Flexural safety cost of optimized reinforced
Transcript of Flexural safety cost of optimized reinforced
International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976 – 6480(Print), ISSN 0976 – 6499(Online) Volume 3, Number 2, July-December (2012), © IAEME
289
FLEXURAL SAFETY COST OF OPTIMIZED REINFORCED CONCRETE SLABS
Mohammed S. Al-Ansari
Civil Engineering Department Qatar University P.O. Box 2713
Doha Qatar Email: [email protected]
ABSTRACT This paper presents an analytical model to estimate the cost of an optimized design of reinforced concrete slab sections base on structural safety. Flexural and optimized slab formulas for four types of reinforced concrete slabs simple one way slab, continuous one way slab, two - way solid slab on stiff beams, and flat plate that is a flat slab without drop panels and capital heads are derived base on ACI building code of design, material cost and optimization. The optimization constraints consist of upper and lower limits of depth and area of steel. Slab depth and area of reinforcing steel to be minimized to yield the optimal section. Optimized slab materials cost of concrete, reinforcing steel and formwork of all sections are computed and compared. Total cost factor TCF and other cost factors are developed to generalize and simplify the calculations of slab material cost. Numerical examples are presented to illustrate the model capability of estimating the material cost of the slab for a desired level of structural safety. Keywords: Margin of Safety, Depth, Concrete, Steel, Formwork, Optimization, Material cost, Cost Factors.
INTRODUCTION
Safety and reliability were used in the flexural design of reinforced concrete slabs of different sections using ultimate-strength design method USD under the
INTERNATIONAL JOURNAL OF ADVANCED RESEARCH IN ENGINEERING AND TECHNOLOGY (IJARET)
ISSN 0976 - 6480 (Print) ISSN 0976 - 6499 (Online) Volume 3, Issue 2, July-December (2012), pp. 289-310 © IAEME: www.iaeme.com/ijaret.asp Journal Impact Factor (2012): 2.7078 (Calculated by GISI) www.jifactor.com
IJARET
© I A E M E
International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976 – 6480(Print), ISSN 0976 – 6499(Online) Volume 3, Number 2, July-December (2012), © IAEME
290
provisions of ACI building code of design (1, 2, 3 and 4). Slabs are very important structure members and the most common shape of reinforced concrete slabs is rectangular cross section. Slabs with single reinforcement are the preliminary types of slabs and the reinforcement is provided near the tension face of the slab. Slab sizes are mostly governed by the ultimate external bending moment Me, and the optimized section of reinforced concrete slabs could be achieved by minimizing the optimization function of slab depth and reinforcing steel area (5, 6 and 7). This paper presents an analytical model to estimate the cost of an optimized design of reinforced concrete slab sections with yield strength of nonprestressed reinforcing 420 MPA and compression strength of concrete 30 MPA base on flexural capacity of the slab section that is the design moment strength and the sum of the load effects at the section that is the external bending moment Me. Slab Flexural and optimized formulas for four types of reinforced concrete slabs, simple one way slab, continuous one way slab, two - way solid slabs on stiff beams, and flat plate that is a flat slab without drop panels and capital heads are derived base on ACI building code of design, material cost and optimization. The optimization of slabs is formulated to achieve the best slab dimension that will give the most economical section to resist the external bending moment Me for a specified value of the design moment strength Mc base on desired level of safety. The optimization is subjected to the design constraints of the building code of design ACI such as maximum and minimum reinforcing steel area and upper and lower boundaries of slab dimensions (8, 9 and 10). The total cost of the slab materials is equal to the summation of the cost of the concrete, steel and the formwork. Total cost factor TCF, cost factor of concrete CFC, Cost Factor of steel CFS, and cost factor of timber CFT are developed to generalize and simplify the estimation of beam material cost. The slab is said to fail when the resistance of the slab is less than the action caused by the applied load. The slab resistance is measured by the design moment strength Mc and the slab action is measured by the external bending moment Me. The slab margin of safety is given by:
� = �� − �� (1) Where
�� = DesignMomentStrength
�� = �xternalbendingmoment
� = Marginofsafety Setting the margin of safety M in percentages will yield the factor of safety (F.S.)
