- Email: [email protected]
A knowledge-based approach for the design of spread footings
C,,,,,pu,ers & Structures Vol. 30. No. 3. pp. 72%735. Printed in Great Britain.
1988
$: 1988 Civil-Comp
004s7949jas $3.00 + 0.00 Ltd and Pergamon Press plc
A KNOWLEDGE-BASED APPROACH FOR THE DESIGN OF SPREAD FOOTINGS NABIL
A. B.
YEHIA~
AHMAD
and
H.
EL-HAJJ~
Structural Engineering Department, Faculty of Engineering, Cairo University, Giza, Egypt
Abstmc-A
knowledge-based system for the design of the general layout of reinforced concrete spread footings is presented. A database., sorting previous design cases, is used to assist the user in obtaining different solutions for each problem. Plotting capability is also incorporated to show all the reinforcement details which could be obtained from a design office. The analysis of single and double footing is carried out using the conventional methods whereas the mat foundation is treated as a plate on elastic foundations and is analyzed by the bending theory of plates using the finite element method.
1. INTRODUCTION The
use of computers has drastically altered the practice of civil engineering particularly in the area of analysis. There are however, many aspects of engineering for which the present programs provide insufficient assistance. These are the ill-structured problems in which the individual engineer’s expertise, acquired from years of experience, plays a key role in the area of design. Such expertise is of particular significance in deciding which design is to be selected, and interpreting the results produced by the design algorithm. In structural design problems, although the process is subject to well defined rules of theory and practice, there are usually several possible correct answers to the same problem. The combinational nature of the variables prevents the investigation of all possible designs. In general, a solution path likely to produce an optimum or near optimum result is taken. This process is highly dependent on the experience and memory of the engineer. Clearly, tools which can help expedite the process of searching for good solutions are beneficial. A powerful tool can be realized if the knowledge of an expert can be incorporated into it. A knowledge-based expert system (KBES) is a tool of such kind. It is a computer program which contains the knowledge and heuristics of one or more experts and simulates the performance of those experts in problem solving in their domain. At a global level, an expert system is also an effective means of collecting, organizing, preserving and propagating valuable knowledge which has been developed and accumulated by experts through years of experience [l]. An early attempt in this area was made by Roony and Smith [2] for designing simply supported steel beams with the limitation to standard wide flange sections. Since the wide flange rolled sections are already listed in steel tables, a static database was
sufficient. The approach was mainly concerned with minimizing the search time spent in finding an acceptable design. Adeli [3] also outlined an algorithm for the development of a computer expert system for CAD of structures with reference to stiffened steel plate girders where the problem solving approach was based on the rule-based system example [4]. In their study, Roberts and Saiidi [5] addressed the bending design of reinforced concrete continuous beams using the moment as the primary search criterion and the frequency of usage as the secondary one. A knowledge based menu driven system for the design of reinforced concrete rectangular short columns under the action of combined axial and bending loads has been recently presented by Yehia and Bechara [6] where a more generalized approach for search criteria is adopted. Since the search criteria depend upon the available information about the specific consideration at hand it allows the user to obtain valid and practical designs for ill-formulated problems. This study discusses the development of a computer program called FOOT. The purpose of this program is to provide the groundwork for the development of a powerful computer-based system to aid in the process of substructure type selection and design. It is actually presenting a part of a long term objective for the development of an expert system which might be able to design the foundation of any structure where the loads and site conditions are the only input. The present work is mainly concerned with the spread footing design providing the ability to Select the appropriate footing type for a given map of columns distribution and loading. Directly design the single footing and combined footing selected earlier. However, a mesh has to be defined by the user in order to design a mat foundation. Provide the user with a plotting of the selection made, and the reinforcement details of every single and double footing.
t Formerly at Civil Engineering Department, University of Pittsburgh, Pittsburgh, PA, U.S.A. 729
NABIL
130
A. B. YEHIAand AHMADH. EL-HAJJ
4. Build a database
for previous cases of design, based on the best selection specified by the user. 2. PROGRAM
DESCRDTION
For any given set of loads and geometry in reinforced concrete structure design, there could be several correct answers. There are well defined methods to determine those. However, the best choice does not necessarily correspond to the one with minimum material cost. To an experienced designer, the best alternative is the one which is: (1) more practical in terms of placing of steel and concrete; (2) less confusing to the draftsman, the engineer in charge of shop drawings and the site engineer; and (3) less likely to lead to problems in design for anchorage of reinforcement. No simple formula or guideline can be found to qualify these parameters [2]. The program described in this paper is an attempt to take most of these parameters into account. However, the best alternative is considered as the one which satisfies the user requirements. A database is employed for this purpose. Each execution of the program will add a new deposit to the databank, making it richer. This phenomenon is similar to the pattern
of human experience accumulation. Algorithmic routines were designed to select the appropriate type of footing for a given set of loads, material properties and bearing capacity of soil. Furthermore, they select the flexural reinforcement required for factored moments in accordance with the ACI-Code [7] limitations. A databank consisting of previous execution results is utilized to assist the user in choosing the appropriate selection of reinforcement. This selection is based on one of the following criteria.
