ADVANCES IN STRUCTURAL CONCRETE

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Nov 15, 2013 (3 years and 7 months ago)

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Association
of

Engineers
,
Gaza Governorates
,
Palestine





ADVANCES IN STRUCTURAL CONCRETE




Mohamed Ziara


Assoc. Prof.

Civil Eng. Dept.,
IUG


Consultant

Center for Engineering and Planning

(CEP)






2
7

March 200
5


2

1.

HISTORICAL DEVELOPMENT

OF STRUCTURA
L CONCRETE



O
ldest

concrete
from the Stone Age around
7000 B.C.

was discovered
in 1985

in
the
Southern Galilee, Palestine.




About
2000 B.C., lime mortar
was used in Crete.



In

third century B.C
., Romans
used

a fine
sandy volcanic ash

mixed with

lime
.




In
A.
D. 126

Romans built the
Pantheon concrete dome
of span


40m.



In
1801
, Coignet published his statement of
principles of concrete construction
.



In
1848,

Lambot constructed a
boat of concrete reinforced with wire.



In
1854,

Wilkinson obtained a patent for a
reinforced concrete floor system
.




In
1861,

Coignet published a
book
illustrating
uses of reinforced concrete.



In
1867,

Monier patented
concrete containers reinforced with
metal frames.



In
1886,
Koenen published the
theory and design of concrete structures
.



In
1906,

Turner developed the first
slab without beams.


T
he
extensive use

of
structural
concrete
began at

the turn of the
twentieth century

where

lot of developments has occurred in the theory, design and construction
.




In
1904,

the first
set of buildin
g regulations
for
reinforced concrete

were
drafted
by

Professor M
ö
rsch of the University of Stuttgart.



Between
1907

and
19
10
,
design regulations for reinforced concrete

were
issued in Britain, Franc, Austria
,

Switzerland
, USA
.



By the year
1910

the
German

C
ommittee for Reinforced Concrete, the
American
Concrete Institute, the
British

Concrete Institute and the
Austrian

Concrete Committee were already established.



By
1920

many
reinforced
concrete structures

were already constructed.



As early as
1920,

the era

of
prestressed
concrete has
beg
u
n

with the pioneer
work Freyssinet.



From
1900

to
1950

the
working stress

method was used universally.



In
1938
u
ltimate strength
design method

was
codified in the
USSR
.



In

1956
u
ltimate strength
design methods were codified

in the
USA

and
UK.



Currently, Limit States Method
is used in most countries in the world.



New
constituent

materials
and
composites
of concrete have been used in the
construction industry for sometimes
(
high
-
strength concrete

exceeding

200MPa, high streng
th steel bars

and

welded wire fabric

(
exceeding

700
MPa
)
and
prestressing steel
of ultimate strength exceeding
2000MPa
)
.


3

2.

USE OF CONCRETE

Concrete is the dominant construction material in the world because of its
advantages characteristics that include:




E
conomy

(availability of its constituent materials)
.



Easy of
c
onstruction
(can be cast in
various

shape
s
, require simple skills)
.



Rigidity

(at working load conditions)
.



Fire
r
esistance.




etc.


C
oncrete posses some adverse characteristics such as
:




Weak tens
ile strength

(use reinforcing steel)
.



Low strength/weight ratio

(use high strength and light weight concrete)
.



Brittleness

(use confinement
).



Time
-
dependant volume change

(use expansion joints, non
-
expansive cement).



etc.


4

3.

MECHANICS OF REINFORCED CONCRET
E



Concrete
is strong in compression and
weak in tension
.




C
racks

develop
when

tension stresses

exceed
tensile strength of concrete


f
t





Tensile stresses may result from

loading, shrinkage or temperature changes.





Fig. 1 demo
nstrates the mechanics of reinforced concrete beams
.




Use of
longitudinal

and
shear reinforcement

to prevent the failure
. The
resulting
composite material

is called reinforced concrete.



