DOI: 10.15680/IJIRSET.2015.0405002 The economy of the structural design of reinforced concrete buildings is usually evaluated by comparing the concrete volume per unit area and rebar weight per unit volume with certain empirical values depending on the type of the structure and the past experience of the judging engineer. The aim of this paper is to refine those empirical values and give that past experience the required scientific base. In order to achieve that goal, simplified methods of design that stated in most of reinforced concrete design codes are used to figure out the required quantities of concrete and reinforcement steel for different structural elements and types. Some reasonable assumptions are used to facilitate the mathematical formulas to be usable and presentable. Produced formulas are accurate enough to be used in rough estimation of concrete and rebar quantities, check quantity surveying results and evaluate the economy of the structural design

1. Int
Copyright to I
A
Lectu
ABSTRACT
the concrete
of the structu
and give tha
that stated in
reinforcemen
mathematica
estimation of
design.
KEYWORD
As : M
As’ : dis
d : De
Fcu : Ch
Fc’ : Ch
Fy : Yi
L : Sh
L’ : Lo
R : As
RFT : Re
ts : To
ws : Un
α,β : loa
γrc : Re
γs : Re
RC Slab is
supports eith
Usually, som
of the most w
ternatio
IJIRSET
EST
QU
C
Assistant Prof
urer, Str. Dpt.,
T: The econom
volume per u
ure and the pa
at past experie
n most of rein
nt steel for di
al formulas
f concrete and
DS: optimum
Main steel reinf
stributary stee
epth of section
haracteristic c
haracteristic c
ield stress of r
hort span of sl
ong span of sla
spect ratio of
einforcement
otal thickness
niformly distr
ad distribution
einforced conc
einforcement
a horizontal c
her beams or c
me empirical v
widely accepte
onal Jou
Eng
(
TIMA
UANT
CONC
Dr.
f., Civil Eng. D
, Faculty of En
my of the stru
unit area and re
ast experience
ence the requi
nforced concr
fferent structu
to be usable
d rebar quanti
quantities, reb
forcement area
el reinforceme
n (cm)
ube strength o
ylinder streng
reinforcement
ab or clear sp
ab (m)
slab (L’/L) ≤
of slab (cm)
ributed load on
n factors in sh
crete density (
steel density (
concrete plate
columns. This
values are use
ed values are
urnal of
gineerin
(An ISO 3297:
Vol. 4,
DOI: 10.1568
TING
TITIE
CRET
Amr Abohas
Dpt., Mataria,
ng. & Tech., F
uctural design
ebar weight p
of the judging
ired scientific
rete design co
ural elements
and presenta
ties, check qu
bar percentage
AB
a (cm2
)
ent area (cm2
)
of concrete aft
gth of concrete
t steel
an of cantilev
≤ 2.0
n slabs (t/m2
)
hort & long dir
(2.5 t/m3
)
(7.85 t/m3
)
I.
e which carrie
s load transfer
d as optimum
(60-80 kg/m3
)
f Innova
ng and T
2007 Certified
Issue 5, Ma
80/IJIRSET.201
G THE
S OF
TE SL
shish 1
, Dr. A
Helwan Uni.,
Future Uni., C
of reinforced
per unit volum
g engineer. Th
c base. In orde
odes are used
and types. So
able. Produced
uantity surveyi
e, concrete sla
BBREVIATIO
fter 28 day
e after 28 day
ver slab (m)
rection of 2 w
INTRODUCTI
es loads perp
r generates ma
m rebar percent
) for solid slab
ative Res
Technol
d Organization
ay 2015
15.0405002
E ECO
DIFF
LAB T
Ahmed M. E
, Cairo, Egypt
Cairo, Egypt, a
concrete buil
me with certain
he aim of this
er to achieve
to figure out
ome reasonab
d formulas ar
ing results an
abs, cost estim
ONS
way solid slab
ION
pendicular to
ainly bending
tage to evalua
b and (120-14
search i
logy
n)
ONOM
FERE
TYPES
bid 2
t, abouhashish
ahmed.abdelk
dings is usual
n empirical va
paper is to re
that goal, sim
the required
le assumption
re accurate en
d evaluate the
mation, quantit
its plane. It t
moments and
ate the econom
40 kg/m3
) of fl
ISSN(Online):
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in Scien
MIC
ENT
S
h@yahoo.com
khaleq@fue.ed
lly evaluated b
alues dependin
fine those em
mplified metho
quantities of
ns are used to
nough to be u
e economy of
ty surveying.
transfers those
d shear stresse
my of certain
lat slabs.
: 2319-8753
2347-6710
nce,
2661
m 1
du.eg 2
by comparing
ng on the type
mpirical values
ods of design
concrete and
o facilitate the
used in rough
the structural
e loads to its
es in the slab.
design. Some
n
d
h

2. Int
Copyright to I
This paper ai
based on the
Normally, de
martials, reb
Slab
is e
are
dire
sma
rang
betw
part
sma
and
So,
own
Con
ben
supp
(wL
supp
end
long
the
supp
rein
con
supp
ana
Continui
Simple
One en
Both end
ternatio
IJIRSET
ims to evaluat
simplified de
esign and qua
ar detailing, ..
b loads: Cons
equal to slab t
widely varied
ectly on the sl
all slabs. Henc
ged between (
ween (0.0 – 0
tition load not
allest slab sho
d partition load
the load/span
n weight are a
ntinuity: Con
nding moment
ported elemen
L2
/8), (wL2
/10
ported and bo
d continuous i
gitudinal reinf
total volume
ported, one en
nforcement st
ntinuity cases
ported, one en
alysis will con
ity M max
e
wL2
8
d
wL2
10
ds
wL2
12
onal Jou
Eng
(
te the optimum
esign methods
antities will b
.etc., hence, in
sists of its ow
thickness time
d according t
abs. Generally
ce, it is expec
(0.15 – 0.25)
0.4) t/m2
[2],[
t both of them
ould has small
d for 4.0m spa
n ratio is range
about 0.090 t/m
nnections betw
t distribution a
nt, one end a
0) and (wL2
/
oth ends conti
identical span
forcement. Fi
e of longitudin
nd continuous
eel for each
and the one
nd continuous
sider the one e
T
Rein
(0.33 As * 0
(A
(1.00 As * 0
(A
(1.00 As * 0
(A
urnal of
gineerin
(An ISO 3297:
Vol. 4,
DOI: 10.1568
m thickness an
s stated in mos
e affected by
n order to faci
wn weight, sup
es the reinforc
to type of fini
y, large slabs
cted that slab
t/m2
, live loa
[3] . It should
m. Assuming th
lest loads and
an is (0.15+0.
