Flexural safety cost of optimized reinforced

International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976
INTERNATIONAL JOURNAL OF ADVANCED RESEARCH IN
– 6480(Print), ISSN 0976 – 6499(Online) Volume 3, Number 2, July-December (2012), © IAEME
ENGINEERING AND TECHNOLOGY (IJARET)
ISSN 0976 - 6480 (Print)
ISSN 0976 - 6499 (Online)
Volume 3, Issue 2, July-December (2012), pp. 289-310
IJARET
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FLEXURAL SAFETY COST OF OPTIMIZED REINFORCED
CONCRETE SLABS

Mohammed S. Al-Ansari
Civil Engineering Department
Qatar University
P.O. Box 2713
Doha Qatar
Email: m.alansari@qu.edu.qa

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

289


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:
‫݁ܯ − ܿܯ = ܯ‬ (1)
Where
‫ = ܿܯ‬Design Moment Strength

‫ܧ = ݁ܯ‬xternal bending moment

‫ = ܯ‬Margin of safety

Setting the margin of safety M in percentages will yield the factor of safety (F.S.)

‫ܯ + 1 = .ܵ .ܨ‬ (2)
And ‫.ܵ .ܨ ∗ ݁ܯ = ܿܯ‬ (2-a)
‫)ܯ + 1( ∗ ݁ܯ = ܿܯ‬ (2-b)

290


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

0.85 f`c
Ac a/2
h d N.A. C = 0.85 f`c Ac
As
T = As fy

b N.A. = Neutral Axis
Fig. 1 Rectangular slab cross section with reinforcement

ܶ = ‫ݕ݂ ݏܣ‬ 3

‫ܿܣ ܿ`݂58.0 = ܥ‬ 3-a

‫ܽ ܾ = ܿܣ‬ 3-b

Having T = C from equilibrium, the compression area
஺௦∗ி௬
‫ = ܿܣ‬଴.଼ହ∗ி௖ 3-c

And the depth of the compression block

ி௬∗஺௦
ܽ = 3-d
଴.଼ହ∗ி௖∗௕

Thus, the design moment strength

௔
‫߮ = ܿܯ‬௕ ‫ ݕ݂ ݏܣ‬ቀ݀ − ଶቁ 3-e

291


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

߮௕ = Bending reduction factor
݂‫ = ݕ‬Specified yield strength of nonprestressed reinforcing
݂`ܿ = Specified compression strength of concrete
‫ = ݏܣ‬Area of tension steel
‫ = ܿܣ‬Compression 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

M

M

L
Fig. 2 Simple one way slab moment per running meter

292


M1

M M

M1

L L

Fig.3 Continuous one way slab moments per running meter

L1

L2

M2
M3
M6 M5
M1
M4
M5

M6

M4

M3
M1

Fig.4 Two way slab moments of internal panel

293


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 ‫߮ = )݀ ,ܾ ,ݏܣ(ܨ‬௕ ‫ ݕ݂ ݏܣ‬ቀ݀ − ଶቁ - Mc (4)

Must satisfy the following constraints:
௅ ௎
݀ௌ ≤ ݀ ≤ ݀ௌ (4-a)

ெ௜௡௜ ெ௔௫
‫ݏܣ‬ௌ ≤ ‫ݏܣ ≤ ݏܣ‬ௌ (4-b)

௙`௖ ଺଴଴
‫ ݏܣ‬ெ௔௫ = 0.75 ∗ ߚ1 ∗ ቀ ቁ ܾ݀ (4-c)
௙௬ ଺଴଴ା௙௬

ଵ.ସ
‫ ݏܣ‬ெ௜௡௜ = ቀ ௙௬ ቁ ܾ݀ (4-d)

ߚ1 = 0.85 ݂‫ܽܲܯ 03 ≤ ܿ`݂ ݎ݋‬ (4-e)

ߚ1 = 0.85 − 0.008(݂`ܿ − 30) ≥ 0.65 ݂‫ܽܲܯ 03 > ܿ`݂ ݎ݋‬ (4-f)
௅ ௅
Where ݀஻ and ݀஻ are slab depth lower and upper bounds the upper bound is equal to

ெ௜௡௜ ெ௔௫
300mm, one meter is constant slab width, and ‫ݏܣ‬஻ and ‫ݏܣ‬஻ 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

‫ܨܣ‬ௌ௅஺஻ = 2(20 ∗ ℎ) + 50 ∗ ܾ (5)

294


20mm sheathing Slab side

50mm Slab bottom (soffit)

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:

்௢௡
ܶ‫݉(݃ܣ ݐݏ݋ܥ ݈ܽݐ݋‬ଶ ) ‫݉(ݏܣ‬ଶ ) ߛ௦ ቀ ௠య ቁ ‫݉(ܨܣ‬ଶ )
= ∗ ‫+ ܿܥ‬ ∗ ∗ ‫+ ݏܥ‬ ∗ ‫)6( ݂ܥ‬
݉ଶ ݉ ݉ ݉ ݉

