ASIAN JOURNAL OF CIVIL ENGINEERING (BUILDING AND HOUSING) VOL.

5, NOS 3-4 (2004)

PAGES 161-174

COST OPTIMIZATION OF REINFORCED CONCRETE

ELEMENTS

Khaled Alreshaid∗, Ibrahim M. Mahdi and Ehab Soliman

Department of Civil Engineering, Kuwait University, P.O. Box 5969, 13060 Kuwait

ABSTRACT

A computer-based systematic approach for optimizing material cost in reinforced concrete

elements is presented. This approach considers the current material cost in the trade-off and
selection of member dimensions and reinforcement design of concrete elements such as
beams and columns. The theoretical framework is to design reinforced concrete structure
based on the cost of available materials and not just on the availability of materials. The
windows-oriented computer program developed for this purpose would also be beneficial to
owners, designers and contractors interested in cost optimization of reinforced concrete
elements.

Keywords: cost optimization, reinforced concrete, reinforcement ratio

BACKGROUND

Optimization in concrete design, as a main building material component, attracted

attention of researchers and professional engineers. Literature on concrete design
shows considerable efforts in the optimization of concrete constituents and mixture
proportions [1], [2] and [3]. Early concrete design procedures, including the mixture
proportions, were based on consecutive trials from which an acceptable design and
composition were selected. The relationships established for optimization were
mainly between the mix composition and the compressive strength, Ref. [2].
Although optimization methods are often applied in concrete design and mixture
proportions, few of these methods consider the costs of both plain concrete and
reinforcement as functions.
Cost optimization remains one of the major factors in construction projects. It is
the responsibility of all members of the design-construction team to consider
analytical procedures for optimizing cost. Maximum impact to be gained on cost is
available at the earliest parts in the life-cycle of a project, Ref. [4]. A major area has
a great contribution to achieve cost optimization is the reinforced concrete system;
specifically during the design phase.

∗
E-mail address of the corresponding author: khaled@civil.kuniv.edu.kw
162 Khaled Alreshaid, Ibrahim M. Mahdi and Ehab Soliman

Cost considerations are lacking in many of these processes. A high influence on

cost can be achieved at the earliest parts in the life-cycle of a project, mainly the
design phase. One aspect of controlling cost during design comes with introduction
of the Design-To-Cost concept [5]. The basis of Design-To-Cost is to make design
converge on cost, instead of the other way around. Design-To-Cost has drawbacks of
extra time and cost of redesigning/re-bidding in the case of value engineering, and
the compromise of quality in the case of Design-To-Cost. In Kuwait, no systematic
procedure has been adopted for cost optimization in reinforced concrete design.
Most design offices do not advocate realistic estimate of material costs, even
though all the specifications set forth by design codes are adequately incorporated.
The practical applications of cost optimization in concrete design are still relatively
rare, and they are usually carried out based on manual consecutive trials of design.
Design offices have the difficult task of convincing their clients (owners) of the cost
efficiency of their designs. Value engineering measures are beginning to be
considered and carried out by major consultant offices for large public projects as an
avenue for cost reduction, but these offices usually ignore the reinforced concrete
systems of the facility under hand, Refs. [4 and 6].
Recent advancement and availability of cheap computing technology have
provided powerful tools for analysis and design of concrete structures and computer
model for optimization problems. Coupled with the extensive power of today’s
personal computers, the available design software are capable of efficiently
performing rapid interactive graphics and databases operations in reinforced concrete
design.
The advantages of computer technology have been incorporated in the
optimization of concrete design and mixture proportions; most notably is the use of
spreadsheets. Spreadsheets are user friendly and exceedingly powerful but are not
being exploited as much as they could be in structural engineering design, Ref. [7].
Spreadsheets and intelligent databases are being used for mix designs, Refs. [8] and
[9], and automation of concrete design, Refs. [1] and [10]. Other approaches used for
reinforced design and mixture proportions such as object-oriented, Ref. [11], and
constraint-based reasoning, Ref. [12], can use the powerful programming tools such
as Visual Basic and C++.
A quick and accurate systematic optimization approach based on the function of
cost in concrete design would reduce the cost of construction and enhance the
design process. This research is concerned with developing a tool that considers the
costs of reinforced concrete materials along with the specifications of the design
codes. The tool would integrate the processes of reinforced concrete design, quantity
take-off and cost estimating. A change in any of the parameters in one process would
have its effects on the other parameters of the other processes. The suggested
optimization approach could set the ground for further research in predicting optimal
design dimensions, mixture proportions and structural designs and systems.
The end product is an easy to use window-oriented tool that is beneficial
to owners, designers and contractors interested in reinforced concrete cost
optimization.
 COST OPTIMIZATION OF REINFORCED CONCRETE ELEMENTS... 163

