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Concrete
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REINFORCED CONCRETE 10423522
Dr. Murat Serdar Kırçıl
İNM 1-024
www.yildiz.edu.tr/~kircil
Betonarme 1 Ders Notları
Yrd.Doç.Dr.Murat Serdar Kırçıl
Fundamental principles and methods for design of reinforced concrete structures
Elastic design (working stress design / Allowable stress design)
The fundamentals of this method has been established in the beginning of
20th century. Both steel and concrete are assumed to be linear elastic and Hooke Law is valid.
This assumption may be valid for service loads (işletme yükleri)
However; it’s not valid anymore in case of failure. For instance, under
the effect of a strong ground motion, the assumption of material
linearity is not valid.
σ
ε
σ = EεE
Analysis and design of a cross-section
Betonarme 1 Ders Notları
Yrd.Doç.Dr.Murat Serdar Kırçıl
Both steel and concrete are assumed to be linear elastic and Hooke Law is valid.
Main assumptions of this method
Concrete can not take any tension (REALISTIC)
Stresses in steel and concrete is considerably changed with time due
to time dependent deformations. That’s why, stresses can not be
calculated with reasonable accuracy.
The little tensile strength of concrete is neglected. However, in the
design of some structures like water tanks, tensile stress is limited for
leak proofing.
Fundamental principles and methods for design of reinforced concrete structures
Elastic design (working stress design / Allowable stress design)
Strength of materials are decreased by safety factors to obtain allowable stresses. The structural element is assumed to be safe if
the maximum stress of section is lower than the allowable stress (NOT
REALISTIC)
Betonarme 1 Ders Notları
Yrd.Doç.Dr.Murat Serdar Kırçıl
Bernouilli-Navier hypothesis is valid (REALISTIC)
Plane sections remain plane after bending.
Main assumptions of this method
Fundamental principles and methods for design of reinforced concrete structures
Elastic design (working stress design / Allowable stress design)
Betonarme 1 Ders Notları
Yrd.Doç.Dr.Murat Serdar Kırçıl
This assumption is valid for service loads. In case of failure it doesn't
represent the real behavior of the RC sections.
fc
εεεεcoεεεεcu
Stress (σ)
Deformation(ε)Valid for this region
Both steel and concrete are assumed to be linear elastic and Hooke Law is valid (NOT REALISTIC)
Main assumptions of this method
Fundamental principles and methods for design of reinforced concrete structures
Elastic design (working stress design / Allowable stress design)
Betonarme 1 Ders Notları
Yrd.Doç.Dr.Murat Serdar Kırçıl
It’s not a realistic assumption since concrete has not a constant elastic
modulus.
There is a modular ratio between concrete and steel reinforcement (NOT REALISTIC!)
Main assumptions of this method
Fundamental principles and methods for design of reinforced concrete structures
Elastic design (working stress design / Allowable stress design)
Betonarme 1 Ders Notları
Yrd.Doç.Dr.Murat Serdar Kırçıl
Limit state design (Limit durumlara göre hesap)
Limit state defines a particular state of a structure which may be
collapse or loss of function, either partial or total. Structures must
be designed so that the probability of reaching a limit state is lower
than prescribed level.
ULTIMATE LIMIT STATE (Son limit durum)
The collapse of a part of a structure or the whole structure.
SERVICEABILITY LIMIT STATE (Kullanılabilirlik limit durumu)
The loss of a function of a structure because of excessive deformation,
wide cracks or vibration under the effect of service loads (dead+live).
For instance, a slab which doesn’t collapse but vibrates.
Fundamental principles and methods for design of reinforced concrete structures
In limit state design, the probability of reaching a limit state is restricted
with a prescribed level (%5-%10) for the design of structures.
The first stage of design making design of a cross-section for the
ultimate limit state and the following step is checking the serviceability
requirements (deformations and cracks).
Betonarme 1 Ders Notları
Yrd.Doç.Dr.Murat Serdar Kırçıl
Cross-sectional design based on the limit state design assumptions is
called Ultimate Strength Theory or Ultimate Strength Design.
Concrete does not take any tension, all tensile stresses are taken by reinforcement.
Bernouilli-Navier hypothesis is valid.
Concrete σ-ε curve is the curve obtained from uniaxialcompression. Reinforcement steel is elastoplastic.
fc
εεεεcoεεεεcu
Gerilme (σ)
Şekil değiştirme (ε)
fy
εεεεsy εεεεsu
Gerilme (σ)
Şekil değiştirme (ε)
Loads are increased by load factors and material strength isdecreased by material factors. Load and material factors arecalled partial safety factors.
Limit state design (Limit durumlara göre hesap)
Fundamental principles and methods for design of reinforced concrete structures
Main assumptions of this method
Betonarme 1 Ders Notları
Yrd.Doç.Dr.Murat Serdar Kırçıl
Probability of reaching or exceeding a limit state of structural
system elements is restricted in limit state design.
What is the
probability of
reaching a limit
state?
