STEELEX: A coupled expert system for integrated design of steel structu res

Y. Paek and H. Adeli Department of Civil Engineering, The Ohio State University, 470 Hitchcock Hall, 2070 Nell Avenue, Columbus, Ohio 43210, USA (Received August 1988)

ABSTRACT

Most expert systems developed so far are concerned with symbolic processing of a knowledge base. Solution of complex engineering problems often requires substantial numerical processing in addition to symbolic processing of heuristics and experiential knowledge. In this paper, we present STEELEX, a prototype knowledge-based expert system for integrated design of building structures consisting of moment-resisting steel frames. STEELEX is a coupled system in which AI symbolic processing is combined with conventional numerical processing. STEELEX produces the final detailed design including the beam-column connections ready for fabrication. In addition, it can explain the basis of design and the principles behind the design specification. STEELEX has been developed using a domain-specific tool called SDL (for Structural Design Language). Implemented in the INTERLISP environment, SDL provides a design problem- solving environment using a hierarchical co- operating specialists paradigm. STEELEX has a debugging facility and provides a multiwindow graphics interface for drawing isometric as well as orthographic views of the steel frame and beam- column connections. 0952-1976/88/030170-1152.00 ~, 1988 Pineridge Ltd

170 Eng. Appli. of AI, 1988, Vol. 1, September

INTRODUCTION

The celebrated first generation expert systems such as MYCIN (an expert system for diagnosis and treatment of meningitis), CADUCEUS (an expert system for diagnosis of diseases of internal medicine), and XCON (an expert system for designing the configuration of VAX-11/780 computer components for Digital Equipment Corporation according to the requests of a customer) 1 basically deal with symbolic processing of a knowledge base. Very little numerical processing is involved in these expert systems. However, solution of complex engineering problems often requires substantial numerical processing in addition to symbolic processing of heuristics and experiential knowledge.

Most of the early expert systems reported in the literature are diagnostic systems. Recently, a number of investigators have presented knowledge- based approaches to engineering design problems. Engineering design may be broadly divided into conceptual design, preliminary design and detailed design. Expert systems reported in the literature are mostly concerned with the conceptual design or preliminary design where little numerical processing is involved 2"3'4"5'6.

In this paper, we present a prototype knowledge- based system for integrated design of a class of structures, called STEELEX. The integrated design should produce the final detailed design ready to be fabricated. STEELEX is an expert system for integrated design of building structures consisting of moment-resisting steel frames. Each frame is made of standard steel wide-flange I-shaped sections (commonly called W shapes) used as beams and columns. The beams and columns are connected to each other by moment connections through the use of plates, bolts, and welds. The detailed design of such structures requires judgement and previous experience, as well as a considerable amount of numerical processing. STEELEX is a coupled

A coupled expert system for design of steel structures." Y. Paek and H. Adefl

Table 1 Properties of W36 ×300 Object: W36 × 300

Attribute Value

Cross sectional area (A) 88.3 Depth (d) 36.74 Web thickness (tw) 0.945 Flange width (bf) 16.655 Flange thickness (tf) 1.68 Distance from outer face of flange to web toe of

fillet (k) 2.8125 Radius of gyration of a section comprising the

compression flange plus 1/3 of the compression web area, taken about an axis in the plane of the web (rT) 4.39

Ratio of the depth to the flange area (d.Af) 1.31 Moment of inertia about the strong axis (Ix) 20300.0 Section modulus about the strong axis (Sx) 1030.0 Radius of gyration about the strong axis (rx) 15.2 Moment of inertia about the weak axis (ly) 1300.0 Section modulus about the weak axis (Sy) 156.0 Radius of gyration about the weak axis (ry) 3.83 Torsional constant (J) 64.2 Plastic modulus about the strong axis (Zx) 1260.0 Plastic modulus about the weak axis (Zy) 241.0

system in which AI symbolic processing and conventional numerical processing are integrated. Research in the area of coupled expert systems is relatively new 7'8'9A°'11,12

AI languages such as Prolog and LISP have been developed primarily for non-numeric symbolic processing. To facilitate the development of expert systems for integrated design of structures, we first developed a Structural Design Language (SDL) in the INTERLISP environment. The integrated design includes the preliminary design, structural analysis, design of members, design of connections, and computer-aided drafting of the final design. It should be noted that a large number of commercial expert system development tools or shells have been developed in recent years 13"14, but practically all of them are most suited to the solution of diagnostic problems. A brief description of the knowledge representation techniques and problem-solving paradigm used in SDL is presented in the following section.