(4 Select the minimum area of steel required by the (b)
w
ACI-Code, which in turn maximizes the depth of concrete section. Select the bar size which furnishes the most exact flexural area of reinforcement required. Maximize the area of steel by reducing the depth of the concrete section to the limit specified by the AC1 (shear criterion).
The program may be divided into four basic components: the decision making segment, the analysis and design of flexural reinforcement of footing, the plotting segment and the database. The flow among different sections is shown in Fig. 1. The program is capable of handling large problems
DOCUMENT AVAILABLE
Fig. I. Basic flow of program FOOT.
ALL
The design of spread footings defined by the user. In such cases a general map of column distribution is requested by the main program in the form of matrix data consisting of the coordinates of columns from a two coordinate system. With these inputs fed to the main program, module DECIDE will select the appropriate footing type, and the design process will be transferred to module DESIGN. If a mat foundation is encountered, the user will be asked to define his mesh for the finite element analysis of the mat. Nevertheless, the program will supply the user with the approximate thickness and area to be furnished for the mat. Moreover, the user can select the type of footing he is willing to design by requesting an interactive data supply to the program. An inappropriate selection made by the user will not be accepted by the program, and a message in that sense will be displayed. The cross sectional areas and diameters of standard rebars are already stored into the program, allowing it to determine different bar sizes that would satisfy the flexural strength requirements and the ACI-Code limitations. Shear reinforcement is not considered here. The program output takes the form of a table consisting of all possible choices which fall inside the code limits on different parameters such as steel ratio, spacing, development length, etc. It should be noted here that a search will be made for every single and double footing, seeking a matching solution from previous executions. If such a matching solution exists, the user will be notified with the solution displayed. However, the user may accept the proposed solution or reject it calling for a full new run of the program. 3. PROGRAM
FLOW
The program consists of four main modules and some different functional subroutines. The function of each module is briefly discussed in the following. (See [8] for a more complete description.) 3.1. Module MAIN This module is the skeleton of the program which accepts the data directly from the user or from a data file prepared earlier. It performs some unit transformations and generates a code matrix which will be used later by module DECIDE to reach a decision. The code number and its location in the code matrix depends on the distance from center line to center line of each of the two columns and the footing dimensions of each column. The main program does not have a databank. Databanks are only provided in module DESIGN which will be described later. 3.2. Module DECIDE Module DECIDE represents the inference engine, and receives the code matrix and the numbering system of columns from MAIN. A ‘zero’ in the code matrix represents a discontinuity between two footings, which implies the identification of single
731
footing. A ‘one’ represents an overlapping of two columns along the x-axis or the y-axis, depending on the position of the ‘one’ in the code matrix. The search inside the code matrix takes the form of an angle moving row by row along the x-axis. A column previously identified may change its identification depending on its nearby column current identification. Figure 2 shows a general map, prepared by the user, which consists of nine columns, one of which is fictitious. The fictitious column does not exist on the site map, however, it is required to be included in the data file, so that the columns distribution will always be rectangular. Ignoring the position of a fictitious column will affect the performance of the program, resulting in a safe decision, but not an accurate one. For instance, if column 5 in Fig. 2 is ignored, column 6 would take its place in the datafile, then, it will be. checked with columns 2, 4 and 8 for combination possibilities, where it is more likely to be combined with column 3 or column 9 if needed. 3.3. Module GRAPH This module utilizes a group of subroutines provided by DISPLA, an integrated software system and language available on the DEC-SYSTEM 10 and VAX/VMS libraries. GRAPH will provide the user with a general map for column distribution and later on with the map of footing distribution. It also contains some arithmetic calculation procedures to be utilized by DISPLA software to plot the reinforcement details of single and double footings. Only the best choice will be plotted. 3.4. Module DESIGN This module receives the Input from MAIN or interactively from the user and starts the search for similar cases in its databank. If a similar case is found from previous executions, the criterion for which the case was being selected will be displayed. The intelligent segment of the program identifies only the best selection based on the user’s criteria. At this point the user may request a complete detail of the design items which shows all the available design possibilities in a matrix form and displays the best choice among these possibilities. The best choice will then be sent to module GRAPH to plot the reinforcement details. Through this process, the databank expands every time the program is used, and future selections are likely to improve. It should be mentioned that for the design of combined footing more input items will be requested, and so will be the output. At least five different locations of reinforcement will be taken care of in the databank and, of course, the search for similar solutions imposes some more elements to be checked. To perform the analysis of mat foundation, a program was adapted from the system described in [9]. The program utilizes a nonconforming element for the analysis of flexural plates based on the
NABIL
732
0.0
4.0
1.0
A. B. YEHLAand
l2.0
le.0
20.0
AHMAD
24.0
H. EL-HAJJ
a.0
X ROWS OF COWMNS
szo
SC0
so.0
I
10
Fig. 2. Column distribution map.
