Preliminary design of double layer grids using aNN

Journal of Structural Engineering Vol. 40, No. 3, August - September 2013 pp. 215-227

No. 40-25

Preliminary design of double layer grids using ann G. S. Deshmukh*,  Email: [email protected]

*Department of Civil Engineering, M. G. M’s College of Engineering, Nanded-431 605, Maharashtra, INDIA. Received: 22 November 2011; Accepted: 29 February 2012

With the industrialization and development of the world there is a demand for efficient and adaptable long-span structures. The Double Layer Grid (DLG) is a valuable tool for the architect or engineer in the search for new forms, due to their wide variety and flexibility. DLG is the truss spanning in three directions to cover large spans without intermediate support. Except the planner beams and trusses all other structures are 3D in sense as they have length, depth and thickness. Beams and trusses are predominantly 2D in their actions as they effectively resist loads applied only in one direction between their supports. But from stability point of view third dimension is also important. Hence 3D action is considered. Groups of DLG were made according to the span range from 25 meter to 100 meter with the  Height of DLG H  two different sets of aspect ratio    Viz- 0.035 to 0.065 and 0.05 to 0.08 with interval of 0.01. The L  Span Length initial analysis and design work of DLG is carried out on STAAD Pro as per IS 800:1984. No of Neural Networks are trained in MATLAB and one networks which gives best results among all is chosen. The results of Artificial Neural Network (ANN) and STAAD for same conditions were analyzed. Keywords: Double layer grid; preliminary design; ann, 3-d truss; space truss in staad pro.

Until the middle of the eighteenth century the main construction materials available to architects and engineers were stone, wood and brick. Metals, being in relatively short supply, were used mainly in the connection of the other materials. Stone and brick are strong in compression but weak in tension than the other widely available materials. Thus they are suitable for 3-D structural forms such as domes and 3-D vaults1. Good quality timber has strength in tension and compression but is naturally available only in limited lengths and with limited cross-section. For large scale 3-D structures connections of timber becomes a major problem. However, with the Industrial revolution, production of iron and high-strength steel materials permitted the construction of more delicate structures of longer span or greater height. At approximately the same time, mathematical techniques were being developed to describe and predict structural behavior.

The understanding of material strengths with the advent of the railway age and the industrialization for commodity production raised the demand for long span structures for bridges, stations, storage buildings and factories. With the wider availability of iron and steel there came a period of development of new structural forms, initially a multiplicity of different truss configurations and eventually three dimensional space grids1,2. Double Layer Grid (DLG) Double layer grid consists of two plane grids forming the top and bottom layers, parallel to each other and interconnected by vertical and diagonal members as shown in Fig. 1(c). DLGs may be lattice grids or true space grids3. The grid pattern of the top layer may be identical with that of the bottom layer, or it may differ. Journal of Structural Engineering Vol. 40, No. 3, August - september 2013

215

Some types of double layer grids are listed below4. • • • •

Square on square offset ( SOS ) Square on diagonal pattern ( SOD ) Diagonal on square ( DOS ) Diagonal on diagonal pattern (DOD )

In present work Square on Square offset (SOS) is considered for the analysis and design. The preliminary analysis and design is carried out using software STAAD Pro5.

(a)

(b)

Configuration processing

Top Member Inclined Member

Y

X

Z

Bottom Member (c)

(d)

Fig. 1 (a) SOS type DLG Top Members (b) SOS type DLG Web or Inclined Members (c) SOS type DLG in Elevation showing various members (d) SOS type DLG 2.5 × 2.5 m Module

Square on Square offset (SOS)

Square on square offset pattern is the most popular geometric solution used in double layer space grids3. This geometry has been used by several commercially available prefabricated systems. The most popular geometry used in the double layer space grid is the square grid. These systems may be classified generally as nodular or modular. Nodular systems are based on proprietary, piece-small, joints or components. Whereas the modular systems consist of prefabricated modules of various types, and shapes and assembled at site by bolting them together1. In the analysis and design of DLGs a large number of nodes and members are involved, making the process