�. �. = 1 + � (2) And �� = �� ∗ �. �. (2-a) �� = �� ∗ (1 + �) (2-b)
International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976 – 6480(Print), ISSN 0976 – 6499(Online) Volume 3, Number 2, July-December (2012), © IAEME
291
FLEXURAL SLAB FORMULAS
Four types of reinforced concrete slabs, simple one way slab, continuous one way slab,
two way solid slab on stiff beams, and flat plate that is a flat slab without drop panels
and capital heads with yield strength of nonprestressed reinforcing fy and compression
strength of concrete f`c. The design moment strength Mc results from internal
compressive force C and an internal force T separated by a lever arm. For the slabs
with single reinforcement, Fig. 1
Fig. 1 Rectangular slab cross section with reinforcement
$ = %&'( 3
) = 0.85'`�%� 3-a
%� = ./ 3-b
Having T = C from equilibrium, the compression area
%� = 01∗234.56∗27 3-c
And the depth of the compression block
/ = 23∗014.56∗27∗8 3-d
Thus, the design moment strength
�� = 98%&'( :; − <=>3-e
T = As fy
C = 0.85 f`c Ac
a/2
h d
N.A.
0.85 f`c
b N.A. = Neutral Axis
Ac
As
International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976 – 6480(Print), ISSN 0976 – 6499(Online) Volume 3, Number 2, July-December (2012), © IAEME
292
From flexural point of view a simple one way slab has a single moment, the
continuous one way slab has two moments, two way solid slabs and flat slabs have six
moments, four edge moments and two middle moments, Figs. 2,3,and 4.
Where
98= Bending reduction factor '( = Specified yield strength of nonprestressed reinforcing '`� = Specified compression strength of concrete %& = Area of tension steel %� = Compression area
; = Effective depth
/ =Depth of the compression block
. =Width of the slab cross section
ℎ =Total depth of the slab cross section
Ag = Gross cross-sectional area of a concrete member
Fig. 2 Simple one way slab moment per running meter
M
M
L
International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976 – 6480(Print), ISSN 0976 – 6499(Online) Volume 3, Number 2, July-December (2012), © IAEME
293
Fig.3 Continuous one way slab moments per running meter
Fig.4 Two way slab moments of internal panel
M1
M M
M1
L L
M 1
M 2
M 4
M 3
M 5 M 6
M 3
M 6
M 1
M 4
M 5
L 1
L 2
International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976 – 6480(Print), ISSN 0976 – 6499(Online) Volume 3, Number 2, July-December (2012), © IAEME
294
SLAB OPTIMIZATION
The optimization of slabs is formulated to achieve the best slab dimension that will
give the most economical section to resist the external bending moment (Me) for a
specified value of the design moment strength (Mc) base on selected margin of safety.
The optimization is subjected to the constraints of the building code of design ACI for
reinforcement and slab size dimensions. The optimization function of slab
Minimize�(%&, ., ;) = 98%&'( :; − <=> - Mc (4)
Must satisfy the following constraints:
;AB ≤ ; ≤ ;AD (4-a)
%&AEFGF ≤ %& ≤ %&AE<H (4-b)
%&E<H = 0.75 ∗ J1 ∗ K`7K3 :L44
L44MK3>.; (4-c)
%&EFGF =:N.OK3> .; (4-d)
J1 = 0.85'PQ'`� ≤ 30�S/ (4-e)
J1 = 0.85 − 0.008('`� − 30) ≥ 0.65'PQ'`� > 30�S/ (4-f)
Where ;WB and;WB are slab depth lower and upper bounds the upper bound is equal to
300mm, one meter is constant slab width, and%&WEFGF and %&WE<H are slab steel
reinforcement area lower and upper bounds.