F
ailure
may also be prevented
by
using

“prestressing tendons”
.
The re
sulting
composite material

is called
prestressed

concrete.



Different applications require
different
configuration of
steel reinforcement.

f
t

f
c

f
t

f
c

f
s

f
t

Fig. 1 Mechanics of reinforced concrete beams.

Brittle flexural failure of
Plain concrete beam.

Brittle
shear

failure of Plain
concrete beam.

Prevention of failure in
reinforced concrete beam

Prevention of failure in
prestressed concrete beam

Prestressing
fo
rce


5

4.

DESIGN OBJECTIVES

The structural design should satisfy structural and nonstructural requirements

in Fig.

2
.



Design Requirements

Structural Requirements

Non
-
Structural Requirements

Strength

Stability

Rigidity

Suitability

Economy

Maintainability

Fig. 2 Requirements of structural design.


6

5.

LIMI
T STATES DESIGN METHOD

T
he design requirements are satisfied using t
hree limit states
in Fig. 3.






A structure reaches its
limit state

when it becomes
unfit
for its use.



Ultimate limit state

is very important since it involv
es
structure
collapse
.

Thus, this limit state should have
low
probability of occurrenc
e.



The
design

is

carried out for the
ultimate limit state
.

T
hen the
serviceability
limit

state is
checked
.



The
special limit state

is considered in case of
abnormal
con
ditions.


Limit States

Serviceability
Limit State

Special Limit
State

Excessive
d
eflection

Excessive
c
rack
w
idth

Excessive
v
ibration

Ultimate
Limit State

Rapture

Progressive
c
ollapse

Instability
/
Loss
of
e
quilibrium

Fatigue

Plastic
m
echanism

Severe
e
arthquake

Explosion,
f
ire, etc.

Environmental
d
eterioration

Chemical
d
eterioration

Fig. 3 Limi
t States Design Method.


7

6.

UNIFIED DESIGN APPROACH FOR
STRUCTURAL CONCRETE




S
tructural concrete

is a unifying name for concrete used for structural
purposes including
plain, reinforced

and
prestressed
concrete.



Previous

research and developments
on structural concrete

h
a
ve

resulted in a
variety of design approaches and codes of practice.



T
he design approach for all types of concrete
(structural concret
e)
should be
consistent

and

unified
, i.e.

t
he unified approach to the design of structural
concrete
.


THE UNIFIED DESIGN

APPROACH

(UDA)



A
ll

regional and national
codes

should be
unified
.




Member

design should
replace

section

design.



More consideration

be given to
:



O
verall structural behavior
.



L
ogical structural systems
.



L
oad paths and flow of forces
.



D
esign concepts
.




Rigor
ous design models and detailing.



Deformation restraints
.



Multi
-
axial
state of
stress/strain
.


8

7.

BUILDING CODES



To ensure
public’s health and safety

the
design and construction

of buildings
is regulated using
municipal bylaws

called
“Building Codes”
.



Each c
ountry

should
have

or
adopt

its own building codes which then become
legal

documents.



Writing

of a code involves a
complex process
.



A number of
building codes

exist for
various applications

including fire
resistance, heat insulation, occupancy, formwork,

design of structural concrete,
etc.



For example
,

ACI

318

code or
BS 8110

are used for t
he design and construction
of
structural concrete.
The
se

codes give
specific requirements

for
material
,
structural analysis
,
member proportioning
,
construction practic
e
, etc.



O
fficial building codes
do
not

exist in the USA
for structural

concrete
.

A
number of
non
-
government
institutions

are responsible for developing and
producing the codes. The
ACI

takes the main role in producing the code
.
The
ACI code is regarded as

an
authoritative statement
of current good practice in
the field of reinforced concrete. It has been
incorporated

in a number of
municipal and regional building codes

that have
legal status

and thus the
ACI

code itself
attain a legal standing
. The
ACI

cod
e has also served as
a model
code for many countries in the
world.




Codes do

not substitute

for

sound engineering
judgment.