ed between (0
m2
times its go
ween consider
along this elem
and both ends
/12) respectiv
inuous spans
n respectively
gure (1) show
nal reinforcem
s & both ends
case. Table (
e end continu
s & both ends
end continuity
Table 1: Conti
nforcement V
0.25 L)+ (0.33
As * L) = 1.28
0.30 L)+(0.33
As * L) = 1.49
0.30 L)+(1.00
As * L) = 1.70
f Innova
ng and T
2007 Certified
Issue 5, Ma
80/IJIRSET.201
nd rebar perce
st reinforced c
several varia
ilitate the stud
perimposed lo
ced concrete d
ishing and the
are more like
load proportio
ad is ranged b
d be noted tha
hat the short s
vice versa. H
.2+0.0=0.35 t/
0.088 - 0.085)
overning span
red bending el
ment. As per m
s continuous
vely [1],[4]. H
are 1.25 & 0.
y. Also, the co
ws the typical
ment are (1.2
s continuous s
(1) shows the
uous case. Th
s continuous s
y with error le
inuity effect o
olume
As * 0.25 L)+
As.L
As * 0.25 L)+
As.L
As * 0.30 L)+
As.L
ative Res
Technol
d Organization
ay 2015
15.0405002
entage of solid
concrete desig
ables such as l
dy, the followi
ads and live l
density, while
e room activi
ly to either be
onally increas
between (0.2 –
at the increas
span of the sla
Hence, the sum
/m2
) and for 1
t/m2
/m. Base
n in meters.
lement and ad
many codes, m
element subj
Hence, the re
.83 times the
ontinuity of t
detail of solid
28 As.L), (1.4
spans respecti
e ratios betw
he ratios are
spans respecti
ess than 7%
on RFT amoun
. M . = .
M 1 side
+
10/8 =
+
10/10 =
+
10/12 =
search i
logy
n)
d, hollow bloc
gn codes.
loads, spans,
ing assumptio
loads. Own w
e the superimp
ity, also there
e public area o
ses with slab a
– 0.6) t/m2
, an
e of loads is
ab is ranged b
mmation of su
10.0m span is
d on this stud
djacent eleme
maximum ben
ected to unifo
equired reinfo
required reinf
the element a
d slabs in AC
49 As.L) & (
ively, where (
ween reinforce
(1.07, 1.00
ively. Based o
nt
As .
As 1side
1.25
1.25
1
=1.00
1.00
1
= 0.83
0.83
1
ISSN(Online):
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in Scien
ck, flat slab an
boundary con
ns are conside
eight is well d
posed loads a
e might be pa
or have partiti
area. Superim
nd partition lo
either due to
between 4.0 to
uperimposed lo
(0.25+0.2+0.
dy, slab loads a
ents have a ma
nding moment
formly distribu
forcement are
forcement are
affects the det
CI-315. Based
1.70 As.L) fo
(As) is the req
ement weight
and 0.95) fo
on this analys
. RFT
RFT 1 s
5*1.28 As.L.γ
1.49 As.L.γs
0*1.49 As.L.γ
1.49 As.L.γs
3* 1.70 As.L.γ
1.49 As.L.γs
: 2319-8753
2347-6710
nce,
2662
nd waffle slab
nditions, used
ered:
defined and it
and live loads
artitions loads
ion loads than
mposed load is
oad is ranged
o live load or
o 10.0 m, then
oad, live load
4=0.85 t/m2
).
apart from its
ajor effect on
t for a simply
uted load are
a for simply
ea for the one
tailing of the
on this detail
or the simply
quired area of
t in the three
or the simply
sis, all further
.
side
γs
= 1.07
γs
= 1.00
γs
= 0.95
d
t
n
d
r
n
d
n
y
y
y
f
y
r

3. Int
Copyright to I
Solid slab is
beams on the
simply suppo
be calculated
For Fy=360
table(2).
Tab
Slab load is
rectangularit
long spans L
ws s
M s
As s
RFT
RFT
Wh
Con
Lea
RFT
RFT
Similarly, th
ternatio
IJIRSET
s the basic typ
e edges. Recta
orted or free.
d as follows:
MPa, this eq
ble 2: Compar
R = L’/ L
ts As ACI-3
(1.6L+L’)/1
distributed in
ty ratio has a
L & L’ respect
short = α . ws
hort = α.ws.L
short = 1.5 M
Tshort = 1.49 A
T/ts = (RFTs
= K ( α.L
here K= (1.5 *
nsidering units
α = (0.5
ts = (1.6
γs = 7.8
ads to the form
T/ts = 8.3 L.
For R =
For R =
T/ts =
he conclusion i
onal Jou
Eng
(
Fig. (1): T
pe of slabs. I
angular solid
According to
ts = [0.8 + Fy
quation could
rison between
L 1.
318 L/4
100 L/3
n both directi
minor effect
tively
L2
/ 10
M short / 0.85 Fy
As short . γs
short + RFTlong )
L2
+ β.L’2
)
1.49 * ws *
s and substitu
R – 0.15)
6L + L’)/100
5
mula below:
( R+5.2)(R+0
1, RFT
2, RFT
10.9 L ±2.0%
is valid in cas
urnal of
gineerin
(An ISO 3297:
Vol. 4,
DOI: 10.1568
Typical rebar d
II.