classical Kirchhoff theory and it provides an automatic mesh generator for rectangular regions with rectangular elements. The results obtained from the mat analysis are sent to an algorithmic subroutine to sort the moments and their locations on the mesh for the completion of the design process. 4. DATABASE
To prepare a databank, it is necessary to know the input and output parameters to be included there. These parameters are primarily the design variables. The structure of the databank affects the search time for best choice. In this study, the guide parameters are placed in first range, the best selection in the second, the user’s criteria in the third, and finally the execution date. In general, the database consists of two main segments, the intelligent segment and the databank segment. 4.1. The intelligent segment The intelligent segment is utilized to consult the database and determine the available designs for the current case. Therefore, it selects the one that agrees with the user’s criteria. This process involves a search through the databank that primarily satisfies the factored loads and the material properties, and secondarily the user’s criteria. The best selection need not necessarily match all the parameters. The follow-
ing tolerance limits were used for different variables: 3% difference in factored loads, 0% difference in each of the bearing capacity, steel yield strength and the 28-day concrete strength, 1 in. difference in concrete thickness, and 3 in. difference in footing lateral dimensions. 4.2. The databank The search process inside the databank is performed quite similarly to a commercial banking machine. An identification number is always used to start with. The identification number, as in this case, might be the design selection criteria as specified by the user. Having the ID entered, the rest of the process might take one of the following two forms. (a) Compatible previous design. This form of search type inside the databank will be performed every time the program is executed. Having selected the design criteria, the material properties, and the bearing capacity of soil, a check for every item will SUCC~Ssively take place. For instance, the factored load input will be compared with the one deposited first; if a difference within the tolerance limit is obtained, the comparison will continue for another item (yield strength of steel might be the other item). However, a complete agreement in value is required now otherwise the searching process will jump to the next set of data. If the comparison result comes out positively, the user will be notified that a similar case was
The design of spread footings
133
handled by the program on the basis of certain criteria and on a specific date. A message in that sense will be displayed on the terminal and documented on an output file for later use to obtain a hardcopy. On the other hand, complete design details could be documented if requested by the user. However, only the best choice will be plotted in order to save CPU time. (b) Design safety check. An alternative way of using the built-in database is to check the safety of an existing structure. The elements needed for that check are the existing dimensions of the proposed footing, the material properties, the bearing capacity of soil, and the area of steel furnished in different directions. The search in this case will take a longer time since more parameters are to be checked. Nevertheless, the safety of the structure depends on some more vita1 elements, such as the current condition of the structure, which are out of scope of this study. 5. EXAMPLE
PROBLEM
Fig. 4. Generated mesh for mat of columns 1, 2 and 4.
In this example, the user inputs a map of columns, as shown in Fig. 2, with the factored loads assumed as 391.5, 381, 288, 379, 0.0, 488, 299, 262.5 and 488 kips for columns l-9 respectively. The selection decisions as concluded by the program are shown in Fig. 3. The design process takes place for single and double footings first until it is altered by the presence of a mat foundation. A mesh is then prepared, as
20.0
X ROWS OF
shown in Fig. 4, to start the program again for the three columns mat and loaded by the loads of columns 1,2 and 4 as nodal loads normal to the plane of the mat. The thickness of the mat is assumed to be 1.5 ft with elasticity modules, shear modulus, and Poissons ratio of 452,700 ksf, 19,512 ksf and 0.16
24.0
COLUMNS
Fig. 3. Selected footings map.