In many applications
,

codes serve as a guide

and
judgment

is made based on

full understanding

of
the

theory of reinforced concrete

a
nd

structural behavior of members at
material level.
However, this doe
s

not

mean that
E
ngineers
can

violate the code
requirements.


9

8.

STRUCTURAL SAFETY

Uncertainties in Resistance


V
ariability in
material strength
,

member
dimensions

and inaccuracy of
design

methods
.

Uncertainties in Load

By nature
actual loads can not be predicted accurately
. In addition,
mathematical
models

do not adequately represent
actual physical models
.
.

Consequence of Failure

The

level of safety

depends on
subjective factors

such as p
otential
loss of life, cost
of failure
and
type of failure
where sudden
brittle

failures need to be prevented
and alternative
load paths
and
load redistribution
need to be allowed.




The
safety

factors

are calculated following
a
probabilistic

approach

in Fig. 4.


In accordance with the
probabilistic

approach

absolute

safety
can

never

be

achieved

even if a large factor of safety was used in the
deterministic

design
approaches. The
probability

of

failure

can however be
reduced

by

increasing

the
resistance

or by
reducing

the
dispersion

of
resistance
.


f
x
(
X
)

Value (
X
)

Resistance (R)

Load (L)

Failure Area
L>R

Fig. 4 Possible combinations of load and resistance


10

9.

LOAD TYPES

Lo
ads can be classified as shown in Fig.
5
.

The following remarks are related to the type of loads:




C
reep

results from
permanent

loads plus
sustain

part of
variable

load
.



I
nfluence of
dynamic loads

can be considered by
multiplying

the
live load
by
impact factors or

by carrying out
dynamic analysis
.



In the
Ultimate Limit State

the
mean value

of the
maximum live

or
wind

load on the structure in its
lifetime

is considered.



In the
Serviceability Limit State

50%

to
60%
of the
mean

value

of the
maximum live

or
wind
load is considered.



For calculating the
sustained

load
deflection

20%

to
30%

of
specified live

load is considered (
ACI code considers the entire specified
live
load
which
result
s

in overestimating creep deflection of slender columns
).

Load

Permanent

(e.g. own wt.)

Accidental

(e.g. explosion)

Variable

(e.g. occupancy)

Sustain

(e.
g. furniture)

Short duration

(e.g. people)

Free

(e.g. traffic)

Fixed

(e.g. crane)

Fig.

5

Classification of loads.

Dynamic

(produce acceleration)

Static

(do not cause acceleration)


11

10.

LOADING SPECIFICATIONS

L
oads

may be

estimated based on the
ASCE Minimum Design Loads for
Buildings and Other Structures (ASCE 7)

formerly known as
ANSI A58.1.
ASCE 7 specifies dead loads
, live loads due to occupancy, snow loads (depend on
the
use categories
), roof loads, construction loads, wind loads (depend on the
use
categories
), earthquake loads (depend on the
use categories
) and other loads (e.g.
floods, soil loads, etc.).


The
Use C
ategories Are As Follows:

I.

Buildings and other structures that represent a low hazard to human life
at failure, e.g., warehouses and agricultural facilities.

II.

Buildings and other structures that do not fall into categories I, III or IV.

III.

Buildings and other s
tructures that represent a substantial hazard to
human life at failure, e.g., schools, buildings host chemical or explosive
materials.

IV.

Buildings and other structures designated as essential facilities, e.g.,
hospital, police stations, power
-
generating stat
ions, communication
centers, etc.


12

11.

STRENGTH DESIGN METHOD

IN ACI

“ACI 318
-
02/318R
-
02: Building Code Requirements for Structural Concrete
Commentary”.




Working
Load
s

>

Factored
Loads

Reduced
Strength



Required
Strength

Design
Strength



Or

Nominal
Strength

Fig.

6

Strength Design Method
.


13

12.

