grid. The area of slab that is
supported by a particular beam is termed
the beam’s tributary area (see figure)
Concept of tributary area; a) square slab, all edge beams support a triangular
area; (b) two edge beam divide load equally; (c) load on a 1 ft of slab in (b).
(d) tributary areas for beams B1 and B2 shown shaded, all diagonal lines slope at 45o;
(e) top figure shows most likely load on beam B2 in figure (d); bottom figure shows
simplified load distribution on beam B2; (f) most likely load on beam B1; (g) simplified
load distribution to beam B1.
• Live Loads
Loads that can be moved on or off a structure
are classified as live loads. Live loads include
the weight of people, furniture, machinery, and
other equipment. Live loads specified by codes
for various types of buildings represent a
conservative estimate of the maximum load
likely to be produced by the intended use of the
building. In addition to long term live load, when
sizing members short term construction loads (if
these loads are large) should be considered.
Live loads are also vertical, but their magnitudes
and locations are not certain. They are mainly
occupancy loads i.e. the weights of human
beings and furniture etc. Every country has a
national standard, which specifies the minimum
magnitudes of the live loads to be used in
design. In ordinary buildings live loads act on
floors. A special kind of live load is the traffic
load on bridges, but they are always specified in
bridge design regulations issued by highway or
railway officials. Live loads specified by the
standards are well over the actual average
values.
• Wind Loads
The magnitude of wind pressure on a
structure depends on the wind velocity, the
shape and stiffness of the structure, the
roughness and profile of the surrounding
ground, and influence of adjacent
structures. As wind pressure may be
computed from wind velocities an
alternative is the equivalent horizontal
wind pressure specified by codes
a) variation of wind velocity with distance
above ground surface; (b) variation of wind
pressure specified by typical building codes
for windward side of building
a) uplift pressure on a sloping roof; (b)
Increased velocity creates negative pressure
(suction) on sides and leeward face
• Earthquake Forces
The ground motions created by major
earthquake forces cause buildings to sway
back and forth. Assuming the building is
fixed at its base, the displacement of floors
will vary from zero at the base to a
maximum at the roof. As the floors move
laterally, the lateral bracing system is
stressed as it acts to resist the lateral
displacement of the floors. The forces
associated are inertia forces and related
with the weight and stiffness of the
structure.
(a) Displacement of floors as building sways;
(b) inertia forces produced by motion of floors
• In reinforced concrete structures, the structural
system is monolithic. That is, slabs, beams,
columns and footings constitute a single threedimensional structure. This system deforms in
three-dimensional space. However, for the
purpose of analysis, structural systems can
suitably be parted to simplify the analysis. For
example, slabs of each floor are analyzed
separately. Frames, which are formed by the
beams and the columns in vertical plane, are
analyzed separately as plane systems.
Mechanical Properties of Concrete
a) Properties in Compression
Properties can be investigated best by
crashing cylindrical specimens under
axial compression and drawing the
stress-strain diagram.
300mm
150mm
b. Tension strength  in
general, neglected in design
since it is low
• A typical set of stress-strain curves of
concrete is:
0.001
0.002
(
)
co

0.003
• Such a curve has initial elastic part (proportional
limit: Fc = Ec ec)
• At certain strain curve becomes nonlinear
• Reach to the maximum strength (compressive
strength of concrete eco=0.002 (app.)
• After peak point stress-strain diagram has a
descending part which ends by crashing.
• Approximately, strain when concrete crash is
ecu=0.003
Classification of Concrete:
Concrete is classified according to
compression strength
Lightweight concrete
Sand lightweight concrete
High strength concrete
Normal weight concrete
Table 2.1 Concrete Classes and Strength Values
Concrete
class
Fck,
characteristic
cylindrical
compressive
strength
(N/mm2)
Equivalent
cubic
compressive
strength
(N/mm2)
Fctk,
characteristic
tensile
strength
(N/mm2)
Ec,
modulus of
elasticity
(28-D)
(N/mm2)
BS16 (C16)
16
20
1.4
27 000
BS18 (C18)
18
22
1.5
27 500
BS20 (C20)
20
25
1.6
28 000
BS25 (C25)
25
30
1.8
30 000
BS30 (C30)
0
37
1.9
32 000
BS35 (C35)
35
45
2.1
33 000
BS40 (C40)
40
50
2.2
34 000
BS45 (C45)
45
55
2.3
36 000
BS50 (C50)
50
60
2.5
37 000
C14, C16, C20 and C25 are normal strength concrete and others are
regarded as high strength concrete.
• Elasticity modulus of concrete at the
age of jth day can be calculated as:
When a member is subjected to bending crashing of
concrete is associated with the maximum strain reached
at the extreme fibers (not maximum stress). Maximum
stress will reach to adjoint fiber as strain increases.
Modification Factor Lightweight
Concrete
Strength Reduction Factor
(NSCP Table 421.2.1)
• END
Any question?