22.0
26.0
40.0
NABILA. B. YEHM and W
734
H. EL-HAJJ
Column No. 9 use minimum of 3in. concrete cover
r’-‘-‘-‘--’ a
3
‘---‘--I a I I -n
8.6ft
I
Fig. 5a. Sample detail of single footing.
Column No.3 and column No.6 use minimum of 3in. concrete cover P
0
1
II
.a ____ ____*I!I_-_-
____ 1:+_-_______
______ *_
II .I
7.I
2i
_._.-.-.-.-.-
!;
.I
I’
I
t
ia
i0
20.3ft Section c-c
b
.208amNa5ut 6in. . 20 9arsNa5 ot 6in. _o ~,_____ _______--_-__ 20 Bare Nra5at_______. 6in .______________ 5 l3are NaS at 6.2in. . ____-____- ---------. 4 Bare No.6 at 6.2 in.c c____________ _______
Fig. 5b. Sample detail of double footing.
The design of spread footings
respectively. The subgrade modulus is assumed to be 50 kcf. A maximum moment of 158 kip. ft/ft is found to exist between columns 1 and 4. A minimum reinforcement of 0.72in2/ft, as recommended by ACI-Code is therefore adopted by the program. A hard-copy of the designed single and double footing may be requested as shown in Figs 5a and 5b. However, this facility is not yet available for mat foundation types. 6. CONCLUSION
The paper presented herein can be considered as a preliminary study into the possibility of building an expert system that eventually will be capable of selecting and designing any type of spread footing. Previous programs that dealt with footing design were almost always limited to a single type of footing. This, however, is impractical, since a footing design problem is most likely to have a column load map where a decision is to be made before the real design steps can take place. Therefore, it was the aim of the present paper to develop a program capable of making decisions and, furthermore, capable of handling single cases of design. There is, however, one part of the problem yet to be worked out. If the program delivers a decision that consists of mat foundations, the execution will be halted until a finite element mesh is supplied by the user. Some of the published works that were referred to earlier [l-5] have based their choices on the frequencies of previous acceptances. This sometimes resulted in limiting the options available to the user because after a certain number of program executions, the databank tends to become strongly biased toward certain selections [5]. The concept discussed in this paper allows the user to select certain design criterion and a best choice corresponding to the most matching area of steel will be based on that criterion. This process will enlarge the databank so that, at certain times, it might contain all the design choices for a certain design case. However, the selec-
C.A.S. ,013-T
135
tion criterion used in the present work minimizes or maximizes either one of the concrete sections or the steel area. Other criteria such as total material weight, market availability or uniformity of steel bar size have not been taken into consideration in the present work. For the part of single and double footing design, the program is so efficient that it uses very little CPU time. However, the explanation facilities, presented by the documented plots, enlarge the memory occupancy so much that the program could not be run interactively when plots are asked for. Another item of interest is the computer language utilized by the program. While most of the programs developed in this area are written in LISP, FORTAN(commonly known as an engineering-oriented language) proved to be efficient in performing the search inside the databank.
REFERENCES 1.
2. 3.
4. 5.
6.
7. 8.
9.
S. J. Fenves, M. L. Maher and D. Sriram; Expert System: CE Potential. Civil Engineering/AXE 54, u7 (1984). M. F. Roony and S. E. Smith, Artificial intelligence in simple beam design. Strut. Div. AXE 108,2344-2348 (1984). G. Adeli, Artificial intelligence in simple beam design. Proceedinns. Fifth ASCE/EMD Snecialitv Conference. Laramie, Wyoming, USA, Augusi 1984.. P. H. Winston, Artificial Intelligence, 2nd Ed. Addison-Weseley, London, U.K. P. Roberts and M. Saiidi, Artificial intelligence for design of R/C beams. 2nd National Conference on Microcomputers in Civil Engineering, Orlando, Florida (1984). N. Yehia and R. Bechara, A simple knowledge-based design of reinforced concrete columns. Concrete Int. 10, PI-55 (1988). AC1 318-83, Building code requirements for reinforced concrete. Detroit, Michigan (1983). A. H. El-Hajj, Knowledge-based system for the design of spread footing. MSc. Thesis, Civil Engineering Dept, University of Pittsburgh, PA (1986). R. E. Dick and N. Yehia, Finite element analysis of plates on elastic foundation-automated approach. Civ. Engng Sys. (to appear).