ADVANCES IN LOAD AND RESISTING FACTORS
IN ACI 318
-
02

Design Strength (Redu
ced Strength)

Design Strength =


Nmi湡l⁓瑲敮e瑨


S
trength reduction factors


´
ACI

9.3
):




㴠=⸹.


for
tension
-
controlled

sections
.



= 0.70



for
compression
-
controlled

sections with
spiral

reinforcement



= 0.65



for other
compression
-
controlled

s
ections



= 0.75



for
shear

and
torsion



= 0.65



for
bearing

on concrete



= 0.75



for
strut

and
-
tie

models



shall be
modified

for
earthquake

resisting
elements
(
ACI 9.3.4
)
.

Required Strength (U)

Load

factors
(
ACI
9.2
)
:

U = 1.4(D + F)









(ACI 9
-
1)

U = 1.2(D + F + T) + 1.6(L + H) + 0.5(L
r

or S or R)



(ACI 9
-
2)

U = 1.2D + 1.6(L
r

or S or R) + (1.0L or 0.8 W)



(ACI 9
-
3)

U = 1.2D + 1.6W + 1.0L + 0.5(L
r

or S or R)




(ACI 9
-
4)

U = 1.2D + 1.0E + 1.0L + 0.2S






(ACI 9
-
5)

U = 0.9D + 1.6W + 1.6H







(ACI 9
-
6)

U = 0.9D + 1.0E + 1.6H







(ACI 9
-
7)

M
odifications

to the
se

factors are
given in Code
for various loading conditions.


Example
:

U
for L and D

loading case
:

U = 1.2D + 1.6 L








(ACI 9
-
2)



14

13.

LOAD AND RESISTING FACTORS
IN ACI 318
-
02

APPENDIX
“C”

A
lternative
S
trength reduction factors


´
ACI
C
.3
)
:



㴠=⸹.


for
tension
-
controlled

sections
.



= 0.7
5



for
compression
-
controlled

sections with
spiral

reinforcement



= 0.
7



for other
compression
-
controlled

sections



= 0.
8
5



for
shear

and
tors
ion



= 0.
7
5



for
bearing

on concrete



= 0.
8
5



for
strut

and
-
tie

models



shall be
modified

for
earthquake

resisting
elements
(ACI
C
.3.4)
.

Alternat
!Unexpected End of Formula

Strength

U


(
ACI C.2
)

U = 1.4D + 1.7L








(C
-
1)

U = 0
.75(1.4D + 1.7L) + (1.6W or 1.0E)




(C
-
2)

U = 0.9D + (1.6W or 1.0E)







(C
-
3)

U = 1.4D + 1.7L + 1.7H







(C
-
4)

U = 0.75(1.4D + 1.4T + 1.7L)






(C
-
5)

U = 1.4(D + T)









(C
-
6)



U = 0.9D + 1.7H



(
In case
L

and
D

reduce effect of
H
)



U = 0.9D + 1.4
F)




(in case
L
and
D

reduce effect of
F
)



F
is

multiplied by
1.4
in
all
load combinations that include
L
.

Notation

D:

Dead load

E:

Seismic Load

F:

Fluid pressure load

H:

Earth pressure load

L:

Live load

L
r
:

Roof live load

R:

Rain load

S:

Snow load

T:

Cum
ulative effects of differential settlement, creep, shrinkage,
expansion or temperature change

U:

Required strength

W:

Wind load


15

14.

ADVANCES IN FLEXURAL THEORY IN ACI 318(02)

Types of Sections



ε
y

0.002

0.002<
ε
s
<0.00
5

ε
s

0.00
5

ε
s
=0.004

ε
s
<0.002

ε
s
=0.004

Over
-
reinforced brittle sections

ε
s
<0.00
4

ε
s

0.00
4

Under
-
reinforced
ductile sections

ε
c
=
0.00
3

ε
c
=
0.00
3

ε
c
=
0.00
3

ε
c
=
0.00
3

ε
c
=
0.00
3

Compression
-
controlled
section

Tension
-
controlled
section

Balanced
section

Transition
section

Transition
section

Fig.