Probability of reaching a limit state is 10-6
The safety of structure can be expressed as given below (R and F are
strength and load, respectively)
FR≥ structure is assumed to be safeIf
610)FR(P
−=<Probability of reaching a limit state is
Limit state design (Limit durumlara göre hesap)
Fundamental principles and methods for design of reinforced concrete structures
Betonarme 1 Ders Notları
Yrd.Doç.Dr.Murat Serdar Kırçıl
Why do we need a probabilistic
approach?
Load and strength are probabilistic variables.
Probability of reaching or exceeding a limit state of structural
system elements is restricted in limit state design.
Limit state design (Limit durumlara göre hesap)
Fundamental principles and methods for design of reinforced concrete structures
Betonarme 1 Ders Notları
Yrd.Doç.Dr.Murat Serdar Kırçıl
We need to know probability distribution of load and strength aswe can determine the safety of structures by using a probabilisticapproach. The probability distribution of them is usuallyassumed as normal (gauss distribution).
Load and strength are probabilistic variables.
Why do we need a probabilistic
approach?
Limit state design (Limit durumlara göre hesap)
Fundamental principles and methods for design of reinforced concrete structures
Betonarme 1 Ders Notları
Yrd.Doç.Dr.Murat Serdar Kırçıl
0 100 200 300 400 500 600 700 800 900 1000 1100 1200 1300
Değişken
0
1
2
3
4
5
6
7
Gözle
m s
ayıs
ı
( )
−−
=
2mx
2
1
x e2
1xf
σ
πσ
m mean value, σ standard deviation
We need to know probability distribution of load and strength aswe can determine the safety of structures by using a probabilisticapproach. The probability distribution of them is usuallyassumed as normal (gauss distribution).
Limit state design (Limit durumlara göre hesap)
Fundamental principles and methods for design of reinforced concrete structures
Betonarme 1 Ders Notları
Yrd.Doç.Dr.Murat Serdar Kırçıl
( )
−−
=
2mx
2
1
x e2
1xf
σ
πσ
smx
=−
σ
( )
−
=
2s
2
1
x e2
1xf
π Toplam alan=1
0 100 200 300 400 500 600 700 800 900 1000 1100 1200 13000
1
2
3
4
5
6
7
0
Standard normal
distribution m=0, σ =1
s
0 100 200 300 400 500 600 700 800 900 1000 1100 1200 13000
1
2
3
4
5
6
7
mx
Limit state design (Limit durumlara göre hesap)
Fundamental principles and methods for design of reinforced concrete structures
Betonarme 1 Ders Notları
Yrd.Doç.Dr.Murat Serdar Kırçıl
smx
=−
σ( )
−
=
2s
2
1
x e2
1xf
π
0 100 200 300 400 500 600 700 800 900 1000 1100 1200 13000
1
2
3
4
5
6
7
0
AsmA
=−
σBs
mB=
−
σ
sA sB
( )BxAp <<
CsmC
=−
σ
sC
( )xCp <
Standard normal
distribution m=0, σ =1
Probability of having a value
between A and B for x?
Probability of having a value
higher than C for x?
Limit state design (Limit durumlara göre hesap)
Fundamental principles and methods for design of reinforced concrete structures
Betonarme 1 Ders Notları
Yrd.Doç.Dr.Murat Serdar Kırçıl
smx
=−
σ( )
−
=
2s2
1
x e2
1xf
π
smx σ+=
0 100 200 300 400 500 600 700 800 900 1000 1100 1200 13000
1
2
3
4
5
6
7
0-2 -1-3-4 4321s-2σ -1σ-3σ 4σ3σ2σ1σ-4σ
sσ
Limit state design (Limit durumlara göre hesap)
Fundamental principles and methods for design of reinforced concrete structures
Betonarme 1 Ders Notları
Yrd.Doç.Dr.Murat Serdar Kırçıl
smx
=−
σ
smx σ+=
0 100 200 300 400 500 600 700 800 900 1000 1100 1200 13000
1
2
3
4
5
6
7
0-2 -1-3-4 4321s-2σ -1σ-3σ 4σ3σ2σ1σ-4σ
sσ
0 100 200 300 400 500 600 700 800 900 1000 1100 1200 13000
1
2
3
4
5
6
7
FmFk
sFF mk σ+=
Characteristic Load: The load
value with the %10 probability of
being exceeded.
σ+= 28.1FF mk
0.1
( ) 1.0xFp k =<
Limit state design (Limit durumlara göre hesap)
Fundamental principles and methods for design of reinforced concrete structures
Betonarme 1 Ders Notları
Yrd.Doç.Dr.Murat Serdar Kırçıl
smx
=−
σ
smx σ+=
0 100 200 300 400 500 600 700 800 900 1000 1100 1200 13000
1
2
3
4
5
6
7
0-2 -1-3-4 4321s-2σ -1σ-3σ 4σ3σ2σ1σ-4σ
sσ
0 100 200 300 400 500 600 700 800 900 1000 1100 1200 13000
1
2
3
4
5
6
7
Rm
sRR mk σ−=
Characteristic strength: Characteristic strength is the
strength below which has 10%
probability will fall.