216

time consuming. Configuration processing and data generation for these structures is also a problem, which can be simplified using concept of FORMEX algebra 336 but now a days many designer are using analysis and design software for many complex structures due to their simplicity in modeling, accuracy and interpretation of results hence in present work one of such tool5 is used for modeling, analysis and preliminary design of DLG. An optimal (minimum weight) analysis is carried out in by several numbers of trials with different member cross sectional area to satisfy the deflection criterion. The design parameters considered are length L, grid aspect ratio and module size of DLG. The configuration and model making of DLG along with analysis and minimum weight designs is performed using analysis and design software5. Additional program is developed for the correct grouping of members in spreadsheet. The hollow circular steel sections (Pipe sections) are used as members of DLGs and the design is carried out as per Indian Code IS: 800, 19843,4,7.

Journal of Structural Engineering Vol. 40, No. 3, August - september 2013

The model considered in this work is a Double-Layer Grid with bar elements, connected by MERO type of joints. One out of five different configurations of double-layer grid is considered. For prediction of minimum weight, maximum deflection and maximum forces, 256 DLGs were analyzed using software. The following data are employed: • • • • • • • •

Span (L): From 25 m to 100 m Grid Configuration: SOS. Aspect Ratio (h/L): Set (1) - 0.035, 0.045, 0.055, 0.065 Set (2) – 0.05, 0.06, 0.07, 0.08 Module Size: 2.5 × 2.5 m and 5 × 5 m Support Condition: Columns are along whole Perimeter Total Load on top layer nodes: 2.5 kN/m2

Due to the practical demands, members are grouped. The grouping of problems is done based on module size and aspect ratio i.e. h/L of DLG as given in Table 1.4

Table 1 Member Grouping Group No. Module Length/span L= (25 Aspect Ratio A.R= size ~ 100 m) L/h Group І:-

L= (25 ~ 100 m)

0.035

2.5 × 2.5

L= (25 ~ 100 m)

0.045

L= (25 ~ 100 m)

0.055

Where σac = permissible stress in axial compression, in N/ mm2. fy = yield stress of steel, in N/mm2. fcc = Elastic critical stress in compression = π2 E/ 2 λ λ = (L/r) = Slenderness ratio of the member L = Effective length of the member. n = factor assumed as 1.4 (Code of Practice for general construction in steel IS: 800, 1984)

L= (25 ~ 100 m)

0.065

Group ІІ:-

L= (25 ~ 100 m)

0.035

5×5

L= (25 ~ 100 m)

0.045

L= (25 ~ 100 m)

0.055

L= (25 ~ 100 m)

0.065

Group ІII:-

L= (25 ~ 100 m)

0.05

Deflection Constraint

5×5

L= (25 ~ 100 m)

0.06

L= (25 ~ 100 m)

0.07

L= (25 ~ 100 m)

0.08

Group ІV:-

L= (25 ~ 100 m)

0.05

2.5 × 2.5

L= (25 ~ 100 m)

0.06

L= (25 ~ 100 m)

0.07

L= (25 ~ 100 m)

0.08

The deflection of the member shall not be such as to impair the strength or efficiency of the structure and lead to damage to finishing. The maximum vertical deflection should not exceed L/325 of the span as specified in Code of Practice for general construction in steel IS: 8007. But in present study, the maximum vertical deflection is restricted to L/400. It has been observed that for a constant length, few compression members of DLG lead to failure due to slenderness for L/325 threshold and not for L/400.