7

Types of sections
.


16

15.


STRENGTH REDUCTION FACTOR “

´







0.65

0.9

0.002

0.00
5

ε
s

0.004

Beams

Fig.

8

Strength reduction factor
.


17

16.

LONGITUDINAL REINFORCEMENT RATIOS


y
y
c
b
f
f
f
y
s




600
600
85
.
0


1
)
(







y
c
f
f
s



1
)
004
.
0
(

max
364
.
0







y
c
f
f
s



1
)
005
.
0
(

319
.
0







For:



=


b







balanced section






b







compression
-
controlled section







)
005
.
0

s

(






tension
-
controlled section



b

<


<


)
005
.
0
(


s






transition

section






max






b
rittle behavior



For design of beams:






max






ductile behavior





y
y
c
f
f
f
4
.
1
4
min








ductile behavior


18

17.

EXAMPLE

Find
M
u

for the shown section

Assume tension
-
controlled s
ection
*

From Equilibrium

C
=

T

b
f
.
f
A
a
c
y
s


85
0

=

73.4

mm

c = a/

1

= 86.4 mm

From strain diagram

ε
s
=
0.01

> 0.005





assumption is ok.

f
s

= f
y

and



㴠=⸹


*

Or
:

Check for





s
=0.005)


0069
.
0
440
*
200
201
*
3




0131
0
414
20
85
0
319
0
005
0
.

.
*
.


ρ
)
.
(
ε
s










s
=0.005)





tension
-
controlled section



)
2
(
a
d
T
M
M
n
u






kN.m

5
.
90
)10
2
73.4
414(440
*
201
*
3
*
0.9
Μ
6
υ






Check


y
y
c
f
f
f
4
.
1
4
min






ρ = 0.0069 > ρ
min
= 0.0034



ok

ε
s

ε
c
=0.003

f
s

0.85
c
f


C

T

200mm

440

c

a

a/2

c
f

=20 MPa

f
y
=414 MPa

3

16


19

18.

ULTRA HIGH STRENGTH CONCRETE

General Properties of the
UHPC



Ultra High Performance concrete
(
UHPC
)
is

a high strength, low porosity
and ductile material.



UHPC is made with
Portland cement, silica fume, quartz flour, fine silica
sand,

high range

water reducer

and

steel or organic

fibres

with very
low

w/c
ratio
.



The

absence of coarse aggregate

is a key asp
ect to
reduce

the

heterogeneity

between the cement matrix and the aggregate.



The

cement content

is more than

1000

kg/m3.




The

density

is high more than
260
0 kg/m3.



The

ductility

is improved by using steel micro

fibres
.



The
compressive strength

is more th
an
200

MPa.



The flexural strength is more than

50

MPa.



It is possible to produce concrete with a strength as high as

700 MPa

in the

laboratory
.



The use of
UHPC

may allow the

elimination

of the

reinforcing steel
.



UHPC

meets all
eight performance criteria

for high performance concrete:

freeze
-
thaw durability, scaling resistance, abrasion resistance, chloride
penetration, compressive strength, modulus of elasticity, shrinkage, and
creep
.



UHPC

is a milestone on the way towards

no
-
maintenance

constructions.



T
he
material

itself is
av
ail
abl
e

and the problem is the ease of

application

and the

price
.



Typical Composition of UHPC

Material

Percent by Weight

Portland
Cement


28.7


Fine Sand


41.1


Silica Fume


9.3


Ground Quartz

8.5


Superplasticize
r


0.5


St
eel Fibres


6.4


Water


5.5




20

Design Properties of UHPC



Valid design
rules

for UHPC
do not

yet
exit
.



A work group of the
German Commission on Reinforced Concrete

has
presented a state of the art report on UHPC. Some of the
main aspects
are:

The Modulus

of elasticity “E
c
” for UHPC


or

E
c

= 16.364 Ln (
f
c
)


34.828 (10
3

N/mm
2
)

Behaviour Under Compression



UHPC shows a
linear

elastic behavior Until about 70 to
80 %

of
f
c
.