STRUCTURAL DESIGN LANGUAGE

a structural frame in a building the static knowledge includes the knowledge of the geometry and properties of beams and columns, and the knowledge of their interconnectivities. Static knowledge is represented by lists, object-attribute- value triplets (OAV), and arrays. As an example of OAV, the properties of a standard steel W shape such as W36 x 300 can be represented by OAV representation, as shown in Table 1. The record package of INTERLISP is used to store the properties of 187 W shapes available in the AISC manual 16. Each record for a W shape contains an object name (for example, W36 x 300) and 17 values for 17 attributes, as shown in Table 1.

Dynamic knowledge includes the knowledge of design constraints that have to be satisfied in a given design problem, and the heuristics that are used to solve the problem effectively. Dynamic knowledge is represented by production rules and functionals via procedural abstraction. Production rules are used to represent design specifications such as the American Institute of Steel Construction (AISC) specifica- tions 16. As an example, Table 2 shows the production system representation of the AISC specification Section 1.5.1.4.1.

Table 2 Production rules for the AISCS 1.5.1.4.1 requirements

(Rule1

(Rule2

(Rule5

(Rule7

(if ( (> Section) has flanges continuously connected to the web))

(then ( (< Section satisfies the flanges continuously connected to the web requirement)))

(if ( (> Section) contains unstiffened elements) (( < Section) has (bf/(2*tf) LT 65/(SQRT Fy))))

(then ( (< Section) satisfies flange local buckling requirement)))

i i f (( > Section) has (fa/Fy GE .16)))

(then ( (< Section) satisfies web local buckling requirement)))

i i f (( > "Section) is a W-shape) (( < Section) has (and (Lc LE 76*bf/(SQRT Fy))

(Lc LE 20000/(d.Af*Fy))))) (then ( (< Section)

satisfies W-shape unsupported length requirement)))

Knowledge representation

The knowledge necessary for structural design is classified into three categories: static knowledge, dynamic knowledge, and graphical knowledge is

Static knowledge is defined as the knowledge necessary for representing the physical structure, its components, and their topology. As an example, for

(Rule12 iif ((>Section) satisfies the flanges continuously connected to the web requirement) (( < Section) satisfies flange local buckling requirement))) (( < Section) satisfies web local buckling requirement))) (( < Section) satisfies W-shape unsupported length requirement))

(then ( (< Section)is Compact)))

Eng. Appli. of AI, 1988, Vol. 1, September 171

A coupled expert system for design of steel structures: Y. Paek and H. Adefi

Graphical knowledge represents the structural configuration in graphical images. Graphical knowledge is represented by bitmaps, windows and m e n u s 15.

Problem solving paradigm

In actual design of structures, often a number of senior and junior engineers, technicians, and draftsmen work co-operatively. In order to solve the complex problem of integrated design of structures,

/ onnectOesign~

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Figure I The hieraChicaltree ofthe FrameDesign specialist

a problem-solving paradigm has been created, based on the concept of co-operating specialists. The complex body of knowledge needed for detailed design of structures is fractionated into smaller and manageable knowledge sources which are then organized into a set of conceptual specialists.

In the case of frame structures, at the topmost level, we have the FrameDesign specialist (Figure 1). This specialist uses the assistance of four other specialists at the second level of the hierarchy. They are the FramePredesign specialist whose task is the preliminary design, the FrameAnalysis specialist whose task is the structural analysis, the SectionDesign specialist whose task is the design of individual members (beams and columns), and the ConnectDesign specialist with the task of designing the connections.

The FramePredesign specialist selects preliminary values for the cross-sectional areas and moments of inertia of beams and columns. The hierarchical tree of the FramePredesign specialist is shown in Figure 2. This specialist uses several lower-level specialists. For example, the PreSection specialist estimates the beam section modulus and the column cross- sectional area and moment of inertia, using knowledge from previous designs.

SDL provides a problem-solving environment for the development of structural design expert systems. SDL has been developed on a Xerox AI machine

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172 Eng. Appli. of AI, 1988, Vol. 1, September

A coupled expert system for design of steel structures: Y. Paek and H. Adefi

Explanation Facility ,I

"1 Package 1"

Knowledge Base

Specialists

IFrameAnalysis

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Knowledge Enginter

Figure 3 A schematic

Procedural i Functions

I Rules

representation of the architecture of STEELEX

STEELEX prompts:

Checking W-shape W14x99.

