2. 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.
3. • 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.
4. • 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.
5. • Concrete cracks even under the normal
loads. The cracks may be invisible, hence
the term “ hairline cracks”.
Reinforcement
A
P1 P2
A
n.a
SECTION A-A
FIG. 1.1
Fig.1.1 shows a reinforced concrete beam under the action of bending
moments.
6. • 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
7. • 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.
+ = or
Mex
Nin
comp.
initial
compression
Bending
stresses
comp. comp.
Tension
FIG. 1.3
8. • 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.
9. 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.
10. • 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.
11. 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.
12. 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.
13. • 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.
14. • 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.
15. • 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)
16. 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).
17. (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.
18. • 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.
19. 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.
20. • In Turkey, TS 498 is used for the load
calculations. The title of this standard is
“The loads to be used for proportioning of
structural elements”. During the structural
analysis certain load combinations are
used. In most of them live load exist.
Important point here is the location of the
live loads.
• To explain this let us investigate the
continuous beam shown in the Fig 1.4a.
21. 1 2 3
M1 M2 M3
+
-
+
-
+
-
+
-
+
- -
+
(b) M1
influence line
(c) M2
influence line
(d) M3
influence line
(e) X1
influence line
(a) Continues beam
FIG.1.4
22. • 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
23. 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
24. • 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.
25. (a) Displacement of floors as building sways;
(b) inertia forces produced by motion of floors
26. • In reinforced concrete structures, the structural
system is monolithic. That is, slabs, beams,
columns and footings constitute a single three-
dimensional 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.
27. 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
28. • A typical set of stress-strain curves of
concrete is:
0.001 0.002
( )
0.003
co
29. • 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
30. Classification of Concrete:
Concrete is classified according to
compression strength
TS 500 (Code of practice for reinforced
cocrete structures) indicates compressive
strength as characteristic strength, fck
32. • Elasticity modulus of concrete at the
age of jth day can be calculated as:
)
/
(kg
140000
10270
)
/
(
14000
3250
2
2
cm
f
E
mm
N
f
E
ckj
cj
ckj
cj
33. (b) Properties in Tension:
Tension strength in general, neglected
in design since it is low
In many cases, tension strength has to be known (uncracked section
analysis etc).
Test to get tension strength of concrete:
• Direct tension test
• Indirect tension test
• Plain concrete test of beams modulus of rupture
• Cylinder splitting test
P=applied load
d= diameter of the cylinder
l= length of the cylinder
dl
P
fcts
2
34. • Tensile strength id related to compressive
strength. TS 500 gives empirical formulas for
the characteristic tensile strength:
)
(kg/cm
1
.
1
)
(N/mm
35
.
0
2
2
ck
ctk
ck
ctk
f
f
f
f
From test results:
fctk=(strength obtained from split tests)/1.5
fctk=(Modulus of rupture)/2
35. Mechanical Properties of Steel
• In TS 500 mainly three grades of steel are
specified:
S220 (BC I)
S420 (BC III)
S500 (BC IV)
Reinforcing bars can be grouped in two classes:
a) Hot rolled steel properties depends on
chemical composition. Larger strain capacity
b) Cold worked steel worked steel in normal
temperature. Larger strength but less strain
capacity (ductility decreases)
36. • For stress-strain diagram see Figure 2.3 of your
text book.
• Steel grades specified by TS 500 is given in
Table 2.4 of your text book
• In TS 500 yield strength id given as
characteristic tensile strength fyk
S220 (BC-I) fyk = 220 N/mm2
In case of energy type loading hot rolled steel
should be preferred (like earthquake).
Hot rolled ductility (so, the energy
absorbtion capacity)
37. • The surface of steel bars are:
– Smooth
– Deformed (generally used to increase the bond
strength between concrete and steel)
• In Europe bars are designated with their sizes
ϕ6, ϕ8, ϕ10, ϕ12, ϕ14, ϕ16, ϕ18, ϕ20, …. ,
ϕ40
Area of a single bar =
There are tables which gives directly area etc.
of the bars. For example see TABLE A-7 of
your text book
4
2
D
38. 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.
39. 1.4. SERVICEABILITY, STRENGTH AND
SAFETY OF THE STRUCTURE
• Any structure should not fail when subjected to
service loads. Service loads are the loads used
in design. They should also be reasonably safe.
Excessive deformations of structural members,
even if they are strong enough may create
problems under the service conditions. Besides,
cracks that form in the concrete should be
invisible, in some structures concrete should not
crack at all. For example, cracks are not
desirable in water tanks, reactor buildings etc.
All these requirements are known as the
serviceability of the structure.
40. There are a number of uncertainties in the analysis, design and
construction processes. For this reason neither strength nor
serviceability of a structure can be defined precisely. However
as it will be explained later, a margin of safety may be provided
for both strength and serviceability.
The main reasons of uncertainties are listed below:
– Actual loads may be different than the assumed ones.
– Distribution of loads may be different than that assumed.
– Calculated load effects (stresses etc.) may be different than the
actual effects because of the assumptions and simplifications
made in analysis.
– Actual behavior of the structure may not be as assumed.
– Errors may be made in the dimensions of the members during the
construction.
– Errors may be made during the placing of reinforcement.
– Actual material strength may be different than the specified
strength.
Margin of safety of a structure should be related to the
probable results of a failure.
41. 1.5. STATISTICAL APPROCH FOR SAFETY
MARGIN
• Maximum load of a structural element during the lifetime
of a structure is not certain. Variation of the load may be
considered random and may be approximated in the
form of a frequency curve, as shown in Fig. 1.5.
Pk
Pm
f(P)
P
FIG. 1.5
42. Shaded area represents the probability of
occurrence of loads larger than Pk. Pm is
mean value of loads. It common practice to
use a conservative value grater than Pm in
design. For example a characteristic value
Pk can be considered for this purpose. If
standard deviation is the following
equation can be written as
Pk = Pm + u. (1.1)
u is a factor depending on the shaded area
in Fig.1.5.
p
p
43. • TS 500, which is code of practice for the design
of reinforced concrete members, specifies the
characteristic load Pk as the load given by TS
498. Therefore, the designer has not to use
equation 1.1.
• Actual strength of material also differ from the
specified design strength. Therefore strength of
material is also considered as a random
variable. Variation of material strength may be
approximated by a frequency curve as shown in
Fig. 1.6.
44. • Rk is the characteristic strength value
whereas Rm is the mean value. Shaded
area represents the probability of
occurrence of strength values less than
Rk.
Rk Rm
f(R)
R
FIG. 1.6
45. Similar to equation 1.1 the following
equation can be given for Rk:
Rk = Rm – u. (1.2)
where is standard deviation for R.
depends on the degree of supervision
and inspection of production. u=1.28 in
Turkey. For the safety of structure Rk Pk
if Rk and Pk are selected as design values.
R
R
R
46. In Fig.1.7 this situation is shown where
double shaded area represents the
probability of failure.
Pm Pk Rk Rm
FIG. 1.7
47. • Statistical calculation shows that the
probability of failure is rather high if Rk and Pk
are used as design values. Hundred percent
safety is not possible but probability of failure
can be reduced by increasing the design
value of load and decreasing the strength
value. This can be achieved by using
appropriate factors. Dividing Rk by a factor
greater than 1 and multiplying Pk by a factor
greater than 1 design values are obtained.
Considering economic results of collapses it
is tried to achieve a probability of failure as
small as 10-5-10-7.