The
failure

of UHPC
without fibres

is of
explosive

nature.



No descending

branch in
the stress
-
strain
-
diagram does exist.



Behavior in Tension



Tensile
strength values may reach
15

MPa.



The
slope

of the
descending
branch depends on the fibre
orientation
,
content

and
type
.



21

Shear Resistance of UHPC Structural Elements

Tests proved th
at it is very
effective

to use steel
fibres as a shear

reinforcement
instead of stirrups
.




Shear failure pattern of the test specimens

A model for the
shear

force capacity of HPC
-
beams
without shear reinforcement

(stirrups) has been proposed by Zink su
ch as:






22

Flexural Design of UHPC Beams

Compressive stress distribution

for UHPC is
trapezoidal
.

ACI
Block
can be used
for strength up to
80

MPa.



Limiting compressive strain

The constant value of strain at extreme concre
te compression fiber of
0.003

prescribed by
ACI 318

represent
s

satisfactorily

the experimental results for
high
-
strength
as well as lower
-
strength concrete, although it is
not as

conservative

for
high
-
strength concrete.

k
3

f
c


c

c

d

T
=A
s

f
y

C=
k
1
k
2

f

c

bc


k
2

c

α

f
c





c

T
=A
s

f
y

T
=A
s

f
y

C=
0.85
f

c

bc


γ

C=
(1
+

)/2

f

c

bc)


Actual for NSC

Block for

NSC

Trapezoidal for

UHPC


23

19.

STRUT
-
AND
-
TIE MODELS

Background



The

strut
-
and
-
tie

method
is based on the
truss analogy
used
for
shear design of
B
-
r
egions

shown in Fig.
9
.



The
strut
-
and
-
tie
model
is

used to idealize the
flow of force

in a
cracked
concrete

beam.



Marti

and
Schlaich

et al. promoted the use of
t
he strut
-
and
-
ti
e method
for
design of

D
-
Regions
.



V
s

V
s

V
s

V
s

Actual beam

Truss analogy

Fig. 9 Tr
uss analogy for shear.


24

20.

B
-

AND D
-

REGIONS

B
-

(Beam or Bernoulli)
Regions

B
-
Regions are parts of a structure in which
B
ernoulli's hypothesis of
straight
-
line
strain

profiles applies.


D
-
(Disturbed or Discontinuity)
R
egions

D
-
Regions

are parts of a structure with a
complex variation

in
strain
.

D
-
Regions include portions near
abrupt
changes in
geometry

(geometrical
d
iscontinuities) or
con
centr
ated forces

(statical
d
iscontinuities).

St. Venant's
P
rinciple

T
he extent of
a
D
-
Region

spans about
one section depth

of the region on
either
side

of the discontinuity

as shown in Fig. 10
.



Fig. 10 B
-

and D
-

regions.


25

21.

GENERAL NOTES ON STM



B
-
Regions

are

adequately
designed
based on
conventional

models, e.g.

design
for
flexure

is based on conventional
beam theory

and

the design for
shear

is
based on the
truss analogy
.



Previous c
ode

provisions provide
d

little guidance

for design of most types of
D
-
Regions

such as
deep beams, corbels, beam
-
column
joints,

and pile
caps
.



D
-
Regions

were

designed by
empirical approaches

or by using
common

detailing practices
.



The
STM

is emerging as a
code
-
worthy methodology

for the design of all types
of
D
-
Regions

in
structural concrete
.



A
lthough the
STM

is equally
a
pplicable

to both
B
-

and
D
-
Region problems, it
is
not practical

to apply the
STM
method to
B
-
Region problems.


,


26

22.

STM DESIGN CONCEPT

STM

is
a
truss model

of a member that is made of
struts
,
ties
and connected at
nodes

capable of transmitting the loads to
supports.