Development of Model

Earlier authors have used FORMIAN6 programming language to develop the DLG, as modeling of DLG is difficult. In present work, DLG is modeled as a 3D truss since all elements are having only axial tension or compression. Design Constraints Axial Stress Constraint



σj = σ Allowable

(1)

For j = 1, 2 … no. of members The permissible stress in axial tension, σat in Mpa on the net effective area of the member is taken as:

 at  0.6  f y

(2)

The permissible stress in axial compression, σac in Mpa on the net effective area of the member is taken as:   

 ac  0.6

fcc  fy 1



(3)

  f n  f n n  y   cc σac should not be greater than 0.6 fy

Assumptions Made and first analysis

Following assumptions are considered: 1. The sum of dead load and live load equal to 2.5 kN/m2 is applied to the top layer nodes. 2. All the nodes are considered as ball and socket (MERO) joints. 3. Member cross sections are not selected from available Standard profile list. 4. Linear analysis is performed. 5. The design is carried out as per Indian Code IS: 8007. The first analysis was based on a preliminary design e.g. a design where all members were assumed to be of the same section like 100 mm outer diameter with thickness of 6 mm. This analysis would give the member forces, and on the basis of this, a “reasonable” design was chosen with a section sizes in each part of the structure (top layer, bottom layer, and diagonal members). A reanalysis was carried out, based upon the new sections and the member forces and deflection Journal of Structural Engineering Vol. 40, No. 3, August - september 2013

217

Data selection and neural networks training In present work a program is prepared to form the ANN (MATLAB V.6.5)10. No. of such programs were prepared with varying hidden layers and neurons in each layer to come at the solutions given by analysis software for unknown problems. Unknown problems are used to validate the ANN whose outputs are known by actual analysis and they are not included in training set. The program which gives nearby results to software results is chosen and tested. The results are given based on the comparison between analysis software results and the ANN results. In program no of hidden layers are three and in first hidden layer we are having 36 neurons, in second layer there are 47 neurons and in third layer there are 36 Neurons. Input layer contains the neurons equal to the no of input i.e. five and output layer contains neurons equal to the no of outputs i.e. three neurons as shown in Fig. 2. In the present work module sizes are of two types only i.e. 2.5 × 2.5 m and 5 × 5 m. In column under 2.5 for 2.5 × 2.5 m size input will be 1 and for column of 5 it will be 0 for one set. In column under 5 for 5 × 5 m size input will be 1 and for column of 2.5 it will be 0 for other set.

time found is of few hours. But for less no of neurons in hidden layer the training time is more. Also training time depends on the function used for training. In this work Radial Basis (RADBAS) function was used to train the data or form the ANN. For initialization of the network Hyperbolic tangent sigmoid transfer (TANSIG) function was used.11,12 Training by ANN

The data given in Table 2, 3, 4 and 5 is given as input in program which trains the neural network. No. of programs were prepared to change hidden layers and no. of neurons in each hidden layer to arrive at the desired solution and minimizing the error between software results and ANN results. Solution to the unknown problems is confirmed from the high end analysis software’s output for same problems. Variation of results observed in software and ANN results is reflected in terms of graphs as given below in Figs. 3 to 5.

Area of member in mm2

is determined. A reanalysis was carried out and the iterative procedure was continued until the difference in weight of the space frame resulting from two successive cycles was insignificant. Normally, 4 to 6 iterations were necessary. For all practical purposes, such iterative process is adopted by designers. This gives minimum weight design for the considered grid type8,9.

500 450 400 350 300 250 200 150 100 50 0

Software Output ANN Output

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Unknown Problems

Fig. 3 Variation in Area by Software (STAAD 2005) and ANN for Unknown Problems

Grid length Cross section Area Central deflection

Height Module size 2.5 × 2.5m

Weight

Module size 5 × 5m Input Layer

3 Hidden Layers

Output Layer

A processing element (Neuron)

Fig. 2 Architecture of Proposed Neural Network

Such method of input is adopted since to minimize the training time for the ANN. Generally the training 218

Journal of Structural Engineering Vol. 40, No. 3, August - september 2013

300 Deflection in mm

Aspect Ratio

Software Output ANN Output

250 200 150 100 50 0

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Unknown problems

Fig. 4 Variation in Deflection by Software (STAAD 2005) and ANN for Unknown Problems