OBJECTIVE

The objective of this article is to present a computer-based systematic approach for

optimizing materials cost in reinforced concrete elements.

PROPOSED SYSTEM FOR REINFORCED CONCRETE ELEMENTS

DESIGN AND COST OPTIMIZATION

The quantities of material for any structural system can be either computed on the past
records of completed buildings or alternatively from first principles by analysis, design and
computation of quantities, Ref. [13]. The accuracy in the case of the first method depends on
whether the various structural components of completed buildings were designed using
methods being adapted to present. The proposed system is dependant on the second method.
This is especially with the availability of the advanced computer systems that can carry out
©
the design process easily such as STAADIII . In addition, the proposed system considers
the updated material costs in the trade-off and selection of member dimensions and
reinforcement design of concrete elements such as isolated footings, beams, columns and
slabs. The theoretical framework is to design reinforced concrete elements based on the cost
of available materials and not just on the availability of materials, Figure 1.

Figure 1. Diagram of the proposed systematic for cost optimization in reinforced concrete
design
164 Khaled Alreshaid, Ibrahim M. Mahdi and Ehab Soliman

RESEARCH METHODOLOGY

The methodology of this research consists of five sequential stages as follows:

Literature review
Establish the concepts of reinforced concrete and its current design applications specified in the
ACI Building code [14]. Then, the relevant equations, parameters and methods of calculation for
the reinforced concrete systems are established. This study is focusing on the two structural
elements, namely columns and beams, to demonstrate the approach of the proposed system.

Cost data
Conduct a study of the materials cost of reinforced concrete for the past two years, and
establish change indicators for these costs. This would require cost data collection from
previous projects (from Kuwait as a practical example), current projects and reinforced
concrete materials suppliers. The collected data will be developed in a database to be used
for cost references.

Cost Parameters
Define the parameters in the reinforced concrete design process that affect the cost of
materials. This would include the dimensions (X, Y, Z) of the different reinforced concrete
elements, the area of reinforcements and ρ limit values, and the different types of concrete
and reinforcement available in the market.

Design phase
The design phase utilizes the automatic calculations and programming powers of the
spreadsheet environment with its Macros capabilities. The design phase consists of four
stages as follows:
i. Structural design computer program. This compute-aided design program
incorporates the reinforced concrete design procedures and equations as per the
ACI code. It automates the design process for accuracy and speed purposes.
ii. Quantity take-off computer program. This program measures the total quantities
of the reinforced concrete systems on the basis and their units of measure through
given set of dimensions and number of elements (inputs).
iii. Cost estimating computer program. The program uses the cost data from the
material cost database and the quantity take-off system to estimate total cost of
materials.
iv. Cost optimization support system. The three programs of reinforced concrete
design, quantity take-off and cost estimating, are integrated into a single system
that would provide different costs for different reinforced concrete designs.

Validation and Implementation

The functionality of the cost optimization support system is then tested in an iterative mode
to ensure reliability prior to final implementation. Upon successful testing, parametric cost
studies are conducted to determine the relationship between the structural element
dimensions and their costs.
 COST OPTIMIZATION OF REINFORCED CONCRETE ELEMENTS... 165

ANALYSIS AND RESULTS

The cost of reinforced concrete consists of two main elements, which includes the concrete
cost and the reinforcement cost. A design process aims to determine the values of concrete
element dimensions and steel area in addition to the steel ratio ρ. Recommended steel ratio ρ
is that ensures the minimum total cost. This section describes the calculation steps to obtain
the recommended steel ratio ρ and then a sensitivity analysis is introduced to demonstrate
the system range of applicability.