It is defined a
slab is the mo
o ACI-318, m
y/1600] / [36
be simplified
n ACI-318 & s
.0 1.2
3.0 L/37
8.5 L/35
ions according
on rebar perc
y . d
/ ts
γs) / ( 8.5 Fy
ting in the pre
0.4) / (R+1.6)2
T/ts = 1.333 *
T/ts = 1.285 *
%
e of two way
f Innova
ng and T
2007 Certified
Issue 5, Ma
80/IJIRSET.201
details for slab
SOLID SLA
as uniform th
ost common sh
inimum solid
+ 9 L’/L]
d to ts= (1.6
simplified for
2 1.4
7.0 L/33
5.7 L/33
g to rectangu
entage of soli
ws long = β
M long = β
As long = 1
RFTlong = 1
. d . ts ),
evious formul
β = 0.35 / R2
d = 0.9 ts
ws = 2.5 ts +
2
* 8.3 * L =
* 8.3 * L =
hollow block
ative Res
Technol
d Organization
ay 2015
15.0405002
bs as per ACI
ABS
hickness horiz
hape, it has fo
d slab thicknes
(in N,m
L + L’)/100
rmula to estim
4 1.6
.0 L/30.
.3 L/31.2
ularity ratio (R
id slabs (abou
. ws
.ws.L’2
/ 10
.5 M long / 0.8
.49 As long . γs
Mult. ≈ 1
as as follows:
2
+ 0.09L
11.1 L
10.7 L
slabs.
search i
logy
n)
315-99 [5]
zontal concret
our edges, and
ss meeting de
mm)
with error le
mate the thickn
1.8
0 L/27.6
2 L/29.4
R), the follow
ut ±2.0%). For
5 Fy . d
s
1.5 M working
L’ = R . L
fy = 3600
ISSN(Online):
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in Scien
te plate suppo
d each edge co
flection requi
ss than 10%,
ness of solid sl
2.0
6 L/25.7
4 L/27.8
wing derivation
r a solid slab
: 2319-8753
2347-6710
nce,
2663
orted by rigid
ould be fixed,
irement could
as shown in
labs
n proves that
with short &
d
d
n
t

4. Int
Copyright to I
Solid slabs th
about 5.0 to
between 6.0
A) One way
Slab
Slab
Ow
Tot
Ben
Mai
Mai
Sec
Shr
Tot
Tot
Min
Min
B) Two way
For
Slab
Slab
Ow
Tot
Ben
Stee
RFT
Shr
Tot
Tot
Min
Min
C) Cantileve
Slab
leng
Slab
Slab
Ow
Tot
Ben
Mai
Mai
Sec
Sec
Tot
Tot
Min
Min
ternatio
IJIRSET
hicker than 16
6.0 m accord
to 10.0m. The
solid slab (L’
b thickness
b depth
wn weight of sl
tal slab load
nding moment
in steel area
in RFT weigh
c. RFT weight
rinkage RFT w
tal RFT weigh
tal RFT weigh
n. slab thickne
n. RFT weight
y solid slab (L’
r 4 sides suppo
b thickness
b depth
wn weight of sl
tal slab load
nding moment
el area for one
T weight per m
rinkage RFT w
tal RFT weigh
tal RFT weigh
n. slab thickne
n. RFT weight
er solid slab
b thickness is
gth in the adja
b thickness
b depth
wn weight of sl
tal slab load
nding moment
in steel area
in RFT weigh
c. RFT area
c. RFT weight
tal RFT weigh
tal RFT weigh
n. slab thickne
n. RFT weight
onal Jou
Eng
(
6 cm should h
ding to rectang
e average wei
’=2L)
lab
t
ht per m2
per m2
weight per m2
ht per m2
ht per m3
ess = 10 cm, H
t per m3
’=L)
orted elastic re
lab
t in one dir.
e dir.
m2
in one dir.
weight per m2
ht per m2
ht per m3
ess = 10 cm, H
t per m3
s about L/10,
acent slab. RF
lab
t
ht per m2
per m2
ht per m2
ht per m3
ess = 10 cm, H
t per m3
urnal of
gineerin
(An ISO 3297:
Vol. 4,
DOI: 10.1568
have top mesh
gularity ratio.
ght of the top
ts (m)
d (m)
(t/m2
)
ws (t/m
M (m.t/m
As (cm2
(kg/m2
)
(kg/m2
)
(kg/m2
)
(kg/m2
)
(kg/m3
)
Hence, L min
(kg/m3
)
ectangular pla
ts (m)
d (m)
(t/m2
)
ws (t/m
M (m.t/m
As (cm2
(kg/m2
)
(kg/m2
)
(kg/m2
)
(kg/m3
)
Hence, L min
(kg/m3
)
the main RF
T in secondar
ts (m)
d (m)
(t/m2
)
ws (t/m
M (m.t/m
As (cm2
(kg/m2
)
As’ (cm
(kg/m2
)
(kg/m2
)
(kg/m3
)
Hence, L min
(kg/m3
)
f Innova
ng and T
2007 Certified
Issue 5, Ma
80/IJIRSET.201
h to resist shrin
The top mesh
mesh is abou
= 0
≈ 0
= 0
m2
) = 0
m’) = w
2
/m) = 1
= 1
= 2
= A
= S
= 0
≈ 3.0 m
= 1
ate, α,β=0.35
= 0
≈ 0
= 0
m2
) = 0
m’) = α
2
/m) = 1
= 1
= A
= S
= 0
≈ 4.0 m
= 1
FT is hook sh
ry direction is
= 0
≈ 0
= 0
m2
) = 0
m’) = w
2
/m) = 1
= 3
m2
/m) = 2
= 1
= S
= 3
≈ 1.0 m
= 1
ative Res
Technol
d Organization
ay 2015
15.0405002
nkage stresses
h is ranged be
ut 0.06L2
.