Table 2 Input and Output of DLG for Group І by Software (STAAD 2005) Input to the STAAD Name

Grid Length (m)

Output from STAAD

Aspect

Height

Ratio=h/L

h =A.R.*L (m)

Module Size

A1 = A2 = A3 Central Weight (kN) (mm2) Deflection (mm) From STAAD

SOS_1

25

0.035

0.875

2.5

82

61.470

196.876

SOS_2

25

0.045

1.125

2.5

53

61.638

125.098

SOS_3

25

0.055

1.375

2.5

39

60.390

90.591

SOS_4

25

0.065

1.625

2.5

30

61.206

68.131

SOS_5

30

0.035

1.05

2.5

106

74.063

380.003

SOS_6

30

0.045

1.35

2.5

68

74.270

244.300

SOS_7

30

0.055

1.65

2.5

49

73.766

176.387

SOS_8

30

0.065

1.95

2.5

38

73.094

136.972

SOS_9

35

0.035

1.225

2.5

131

86.451

659.963

SOS_10

35

0.045

1.575

2.5

84

86.289

431.023

SOS_11

35

0.055

1.925

2.5

60

85.898

313.476

SOS_12

35

0.065

2.275

2.5

46

85.500

244.353

SOS_13

40

0.035

1.4

2.5

157

98.579

1064.632

SOS_14

40

0.045

1.8

2.5

100

98.717

700.091

SOS_15

40

0.055

2.2

2.5

71

98.374

512.956

SOS_16

40

0.065

2.6

2.5

54

98.183

401.702

SOS_17

45

0.035

1.575

2.5

182

111.663

1607.707

SOS_18

45

0.045

2.025

2.5

116

111.396

1070.963

SOS_19

45

0.055

2.475

2.5

82

111.047

790.346

SOS_20

45

0.065

2.925

2.5

62

111.036

621.896

SOS_21

50

0.035

1.75

2.5

208

124.323

2334.125

SOS_22

50

0.045

2.25

2.5

132

124.231

1565.092

SOS_23

50

0.055

2.75

2.5

93

123.842

1162.855

SOS_24

50

0.065

3.25

2.5

70

124.005

919.265

SOS_25

55

0.035

1.925

2.5

235

136.546

3282.734

SOS_26

55

0.045

2.475

2.5

149

136.206

2221.468

SOS_27

55

0.055

3.025

2.5

104

136.719

1649.378

SOS_28

55

0.065

3.575

2.5

78

137.068

1309.585

SOS_29

60

0.035

2.1

2.5

261

149.490

4462.112

SOS_30

60

0.045

2.7

2.5

165

149.217

3038.063

SOS_31

60

0.055

3.3

2.5

115

149.654

2270.497

SOS_32

60

0.065

3.9

2.5

87

148.360

1832.711

SOS_33

65

0.035

2.275

2.5

288

161.93

5941.525

SOS_34

65

0.045

2.925

2.5

182

161.343

4077.974

SOS_35

65

0.055

3.575

2.5

127

161.293

3073.888

SOS_36

65

0.065

4.225

2.5

95

161.603

2467.160

SOS_37

70

0.035

2.45

2.5

314

175.000

7722.021

SOS_38

70

0.045

3.15

2.5

198

174.425

5328.963

SOS_39

70

0.055

3.85

2.5

138

174.334

4037.882



Journal of Structural Engineering Vol. 40, No. 3, August - september 2013

219

Table 2 Input and Output of DLG for Group І by Software (STAAD 2005) Input to the STAAD Name

Grid Length (m)

Output from STAAD

Aspect

Height

Ratio=h/L

h =A.R.*L (m)