SLAB FORMWORK MATERIALS
The form work material is limited to slab bottom of 50 mm thickness and two sides of
20 mm thickness each, Fig.5 .The formwork area AF of the slab
%�AB0W = 2(20 ∗ ℎ) + 50 ∗ . (5)
International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976 – 6480(Print), ISSN 0976 – 6499(Online) Volume 3, Number 2, July-December (2012), © IAEME
295
Fig. 5 Rectangular slab formwork material for sides and bottom
SLAB COST ANALYSIS
The total cost of the beam materials is equal to the summation of the cost of the
concrete, steel and the formwork per square meter:
$PY/Z)P&Y[= = %\([
=)[ ∗ )� + %&([
=)[ ∗
]1 :^_G`a >[ ∗ )& + %�([
=)[ ∗ )'(6)
For simple one way slab
$PY/Z)P&Y[= = %\([
=)[ ∗ )� + (%& + %&Y)([
=)[ ∗
]1 :^_G`a >[ ∗ )& + %�([
=)[ ∗ )'(7)
For continuous one way slab
$PY/Z)P&Y[= = %\([
=)[ ∗ )� + (%& + %&Y)([
=)[ ∗
]1 :^_G`a >[ ∗ )& + %�([
=)[ ∗ )'
+J ∗ b(%&1)([=)
[ ∗]1 :^_G`a >[ ∗ )&(8)
Where
Cc = Cost of 1 m3 of ready mix reinforced concrete in dollars
20mm sheathing Slab side
50mm Slab bottom (soffit)
International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976 – 6480(Print), ISSN 0976 – 6499(Online) Volume 3, Number 2, July-December (2012), © IAEME
296
Cs = Cost of 1 Ton of steel in dollars
Cf = Cost of 1 m3timber in dollars
γd = Steeldensity= 7.843 ^_G`a
Ast = Temperature and shrinkage area of steel
β = 1 for external panel and 2 for internal panel base on top reinforcement in the panel
α = Coefficient required to determine top reinforcement length and is equal to 0.3 for
ACI code
Total Cost Factor TCF and other cost factors are developed to generalize and simplify
the calculations of slab material cost.
)�) = ()Pf�Q�Y�)P&Y)[= =%\([=)
[ ∗ )�(9)
)�� = �Y��Z)P&Y[= =%&([=)
[ ∗ ]1 h$Pf[i j ∗ )&(10)
)��1 = �Y��Z)P&Y[= = (%& + %&Y)([=)
[ ∗ ]1 h$Pf[i j ∗ )&(10 − 1)
)�$ = $k[.�Q)P&Y[= =%�([=)
[ ∗ )'(11)
And
$)� = )�) + )�� + )�$ = ^_l<mn_1l
`o (12)
$)�1 = )�) + )��1 + )�$ = ^_l<mn_1l
`o (12-1)
Where
CFC = Cost Factor of Concrete
CFS = Cost Factor of Steel
International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976 – 6480(Print), ISSN 0976 – 6499(Online) Volume 3, Number 2, July-December (2012), © IAEME
297
CFS1 = Cost Factor of Steel - One Way Slab
CFT = Cost Factor of Timber
TCF = Total Cost Factor
TCF1 = Total Cost Factor – One Way Slab
Fig. 6 The process of estimating Slab cost for a selected M
pqrstuvwxyzsur Me
Safety and Reliability: 1- Margin of safety M
2- {s|}~uxyzsur�rtsu~r� Mc (equation 2-b)
Optimization: 1- Flexural formulas
2- Constraints
3- Slab dimensions and area of steel
Material quantities per square meter: 1- Concrete
2- Steel
3- Timber
Cost Analysis: 1- Concrete cost
2- Steel cost
3- Formwork cost
4- Total cost
International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976 – 6480(Print), ISSN 0976 – 6499(Online) Volume 3, Number 2, July-December (2012), © IAEME
298
RESULT AND DISCUSSION
Base on the selected margin of safety M for externalbendingmoment Me, the slabs
were analyzed and designed optimally to ACI code of design in order to minimize the
total cost of slabs that includes cost of concrete, cost of steel, and cost of formwork,
Fig. 6. To relate the safety margins to analysis, design, and cost of reinforced concrete
slabs, the slabs were subjected to different externalbendingmoment Me with
selected range of margins of safety. In order to optimize the slab section, a list of
constraints (equations 4-4f) that contain the flexural formulas (equations 3-3e) have to
be satisfied to come up with the most economical slab dimensions. The
designmomentstrength Mc (equation 2-b) that is selected base on margin of safety
is an input in the optimization function of the slab (equation 4). Once the optimum
slab thickness and reinforcing steel area are determined, the optimized section design
moment strength Mo is computed base on ACI flexural equation (equation 3-e) and
compared with the design moment strength Mc selected base on the margin of safety,
Table 1.
