Flexural safety cost of optimized reinforced concrete slabs

22
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

Transcript of Flexural safety cost of optimized reinforced concrete slabs

Page 1: Flexural safety cost of optimized reinforced concrete slabs

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

Page 2: Flexural safety cost of optimized reinforced concrete slabs

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)

Page 3: Flexural safety cost of optimized reinforced concrete slabs

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

Page 4: Flexural safety cost of optimized reinforced concrete slabs

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

Page 5: Flexural safety cost of optimized reinforced concrete slabs

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

Page 6: Flexural safety cost of optimized reinforced concrete slabs

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)

Page 7: Flexural safety cost of optimized reinforced concrete slabs

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)

Page 8: Flexural safety cost of optimized reinforced concrete slabs

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

Page 9: Flexural safety cost of optimized reinforced concrete slabs

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

Page 10: Flexural safety cost of optimized reinforced concrete slabs

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

Page 11: Flexural safety cost of optimized reinforced concrete slabs

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

Page 12: Flexural safety cost of optimized reinforced concrete slabs

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.

Page 13: Flexural safety cost of optimized reinforced concrete slabs

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

)

Page 14: Flexural safety cost of optimized reinforced concrete slabs

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

Page 15: Flexural safety cost of optimized reinforced concrete slabs

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

Page 16: Flexural safety cost of optimized reinforced concrete slabs

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

)

Page 17: Flexural safety cost of optimized reinforced concrete slabs

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

Page 18: Flexural safety cost of optimized reinforced concrete slabs

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

Page 19: Flexural safety cost of optimized reinforced concrete slabs

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

)

Page 20: Flexural safety cost of optimized reinforced concrete slabs

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

Page 21: Flexural safety cost of optimized reinforced concrete slabs

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.

Page 22: Flexural safety cost of optimized reinforced concrete slabs

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.