For simple one way slab

்௢௡
ܶ‫݉(݃ܣ ݐݏ݋ܥ ݈ܽݐ݋‬ଶ ) (‫݉()ݐݏܣ + ݏܣ‬ଶ ) ߛ௦ ቀ ௠య ቁ ‫݉(ܨܣ‬ଶ )
= ∗ ‫+ ܿܥ‬ ∗ ∗ ‫+ ݏܥ‬ ∗ ‫)7( ݂ܥ‬
݉ଶ ݉ ݉ ݉ ݉

For continuous one way slab

்௢௡
ܶ‫݉(݃ܣ ݐݏ݋ܥ ݈ܽݐ݋‬ଶ ) (‫݉()ݐݏܣ + ݏܣ‬ଶ ) ߛ௦ ቀ ௠య ቁ ‫݉(ܨܣ‬ଶ )
= ∗ ‫+ ܿܥ‬ ∗ ∗ ‫+ ݏܥ‬ ∗ ‫݂ܥ‬
݉ଶ ݉ ݉ ݉ ݉
்௢௡
ߚ ∗ ߙ(‫݉()1ݏܣ‬ଶ ) ߛ௦ ቀ ௠య ቁ
+ ∗ ∗ ‫)8( ݏܥ‬
݉ ݉

Where

Cc = Cost of 1 m3 of ready mix reinforced concrete in dollars

295


Cs = Cost of 1 Ton of steel in dollars

Cf = Cost of 1 m3timber in dollars
்௢௡
γୱ = Steel density = 7.843 ௠య

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.

(‫)ݐݏ݋ܥ ݁ݐ݁ݎܿ݊݋ܥ‬ ‫݉(݃ܣ‬ଶ )
‫= ܥܨܥ‬ = ∗ ‫)9( ܿܥ‬
݉ଶ ݉

ܵ‫ݐݏ݋ܥ ݈݁݁ݐ‬ ‫݉(ݏܣ‬ଶ ) ܶ‫݊݋‬
‫= ܵܨܥ‬ = ∗ ߛ௦ ൬ ଷ ൰ ∗ ‫)01( ݏܥ‬
݉ ଶ ݉ ݉

ܵ‫ݐݏ݋ܥ ݈݁݁ݐ‬ (‫݉()ݐݏܣ + ݏܣ‬ଶ ) ܶ‫݊݋‬
‫= 1ܵܨܥ‬ = ∗ ߛ௦ ൬ ଷ ൰ ∗ ‫)1 − 01( ݏܥ‬
݉ଶ ݉ ݉

ܾܶ݅݉݁‫ݐݏ݋ܥ ݎ‬ ‫݉(ܨܣ‬ଶ )
‫= ܶܨܥ‬ = ∗ ‫)11( ݂ܥ‬
݉ଶ ݉

And

்௢௧௔௟ ஼௢௦௧
ܶ‫= ܶܨܥ + ܵܨܥ + ܥܨܥ = ܨܥ‬ (12)
௠మ

்௢௧௔௟ ஼௢௦௧
ܶ‫= ܶܨܥ + 1ܵܨܥ + ܥܨܥ = 1ܨܥ‬ (12-1)
௠మ

Where

CFC = Cost Factor of Concrete

CFS = Cost Factor of Steel

296


CFS1 = Cost Factor of Steel - One Way Slab

CFT = Cost Factor of Timber

TCF = Total Cost Factor

TCF1 = Total Cost Factor – One Way Slab

۳‫ ܜܖ܍ܕܗۻ ܔ܉ܖܚ܍ܜܠ‬Me

Safety and Reliability:
1- Margin of safety M
2- ۲‫ ܐܜ܏ܖ܍ܚܜ܁ ܜܖ܍ܕܗۻ ܖ܏ܑܛ܍‬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

Fig. 6 The process of estimating Slab cost for a selected M

297


RESULT AND DISCUSSION

Base on the selected margin of safety M for external bending moment 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 external bending moment 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

design moment strength 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 M Mc Optimized Section Mo
kN.m % kN.m Dimensions kN.m
b As d Flexural
mm mm2 mm 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

298


START

Next i
i = 1 .. 680 Me Range

Next j
j = 0.01 .. 1.00 M Range

ࡹࢋ࢏ = ࢏ External Moment

ࡹ࢐ = ࢐ Safety Margin

ࡹࢉ࢏࢐ = ࡹࢋ࢏ ൫ࡹ࢐ + ૚൯ Design Moment Strength

New As,d
Initial Design Parameters (As, d)

Optimization

No
Constraints

yes
Material Quantities Steel As, Concrete Ag, Timber AF

Beam Cost Factors Equations 9-12
21

࢐>૚ No

yes

࢏ > ૟ૡ૙ No

yes

END

Fig. 7 The Process of Computing Cost Factors

299


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.