Module Size

A1 = A2 = A3 Central Weight (kN) (mm2) Deflection (mm) From STAAD

SOS_40

70

0.065

4.55

2.5

103

174.921

3251.290

SOS_41

75

0.035

2.625

2.5

342

186.980

9921.902

SOS_42

75

0.045

3.375

2.5

215

186.628

6874.586

SOS_43

75

0.055

4.125

2.5

149

187.413

5208.991

SOS_44

75

0.065

4.875

2.5

112

186.540

4246.780

SOS_45

80

0.035

2.8

2.5

370

199.005

12546.154

SOS_46

80

0.045

3.6

2.5

231

199.747

8688.341

SOS_47

80

0.055

4.4

2.5

161

199.239

6657.527

SOS_48

80

0.065

5.2

2.5

121

198.281

5451.305

SOS_49

85

0.035

2.975

2.5

396

212.143

15564.806

SOS_50

85

0.045

3.825

2.5

248

211.999

10878.538

SOS_51

85

0.055

4.675

2.5

173

211.135

8384.090

SOS_52

85

0.065

5.525

2.5

129

211.844

6863.308

SOS_53

90

0.035

3.15

2.5

423

224.744

19132.267

SOS_54

90

0.045

4.05

2.5

265

224.279

13451.796

SOS_55

90

0.055

4.95

2.5

184

224.349

10363.486

SOS_56

90

0.065

5.85

2.5

138

223.779

8532.538

SOS_57

95

0.035

3.325

2.5

450

237.351

23267.706

SOS_58

95

0.045

4.275

2.5

281

237.444

16390.163

SOS_59

95

0.055

5.225

2.5

196

236.356

12738.199

SOS_60

95

0.065

6.175

2.5

146

237.505

10448.198

SOS_61

100

0.035

3.5

2.5

477

249.963

28027.392

SOS_62

100

0.045

4.5

2.5

298

249.766

19848.238

SOS_63

100

0.055

5.5

2.5

207

249.660

15417.978

SOS_64

100

0.065

6.5

2.5

155

249.629

12753.441

Table 3 Input and Output of DLG for Group II by Software (STAAD 2005) Input to the STAAD Name

Output from STAAD

Grid Length

Aspect

Height

(m)

Ratio=h/L

h =A.R.*L (m)

SOS_65

25

0.035

0.875

SOS_66

25

0.045

1.125

SOS_67

25

0.055

SOS_68

25

SOS_69

30

SOS_70 SOS_71

220

A1 = A2 = A3 (mm2)

Central

Weight (kN)

Deflection (mm)

From STAAD

5

89

62.381

103.866

5

58

61.351

65.585

1.375

5

41

62.404

44.566

0.065

1.625

5

32

61.747

33.474

0.035

1.05

5

128

74.212

221.015

30

0.045

1.35

5

81

74.432

137.377

30

0.055

1.65

5

57

74.986

94.662

Journal of Structural Engineering Vol. 40, No. 3, August - september 2013

Module Size

Table 3 Input and Output of DLG for Group II by Software (STAAD 2005) Input to the STAAD Name

Output from STAAD

Grid Length

Aspect

Height

Module Size

A1 = A2 = A3 (mm2)

Central

Weight (kN)

(m)

Ratio=h/L

h =A.R.*L (m)

Deflection (mm)