W-shape W14x99 is compact.

(WHY?)

"Rulel says W14x99 satisfies continuously connected flange and web requirement"

"Rule2 says W14x99 satisfies flange local buckling requirement" "Rule7 says W14x99 satisfies web local buckling requirement" "Rule9 says W14x99 satisfies unsupported len~-~da requirement" "Rule 16 says W 14x99 is compact"

Figure 4 An example of explanations provided by the WHY? function

equipped with Xerox 1108 monitors, having a resolution of 1020 by 820.

are implemented in STEELEX:

1. preliminary design of the members of the moment-resisting frame,

2. analysis of the structure, 3. detailed and final design of the structure,

including connections, and 4. drawing of the final design.

The architecture of STEELEX is presented schematically in Figure 3. STEELEX uses the four topmost specialists provided by SDL (see Figure 1).

Explanation facility

The explanation facility for STEELEX consists of three different types of explanations: WHY?, HOW?, and WHAT? The WHY? function uses production rules with forward chaining, based on matching rules to given facts. It provides reasoning about the domain knowledge when the user inquires about the conclusions made by STEELEX. An example of explanations provided by the WHY? function is given in Figure 4.

The HOW? function is used to obtain detailed explanations about rules when the user asks for deeper knowledge about the production rules provided by the WH Y? function. In other words, the HOW? function explains the underlying reasoning or theory behind each rule. As an example, Figure 5 shows the detailed information about Rule2.

Finally, the WHAT? function provides explanations about the terminologies and equations used in the production rules. As mentioned earlier, the AISC design specifications 16 have been represented by IF-THEN rules and functionals. Some of these rules contain long equations. If equations are used directly in the IF-THEN rules, they become cumbersome and complicated. Hence, equation numbers are used in the production rules instead of the equations themselves. However, when

(HOW? Rule2)

STEELEX

Architecture

STEELEX is a prototype knowledge-based expert system for the integrated design of steel buildings consisting of moment-resisting frames. STEELEX has been developed using SDL. The basis of design is the AISC specification 16. The following activities

Then, STEELEX will respond:

"(Rule2 (if ((> Section) contains unstiffened elements) ((< Section) satisfies EQI.5-4))

(then ((< Section) satisfies flange local buckling requirement)))

The high compression strain necessary to develop plastic moment (Mp) may occur prior to achieving the local buckling of the compression flange. Ref. 'Steel Structures' by Salmon & Johnson page, 342"

Figure 5 An example of explanations provided by the HOW? function

Eng. Appli. of AI, 1988, Vol. 1, September 173

A coupled expert system for design of steel structures. Y. Paek and H. Adefi

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the user wishes to see the equation itself, the WHAT? function displays the equation.

Graphics interface

Jain and Maher tv discuss three approaches for combining expert systems and computer graphics: writing an expert system inside a drafting package, writing a graphics package inside the expert system, and using a drafting package for graphics and an expert system package for rules. The second integrated approach is used in developing STEELEX. STEELEX provides a multiwindow graphics interface through the use of Frame- Predesign and ConnectDesign specialists. The graphics interface is capable of displaying both the orthographic and isometric views of the frame structure and beam-column connections. The screen is divided into eight windows, as shown in the

example of Figure 6, generated by the Frame- Predesign specialist. The Prompt Window displays the status of the computer executions. The Executive Window is used for entering the input data inter- actively and displaying the output. These windows are the two primitive windows provided by INTER- LISP-D. The ((LEGEND and NOTE)) window is used to display the explanatory notes. STEELEX provides three types of supports, that is fixed, hinged, and roller supports. These support types are displayed in the window ((SUPPORT TYPES)). The ((MEMBER PROPERTY)) window is used to display the output of the FramePredesign specialist. The ((ISOMETRIC FRAME)) window is used to display the isometric view of the three-dimensional frame. The isometric view can be displayed from various angles by selecting the desired rotations about the x and y axes.

The window ((MEMBERS, NODES, LOADS,

174 Eng. Appli. of AI, 1988, Vol. 1, September

A coupled expert system for design of steel structures." Y. Pack and H. Adefi

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connection from various angles by selecting desired rotat ions about the x (horizontal) and y (vertical) axes. Figures 11 to 13 show examples of connections graphics in the windows ( (FRONT VIEW)), ((SIDE VIEW)), and ( (TOP VIEW)), respect- ively• It should be noted that the three orthographic views contain all the necessary details for fabricating the connection.