Simple STM is shown in Fig. 11.

Types of Nodes


Types of Struts




C

C

C

C

C

C

T

T

T

T

T

T

CCC Node

TTT Node

CCT Node

CTT Node

Strut

Tie

Node

Prismatic

Bottle

Fan

Fig. 11 Strut and Tie Model (STM).


27

23.

DESIGN PRO
CESS

The design process using STM involves five major steps

that are illustrated for
dapped
-
ended beam in Fig. 12.


1.

Define the
boundarie
s

of the
D
-
Region

and determine the
boundary forces
.

2.

Sketch the
truss

and
solve

for the truss member
forces
.

3.

Select

steel

reinforc
ement

that is
properly
anchored

in
to

the
nodes

to provide
the necessary
tie

capacity
.


4.

Evaluate the
dimensions

of the
struts

a
nd
nodes

to carry the forces.

5.

Provide
distributed reinforcement

to ensure
ductile

behavior of the
D
-
Region
.





Fig. 12 Design steps of STM.


28

24.

STRENGTH OF MODEL MEMBERS

(
ACI 318
-
02 Appendix A
)

Strength of Struts

F
u




F
n
s

F
ns

= f
cu

A
c


Where



= 0.75



s

= 1
.0

for prismatic struts in
uncracked

compression zones.


= 0.4
for struts in
tension

member
s.


= 0.
75

for
bottle shaped struts
with

crack control reinforcement
*
.


= 0.6

for all other cases.

*

C
rack control reinforcement

=



= steel ratio of reinforcement crossing the strut under review
.


= angle between the axis of the strut and the bars.

Strength of
Node
s

F
u




F
nn

F
nn

= f
cu

A
n


Where



= 0.75



n

= 1
.0

for

nodes bounded by struts and/or bearing areas.


= 0.
8

for
nodes

anchor only one tie
.


= 0.6

for nodes

anchor
more than

one tie
.

Strength of
Ties

F
u




F
nt

F
nt

= f
y

A
s


Where



= 0.75









29

25.

DESIGN EXAMP
LE: DEEP BEAM

and




Check Bearing Strength

Bearing strength at points of loading

=


= 0.75(0.85)(25)(1.0)(450)(500)/1000

= 3586 kN > 1600 kN




OK


B
earing strength at s
upports

=


= 0.75(0.85)(25)(0.80)(450)(500)/1000

= 2868 kN > 1600 kN



OK

Strut
-
and
-
Tie Model



30

Member Forces and Dimensions

Note that t
he entire
deep beam

is a
disturbed
D
-
re
gion
.


F
BC

=
F
AD

=

1850
kN
,
F
BC
=
2444

kN


Check capacity of

prismatic

strut
BC
:


= 0.75(0.85)(1.0)(25)(500)(240
#
)/1000

=
= 1912 kN



OK

#

width of strut
.

Check Capacity of
bo
ttled
-
shape

strut AB:


= 0.75(0.85)(0.75)(25)(500)(476)/1000

= 2885 kN > 2444 kN








OK


Use crossing vertical and horizontal
(
1 #13 on each face at
s
h

= 300 mm) and
vertical (
1 #16 on each face at
s
v

= 300 mm)
reinforcement in this strut (

s

= 0.75
).


= 0.00312 > 0.003
OK

Tie
AD
:


Use

2 layers of 5 #29 bars = 6450 mm
2

@ 80 mm and 220 mm from bottom
.



31

26.

SPECIAL ADVANCES IN STRUCTURAL CONCRETE

1.

Mohamed Ziara,

Structural Reha
bilitation of Reinforced Concrete Water
Tanks
,”

The Ninth Arab Structural Engineering Conference (9ASEC),
November 29
-
December 1, 2003, Abu Dhabi, United Arab Emirates, pp 479


486.

2.