From STAAD

SOS_72

30

0.065

1.95

5

44

74.011

71.610

SOS_73

35

0.035

1.225

5

173

86.897

414.327

SOS_74

35

0.045

1.575

5

109

86.977

259.306

SOS_75

35

0.055

1.925

5

77

86.512

181.871

SOS_76

35

0.065

2.275

5

58

86.892

135.838

SOS_77

40

0.035

1.4

5

214

99.452

678.717

SOS_78

40

0.045

1.8

5

135

99.128

428.812

SOS_79

40

0.055

2.2

5

94

99.747

298.942

SOS_80

40

0.065

2.6

5

79

99.428

226.218

SOS_81

45

0.035

1.575

5

263

111.924

1069.542

SOS_82

45

0.045

2.025

5

165

112.037

676.912

SOS_83

45

0.055

2.475

5

116

111.305

480.759

SOS_84

45

0.065

2.925

5

87

111.358

364.384

SOS_85

50

0.035

1.75

5

306

124.580

1554.286

SOS_86

50

0.045

2.25

5

192

124.601

990.141

SOS_87

50

0.055

2.75

5

134

124.553

702.766

SOS_88

50

0.065

3.25

5

101

123.701

539.369

SOS_89

55

0.035

1.925

5

357

137.037

2220.251

SOS_90

55

0.045

2.475

5

224

137.047

1423.285

SOS_91

55

0.055

3.025

5

156

137.138

1014.782

SOS_92

55

0.065

3.575

5

117

136.635

780.108

SOS_93

60

0.035

2.1

5

403

149.245

3017.226

SOS_94

60

0.045

2.7

5

253

149.141

1946.522

SOS_95

60

0.055

3.3

5

176

149.267

1394.687

SOS_96

60

0.065

3.9

5

131

149.696

1070.097

SOS_97

65

0.035

2.275

5

454

162.227

4036.317

SOS_98

65

0.045

2.925

5

285

162.151

2618.669

SOS_99

65

0.055

3.575

5

198

162.375

1884.665

SOS_100

65

0.065

4.225

5

148

161.882

1400.747

SOS_101

70

0.035

2.45

5

501

174.648

5226.906

SOS_102

70

0.045

3.15

5

315

174.253

3415.025

SOS_103

70

0.055

3.85

5

219

174.217

2472.980

SOS_104

70

0.065

4.55

5

163

174.267

1918.173

SOS_105

75

0.035

2.625

5

554

187.277

6715.591

SOS_106

75

0.045

3.375

5

348

187.031

4406.980

SOS_107

75

0.055

4.125

5

242

186.797

3204.701

SOS_108

75

0.065

4.875

5

180

186.752

2499.359

SOS_109

80

0.035

2.8

5

605

198.804

8446.551



Journal of Structural Engineering Vol. 40, No. 3, August - september 2013

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Table 3 Input and Output of DLG for Group II by Software (STAAD 2005) Input to the STAAD Name

Output from STAAD

Grid Length

Aspect

Height

Module Size

A1 = A2 = A3 (mm2)

Central

Weight (kN)

(m)

Ratio=h/L

h =A.R.*L (m)

Deflection (mm)

From STAAD

SOS_110

80

0.045

3.6

5

378

199.558

5541.147

SOS_111

80

0.055

4.4

5

263

199.044

4056.296

SOS_112

80

0.065

5.2

5

195

199.484

3165.404

SOS_113

85

0.035

2.975

5

657

212.050

10483.757

SOS_114

85

0.045

3.825

5

412

212.019

6937.887

SOS_115

85

0.055

4.675

5

286

211.798

5090.647

SOS_116

85

0.065

5.525

5

212

212.116

3985.958

SOS_117

90

0.035

3.15

5

705

224.924

12770.311

SOS_118

90

0.045

4.05

5

443

224.322

8509.291

SOS_119

90

0.055

4.95

5

307

224.308

6260.373

SOS_120

90

0.065

5.85

5

228

224.072

4930.751

SOS_121

95

0.035

3.325

5

760

237.382

15534.521

SOS_122

95

0.045

4.275

5

477

236.931

10387.558

SOS_123

95

0.055

5.225

5

330

237.146

7661.263

SOS_124

95

0.065

6.175

5

245

236.804

6054.522

SOS_125

100

0.035

3.5

5

810

249.884

18580.561

SOS_126

100

0.045

4.5

5

510

248.463

12520.733

SOS_127

100

0.055

5.5

5

352

249.117

9249.374

SOS_128

100

0.065

6.5

5

260

249.963

7296.664

Table 4 Input and Output of DLG for Group III by Software (STAAD 2005) Input to the STAAD Name

Grid Length (m)

Output from STAAD

Aspect

Height

Ratio=h/L

h =A.R.*L (m)