Debugging facility

The debugging facility consists of two different types of debugging, that is numerical debugging and

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• -"(<: 180METRIG-VIEW. ~ ) - .. . . . . . " : ,_.';i . AND DIMENSIONS)) is used to display the two- dimensional flame including the member numbers (inside circles), node numbers, dimensions, and the loading, as shown in Figure 7. This window has the option of displaying the flame with member and node numbers and dimensions but without the loading, as shown in Figure8. The last window is the window ((DEGREES OF FREEDOM)) for displaying the nodal displacement degrees of freedom, as shown in Figure 9.

The ConnectDesign specialist also provides a multiwindow graphics interface for displaying the isometric view and three orthographic views of the moment-resisting connection. An efficient priority list algorithm with back-face elimination has been used for the orthographic views. A five-test algorithm has been employed for efficient drawing of the isometric views 18. Figure 10 shows an example of the connection graphics displayed in the window ((ISOMETRIC HEW)). The user can see the

I

Figure 10 The w indow displaying an isometric v iew of the moment-resisting connection

Eng. App l i . o f AI, 1988, Vol. 1, Sep tember 175

A coupled expert system for design of steel structures." Y.

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geometrical debugging. All numerical input data are treated as list formations. The numerical debugging checks the format of the input data and makes sure that they are valid list formations.

The geometric debugging discovers errors in the input data for the coordinates of members, and errors in the input data for numbering of nodes. Member connectivity data is represented as a list (i j) where i and j are the two end nodes of the member.

Paek and H. Adefi

Node i is the left (or lower) and nodej is the right (or upper) node of the member. For the example frame of Figure 8, member connectivity data for members 1 through 8 are represented as (1 2), (2 3), (2 5), . . . , and (7 8). The connectivity data for all the members are stored in a list with the name of Datal as follows:

((1 2)(2 3)(2 5)(3 6)(4 5)(5 6)(6 8)(7 8))

In STEELEX, the coordinates of nodes are not entered individually in the global coordinates system. Rather, the user needs to input the coordinates of the two end nodes of each member in the local coordinates system of the member. For the local coordinates, the x axis is horizontal and the y axis is vertical, with the origin being at the node i of the member. This approach for entering the nodal coordinates is easier and less error-prone than the traditional approach of entering the nodal coordinates with respect to one set of global axes. Thus, the coordinate data for the eight members of the example frame of Fioure 8 are stored in a list Data2 as follows:

((0 150)(0 150)(300 0)(300 0)

(0 150)(0 150)(300 0)(0 300))

The FramePredesign specialist

The FramePredesign specialist handles the preliminary design of two-dimensional frames. Performing the preliminary design requires considerable design experience (i.e. accumulated heuristic knowledge). The preliminary design is initially based on the gravity (vertical) loads only. The preliminary selection of members can be divided into two categories, that is beam and column members. The first step in the preliminary selection of members is to distinguish whether a member is a

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Figure 13 The window displaying the top face view of the moment-resisting connection

176 Eng. Appli. of AI, 1988, Vol. 1, September

A coupled expert system for design of steel structures: Y. Pack and H. Adefi

Type I Type 2 Type 3

I Type 4 Type 5 Type 6

Type 7"

Figure 14

Type 8 Type 9

Classification of beam types for the purpose of the preliminary design

beam or a column. For the purpose of the preliminary design, when a member has a slope of more than 45 degrees with the horizontal it is considered a column member; otherwise, it is considered a beam member. Beam i is subjected to a uniformly-distributed vertical load of intensity wi. The preliminary design of beams is independent of the number of storeys; but the preliminary design of columns depends on the number of storeys above the column under consideration.

Preliminary selection of beam members

The preliminary selection of beam members is done first because beams are independent of the floor levels. The various beam types are classified into 9 categories, as shown in Figure 14. For the preliminary selection of beam members, the node numbering data for node i (left or lower node) and node j (right or upper node) of the beams, member types, and member lengths are required. The connectivity data for the example frame of Figure 8 are stored in a list Datal , as described in a previous section. Member lengths and member types for the frame of Figure 8 are stored in a list under the name of Data4 as follows:

The first one denotes the length of the beam. The second one is a list containing two atoms representing the number of columns and beams attached to the end i of the beam, respectively. The third element is a similar list for the end j of the member.