CALCULATION STEPS

1. Suppose the concrete structure element is exposed to external forces.

2. Use STAAD III to design the safe cross sections with variable sections elements (b-
section breadth, d-depth of the concrete cross section and steel ratio ρ). All the
designed sections will be safe under the supposed external forces based on ACI code.
3. Calculate the required concrete and steel quantities using spread sheet (Microsoft
Excel).
4. Calculate the cost of concrete and steel using the recent available database for
construction material costs.

A sample of the summarized calculations for getting the minimum cost for a beam
exposed to external bending moment of 300 kN.m is presented in Table 1. All the eight
sections are safe based on f′c= 25MPa and fy = 400 MPa. The calculation of total cost is the
summation of longitudinal steel bars cost and ready mix concrete for 100 meters of beam
lengths of prismatic section. Section number 2 has the least total cost which means that
section of 300mm breadth and 700 mm in depth is the optimum section for this external
bending moment of 300 kN.m.

Table 1. Sample of spread sheet calculation for beams

Conc. Steel Conc. Conc. Steel Total
Moment B H Ac As Steel unit
No. ρ Qty Qty unit Cost Cost Cost
(kN.m) (mm) (mm) (m2) (mm2) Price Price
(M3) (Kg) (KD) (KD) (KD)
(KD/m3) (KD/kg)
1 300 600 300 0.18 0.04 5853 18 4595 18 0.1 324 459.5 783.5
2 300 700 300 0.21 0.03 4856 21 3812 18 0.1 378 381.2 759.2
3 300 800 300 0.24 0.02 4498 24 3531 18 0.1 432 353.1 785.1
4 300 900 300 0.27 0.02 4293 27 3370 18 0.1 486 337.0 823.0
5 300 1000 300 0.3 0.02 4157 30 3263 18 0.1 540 326.3 866.3
6 300 1100 300 0.33 0.02 4059 33 3186 18 0.1 594 318.6 912.6
7 300 1200 300 0.36 0.01 3984 36 3128 18 0.1 648 312.8 960.8
8 300 1300 300 0.39 0.013 3898 39 3060 18 0.1 702 306.0 1008.
166 Khaled Alreshaid, Ibrahim M. Mahdi and Ehab Soliman

RECOMMENDED STEEL RATIO FOR COLUMN

Column concrete section is tested under four different compressive loads varying from 1500
kN to 3750 kN, which are common in residential (not high rise) buildings. Different safe
cross section can be obtained from STAAD III, for example different combinations of b, d, ρ
can safely resist a 1500 kN compressive force.

900

800

700

600

500
Cost

400

300

200

100

0
0.0 2.0 4.0 6.0 8.0
Steel reinforcement ratio (%)

Figure 2. Depicts the relationship between the steel ratio and the total cost of concrete
section

Figure (2) Relationship Between Steel Ratio % and Total Cost for Columns Subjected to
Different Compressive Loads
The steel ratio that ascertains the minimum cost for all sections is about 1.2 % of the
concrete cross section (average steel ration is 1.216, min, 1.07, max 1.61).
The trend at different levels is similar, where the total cost of the element increases with
increasing steel ratio. This trend is caused by the fact that the cost of steel is higher than that
of concrete.

SENSITIVITY ANALYSIS FOR COLUMNS

A sensitivity analysis is performed to assess the impact of variation in the cost of the
concrete and steel. In Figure 3, the range of steel and concrete cost varies between + 30% to
 COST OPTIMIZATION OF REINFORCED CONCRETE ELEMENTS... 167

–30% from the initial estimate cost. It is noticed in general that there is no remarked impact
of changes of steel and concrete cost on the recommended steel ratio ρ.
The steel recommended steel ratio for compressive load 1500 kN were increased to be
1.58 instead of 1.1 if the concrete cost increased by 20% and 30%. This can be due to the
percentage of cost contribution to the total cost in small compressive loads.