.01 (1.6 L + 2
.032 L
.036L * 2.5
.09L + 0.09L
ws. L2
/ 10
.5E+5 . M / 0
.49 As γs
0% Main RFT
Avenge value
Sum of weight
.460 L2
/ 0.03
2.8 * 3m
.01 (1.6 L + L
.023 L
.026L * 2.5
.065L + 0.09L
α.ws. L2
/ 10
.5E+5 . M / 0
.49 As γs
Avenge value
Sum of weight
.338 L2
/ 0.02
3.0 * 4m
hape, and the
20% of the m
.10 L
.08 L
.10 L * 2.5
.25L + 0.09L
ws. L2
/ 2
.5E+5 . M / 0
.55 As γs
x20% As
.00 As’ γs
Sum of weight
.337 L2
/ 0.10
1.1 * 1m
search i
logy
n)
s. For 18 cm t
etween 5φ6/m
2 L) = 0
= 0
= 0
= 0
.85 fy.d = 0
= 0
T = 0
= 0
ts/m2
= 0
36 L = 1
= 3
L ) = 0
= 0
L = 0
= 0
.85 fy.d = 0
= 0
= 0
ts/m2
= 0
26 L = 1
= 5
upper bars e
main steel at to
= 0
= 0
= 0
= 0
.85 fy.d = 1
= 3
= 0
= 0
ts/m2
= 3
00 L = 3
= 3
ISSN(Online):
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thick slab, the
m to 5φ10/m f
0.036 L
0.090 L
0.180 L
0.018 L3
0.285 L2
0.333 L2
0.066 L2
0.060 L2
0.460 L2
2.80 L
8.5
0.026 L
0.065 L
0.155 L
0.005 L3
0.118 L2
0.139 L2
0.060 L2
0.338L2
3.00 L
52.0
xtend 1.5 tim
op and bottom
0.10 L
0.250 L
0.340 L
0.170 L3
.072 L2
.000 L2
0.429 L2
0.337 L2
.337 L2
3.37 L
3.37
: 2319-8753
2347-6710
nce,
2664
e short span is
for short span
mes cantilever
m of the slab.
n
r

5. Int
Copyright to I
Hollow bloc
or foam bloc
used) and the
Due to the la
slabs (α+β=0
previous ass
addition to th
• Tot
• Ow
• Ow
• Ow
• Rib
• Spa
• Rib
• Top
A) One way
Slab
Slab
Ow
Tot
Ben
Mai
Mai
Rib
Top
Tot
Tot
Min
Min
B) Two way
Usi
Slab
Slab
Ow
Tot
Ben
Stee
RFT
Rib
Top
Tot
Tot
Min
Min
ternatio
IJIRSET
ck slab is a rib
cks. Due to th
e minimum to
ack of torsiona
0.80). It is a c
sumptions for
he following a
tal slab thickne
wn weight of on
wn weight of tw
wn weight of ca
b spacing is ab
an ranges betw
b ties range bet
p slab mesh ra
hollow block
b thickness
b depth
wn weight of sl
tal slab load
nding moment
in steel area
in RFT weigh
bs ties weight p
p slab mesh w
tal RFT weigh
tal RFT weigh
n. slab thickne
n. RFT weight
y hollow block
ng Markus di
b thickness
b depth
wn weight of sl
tal slab load
nding moment
el area for one
T weight per m
bs ties weight p
p slab mesh w
tal RFT weigh
tal RFT weigh
n. slab thickne
n. RFT weight
onal Jou
Eng
(
bbed slab form
e limitation of
otal depth of s
al rigidity and
common pract
r solid slab th
assumptions:
ess ≈ 1.5 slab
ne way H.B. s
wo ways H.B.
antilever H.B
bout 0.5m.
ween 5 to 10 m
tween φ6-300
anges between
k slab
lab
t
ht per m2
per m2
weight per m2
ht per m2
ht per m3
ess = 20 cm, H
t per m3
k slab (L’=L)
stribution para
lab
t in one dir.
e dir.
m2
in one dir.
per m2
weight per m2
ht per m2
ht per m3
ess = 20 cm, H
t per m3
urnal of
gineerin
(An ISO 3297:
Vol. 4,
DOI: 10.1568
III. HOLL
med using blo
f the block siz
slab is limited
d corner effect
tice to evalua
hickness, load
thickness of e
slab ≈ 0.5 own
slab ≈ 0.66 o
. slab ≈ 0.5 ow
m.
0 to φ8-200, av
n φ6-200 to φ1
ts (m)
d (m)
(t/m2
)
ws (t/m
M (m.t/m
As (cm2
(kg/m2
)
(kg/m2
)
(kg/m2
)
(kg/m2
)
(kg/m3
)
Hence, L min
(kg/m3
)
ameters, α,β=
ts (m)
d (m)
(t/m2
)
ws (t/m
M (m.t/m
As (cm2
(kg/m2
)
(kg/m2
)
(kg/m2
)
(kg/m2
)
(kg/m3
)
Hence, L min
(kg/m3
)
f Innova
ng and T
2007 Certified
Issue 5, Ma
80/IJIRSET.201
LOW BLOC
ocks of a mate
ze, the spacing
by 20cm. Ho
t, Markus para
ate the rebar w
d and continu
equivalent sol
n weight of eq
own weight of
wn weight of e
verage weight
10-200, averag
= 0
≈ 0
= 0
m2
) = 0
m’) = w
2
/m) = 1
= 1
= av
= av
= S
= 0
≈ 4.0 m
= 5
0.40
= 0
≈ 0
= 0
m2
) = 0
m’) = α
2
/m) = 1
= 1
= av
= av
= S
= 0
≈ 5.0 m
= 9
ative Res
Technol
d Organization
ay 2015
15.0405002
K SLABS
erial lighter th
g between rib
ollow block sla
ameters are us
weight ratio re
uity are still v
lid slab
quivalent solid
f equivalent so
equivalent sol
t/m2
is 0.040 L
ge weight/m2
.01 (1.6 L + 2
.050 L
.054 L * 2.5 *
.068L + 0.09L
ws. L2
/ 10
.5E+5 . M / 0
.49 As γs
verage value
verage value
Sum of weight
.300 L2
/ 0.05
.60 * 4m
.01 (1.6 L + L
.035 L
.039 L * 2.5 *
.065L + 0.09L
α.ws. L2
/ 10
.5E+5 . M / 0
.49 As γs
verage value
verage value
Sum of weight
.365 L2
/ 0.03
.3 * 5m
search i
logy
n)
han concrete, u
s is limited by
ab could be ei
sed to distribu
elative to the
valid in case
d slab
olid slab
lid slab
L2
is 0.075 L2
2 L)x 1.5 = 0
* 0.5 = 0
L = 0
= 0
.85 fy.d = 0
= 0
= 0
= 0
ts/m2
= 0
54 L = 5
= 2
L)x 1.5 = 0
* 0.66 = 0
L = 0
= 0
.85 fy.d = 0
= 0
= 0
= 0
ts/m2
= 0
39 L = 9
= 4
ISSN(Online):
ISSN (Print):
in Scien
usually hollow
y 0.6m (0.5m
ither one way
ute the load in
total thicknes
of hollow b
0.054 L
0.068 L
0.158 L
0.016 L3
0.160 L2
0.187 L2
0.040 L2
0.075 L2
0.300 L2
5.600 L
22.5
0.039 L
0.065 L
0.155 L
0.006 L3
0.089 L2
0.104 L2
0.080 L2
0.075 L2
0.365 L2
9.300 L
47.0
: 2319-8753
2347-6710
nce,
2665
w clay blocks
is commonly
or two ways.