Table 1. Safety and optimization of reinforced concrete slabs Me
kN.m M %
Mc kN.m
Optimized Section Dimensions
Mo kN.m
b mm
As mm2
d mm
Flexural ACI - Equation
10 100 20 1000 450 125 20.667 20 50 30 540 155 30.781
50 20 60 750 225 62.134 100 40 140 1280 *300 140.335 150 33 200 1855 *300 200.24
International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976 – 6480(Print), ISSN 0976 – 6499(Online) Volume 3, Number 2, July-December (2012), © IAEME
299
Fig. 7 The Process of Computing Cost Factors
START
i = 1 .. 680 Me Range
j = 0.01 .. 1.00 M Range
��� = �External Moment
�� = � Safety Margin
���� = ������ + �� Design Moment Strength
Initial Design Parameters (As, d)
Optimization
Constraints No
New As,d
Material Quantities Steel As, Concrete Ag, Timber AF
Beam Cost Factors Equations 9-12 21
� > � No
� > ���
yes
yes
No
yes
Next j
Next i
END
International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976 – 6480(Print), ISSN 0976 – 6499(Online) Volume 3, Number 2, July-December (2012), © IAEME
300
Areas of Concrete, reinforcing steel and area of timber of the form work AF (equation
5) are computed based on optimum slab dimensions. The formwork area AF of the
slab cross section is made of two vertical sides of 20mm thickness and height of slab
total depth, slab bottom of 50 mm thickness and width equals slab width.
The total cost of slab material is calculated using equations 6,7 and 8, base on Qatar
and USA prices respectively of $100,$131 for 1 m3 of ready mix concrete,
$1070,$1100 for 1 ton of reinforcing steel bars, and $531.$565 for 1 m3 of timber,
(11). Total Cost Factor TCF, Cost Factor of concrete CFC, Cost Factor of steel CFS,
and Cost Factor of Timber CFT, are developed in equations 9 - 12 to generalize and
simplify the calculation of slab material cost. To determine the cost factors that are to
be used for estimating the slab material cost, an iterative cost safety procedure of
estimating the slab material cost base on safety and optimal criteria is applied to
external bending moment range of 5 kN.m to 680 kN.m as the maximum moment for
an upper bound of depth equals 300mm and a maximum area of steel base on f`c
equals 30MPa and fy equals 420Mpa.The margin of safety range of 1% to 100% for
each moment, Fig. 7. Once the TCF is determined, then the total cost is equal to the
product of the TCF value that corresponds to the moment Mc and the slab panel area,
Figs. 8 and 9. The following examples will illustrate the use of the proposed method.
International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976 – 6480(Print), ISSN 0976 – 6499(Online) Volume 3, Number 2, July-December (2012), © IAEME
301
0 200 400 600 800
20
40
60
80
100
120
140
160
Qatar
USA
Design moment strength Mc (kN. m) Fig. 8 Total Material Cost of One Way Slab $
0 200 400 600 800
20
40
60
80
100
120
140
160
USA
Qatar
Design moment strength Mc (kN.m) Fig. 9 Total Material Cost of Two Way Slab $
TC
F (
$ /
m 2
)
TC
F (
$ /
m 2
)
International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976 – 6480(Print), ISSN 0976 – 6499(Online) Volume 3, Number 2, July-December (2012), © IAEME
302
Example 1: Simple one way reinforced concrete slab panel of 2 m by 6 meter with
external bending moment Me magnitude of 54��.`
` and margin of safety of 25%,
Fig. 10. To determine the slab cost, first the safety margin of 25% will require a design
strength moment Mc equal to N44��.`
` (equation 2-b). Second the total cost factor
TCF is determined base on the Mc magnitude (Fig. 8) and it is equal to 81 and 85 base
on Qatar and USA prices respectively. Finally, the slab cost is equal to the product of
TCF and panel area yielding $972 in Qatar and $1020 in USA. The cost of simple one
way slab with different safety margins is shown in Table 2.
Simple One way Slab Panel Reinforcement Detailing Fig. 10 Simple One Way Slab
Table 2. Material Cost of Simple One Way Slab Me
kN.m M%
Mc kN.m
TotalCost Factor TCF1
Panel Area m2
Total Cost $
Qatar USA Qatar USA
80 25 100 81 85 12 972 1020 50 120 85 89 1020 1068 75 140 87 91 1044 1092
L 2
L 1 L 1
Ast
As
h
International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976 – 6480(Print), ISSN 0976 – 6499(Online) Volume 3, Number 2, July-December (2012), © IAEME
303
Example 2: Internal flat plate panel 6m by 8m with 4 external bending moments Me
i4��∙`` , ==.6��∙`` ,N���∙`` , N6��∙`` and margin of safety of 20%, Fig.