Using the above-described scheme, the nine different types of beams in Figure 14 are identified by list formations as follows (L is the span length):

Beam type 1: (L (1 0) (1 0)) Beam type 2: (L (1 1) (1 0)) Beam type 3: (L (1 1)(1 1)) Beam type 4: (L (2 0) (1 0)) Beam type 5: (L (2 1) (1 0)) Beam type 6: (L (2 1) (1 1)) Beam type 7: (L (2 0) (2 0)) Beam type 8: (L (2 1) (2 0)) Beam type 9: (L (2 1) (2 1))

Beams are designed primarily for the maximum bending moment over their span. Assuming each beam is subjected to a distributed load of intensity w, the maximum bending moment Over the beam span can be expressed approximately as M =bwL 2. The coefficient b depends on the boundary conditions and locations of the beam in the frame. We can find approximate values for the coefficient b by assuming the locations of the inflection points in each beam using the knowledge of the frame behaviour. A beam may be connected to just one column (type A), to two columns (type B), to two columns and one beam (type C), or to one column and one beam (type D), as shown in Figure 15. The assumed approximate locations of the inflection points for the four beam types are also indicated in Figure 15.

Type A Type 8

(NIL NIL (300 (2 0) (2 0)) (300 (1 0) (1 2))

NIL NIL (300 (1 2) (1 0)) NIL)

This list consists of eight sublists, corresponding to the eight members of the frame. Note that the first, second, fifth, sixth, and eighth elements are assigned NIL because they are not beam members. Each remaining sublist consists of three elements. Figure 15 Classification of beam types in a frame on the basis of the

rough location of the inflection point

Eng. Appli. of AI, 1988, Vol. 1, September 177

A coupled expert system for design of steel structures. Y. Paek and H. Adefi

Table 3 Cross-sectional properties of the selected W shapes

Selected W shape Given section modulus Moment of inertia Area (Sx) W shape (Ix) (A)

1110 W36 x 300 20300 88.3 1030 W36 × 280 18900 82.2 953 W36 x 260 17300 76.5 895 W36 × 245 16100 72.1 837 W36 × 230 15000 67.6 757 W33 x 221 12800 65.0 684 W33 x 201 11500 59.1 598 W30 x 191 9170 56.1 542 W36 × 160 9750 47.0 448 W33 × 141 7450 41.6 406 W33 x 130 6710 38.3 359 W33 x 118 5900 34.7 299 W30 × 108 4470 31.7 269 W30 x 99 3990 29.1 222 W24 x 94 2700 29.7 196 W24 x 84 2370 24.7 176 W24 x 76 2100 22.4 154 W24 × 68 1830 20.1 131 W24 x 62 1550 18.2 114 W24 x 55 1350 16.2 94.5 W21 × 50 984 14.7 81,6 W21 x 4 4 843 13.0 68.4 Wl 8 x 40 612 11.8 57,6 Wl 8 x 35 510 10.3 48.6 Wl 4 x 34 340 10.0 42.0 Wl 4 × 30 291 8.85 38.6 Wl 2 × 30 238 8.79 33.4 Wl 2 x 26 204 7.65 29.0 Wl 4 × 22 156 6.48 23.2 Wl 0 × 22 118 6.49 17.1 W 1 2 x 1 6 103 4.71 14.9 W 1 2 × 1 4 88.6 4.16 11.8 W8 x 15 48.0 4.44 9.9 W8 × 13 39.6 3.84 7.3 W6 × 12 22.1 3.55 5.6 W6 × 9 16.4 2.68

Using the above-described scheme, the nine different types of beams in Figure 14 can be analyzed approximately by superimposing the four beam types in Figure 15 as follows:

Beam type 1: Beam type A + Beam type A Beam type 2: Beam type D + Beam type A Beam type 3: Beam type D + Beam type D Beam type 4: Beam type B + Beam type A Beam type 5: Beam type C + Beam type A Beam type 6: Beam type C + Beam type D Beam type 7: Beam type B + Beam type B Beam type 8: Beam type C + Beam type B Beam type 9: Beam type C + Beam type C

Based on the above classification and superposition procedure, the nine beam types in Figure 14 can be analyzed as statically determinate beams.