the two ways
ss of slab. All
lock slabs in
y
n

6. Int
Copyright to I
C) Cantileve
Slab
Slab
Ow
Tot
Ben
Mai
Mai
Rib
Top
Tot
Tot
Min
Min
Flat slab is d
variable thic
equal spans
moment in th
depending on
The conside
reinforcemen
directions an
the four side
better to repr
A) Uniform
Acc
calc
Wh
Slab
Slab
Ow
Tot
For
Pos
Bot
Bot
Neg
Top
Top
Top
Tot
ternatio
IJIRSET
er hollow bloc
b thickness
b depth
wn weight of sl
tal slab load
nding moment
in steel area
in RFT weigh
bs ties weight p
p slab mesh w
tal RFT weigh
tal RFT weigh
n. slab thickne
n. RFT weight
defined as the
ckness (flat sla
flat slabs, a
he span and d
n the uniform
ered reinforce
nt above colu
nd top mesh w
es supported s
resent the rein
thickness flat
cording to sim
culated as foll
here L1 is the s
b thickness
b depth
wn weight of sl
tal slab load
r long direction
sitive bending
ttom steel area
ttom RFT wei
gative bending
p steel area
p col. RFT we
p mesh RFT w
tal RFT weigh
onal Jou
Eng
(
ck slab
lab
t
ht per m2
per m2
weight per m2
ht per m2
ht per m3
ess = 20 cm, H
t per m3
slab that is su
ab with dropp
simplified de
distribute it in
ity of slab thic
ement detail
umns designed
with area equa
slabs, flat & w
nforcement we
slab
mplified desig
ows:
Mo = ws.L1
2
Column & fi
M-ve max =
M+ve max =
span in consid
lab
n:
moment
a
ght per m2
g moment
eight per m2
weight per m2
ht per m2
urnal of
gineerin
(An ISO 3297:
Vol. 4,
DOI: 10.1568
ts (m)
d (m)
(t/m2
)
ws (t/m
M (m.t/m
As (cm2
(kg/m2
)
(kg/m2
)
(kg/m2
)
(kg/m2
)
(kg/m3
)
Hence, L min
(kg/m3
)
IV
upported direc
ped panels). A
esign method
both positive
ckness and the
is bottom m
d for the max
als to 25% of t
waffle slabs th
eight per cubic
gn method po
2
.L2/8,
ield strips wid
= 50% Mo (/s
= 30% Mo (/s
dered direction
ts (m)
d (m)
(t/m2
)
ws (t/m
M+ve (m
As (cm2
(kg/m2
)
M-ve (m
As (cm2
(kg/m2
)
(kg/m2
)
(kg/m2
)
f Innova
ng and T
2007 Certified
Issue 5, Ma
80/IJIRSET.201
= 0
≈ 0
= 0
m2
) = 0
m’) = w
2
/m) = 1
= 3
= av
= av
= S
= 1
≈ 1.5 m
= 1
V.FLAT SLA
ctly on the co
Also it could b
is stated in m
e and negative
e stiffness of m
mesh designed
ximum negati
the top reinfor
hickness is do
c meter as a fu
ositive and ne
dth = 0
strip) = w
strip) = w
n, L2 is the spa
= 0
≈ 0
= 0
m2
) = 0
m.t/m’) = w
2
/m) = 1
= 1
m.t/m’) = w
2
/m) = 1
= 0
= 0
= S
ative Res
Technol
d Organization
ay 2015
15.0405002
.15 L
.12 L
.15 L * 2.5 *
.188L + 0.09L
ws. L2
/ 2
.5E+5 . M / 0
.55 As γs
verage value
verage value
Sum of weight
.750 L2
/ 0.15
1.6 * 1.5m
ABS
olumns. It cou
e solid or ribb
most codes de
e in field and c
marginal beam
d for the max
ive moment a
rcement abov
ominated by th
unction of (L’
egative bendi
.5 L2
ws.L1
2
/ 8
ws.L1
2
/ 13.3
an perpendicu
.033 L’
.030 L’
.033L’ * 2.5
.083L’ + 0.09
ws. L’2
/ 13.3
.5E+5 . M+ve /
.00 As γs
ws. L’2
/ 8
.5E+5 . M-ve /
.3 * 0.3 As γs
.25 * 0.91 * A
Sum of weight
search i
logy
n)
= 0
0.5 = 0
L = 0
= 0
.85 fy.d = 0
= 1
= 0
= 0
ts/m2
= 1
50 L = 1
= 1
uld have unifo
bed (Waffle s
epends on cal
column strips
m.