1.8
1.6
1.4 no changes
1.2 concret + 10%
concret +20%
steel ratio

1
concret +30%
0.8
steel +10%
0.6 steel + 20%
0.4 steel + 30%
0.2
0
1500 2250 3000 3750
Compressive Loads (kN)

Figure 3. Changes in original cost estimate

RECOMMENDED STEEL RATIO FOR BEAMS

Four bending moments of 300, 500, 700 and 900 kN.m were chosen as external forces to
check which of the safe sections will ascertain the minimum cost. The range of moments
from 300 kN.m to 900 kN.m is representing the range of forces that most of residential
building beams can expose to. The beam sections that can be safe under each of these
external forces were calculated. Beam breadths ranged from 200 to 900 mm.
The total cost was calculated for varied cases of moment, breadth, steel ratio ρ and depth.
Figures (4 to 7) show the relationship between total cost of the cross section and the steel
ratio ρ. The figures show a similar trend for all sections that total cost is high for small
values of steel ratio, and then decreases to the minimum at the recommended steel ratio, and
then increases again.
168 Khaled Alreshaid, Ibrahim M. Mahdi and Ehab Soliman

Figure 4. Total costs for different breadths for beam cross sections exposed to 300 kN.m the
minimum total cost for each checked moment is represented in Table (2).

Figure 5. Total costs for different breadths for cross sections exposed to 500 kN.m
 COST OPTIMIZATION OF REINFORCED CONCRETE ELEMENTS... 169

Figure 6. Total costs for different breadths for cross sections exposed to 700 kN.m

Figure 7. Total costs for different breadths for cross sections exposed to 900 kN.m
170 Khaled Alreshaid, Ibrahim M. Mahdi and Ehab Soliman

The Average recommended ρ from all sections that can establish the optimum cost is
0.01535; maximum recommended is 0.02056 and the minimum is 0.01. In other words the
recommended ρ range from 0.01 to 0.02.
Table 2 represents the recommended design criteria. Designers can use this table to
establish the optimum beam cross section that can achieve the minimum cost for each
external load. The designer may choose another section to match with architecture or any
other requirements, it can use another section and determine the percentage of cost increase
due to minimum cost by using figures such as Figure 8 for moment 900 MN.
The recommended value for ρ may be sensitive for the current cost of steel and concrete,
so sensitivity analysis was conducted to test the effect of changes of these estimate values.

M= 900 kNm

2.00
1.80 b =200
Percentage of cost increase

1.60 b = 300
1.40 b = 400
b = 500
1.20
b = 600
1.00 b = 700
0.80 b = 800
0.60 b = 900

0.40
0 0.01 0.02 0.03 0.04 0.05
Steel Ratio

Figure 8. Percentage of total cost increase over the optimum cost

SENSITIVITY ANALYSIS FOR BEAMS

The total cost is recalculated due to changes in the estimate cost of steel and concrete by-
30% to +30%.
As shown in Figure 9, there is no impact for changing steel and concrete cost if the
inflation affects the cost of both materials by the same percentage.
If the steel cost changed and the cost of concrete does not change, the average
recommended steel ratio ρ is between 0.012 to 0.0198, while, if the concrete and steel costs
 COST OPTIMIZATION OF REINFORCED CONCRETE ELEMENTS... 171

change in opposite directions, the average recommended steel ratio ρ will be between 0.0129
to 0.0185.
The recommended steel ratio is averaged between 0.01 and 0.02 in all cases.

Table 2. Recommended design criteria for external bending moment

Moment Beam breadth Beam Height Steel Ratio

(kN.m) (mm) (mm) (ρ)
200 600 0.01682
300 500 0.01705
400 500 0.01207
300 500 400 0.01739
600 400 0.01391
700 400 0.01162
800 400 0.00999
900 300 0.02056
200 800 0.01439
300 600 0.01924
400 600 0.01348
500 500 0.01705
500
600 500 0.01366
700 500 0.01141
800 400 0.01832
900 400 0.0158
200 900 0.01586
300 800 0.01326
400 700 0.01335
500 600 0.01544
700
600 600 0.01243
700 500 0.01705
800 500 0.01447
900 500 0.01259
200 1000 0.01635
300 800 0.01802
400 700 0.01816
500 700 0.01381
900
600 600 0.01682
700 600 0.01394
800 500 0.01984
900 500 0.01705
172 Khaled Alreshaid, Ibrahim M. Mahdi and Ehab Soliman