Assuming the allowable bending stress (Fb) for the preliminary design to be 60~o of the yield stress of steel (Fy), the required section modulus is estimated

from Sx=M/F b. After calculating the section modulus from this equation, the area and moment of inertia of the beam are determined from Table 3 which shows the lightest W shape for a given section modulus. It should be noted that the beams and columns of a steel structure are selected from among 187 W shapes whose properties are tabulated in the AISC manual ~6. The W shapes in Table 3 are the bold-faced shapes in the Allowable Stress Design Selection Table of the AISC manual. Each bold-face W shape is the lightest in its group.

To determine the proper W shape from Table 3, on the average 18 comparisons have to be performed. In order to reduce the execution time, a searching scheme has been developed using 21 COND functions. This is presented in Figure 16. Using this method at most 5 comparisons are needed for selecting the right W shape.

Preliminary selection of column members

The preliminary design of columns comes after the preliminary design of beams because loads are carried from beams to columns and the design of a

(COND (((;E Sx 542)

(COND ((GE Sx 953) (COND ((GE Sx 1110) (setq Mx 20300) (setq A 88.3)) ((GE Sx 1030) (setq Mx 18900) (setq A 82.2)) (T (setq Mx 17300) (setq A 76-5)1

((GE Sx 757) (COND ((GE Sx 895) (setq Mx 16100) (setq A 72.1)) ((GE Sx 837) (setq Mx 15000) (setq A 67.6)) (T (setq Mx 12800) (setq A 65.0)]

(T (COND ((GE Sx 684) (setq Mx 11500) (setq A 59.1)) ((GE Sx 598) (setq Mx 9170) (setq A 56.1)) (T (setq Mx 9750) (setq A 47.0)1

((GE Sx 154) (COND ((GE Sx 359) (COND ((GE Sx 448) (setq Mx 7450) (setq A 41.6))

((GE Sx 406) (setq Mx 6710) (setq A 38_3)) (T (setq Mx 5900) (secq A 34.7)]

((GE Sx 222) (COND ((GE Sx 299) (setq Mx 4470) (setq A 31.7)) ((GE Sx 269) (setq Nix 3990) (setq A 29.1)) (T (setq Mx 2700) (setq A 29.7)]

(T (COND ((GE Sx 196) (setq Mx 2370) (setq A 24.7)) ((GE Sx 176) (setq Mx 2100) (setq A 22.4)) (T (oe;q Mx 1830) (setq A 20.1)]

((GE Sx 38.6) (COND ((GE Sx 94.5) (COND ((GE Sx 131) (setq Mx 1550) (setq A 18.2))

((GE Sx t 14) (setq Mx 1350) (setq A 16.2)) (T (setq Mx 984) (setq A 14.7)]

((GE Sx 57.6) (COND ((GE Sx 81.6) (setq Mx 843) (setq A 13.0)) ((GE Sx 64.7) (setq Mx 612) (setq A 11.8)) (T (setq Mx 510) (setq A 10.3)1

(T (COND ((GE Sx 48.6) (setq Mx 340) (setq A 10.0)) ((GE Sx 42.0) (setq Mx 291) (setq A 8.85)) (T (setq Mx 238) (setq A 8.79)]

(T (COND ((GE Sx 23.2) (COND ((GE Sx 33.4) (setq Nix 204) (setq A 7.65))

((GE Sx 29.0) (setq Mx 156) (setq A 6.48)) (T (setq Mx 118) (setq A 6.49)]

((GE Sx 11.8) (COND ((GE Sx 17.1) (setq Mx 103) (setq A 4.71)) ((GE Sx 14.9) (setq Mx 88.6) (setq A 4.16)) (T (setq Mx 48.0) (setq A 4.44) 1

(T (COND ((GE Sx 9.9) (setq Mx 39.6) (setq A 3.84)) ((GE Sx 7.3) (setq Mx 22.1) (setq A 3.55)) (T (setq Mx 16.4) (setq A 2.68)]

Figure 16 Searching method for the preliminary selection of beams using COND functions

178 Eng. Appli. of AI, 1988, Vol. 1, September

A coupled expert system for design of steel structures." Y. Paek and H. Adefi

W shape Sx

Wl6xl ( )0 175 W21x83 171 W18x86 166 W12.x120 163 W14x99 157 W16x89 155 W24x68 * 154 W21x73 15t W18x76 146 W12x106 145 W14xg0 143 W21x68 * 140 W16x77 134 W24x62 * 131 W l 0 x I [ 2 126 W18x71 127 W21x62 * 127