ximum positi
and extends o
ve columns (se
he long direct
) instead of (L
ing moments
(/m)
(/m)
ular on L1
= 0
9L’ = 0
= 0
/ 0.85 fy.d= 0
= 0
= 0
/ 0.85 fy.d = 0
s = 0
As γs = 0
ts/m2
= 0
ISSN(Online):
ISSN (Print):
in Scien
0.15 L
0.188 L
0.278 L
0.139 L3
0.584 L2
.628 L2
0.040 L2
0.075 L2
.750 L2
1.60 L
7.40
rm thickness
lab). For unif
lculating the
according to
ive bending
one sixth the
eismic require
tion span (L’)
L) for flat and
in column st
0.083 L’
0.173 L’
0.013 L’3
0.219 L’2
0.172 L’2
0.022 L’3
0.364 L’2
0.026 L’2
0.065 L’2
0.265 L’2
: 2319-8753
2347-6710
nce,
2666
(flat plate) or
formly loaded
total bending
certain ratios
moment, top
span in both
ement).Unlike
). Hence, it is
d waffle slabs.
trip could be
r
d

7. Int
Copyright to I
For
Pos
Bot
Bot
Neg
Top
Top
Top
Tot
Sum
Tot
Tot
Min
Min
B) Flat slab w
For
drop
ben
Wh
Slab
Slab
Dro
Dro
Ave
Ow
Tot
For
Pos
Bot
Bot
Neg
Top
Top
Top
Tot
For
Pos
Bot
Bot
Neg
Top
Top
ternatio
IJIRSET
r short directio
sitive bending
ttom steel area
ttom RFT wei
gative bending
p steel area
p col. RFT we
p mesh RFT w
tal RFT weigh
mmation of bo
tal RFT weigh
tal RFT weigh
n. slab thickne
n. RFT weight
with dropped
r variable thick
p panel is abo
nding moment
here L1 is the s
b thickness
b depth
op panel thickn
op panel depth
erage thicknes
wn weight of sl
tal slab load
r long direction
sitive bending
ttom steel area
ttom RFT wei
gative bending
p steel area
p col. RFT we
p mesh RFT w
tal RFT weigh
r short directio
sitive bending
ttom steel area
ttom RFT wei
gative bending
p steel area
p col. RFT we
onal Jou
Eng
(
on:
moment
a
ght per m2
g moment
eight per m2
weight per m2
ht per m2
oth directions:
ht per m2
ht per m3
ess = 20 cm, H
t per m3
panels
kness flat slab
out 1.5 times t
s in column st
Mo = ws.L1
2
Column strip
M-ve max =
M+ve max =
span in consid
ness
h
ss
lab
n:
moment
a
ght per m2
g moment
eight per m2
weight per m2
ht per m2
on:
moment
a
ght per m2
g moment
eight per m2
urnal of
gineerin
(An ISO 3297:
Vol. 4,
DOI: 10.1568
M+ve (m
As (cm2
(kg/m2
)
M-ve (m
As (cm2
(kg/m2
)
(kg/m2
)
(kg/m2
)
(kg/m2
)
(kg/m3
)
Hence, L=L’ m
(kg/m3
)
b, drop panels
the slab thickn
trip could be c
2
.L2/8,
p width = 0.33
= 43.3% Mo (
= 23.3% Mo (
dered direction
ts (m)
d (m)
td (m)
dd (m)
tsavg (m
(t/m2
)
ws (t/m
M+ve (m
As (cm2
(kg/m2
)
M-ve (m
As (cm2
(kg/m2
)
(kg/m2
)
(kg/m2
)
M+ve (m
As (cm2
(kg/m2
)
M-ve (m
As (cm2
(kg/m2
)
f Innova
ng and T
2007 Certified
Issue 5, Ma
80/IJIRSET.201
m.t/m’) = w
2
/m) = 1
= 1
m.t/m’) = w
2
/m) = 1
= 0
= 0
= S
= 0
= 0
= 8
min ≈ 6.0 m
= 1
extend one si
ness. Accordi
calculated as f
3 L2, fiel
(/strip) = w
(/strip) = w
n, L2 is the spa
= 0
≈ 0
= 0
≈ 0
m) = (0
= 0
= 0
m2
) = 0
m.t/m’) = w
2
/m) = 1
= 1
m.t/m’) = w
2
/m) = 1
= 0
= 0
= S
m.t/m’) = w
2
/m) = 1
= 1
m.t/m’) = w
2
/m) = 1
= 0
ative Res
Technol
d Organization
ay 2015
15.0405002
ws. L2
/ 13.3
.5E+5 . M+ve /
.00 As γs
ws. L2
/ 8
.5E+5 . M-ve /
.3 * 0.3 As γs
.25 * 1.00 As
Sum of weight
.265 L’2
+ 0.2
.265 (L’2
+L2
)
.00 L’. [1 + (L
6.0 * 6m
ixth the span i
ing to simplifi
follows:
ld strip width =
ws.L1
2
/ 6.15
ws.L1
2
/ 11.4
an perpendicu
.028 L’
.025 L’
.040 L’
.037 L’
0.75 * 0.028 L
.031 L’
.031L’ * 2.5
.078L’ + 0.09
ws. L’2
/ 11.4
.5E+5 . M+ve /
.00 As γs
ws. L’2
/ 6.15
.5E+5 . M-ve/0
.3 * 0.3 As γs
.25 * 0.91 * A
Sum of weight
ws. L2
/ 11.4
.5E+5 . M+ve /
.00 As γs
ws. L2
/ 6.15
.5E+5 . M-ve/0
.3 * 0.3 As γs
search i
logy
n)
= 0
/ 0.85 fy.d= 0
= 0
= 0
/ 0.85 fy.d = 0
s = 0
γs = 0
ts/m2
= 0
265 L2
)/ 0.033 L’
L/L’)2
]
= 96.0
in both directi
ied design me
= 0.66 L2
(/m)
(/m)
ular on L1
L’ + 0.25 * 0.0
= 0
9L’ = 0
= 0
/ 0.85 fy.d= 0
= 0
= 0
0.85 fy.dd = 0
s = 0
As γs = 0
ts/m2
= 0
= 0
/ 0.85 fy.d= 0
= 0
= 0
0.85 fy.dd = 0
s = 0
ISSN(Online):
ISSN (Print):
in Scien
0.013 L’L2
0.219 L2
0.172 L2
0.022 L’L2
0.364 L2
0.026 L2
0.065 L2
0.265 L2
ions are used.