300


160

140 Qatar
USA
120
TCF ( $ / m 2)

100

80

60

40

20
0 200 400 600 800

Design moment strength Mc (kN. m)

Fig. 8 Total Material Cost of One Way Slab $

160

140 USA
Qatar
120
TCF ( $ / m 2)

100

80

60

40

20
0 200 400 600 800

Design moment strength Mc (kN.m)

Fig. 9 Total Material Cost of Two Way Slab $

301


Example 1: Simple one way reinforced concrete slab panel of 2 m by 6 meter with

଼଴ ௞ே.௠
external bending moment Me magnitude of and margin of safety of 25%,
௠

Fig. 10. To determine the slab cost, first the safety margin of 25% will require a design

ଵ଴଴ ௞ே.௠
strength moment Mc equal to (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.

L2
Ast
h

As
L1 L1

Simple One way Slab Panel Reinforcement Detailing

Fig. 10 Simple One Way Slab

Table 2. Material Cost of Simple One Way Slab
Me M Mc TotalCost Panel Total Cost
kN.m % kN.m Factor Area $
TCF1 m2
Qatar USA Qatar USA
80 25 100 81 85 12 972 1020
50 120 85 89 1020 1068
75 140 87 91 1044 1092

302


Example 2: Internal flat plate panel 6m by 8m with 4 external bending moments Me

ଷ଴ ௞ே∙௠ ଶଶ.ହ ௞ே∙௠ ଵଽ ௞ே∙௠ ଵହ ௞ே∙௠
, , , and margin of safety of 20%, Fig.
௠ ௠ ௠ ௠

11. To determine the slab cost, first the safety margin of 20% requires design moments

36 ݇ܰ∙݉ 27 ݇ܰ∙݉ ଵ଼ ௞ே∙௠
Mc equal to
݉
, ݉ , 23 ݇ܰ∙݉ ,
݉
(equation 2-b)
௠

respectively. Second the total cost factor TCF is determined base on maximum

ଷ଺ ௞ே∙௠
design moment Mc magnitude of , 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.

L1

Internal
L1
Panel

L

L

Floor Plan Reinforcement Detailing of Internal Panel

Fig. 11 Flat Plate

303


70

USA
60 Qatar

50

40
CFS ($ / m 2)

30

20

10

0

0 200 400 600 800


Fig. 12 Two way Slab Reinforcing Steel Cost $

Table 3. Material Cost of Flat Plate
Me M% Mc Cost Factor Panel Cost
Area Qatar USA
Qatar USA m2 $ S
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

304


Example 3: Internal continuous one way slab panel 3m by 7m with 2 external

ଷ଴ ௞ே∙௠ ଷ଼ ௞ே∙௠
bending moments Me , and margin of safety of 30%, Fig. 13.
௠ ௠

To determine the slab cost, first the safety margin of 30% requires design moments Mc

39 ݇ܰ∙݉ 49.4 ݇ܰ∙݉
equal to
݉
, ݉
(equation 2-b) respectively. Second the cost factors
CFC and CFT are determined base on maximum design moment Mc magnitude of

ସଽ.ସ ௞ே∙௠
, 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.

Internal
Panel
External 0.3 L1 typical
L2 Panel

Ast
h

As
L1 L1 L1 L1 L1 L1

Continuous One way Slab Panels Reinforcement Detailing

Fig. 13 Continuous One Way Slab

305


45
Maximum Depth of 300mm
40

35

30
( $ / m 2)

25
Qatar - CFC
Qatar - CFT
20
USA - CFC
USA - CFT
15

10

5
0 200 400 600 800

Design moment strength Mc (kN.m)

Fig. 14 Cost Factors CFC and CFT

Table 4. Material Cost of Continuous One Way Slab
Area Qatar USA
2
Qatar USA m $ S
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

306


80

70 Q
USA
60
CFS ($ / m 2)

50

40

30

20

10

0
0 200 400 600 800


Fig. 15 One Way Slab Reinforcing Steel Cost $

Example 4: Two-way solid slab internal panel 6m by 8m with 4 external bending

ଷ଴ ௞ே∙௠ ଶଶ.ହ ௞ே∙௠ ଵଽ ௞ே∙௠ ଵହ ௞ே∙௠
moments Me , , , and margin of
௠ ௠ ௠ ௠

safety of 20%, Fig. 16. To determine the slab cost, first the safety margin of 20%

36 ݇ܰ∙݉ 27 ݇ܰ∙݉
requires design moments Mc equal to
݉
, ݉ , 23 ݇ܰ∙݉ ,
݉

ଵ଼ ௞ே∙௠
(equation 2-b) respectively. Second the cost factors CFC and CFT are
௠

ଷ଺ ௞ே∙௠
determined based on maximum design moment Mc magnitude of , Fig.13.
௠

Third the cost factor of steel CFS is determined based on the moment’s magnitudes,

307


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.

0.3 L 1

L1

Internal
L1 0.3 L
Panel

L

L

Floor Plan Reinforcement Detailing of Internal Panel

Fig. 16 Two Way Solid Slab on Stiff Beams

308


Table 5. Material Cost of Two way Solid Slab
Area Qatar USA
Qatar USA m2 $ S
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.

309


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.

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