11. To determine the slab cost, first the safety margin of 20% requires design moments
Mc equal to 36��∙[[ , 27��∙[[ ,23��∙[[ , N5��∙`` (equation 2-b)
respectively. Second the total cost factor TCF is determined base on maximum
design moment Mc magnitude of iL��∙`
` , and TCF is equal to 58 and 60 base on
Qatar and USA prices respectively, Fig.9. Third the cost factor of steel CFS is
determined base on the remaining moment’s magnitudes, Fig.12. Finally, the flat plate
cost is equal to the product of cost factors and panel area yielding $ 3358.2 and
$3459.84 in Qatar and USA prices respectively, Table 3.
Floor Plan Reinforcement Detailing of Internal Panel Fig. 11 Flat Plate
L 1
L
Internal Panel
L 1
L
International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976 – 6480(Print), ISSN 0976 – 6499(Online) Volume 3, Number 2, July-December (2012), © IAEME
304
0 200 400 600 800
0
10
20
30
40
50
60
70
USA
Qatar
Design moment strength Mc (kN. m) Fig. 12 Two way Slab Reinforcing Steel Cost $ Table 3. Material Cost of Flat Plate
Me M% Mc Cost Factor
Panel Area m2
Cost Qatar
$ USA
S Qatar USA 30 20 36 *58 60 48 2784 2880
22.5 20 27 **4.3 4.4 206.4 211.2 19 20 23 **3.97 4.08 190.56 195.84
15 20 18 **3.6 3.7 172.8 178.08 Total Cost 3353.76 3465.12
*TCF **SCF
CF
S (
$ /
m 2
)
International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976 – 6480(Print), ISSN 0976 – 6499(Online) Volume 3, Number 2, July-December (2012), © IAEME
305
Example 3: Internal continuous one way slab panel 3m by 7m with 2 external
bending moments Me i4��∙`
` , i5��∙`` and margin of safety of 30%, Fig. 13.
To determine the slab cost, first the safety margin of 30% requires design moments Mc
equal to 39��∙[[ , 49.4��∙[[ (equation 2-b) respectively. Second the cost factors
CFC and CFT are determined base on maximum design moment Mc magnitude of
O�.O��∙`` , Fig.14. Third the cost factor of steel CFS is determined base on the
moment’s magnitudes, Fig.15. Finally, the Internal continuous one way slab cost is
equal to the product of cost factors and panel area yielding $ 1293.7 and $1363 in
Qatar and USA prices respectively, Table 4.
Continuous One way Slab Panels Reinforcement Detailing Fig. 13 Continuous One Way Slab
L 2
L 1 L 1
Ast
As
h
L 1 L 1
0.3 L1 typical
L 1 L 1
Internal Panel
External Panel
International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976 – 6480(Print), ISSN 0976 – 6499(Online) Volume 3, Number 2, July-December (2012), © IAEME
306
0 200 400 600 800
5
10
15
20
25
30
35
40
45
Qatar - CFC
Qatar - CFT
USA - CFC
USA - CFT
Design moment strength Mc (kN.m) Fig. 14 Cost Factors CFC and CFT Table 4. Material Cost of Continuous One Way Slab
Me M% Mc Cost Factor
Panel Area m2
Cost Qatar
$ USA
S Qatar USA 38 30 49.4 *24.5 25.4 21 514.5 533.4
**30.4 32.6 638.4 684.6 ***9.5 9.7 β(0.3)21=12.6 119.7 122.2
30 30 39 ***8.6 8.8 21 180.6 184.8 Total Cost 1453.2 1525
*CFC , **CFT, ***CFS1, β = 2
( $
/ m
2)
Maximum Depth of 300mm
International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976 – 6480(Print), ISSN 0976 – 6499(Online) Volume 3, Number 2, July-December (2012), © IAEME
307
0 200 400 600 800
0
10
20
30
40
50
60
70
80
Q
USA
Design moment strength Mc (kN. m) Fig. 15 One Way Slab Reinforcing Steel Cost $
Example 4: Two-way solid slab internal panel 6m by 8m with 4 external bending
moments Me i4��∙`
` , ==.6��∙`` ,N���∙`` , N6��∙`` and margin of
safety of 20%, Fig. 16. To determine the slab cost, first the safety margin of 20%
requires design moments Mc equal to 36��∙[[ , 27��∙[[ ,23��∙[[ , N5��∙`
` (equation 2-b) respectively. Second the cost factors CFC and CFT are
determined based on maximum design moment Mc magnitude of iL��∙`
` , Fig.13.