( ) 1.0Rxp k =<
Rk
σ−= 28.1RR mk
0.1
Limit state design (Limit durumlara göre hesap)
Fundamental principles and methods for design of reinforced concrete structures
Betonarme 1 Ders Notları
Yrd.Doç.Dr.Murat Serdar Kırçıl
smx
=−
σ
smx σ+=
0 100 200 300 400 500 600 700 800 900 1000 1100 1200 13000
1
2
3
4
5
6
7
0-2 -1-3-4 4321s-2σ -1σ-3σ 4σ3σ2σ1σ-4σ
sσ
0 100 200 300 400 500 600 700 800 900 1000 1100 1200 13000
1
2
3
4
5
6
7
Fm-2 -1-3-4 Fk
Limit state design (Limit durumlara göre hesap)
Fundamental principles and methods for design of reinforced concrete structures
Betonarme 1 Ders Notları
Yrd.Doç.Dr.Murat Serdar Kırçıl
Fm Fk RmRk
The dashed area shows the probability of collapse.
Fk should be increased and Rk should be decreased to reduce the
probability of collapse.
kf
m
k FR
γ≥γ
γm ve γf partial safety factors (kısmi güvenlik katsayıları)
1m >γ 1f >γ
FR≥ structure is assumed to be safeIf
Limit state design (Limit durumlara göre hesap)
Fundamental principles and methods for design of reinforced concrete structures
Betonarme 1 Ders Notları
Yrd.Doç.Dr.Murat Serdar Kırçıl
The probability of collapse is assumed to reduce to predetermined value
(10-6) by increasing characteristic loads with load factors (γf) and
decreasing the characteristic strength with material factors (γm).
kf
m
k FR
γ≥γ
1m >γ 1f >γ
γm ve γf partial safety factors (kısmi güvenlik katsayıları)
Limit state design (Limit durumlara göre hesap)
Fundamental principles and methods for design of reinforced concrete structures
Betonarme 1 Ders Notları
Yrd.Doç.Dr.Murat Serdar Kırçıl
MALZEME KATSAYILARI – TS500
BETON ÇELİK
5.1mc =γCast in place concrete (yerinde dökme beton)
4.1mc =γ
7.1mc =γ
Precast structural elements (prefabrike elemanlar)
If standard control is not available
15.1ms =γ
mc
ckcd
ff
γ=
ms
yk
yd
ff
γ=
mc
ctkctd
ff
γ=
fck:Characteristic compressive strength of concrete (Betonun karakteristik basınç dayanımı)
fctk: Characteristic tensile strength of concrete (Betonun karakteristik çekme dayanımı)
fyk: Characteristic yield strength of reinforcement steel (Çeliğin karakteristik akma dayanımı)
fcd:Design compressive strength of concrete (betonun hesap basınç dayanımı)
fctd: Design tensile strength of concrete (Betonun hesap çekme dayanımı)
fyd: Design yield strength of reinforcement steel (Çeliğin hesap akma dayanımı)
Limit state design (Limit durumlara göre hesap)
Betonarme 1 Ders Notları
Yrd.Doç.Dr.Murat Serdar Kırçıl
STRENGTH REDUCTION FACTORS (Kapasite azaltma katsayıları)–ACI318
900 .=φ Pure bending (Basit eğilme)
ACI318 gives strength reduction factors (Ø) instead of material factors
900 .=φ Axial tension (Eksenel çekme)
900700 .. −=φ Axial force and flexure (Bileşik eğilme)
750700 .. −=φ Axial compression (Eksenel basınç)
MATERIAL COEFFICIENTS– CEB
5.1mc =γ
4.1mc =γ
15.1ms =γ
Limit state design (Limit durumlara göre hesap)
Betonarme 1 Ders Notları
Yrd.Doç.Dr.Murat Serdar Kırçıl
Limit state design (Limit durumlara göre hesap )
LOAD COEFFICIENT – TS500
Q6.1G4.1 +
Only vertical loads
G:Dead load (Dead Load Zati yük / ölü yük))
T2.1Q2.1G0.1 ++ Q:Live load (Hareketli yük)
T:Temparature, differetial settlement, creep (Sıcaklık farkı, Farklı oturma, sünme)
Vetical loads + WindIn addition to (1)
(1)
W3.1Q3.1G0.1 ++
W3.1G9.0 +
W:Wind load (Rüzgar yükü)
In case of earthquake
E0.1Q0.1G0.1 ++
E0.1G9.0 +
E:Deprem yükü (Earthquake Load)
In case of lateral earth pressure
H6.1Q6.1G4.1 ++
H6.1G9.0 +
H: Lateral earth pressure (Yanal toprak itkisi)
In addition to (1)
In addition to (1)
Betonarme 1 Ders Notları
Yrd.Doç.Dr.Murat Serdar Kırçıl
HOMEWORKİlhan Berktay, BETONARME 1, İMO İstanbul şubesi publication
Study examples : 2.4.1, 2.4.2, 2.4.3, 2.4.4 ve 2.4.5
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