RequiredSx = 100] TargetWt = 68 J

W14x82 123WList0 W16x67 * 117 WlSx65 * 117 W24x55 * 114 WI4x74 112 W21x57* 111 WI8x60 * 108 WI2x79 107 W14x68 * 103 W10x88 98.5 WlSx55 98.3 W12x72 97.4

.... >

WList 1 . . . . WLis~

Figure 17 Search technique for the f inal selection of beams

column depends on the number of storeys above the column. Columns are designed for combined axial force and bending moment. The bending moment is customarily converted into an equivalent axial load, and then a section is selected from the column tables of the AISC manual. In the actual design of steel structures, an experienced designer seldom starts from scratch, but uses the results of previous designs. The results of thousands of column designs with various lengths and two different steel types (with yield stress of 36 ksi and 50 ksi) are tabulated in the AISC manual. STEELEX tries to simulate an experienced designer of steel structures. The results of the previous column designs given in the AISC manual have been used in the knowledge base of STEELEX, after employing a data-reduction scheme. This data-reduction scheme is based on heuristics found after plotting the cross-sectional areas of the columns, versus their equivalent axial load capacities.

The SectionDesign specialist

The task of this specialist is the final selection of beams and columns. We will describe here only the search technique for the selection of beams. It should be noted that in the preliminary design, beams are selected from among 36 shapes given in Table 3. The

final selection of beams, however, should be based on the 187 W shapes available.

Figure 17 shows the search technique for the final selection of beams. The problem is to select the lightest section among the 187 W shapes satisfying the design requirements of the AISC specification 16. Considering that this must be done for every beam in the structure, development of an efficient search technique becomes of paramount importance for the overall efficiency of the design expert system. Initially, the 187 W shapes are sorted in an increasing order of the value of the elastic section modulus and stored in a list with the name WList0. The required elastic section modulus (RequiredSx) is compared with the elastic section moduli in the WList0, starting with the smallest one. Those sections with section modulus less than RequiredSx are thrown out and the remaining part of the WList0 list is stored in another list under the name of WList 1. Next, the weight per unit length of the last W shape (the section with the smallest section modulus) in the list WList 1 is set as TargetWt. Then, those sections with the weight greater than TargetWt are thrown out and the remaining sections are stored in a new list with the name WList. Finally, the sections in the list WList are sorted in an increasing order of the value of the weight per unit length. The first section in the revised WList is the first candidate for the beam selection. Its adequacy is checked in accordance with the AISC specification16.

As an example, suppose the required section modulus to be RequiredSx= 100. In this case, the three lists WList0, WList 1, and WList are identified in Fiyure 17. The quantity TargetWt is 68. The final WList is as follows:

(w24x55 w21x57 w18x60 w21x62 w24x62 w18x65 w16x67 w14x68 w21x68 w24x68)

The section W24X55 is the first candidate for the beam design.

CONCLUDING REMARKS

In this paper, we have presented the development of a prototype knowledge-based expert system called STEELEX for integrated design of steel buildings consisting of moment resisting frames. STEELEX is a coupled or hybrid expert system that uses both AI- based symbolic processing and conventional numerical processing. It has been developed using the domain-specific expert system tool SDL.

Eng. Appli. of AI, 1988, Vol. 1, September 179

A coupled expert system for design of steel structures." Y. Pack and H. Adefi

Designers of steel structures usually start with a preliminary design using their previous knowledge, as well as the results of thousands of designs tabulated in the authoritative manual of steel construction 16. These preliminary designs are subsequently checked for their adequacy in accordance with the AISC specification. On one hand, STEELEX tries to simulate the experience of an experienced designer. On the other hand, it can be considered as an electronic version of the AISC manual and specification. In addition, STEELEX not only presents the final detailed design ready to be fabricated, but also it can explain the basis of the design and the principles behind the design specification.

The expert system STEELEX has a hierarchical structure which is fundamentally different from the structure of the conventional CAD programs. The user can see inside the program and how it works clearly. Another advantage of the new program structure is that different portions of the system (for example, various specialists) can be executed independently. Also, the program can be interrupted by the user at the end of each step, and can be resumed again without any need to start all over again.

ACKNOWLEDGEMENT

The research presented in this paper has been partially supported by the Ohio State University Office of Research and Graduate Studies. This research has been performed at the OSU Laboratory for AI Research.

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