1988
$: 1988 Civil-Comp
004s7949jas $3.00 + 0.00 Ltd and Pergamon Press plc
A KNOWLEDGE-BASED APPROACH FOR THE DESIGN OF SPREAD FOOTINGS NABIL
A. B.
YEHIA~
AHMAD
and
H.
EL-HAJJ~
Structural Engineering Department, Faculty of Engineering, Cairo University, Giza, Egypt
Abstmc-A
knowledge-based system for the design of the general layout of reinforced concrete spread footings is presented. A database., sorting previous design cases, is used to assist the user in obtaining different solutions for each problem. Plotting capability is also incorporated to show all the reinforcement details which could be obtained from a design office. The analysis of single and double footing is carried out using the conventional methods whereas the mat foundation is treated as a plate on elastic foundations and is analyzed by the bending theory of plates using the finite element method.
1. INTRODUCTION The
use of computers has drastically altered the practice of civil engineering particularly in the area of analysis. There are however, many aspects of engineering for which the present programs provide insufficient assistance. These are the ill-structured problems in which the individual engineer’s expertise, acquired from years of experience, plays a key role in the area of design. Such expertise is of particular significance in deciding which design is to be selected, and interpreting the results produced by the design algorithm. In structural design problems, although the process is subject to well defined rules of theory and practice, there are usually several possible correct answers to the same problem. The combinational nature of the variables prevents the investigation of all possible designs. In general, a solution path likely to produce an optimum or near optimum result is taken. This process is highly dependent on the experience and memory of the engineer. Clearly, tools which can help expedite the process of searching for good solutions are beneficial. A powerful tool can be realized if the knowledge of an expert can be incorporated into it. A knowledge-based expert system (KBES) is a tool of such kind. It is a computer program which contains the knowledge and heuristics of one or more experts and simulates the performance of those experts in problem solving in their domain. At a global level, an expert system is also an effective means of collecting, organizing, preserving and propagating valuable knowledge which has been developed and accumulated by experts through years of experience [l]. An early attempt in this area was made by Roony and Smith [2] for designing simply supported steel beams with the limitation to standard wide flange sections. Since the wide flange rolled sections are already listed in steel tables, a static database was
sufficient. The approach was mainly concerned with minimizing the search time spent in finding an acceptable design. Adeli [3] also outlined an algorithm for the development of a computer expert system for CAD of structures with reference to stiffened steel plate girders where the problem solving approach was based on the rule-based system example [4]. In their study, Roberts and Saiidi [5] addressed the bending design of reinforced concrete continuous beams using the moment as the primary search criterion and the frequency of usage as the secondary one. A knowledge based menu driven system for the design of reinforced concrete rectangular short columns under the action of combined axial and bending loads has been recently presented by Yehia and Bechara [6] where a more generalized approach for search criteria is adopted. Since the search criteria depend upon the available information about the specific consideration at hand it allows the user to obtain valid and practical designs for ill-formulated problems. This study discusses the development of a computer program called FOOT. The purpose of this program is to provide the groundwork for the development of a powerful computer-based system to aid in the process of substructure type selection and design. It is actually presenting a part of a long term objective for the development of an expert system which might be able to design the foundation of any structure where the loads and site conditions are the only input. The present work is mainly concerned with the spread footing design providing the ability to Select the appropriate footing type for a given map of columns distribution and loading. Directly design the single footing and combined footing selected earlier. However, a mesh has to be defined by the user in order to design a mat foundation. Provide the user with a plotting of the selection made, and the reinforcement details of every single and double footing.
t Formerly at Civil Engineering Department, University of Pittsburgh, Pittsburgh, PA, U.S.A. 729
NABIL
130
A. B. YEHIAand AHMADH. EL-HAJJ
4. Build a database
for previous cases of design, based on the best selection specified by the user. 2. PROGRAM
DESCRDTION
For any given set of loads and geometry in reinforced concrete structure design, there could be several correct answers. There are well defined methods to determine those. However, the best choice does not necessarily correspond to the one with minimum material cost. To an experienced designer, the best alternative is the one which is: (1) more practical in terms of placing of steel and concrete; (2) less confusing to the draftsman, the engineer in charge of shop drawings and the site engineer; and (3) less likely to lead to problems in design for anchorage of reinforcement. No simple formula or guideline can be found to qualify these parameters [2]. The program described in this paper is an attempt to take most of these parameters into account. However, the best alternative is considered as the one which satisfies the user requirements. A database is employed for this purpose. Each execution of the program will add a new deposit to the databank, making it richer. This phenomenon is similar to the pattern
of human experience accumulation. Algorithmic routines were designed to select the appropriate type of footing for a given set of loads, material properties and bearing capacity of soil. Furthermore, they select the flexural reinforcement required for factored moments in accordance with the ACI-Code [7] limitations. A databank consisting of previous execution results is utilized to assist the user in choosing the appropriate selection of reinforcement. This selection is based on one of the following criteria.