Module Size

A1 = A2 = A3 Central Weight (kN) (mm2) Deflection (mm) From STAAD

SOS_193

25

0.05

1.25

5

50

59.364

55.749

SOS_194

25

0.06

1.5

5

40

54.668

43.524

SOS_195

25

0.07

1.75

5

30

58.519

31.086

SOS_196

25

0.08

2

5

25

58.405

24.932

SOS_197

30

0.05

1.5

5

70

71.438

117.977

SOS_198

30

0.06

1.8

5

50

73.985

82.272

SOS_199

30

0.07

2.1

5

40

72.379

64.601

SOS_200

30

0.08

2.4

5

33

72.038

52.207

SOS_201

35

0.05

1.75

5

100

78.094

238.635

SOS_202

35

0.06

2.1

5

70

81.714

165.513

SOS_203

35

0.07

2.45

5

55

80.676

129.353

SOS_204

35

0.08

2.8

5

43

84.380

99.864

SOS_205

40

0.05

2

5

115

96.188

366.154

SOS_206

40

0.06

2.4

5

85

94.646

271.561

222

Journal of Structural Engineering Vol. 40, No. 3, August - september 2013

Table 4 Input and Output of DLG for Group III by Software (STAAD 2005) Input to the STAAD Name

Grid Length (m)

SOS_207

40

SOS_208

40

SOS_209

45

SOS_210

Output from STAAD

Aspect

Height

Module Size

Ratio=h/L

h =A.R.*L (m)

0.07

2.8

5

0.08

3.2

5

0.05

2.25

5

45

0.06

2.7

5

A1 = A2 = A3 Central Weight (kN) (mm2) From STAAD Deflection (mm) 65

95.871

207.991

53

95.110

170.194

140

109.076

577.795

100

110.993

416.690

SOS_211

45

0.07

3.15

5

80

106.688

337.984

SOS_212

45

0.08

3.6

5

65

105.716

278.070

SOS_213

50

0.05

2.5

5

160

123.539

832.225

SOS_214

50

0.06

3

5

120

119.209

636.313

SOS_215

50

0.07

3.5

5

90

122.474

485.313

SOS_216

50

0.08

4

5

72

123.195

395.217

SOS_217

55

0.05

2.75

5

187

135.574

1202.443

SOS_218

55

0.06

3.3

5

135

135.953

889.284

SOS_219

55

0.07

3.85

5

105

134.106

709.587

SOS_220

55

0.08

4.4

5

85

132.774

589.344

SOS_221

60

0.05

3

5

210

148.358

1639.678

SOS_222

60

0.06

3.6

5

155

145.211

1248.434

SOS_223

60

0.07

4.2

5

117

147.578

971.165

SOS_224

60

0.08

4.8

5

95

145.453

813.686

SOS_225

65

0.05

3.25

5

240

158.884

2245.252

SOS_226

65

0.06

3.9

5

175

157.291

1697.946

SOS_227

65

0.07

4.55

5

135

155.978

1358.966

SOS_228

65

0.08

5.2

5

105

160.563

1093.893

SOS_229

70

0.05

3.5

5

265

170.861

2932.909

SOS_230

70

0.06

4.2

5

190

171.953

2191.198

SOS_231

70

0.07

4.9

5

145

172.297

1742.469

SOS_232

70

0.08

5.6

5

115

173.626

1438.208

SOS_233

75

0.05

3.75

5

290

185.122

3758.076

SOS_234

75

0.06

4.5

5

210

184.230

2850.703

SOS_235

75

0.07

5.25

5

160

184.678

2273.769

SOS_236

75

0.08

6

5

130

181.209

1933.394

SOS_237

80

0.05

4

5

320

194.308

4813.505

SOS_238

80

0.06

4.8

5

225

199.119

3559.495

SOS_239

80

0.07

5.6

5

175

195.263

2912.500

SOS_240

80

0.08

6.4

5

140

194.644

2446.207

SOS_241

85

0.05

4.25

5

345

208.678

5974.339

SOS_242

85

0.06

5.1

5

250

207.155

4576.749

SOS_243

85

0.07

5.95

5

190

207.836

3671.698

SOS_244

85

0.08

6.8

5

150

209.899

3052.607

SOS_245

90

0.05

4.5

5

370

221.291

7324.630



Journal of Structural Engineering Vol. 40, No. 3, August - september 2013

223

Table 4 Input and Output of DLG for Group III by Software (STAAD 2005) Input to the STAAD Name