ethod positive
040 L’)
0.078 L’
0.168 L’
0.015 L’3
0.300 L’2
0.230 L’2
0.027 L’3
0.344 L’2
0.025 L’2
0.061 L’2
0.316 L’2
0.015 L’L2
0.300 L2
0.230 L2
0.027 L’L2
0.344 L2
0.025 L2
: 2319-8753
2347-6710
nce,
2667
Thickness of
and negative
f

8. Int
Copyright to I
Top
Tot
Sum
Tot
Tot
C) Waffle sla
Sam
dire
Tot
Ow
Rib
hen
Acc
as f
Wh
Slab
Slab
Ow
Tot
For
Pos
Bot
Bot
Neg
Top
Top
Top
Rib
Tot
For
Pos
Bot
Bot
Neg
Top
Top
Top
Rib
Tot
ternatio
IJIRSET
p mesh RFT w
tal RFT weigh
mmation of bo
tal RFT weigh
tal RFT weigh
Min. sla
Min. RF
ab
me criteria of
ections above
tal waffle slab
wn weight of w
b spacing is ab
nce, the averag
cording to cod
follows:
here L1 is the s
b thickness
b depth
wn weight of sl
tal slab load
r long direction
sitive bending
ttom steel area
ttom RFT wei
gative bending
p col. steel are
p RFT weight
p mesh RFT w
b ties weight p
tal RFT weigh
r short directio
sitive bending
ttom steel area
ttom RFT wei
gative bending
p steel area
p RFT weight
p mesh RFT w
b ties weight p
tal RFT weigh
onal Jou
Eng
(
weight per m2
ht per m2
oth directions:
ht per m2
ht per m3
ab thickness =
FT weight per
f uniform thic
columns.
thickness is t
waffle slab is 0
bout 0.8m. R
ge weight/m2
i
des, empirical
Mo = ws.L1
2
Column strip
M-ve max =
M+ve max =
span in consid
lab
n:
moment
a
ght per m2
g moment
ea
per m2
weight per m2
per m2
ht per m2
on:
moment
a
ght per m2
g moment
per m2
weight per m2
per m2
ht per m2
urnal of
gineerin
(An ISO 3297:
Vol. 4,
DOI: 10.1568
(kg/m2
)
(kg/m2
)
(kg/m2
)
(kg/m3
)
= 20 cm, Henc
m3
(kg/m3
)
ckness flat sla
the same of th
0.66 of the equ
Rib ties range
is about 0.025
method could
2
.L2/8,
p width = 0.33
= 43.3% Mo (
= 23.3% Mo (
dered direction
ts (m)
d (m)
(t/m2
)
ws (t/m
M+ve (m
As (cm2
(kg/m2
)
M-ve (m
As (cm2
(kg/m2
)
(kg/m2
)
(kg/m2
)
(kg/m2
)
M+ve (m
As (cm2
(kg/m2
)
M-ve (m
As (cm2
(kg/m2
)
(kg/m2
)
(kg/m2
)
(kg/m2
)
f Innova
ng and T
2007 Certified
Issue 5, Ma
80/IJIRSET.201
= 0
= S
= 0
= 0
= 1
e, L=L’ min ≈
= 2
ab are consid
he equivalent f
uivalent flat sl
between φ6-2
5L2
.
d be used for u
3 L2, fiel
(/strip) = w
(/strip) = w
n, L2 is the spa
= 0
≈ 0
= 0
m2
) = 0
m.t/m’) = w
2
/m) = 1
= 1
m.t/m’) = w
2
/m) = 1
= 0
= 0
= A
= S
m.t/m’) = w
2
/m) = 1
= 1
m.t/m’) = w
2
/m) = 1
= 0
= 0
= A
= S
ative Res
Technol
d Organization
ay 2015
15.0405002
.25 * 0.91 * A
Sum of weight
.316 L’2
+ 0.3
.316 (L’2
+L2
)
0.2 L’. [1 + (L
≈ 7.0 m
0.4 * 7.0m
dered. Solid p
flat slab with d
lab with dropp
200 to φ8-20
uniformly load
ld strip width =
ws.L1
2
/ 6.15
ws.L1
2
/ 11.4
an perpendicu
.040 L’
.037 L’
.040L’ * 0.66
.066L’ + 0.09
ws. L’2
/ 11.4
.5E+5 . M+ve /
.00 As γs
ws. L’2
/ 6.15
.5E+5 . M-ve /
.3 * 0.3 As γs
.25 * 0.91 * A
Average value
Sum of weight
ws. L2
/ 17.8
.5E+5 . M+ve /
.00 As γs
ws. L2
/ 5.3
.5E+5 . M-ve /
.3 * 0.3 As γs
.25 * 0.91 * A
Average value
Sum of weight
search i
logy
n)
As γs = 0
ts/m2
= 0
316 L2
)/ 0.031 L’
L/L’)2
]
= 143
part extends o
dropped panel
ped panel.