(4 Select the minimum area of steel required by the (b)
w
ACI-Code, which in turn maximizes the depth of concrete section. Select the bar size which furnishes the most exact flexural area of reinforcement required. Maximize the area of steel by reducing the depth of the concrete section to the limit specified by the AC1 (shear criterion).
The program may be divided into four basic components: the decision making segment, the analysis and design of flexural reinforcement of footing, the plotting segment and the database. The flow among different sections is shown in Fig. 1. The program is capable of handling large problems
DOCUMENT AVAILABLE
Fig. I. Basic flow of program FOOT.
ALL
The design of spread footings defined by the user. In such cases a general map of column distribution is requested by the main program in the form of matrix data consisting of the coordinates of columns from a two coordinate system. With these inputs fed to the main program, module DECIDE will select the appropriate footing type, and the design process will be transferred to module DESIGN. If a mat foundation is encountered, the user will be asked to define his mesh for the finite element analysis of the mat. Nevertheless, the program will supply the user with the approximate thickness and area to be furnished for the mat. Moreover, the user can select the type of footing he is willing to design by requesting an interactive data supply to the program. An inappropriate selection made by the user will not be accepted by the program, and a message in that sense will be displayed. The cross sectional areas and diameters of standard rebars are already stored into the program, allowing it to determine different bar sizes that would satisfy the flexural strength requirements and the ACI-Code limitations. Shear reinforcement is not considered here. The program output takes the form of a table consisting of all possible choices which fall inside the code limits on different parameters such as steel ratio, spacing, development length, etc. It should be noted here that a search will be made for every single and double footing, seeking a matching solution from previous executions. If such a matching solution exists, the user will be notified with the solution displayed. However, the user may accept the proposed solution or reject it calling for a full new run of the program. 3. PROGRAM
FLOW
The program consists of four main modules and some different functional subroutines. The function of each module is briefly discussed in the following. (See [8] for a more complete description.) 3.1. Module MAIN This module is the skeleton of the program which accepts the data directly from the user or from a data file prepared earlier. It performs some unit transformations and generates a code matrix which will be used later by module DECIDE to reach a decision. The code number and its location in the code matrix depends on the distance from center line to center line of each of the two columns and the footing dimensions of each column. The main program does not have a databank. Databanks are only provided in module DESIGN which will be described later. 3.2. Module DECIDE Module DECIDE represents the inference engine, and receives the code matrix and the numbering system of columns from MAIN. A ‘zero’ in the code matrix represents a discontinuity between two footings, which implies the identification of single
731
footing. A ‘one’ represents an overlapping of two columns along the x-axis or the y-axis, depending on the position of the ‘one’ in the code matrix. The search inside the code matrix takes the form of an angle moving row by row along the x-axis. A column previously identified may change its identification depending on its nearby column current identification. Figure 2 shows a general map, prepared by the user, which consists of nine columns, one of which is fictitious. The fictitious column does not exist on the site map, however, it is required to be included in the data file, so that the columns distribution will always be rectangular. Ignoring the position of a fictitious column will affect the performance of the program, resulting in a safe decision, but not an accurate one. For instance, if column 5 in Fig. 2 is ignored, column 6 would take its place in the datafile, then, it will be. checked with columns 2, 4 and 8 for combination possibilities, where it is more likely to be combined with column 3 or column 9 if needed. 3.3. Module GRAPH This module utilizes a group of subroutines provided by DISPLA, an integrated software system and language available on the DEC-SYSTEM 10 and VAX/VMS libraries. GRAPH will provide the user with a general map for column distribution and later on with the map of footing distribution. It also contains some arithmetic calculation procedures to be utilized by DISPLA software to plot the reinforcement details of single and double footings. Only the best choice will be plotted. 3.4. Module DESIGN This module receives the Input from MAIN or interactively from the user and starts the search for similar cases in its databank. If a similar case is found from previous executions, the criterion for which the case was being selected will be displayed. The intelligent segment of the program identifies only the best selection based on the user’s criteria. At this point the user may request a complete detail of the design items which shows all the available design possibilities in a matrix form and displays the best choice among these possibilities. The best choice will then be sent to module GRAPH to plot the reinforcement details. Through this process, the databank expands every time the program is used, and future selections are likely to improve. It should be mentioned that for the design of combined footing more input items will be requested, and so will be the output. At least five different locations of reinforcement will be taken care of in the databank and, of course, the search for similar solutions imposes some more elements to be checked. To perform the analysis of mat foundation, a program was adapted from the system described in [9]. The program utilizes a nonconforming element for the analysis of flexural plates based on the
NABIL
732
0.0
4.0
1.0
A. B. YEHLAand
l2.0
le.0
20.0
AHMAD
24.0
H. EL-HAJJ
a.0
X ROWS OF COWMNS
szo
SC0
so.0
I
10
Fig. 2. Column distribution map.