Mohamed Arafa and Mohamed Ziara,
“Non
-
Linear Finite Element Analysis
of R
C Beams With Special Detailing of Stirrups,”

Proceedings of the
International Conference on Engineering and City Development, the Islamic
University, 22
-

23 September 2003, Gaza, Palestine, pp C
-
038
-

C050.

3.

Mohamed M. Ziara, Hasan S. Dweik and Mohammed S.

Hadidoun,
“Engineering Properties of Concrete made with Ground Melamine
-
Formaldehyde Thermosetting Plastics as Sand Replacement,”
The Sixth
International Conference on Concrete Technology for Developing Countries,
Amman, Jordan,
21
-
23 October 2002
.

4.

Moham
ed M. Ziara and David Haldane,
“Flexure
-
Shear Model for
Prevention of Diagonal Failures in Beams Made with High Strength
Concrete,”

The Eighth East Asia
-
Pacific Conference on Structural
Engineering and Construction: Challenges in the 21
st

Century, Singapor
e,

5
-
7
December 2001
.

5.

Mohamed M. Ziara,

“Structural Upgrading of RC Beams Using Composite
Overlays,”

Journal of Construction and Building Materials, UK, Vol. 14, No.
8,
December 2000,

pp. 397
-
406.

6.

Mohamed M. Ziara, David Haldane and Stuart Hood,
“Proposed
Changes to
flexural Design in BS 8110 to Allow Over
-
Reinforced Sections to Fail in a
Ductile Manner,”

Magazine of Concrete Research (London), UK, Vol. 52,
No. 6,
December 2000,
pp. 443
-
454
.

7.

Mohamed M. Ziara,
“The Use of Under, Over and Highly
-
Over Reinforc
ed
Flexural Members Made With Normal And High Strength Concrete,”
The
4
th

Technical Congress, Advances in Civil Engineering, Gazimagusa, TRNC,

1
-
3 November 2000.

8.

D. Haldane and Mohamed M. Ziara,
“Strengthening of Reinforced Concrete
Girders with
"
Π
"

and
"T"

Cross Sections,”

The Institute of Civil
Engineering, Structures and Building Journal, UK,

Vol. 140,

Feb. 2000,

pp.
61
-
72.

9.

Mohamed M. Ziara, David Haldane and A. S. Kuttab,
“Prevention of
Diagonal Tension Failures in Beams Using a Flexural
-
Shear
Interaction
Approach,”

Magazine of Concrete Research (London),
UK,

Vol. 51, No. 4,
August 1999
, pp. 275
-
289.


32

10.

S. Jada and Mohamed M. Ziara
“Repair and Strengthening of Slabs Using
Bonded Concrete Overlays,”

IABSE Symposium, Long
-
Span and High
-
Rise
Structure
s, Kobe, Japan,
September 2
-
4, 1998
, pp. 373
-
375.

11.

Mohamed M. Ziara, R. Rustom, M. El
-
Bayya and A. Amer,
“Codes,
Standards and Regulations in Palestine,”
The Reconstruction of Palestine:
Issues, Options, and Strategies, edited by A. B. Zahlan, Published by
Kegan
Paul International, London and New York,
1997,

pp. 71
-
79.

12.

Mohamed M. Ziara,
“The Strength and Ductility of Structural Concrete
Members in Earthquake Regions,”

First Palestinian Symposium for
Earthquake Hazard Mitigation, An
-
Najah National University,

Nablus,
Palestine,
18
-
20 June 1996
.

13.

Mohamed M. Ziara, D. Haldane and A. Kuttab,
“Flexural Behavior of Beams
with Confinement,”

American Concrete Institute ACI, Structural Journal,
USA,

Vol. 92, No. 1,
January
-
February 1995
, pp. 103
-
114.

14.

Mohamed M. Ziara,

D. Haldane and A. Kuttab,
“Shear and Flexural
Strengths Resulting from Confinement of the Compression Region in
Circular Section Structural Concrete Beams,”

Magazine of Concrete
Research

(London), UK, Vol. 45 (No. 164),
September 1993
, pp. 211
-
219.