0 for spans r
ded equal span
= 0.66 L2
(/m)
(/m)
ular on L1
6 * 2.5 = 0
9L’ = 0
= 0
/ 0.85 fy.d= 0
= 0
= 0
/ 0.85 fy.d = 0
s = 0
As γs = 0
= 0
ts/m2
= 0
= 0
/ 0.85 fy.d= 0
= 0
= 0
/ 0.85 fy.d = 0
s = 0
As γs = 0
= 0
ts/m2
= 0
ISSN(Online):
ISSN (Print):
in Scien
0.061 L2
0.316 L2
one sixth the
l.
anges betwee
ns
0.066 L’
0.156 L’
0.015 L’3
0.205 L’2
0.160 L’2
0.025 L’3
0.341 L’2
0.024 L’2
0.061 L’2
0.025 L’2
0.270 L’2
0.015 L’L2
0.205 L2
0.160 L2
0.025 L’L2
0.341 L2
0.024 L2
0.061 L2
0.025 L2
0.270 L2
: 2319-8753
2347-6710
nce,
2668
span in both
en 7 to 12 m,
h

9. Int
Copyright to I
Sum
Tot
Tot
Results of th
S
One w
Two w
Cantile
One w
Two w
Cantile
Uniform th
Flat slab
W
Wh
Values in the
‐
‐
‐
‐
[1] BS-6399
[2] SEI/ASC
[3] BS-8110
[4] ACI-318
[5] ACI -315
[6] BS-CP-1
[7] David A
89312-12
[8] R. S. Nar
And Rule
[9] C. H. Go
ternatio
IJIRSET
mmation of bo
tal RFT weigh
tal RFT weigh
Min. sla
Min. RF
his study could
Table
Slab type
way solid slab
way solid slab
ever solid slab
way H.B. Slab
way H.B. Slab
ever H.B. Slab
hickness flat s
with drop pan
Waffle slab
here: L & L’ ar
e table (3) are
Residential &
Spans betwe
High strengt
Characteristi
-1-1996, “Loadin
CE-7-2005, “Mini
-1-1997, “Structu
-2005, “Building
5-1999, “Manual
10-1987,” Code
. Fanella and S.
29-0.
rayanan & A. Be
es For Buildings
oodchild, “Econom
onal Jou
Eng
(
oth directions:
ht per m2
ht per m3
ab thickness =
FT weight per
d be summariz
e 3: Estimated
Tota
thic
(
L
L/60 +
b L
L
L/40
b L
slab L’
nel L’/ 36
L’
re short & Lon
valid under th
& office build
een 4.0 to 12.0
th steel ( Fy =
ic concrete str
ng for buildings-P
imum Design Loa
ural use of concre
g Code Requireme
of standard pract
Of Practice For T
K. Ghosh, “Sim
eeby. “Designers'
And Structural F
mic Concrete Fra
urnal of
gineerin
(An ISO 3297:
Vol. 4,
DOI: 10.1568
(kg/m2
)
(kg/m3
)
= 25 cm, Henc
m3
V.
zed in the foll
economic qua
al Slab
ckness
(m)
L / 27
+ L’/100
L / 10
L / 18
+ L’/66
/ 6.6
’ / 30
& L’/ 24
’ / 24
ng span of the
he following c
ding (live load
0 m
3600 to 4000
rength (Fcu =
Part 1: Code of pr
ads for buildings
ete-Part 1: Code o
ents for Structura
tice for detailing r
The Structural Us
mplified Design R
Guide To En 19
ire Design”, © Th
ame Elements“,©
f Innova
ng and T
2007 Certified
Issue 5, Ma
80/IJIRSET.201
= 0
= 0
= 6
e, L=L’ min ≈
(kg/m3
)
CONCLUSI
owing table:
antities of diff
RC vol. /m2
(m3
/m2
)
L / 27
L/60 + L’/10
L / 10
L / 36
L/60 + L’/10
L / 13
L’ / 30
L’ / 32
L’ / 36
e slab respecti
conditions:
d up to 300 kg/
0 kg/cm2
)
250 to 350 kg
REFERENCES
ractice for dead a
and other Structu
of practice for des
al Concrete”, © (A
reinforced concre
se Of Concrete, D
Reinforced Concr
92-1-1and En 19
he authors and Th
British Cement A
ative Res
Technol
d Organization
ay 2015
15.0405002
.270 L’2
+ 0.2
.270 (L’2
+L2
)
.75 L’. [1 + (L
≈ 7.0 m
= 13.5 *
ION
fferent concret
2
R
(Gros
(
0
0
6.75 L’
ively
/m2
)
g/cm2
)
S
and imposed loads
ures”, © (ASCE)
sign and construc
ACI), ISBN 978-
ete structures”, ©
Design, materials
rete Buildings of
992-1-2, Eurocod
homas Telford L
Association 1997
search i
logy
n)
270 L2
)/ 0.040 L’
L/L’)2
]
* 7.0m = 9
te slab types (±
RFT / m3
ss RC vol.)
(kg/m3
)
1
1
3
5.6 L
9.3 L
11.6 L
8.0 L’. [
10.2 L’. [
. [1 + (L/L’)2
]
s”, © BSI, ISBN
, ISBN 0-7844-08
ction”, © BSI, ISB
0-87031-745-3.
© (ACI).
and workmanship
f Moderate Size
e 2: Design Of C
imited 2005, ISB
7, ISBN 0-7210-1
ISSN(Online):
ISSN (Print):
in Scien
95
±10%)
RFT
(Net R
(kg
13 L
13 L
33 L
11
14
23
1 + (L/L’)2
]
[1 + (L/L’)2
]
] 10.1 L’. [1
0-580-26239-1
831-9
BN 0-580-26208
p”,© BSI, ISBN
and Height”, ©
Concrete Structure
BN: 07277 3105 X
488-7
: 2319-8753
2347-6710
nce,
2669
T / m3
RC vol.)
g/m3
)
.2 L
4 L
3 L
1 + (L/L’)2
]
-1
0-580-07488-9
(PCA), ISBN 0-
es General Rules
X

10. INTERNATIONAL JOURNAL OF INNOVATIVE RESEARCH IN
SCIENCE, ENGINEERING AND TECHNOLOGY
ISSN (Online) : 2319 – 8753 ISSN (Print) : 2347 - 6710
PUBLICATION CERTIFICATE
This is to certify that
DR.AHMED M. EBID
Lecturer, Str. Dpt., Faculty of Eng. & Tech., Future Uni., Cairo, Egypt
Published a research paper titled
“ESTIMATING THE ECONOMIC QUANTITIESOF DIFFERENT CONCRETE SLAB TYPES”
in IJIRSET, Volume 4, Issue 5, May 2015
Editor-in-Chief
IJIRSET
Certificate No: V4I05C275
Date: 15th
May 2015
IJIRSET
Impact Factor: 5.442
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