Figure 9. Sensitivity analysis for steel ratio ρ

CONCLUSIONS

Cost indicators are important during the design phase to minimize the construction cost.
Excellent designers must have the capacity for organization and management to conduct the
process of design so that it includes cost consideration during the design process. This
research presented a model for cost optimization of reinforced concrete design. The focus
has been on the reinforced concrete elements since they represent about one third of the total
cost of the constructed facility.
 COST OPTIMIZATION OF REINFORCED CONCRETE ELEMENTS... 173

Implementation of the suggested reinforced concrete cost optimization model for material
cost data obtain from Kuwait’s market resulted in the following steel ratio
recommendations:
Recommended steel ratio ρ for column design is 1.216 % of the concrete cross section.
Recommended steel ratio ρ for beam design is about 0.015% of the concrete cross
section.
The above design recommendations will vary with any changes in the cost of reinforced
concrete materials. The developed system is updated with most recent market cost of
reinforced concrete materials; thus ensuring valid, meaningful and up-to-date results of
design recommended ratios.

Acknowledgement: The author acknowledges the financial support of this project, Project
# EV-01/99 by Kuwait University- Research Administration.

REFERENCES

1. Balling and Richard, J., How to optimize reinforced concrete systems. Proceedings of
the Symposium on Structural Engineering in Natural Hazards Mitigation. ASCE
(1993), Irvine, CA, USA.
2. Brandt, A. M. Optimization Methods for Material Design of Cement-Based
Composites. Modern Concrete Technology 7. E& FN SPON, (an imprint of Rout
ledge), USA, 1998.
3. Mather, K. and Rashwan, Sh., Model for ready-mix concrete optimization,
Proceedings of the 1997 Annual Canadian Society for Civil Engineering. Part 2,
Canada, 1997.
4. Young III and James, A. Design phase cost control. Transactions of American
Association of Cost Engineers, Morgantown. ISSN: 10747397 (1997) Page 24-27.
5. Vitaliano, Wm. J. Three design-to-cost myths. SAVE Annual Proceeding. New
Orleans. USA, 1994.
6. Kwakye, A. A Construction Project Administration in Practice. (Addison Wesley
Longman), USA, 1997.
7. Goodchild, C. H. and Lupton, J. (1999) Spreadsheets and the structural engineer. The
Structural Engineer, 77(1999)326-334.
8. de Larrard, F. and Sedran, T. Computer-Aided Mix Design: Predicting Final Results The
Magazine of the American Concrete Institute 18(1996)178-186.
9. Ganju, T. N. Spread sheeting Mix Designs. The Magazine of the American Concrete
Institute 18(1996)187-198.
10. Walden, N. Lee and Wilkerson, Steve. Automation of Concrete Design. The Magazine of
the American Concrete Institute. 18(1996)148-156.
11. Kulkarni, A. B. and Rojiani, K. B. Object-oriented approach for reinforced concrete
design. Proceedings of the 1st Congress on Computing in Civil Engineering. Part 1 of
2. ASCE., pp. 161-168. New York, USA, 1994.
174 Khaled Alreshaid, Ibrahim M. Mahdi and Ehab Soliman

12. Lucas, W. K.; Roddis, W.M. Kim. Constraint-based reasoning for optimal concrete design
and detailing. Proceedings of the 12th Conference on Analysis and Computation. ASCE,
pp. 154-165, New York, USA, 1996.
13. Singh, S., Cost Model for approximate cost estimation of structure systems in
commercial high rise buildings, thesis submitted to the National University of
Singapore, un fulfillment of the requirements for the degree of Doctor of Philosophy,
Singapore, 1986.
14. ACI, 318/98, Code of the American Concrete Institute. Detroit: American Concrete
Institute, USA, 1999.