Third the cost factor of steel CFS is determined based on the moment’s magnitudes,
CF
S (
$ /
m 2
)
International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976 – 6480(Print), ISSN 0976 – 6499(Online) Volume 3, Number 2, July-December (2012), © IAEME
308
Fig.12. Finally, the two way solid slab cost is equal to the product of cost factors and
panel area yielding $3085 and $3435in Qatar and USA prices respectively, Table 5.
It is worth noting that in examples 3 and 4 CFC and CFT in step 2 were computed
instead of TCF base on maximum moment magnitude, because the maximum moment
reinforcement is top reinforcement and it had to be computed separately since it does
not extend over the panel length. Another point of interest is the comparison of the
cost of flat plate with two-way solid slab on stiff beam that were determined based on
the same external moments, yielding higher cost for the flat plate than two-way solid
slab on beams. Even though the calculation showed that the flat plate cost is higher,
the fact is flat plate is more economical because the cost of two-way solid slab on stiff
beam exclude the beams cost.
Floor Plan Reinforcement Detailing of Internal Panel Fig. 16 Two Way Solid Slab on Stiff Beams
L 1
0.3 L 1
L
0.3 L Internal Panel
L 1
L
International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976 – 6480(Print), ISSN 0976 – 6499(Online) Volume 3, Number 2, July-December (2012), © IAEME
309
Table 5. Material Cost of Two way Solid Slab
Me M% Mc Cost Factor
Panel Area m2
Cost Qatar
$ USA
S Qatar USA 30 20 36 *21.2 21.9 48 1017.6 1051.2
**30.01 32.23 1440 1547.04
***5 5.1 β(0.3)48=28.8 144 146.88 22.5 27 ***4.3 4.4 β(0.3)48=28.8 123.84 126.72 19 23 ***3.9 4.1 48 187.2 196.8 15 18 ***3.6 3.71 48 172.8 178.08
Total Cost 3085.44 3246.72 *CFC , **CFT, ***CFS, β = 2
CONCLUSIONS Flexural analytical model is developed to estimate the cost of slab materials base on selected margin of safety under various design constraints. Margin of safety have a direct impact on the slab optimum design for a desired safety level and consequently it has a big effect on beam material cost. Total cost factor TCF, cost factor of concrete CFC, Cost Factor of steel CFS, and cost factor of timber CFT are developed and presented as formulas to approximate material cost estimation of optimized reinforced concrete slab sections base on ACI code of design. Cost factors were used to produce slab cost charts that relate design moment strength Mc to the slab material cost for the desired level of safety. The model could be used base on selected safety margin for other codes of design by modifying equations of flexural and optimization, and checking the material cost estimates for different types of slabs. REFERENCES
1. Madsen, Krenk, and Lind. (1986). Methods of Structural Safety, Dover Publication, INC., New York.
2. Park, and Gamble. (2000). Reinforced Concrete Slabs, Wiley Publication, INC., New York.
3. Brown, R. H., (1975). “Minimum Cost Selection of One-way Slab Thickness” Structural Division, ASCE, Vol. 101, No. 12, pp.2586-2590
4. American Concrete Institute (ACI).(2008). “Building Code and Commentary”. ACI-318M-08, Detroit.
5. Ahmad, F., and Adeli, H. (2005). “Optimum cost design of reinforced concrete slab using neural dynamics model” Artificial
intelligence, Elsevier, Vol. 18, pp.65-72.
International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976 – 6480(Print), ISSN 0976 – 6499(Online) Volume 3, Number 2, July-December (2012), © IAEME
310
6. McCormac, and Brown. (2009). Design of Reinforced Concrete, Wiley, 8thedition. New Jersey.
7. Hassoun, and Al-Manaseer. (2005). Structural Concrete Theory and Design, Wiley, 3rd edition, New Jersey.
8. MATHCAD (2007).MathSoft Inc., 101 Main Street, Cambridge, Massachusetts, 02142, USA.
9. Merta, I. T., and Kravanja, S. (2010). “Cost Optimum Design of Reinforced Concrete Simply Supported One-Way Slabs ”, Earth and
Space Conference , ASCE, pp.2670-2678. 10. Singh, M. S., (1990). “Cost Model For Reinforced concrete Beam
And Slab Structures in Building” Journal of Construction
Enginnering and Management, Vol. 116, pp.54-67. 11. Waier, P.R., (2010). RSMEANS-Building Construction Cost Data,
68TH Annual Edition,RSMeans, MA 02364-3008, USA.