classical Kirchhoff theory and it provides an automatic mesh generator for rectangular regions with rectangular elements. The results obtained from the mat analysis are sent to an algorithmic subroutine to sort the moments and their locations on the mesh for the completion of the design process. 4. DATABASE
To prepare a databank, it is necessary to know the input and output parameters to be included there. These parameters are primarily the design variables. The structure of the databank affects the search time for best choice. In this study, the guide parameters are placed in first range, the best selection in the second, the user’s criteria in the third, and finally the execution date. In general, the database consists of two main segments, the intelligent segment and the databank segment. 4.1. The intelligent segment The intelligent segment is utilized to consult the database and determine the available designs for the current case. Therefore, it selects the one that agrees with the user’s criteria. This process involves a search through the databank that primarily satisfies the factored loads and the material properties, and secondarily the user’s criteria. The best selection need not necessarily match all the parameters. The follow-
ing tolerance limits were used for different variables: 3% difference in factored loads, 0% difference in each of the bearing capacity, steel yield strength and the 28-day concrete strength, 1 in. difference in concrete thickness, and 3 in. difference in footing lateral dimensions. 4.2. The databank The search process inside the databank is performed quite similarly to a commercial banking machine. An identification number is always used to start with. The identification number, as in this case, might be the design selection criteria as specified by the user. Having the ID entered, the rest of the process might take one of the following two forms. (a) Compatible previous design. This form of search type inside the databank will be performed every time the program is executed. Having selected the design criteria, the material properties, and the bearing capacity of soil, a check for every item will SUCC~Ssively take place. For instance, the factored load input will be compared with the one deposited first; if a difference within the tolerance limit is obtained, the comparison will continue for another item (yield strength of steel might be the other item). However, a complete agreement in value is required now otherwise the searching process will jump to the next set of data. If the comparison result comes out positively, the user will be notified that a similar case was
The design of spread footings
133
handled by the program on the basis of certain criteria and on a specific date. A message in that sense will be displayed on the terminal and documented on an output file for later use to obtain a hardcopy. On the other hand, complete design details could be documented if requested by the user. However, only the best choice will be plotted in order to save CPU time. (b) Design safety check. An alternative way of using the built-in database is to check the safety of an existing structure. The elements needed for that check are the existing dimensions of the proposed footing, the material properties, the bearing capacity of soil, and the area of steel furnished in different directions. The search in this case will take a longer time since more parameters are to be checked. Nevertheless, the safety of the structure depends on some more vita1 elements, such as the current condition of the structure, which are out of scope of this study. 5. EXAMPLE
PROBLEM
Fig. 4. Generated mesh for mat of columns 1, 2 and 4.
In this example, the user inputs a map of columns, as shown in Fig. 2, with the factored loads assumed as 391.5, 381, 288, 379, 0.0, 488, 299, 262.5 and 488 kips for columns l-9 respectively. The selection decisions as concluded by the program are shown in Fig. 3. The design process takes place for single and double footings first until it is altered by the presence of a mat foundation. A mesh is then prepared, as
20.0
X ROWS OF
shown in Fig. 4, to start the program again for the three columns mat and loaded by the loads of columns 1,2 and 4 as nodal loads normal to the plane of the mat. The thickness of the mat is assumed to be 1.5 ft with elasticity modules, shear modulus, and Poissons ratio of 452,700 ksf, 19,512 ksf and 0.16
24.0
COLUMNS
Fig. 3. Selected footings map.
22.0
26.0
40.0
NABILA. B. YEHM and W
734
H. EL-HAJJ
Column No. 9 use minimum of 3in. concrete cover
r’-‘-‘-‘--’ a
3
‘---‘--I a I I -n
8.6ft
I
Fig. 5a. Sample detail of single footing.
Column No.3 and column No.6 use minimum of 3in. concrete cover P
0
1
II
.a ____ ____*I!I_-_-
____ 1:+_-_______
______ *_
II .I
7.I
2i
_._.-.-.-.-.-
!;
.I
I’
I
t
ia
i0
20.3ft Section c-c
b
.208amNa5ut 6in. . 20 9arsNa5 ot 6in. _o ~,_____ _______--_-__ 20 Bare Nra5at_______. 6in .______________ 5 l3are NaS at 6.2in. . ____-____- ---------. 4 Bare No.6 at 6.2 in.c c____________ _______
Fig. 5b. Sample detail of double footing.
The design of spread footings
respectively. The subgrade modulus is assumed to be 50 kcf. A maximum moment of 158 kip. ft/ft is found to exist between columns 1 and 4. A minimum reinforcement of 0.72in2/ft, as recommended by ACI-Code is therefore adopted by the program. A hard-copy of the designed single and double footing may be requested as shown in Figs 5a and 5b. However, this facility is not yet available for mat foundation types. 6. CONCLUSION
The paper presented herein can be considered as a preliminary study into the possibility of building an expert system that eventually will be capable of selecting and designing any type of spread footing. Previous programs that dealt with footing design were almost always limited to a single type of footing. This, however, is impractical, since a footing design problem is most likely to have a column load map where a decision is to be made before the real design steps can take place. Therefore, it was the aim of the present paper to develop a program capable of making decisions and, furthermore, capable of handling single cases of design. There is, however, one part of the problem yet to be worked out. If the program delivers a decision that consists of mat foundations, the execution will be halted until a finite element mesh is supplied by the user. Some of the published works that were referred to earlier [l-5] have based their choices on the frequencies of previous acceptances. This sometimes resulted in limiting the options available to the user because after a certain number of program executions, the databank tends to become strongly biased toward certain selections [5]. The concept discussed in this paper allows the user to select certain design criterion and a best choice corresponding to the most matching area of steel will be based on that criterion. This process will enlarge the databank so that, at certain times, it might contain all the design choices for a certain design case. However, the selec-
C.A.S. ,013-T
135
tion criterion used in the present work minimizes or maximizes either one of the concrete sections or the steel area. Other criteria such as total material weight, market availability or uniformity of steel bar size have not been taken into consideration in the present work. For the part of single and double footing design, the program is so efficient that it uses very little CPU time. However, the explanation facilities, presented by the documented plots, enlarge the memory occupancy so much that the program could not be run interactively when plots are asked for. Another item of interest is the computer language utilized by the program. While most of the programs developed in this area are written in LISP, FORTAN(commonly known as an engineering-oriented language) proved to be efficient in performing the search inside the databank.
REFERENCES 1.
2. 3.
4. 5.
6.
7. 8.
9.
S. J. Fenves, M. L. Maher and D. Sriram; Expert System: CE Potential. Civil Engineering/AXE 54, u7 (1984). M. F. Roony and S. E. Smith, Artificial intelligence in simple beam design. Strut. Div. AXE 108,2344-2348 (1984). G. Adeli, Artificial intelligence in simple beam design. Proceedinns. Fifth ASCE/EMD Snecialitv Conference. Laramie, Wyoming, USA, Augusi 1984.. P. H. Winston, Artificial Intelligence, 2nd Ed. Addison-Weseley, London, U.K. P. Roberts and M. Saiidi, Artificial intelligence for design of R/C beams. 2nd National Conference on Microcomputers in Civil Engineering, Orlando, Florida (1984). N. Yehia and R. Bechara, A simple knowledge-based design of reinforced concrete columns. Concrete Int. 10, PI-55 (1988). AC1 318-83, Building code requirements for reinforced concrete. Detroit, Michigan (1983). A. H. El-Hajj, Knowledge-based system for the design of spread footing. MSc. Thesis, Civil Engineering Dept, University of Pittsburgh, PA (1986). R. E. Dick and N. Yehia, Finite element analysis of plates on elastic foundation-automated approach. Civ. Engng Sys. (to appear).