Grid Length (m)

SOS_246

90

SOS_247 SOS_248

Output from STAAD

Aspect

Height

Module Size

A1 = A2 = A3 Central Weight (kN) (mm2) From STAAD Deflection (mm)

Ratio=h/L

h =A.R.*L (m)

0.06

5.4

5

265

222.170

5567.392

90

0.07

6.3

5

200

224.429

4450.432

90

0.08

7.2

5

160

223.572

3763.138

SOS_249

95

0.05

4.75

5

400

232.697

8997.312

SOS_250

95

0.06

5.7

5

285

234.675

6829.779

SOS_251

95

0.07

6.65

5

220

231.474

5607.308

SOS_252

95

0.08

7.6

5

175

231.822

4728.807

SOS_253

100

0.05

5

5

420

248.462

10669.478

SOS_254

100

0.06

6

5

300

249.818

8149.359

SOS_255

100

0.07

7

5

230

248.116

6664.688

SOS_256

100

0.08

8

5

185

245.726

5700.796

Table 5 Input and Output of DLG for Group IV by Software (STAAD 2005) Input to the STAAD Name

Grid Length (m)

Output from STAAD

Aspect

Height

Ratio=h/L

h =A.R.*L (m)

Module Size

A1 = A2 = A3 Central Weight (kN) (mm2) Deflection (mm) From STAAD

SOS_257

25

0.05

1.25

2.5

45

60.977

105.379

SOS_258

25

0.06

1.5

2.5

35

58.577

80.935

SOS_259

25

0.07

1.75

2.5

28

58.454

63.553

SOS_260

25

0.08

2

2.5

25

53.492

56.557

SOS_261

30

0.05

1.5

2.5

60

70.058

217.016

SOS_262

30

0.06

1.8

2.5

45

69.347

163.386

SOS_263

30

0.07

2.1

2.5

35

70.609

126.864

SOS_264

30

0.08

2.4

2.5

28

73.553

100.568

SOS_265

35

0.05

1.75

2.5

70

86.432

362.367

SOS_266

35

0.06

2.1

2.5

53

84.147

279.854

SOS_267

35

0.07

2.45

2.5

42

83.157

225.643

SOS_268

35

0.08

2.8

2.5

35

81.575

191.321

SOS_269

40

0.05

2

2.5

83

99.047

590.191

SOS_270

40

0.06

2.4

2.5

62

97.337

455.095

SOS_271

40

0.07

2.8

2.5

48

98.213

361.908

SOS_272

40

0.08

3.2

2.5

39

98.797

301.212

SOS_273

45

0.05

2.25

2.5

97

110.646

915.579

SOS_274

45

0.06

2.7

2.5

72

108.981

709.359

SOS_275

45

0.07

3.15

2.5

55

111.070

562.039

SOS_276

45

0.08

3.6

2.5

46

107.594

488.719

SOS_277

50

0.05

2.5

2.5

110

123.634

1340.128

224

Journal of Structural Engineering Vol. 40, No. 3, August - september 2013

Table 5 Input and Output of DLG for Group IV by Software (STAAD 2005) Input to the STAAD Name

Grid Length (m)

Output from STAAD

Aspect

Height

Ratio=h/L

h =A.R.*L (m)

Module Size

A1 = A2 = A3 Central Weight (kN) (mm2) Deflection (mm) From STAAD

SOS_278

50

0.06

3

2.5

80

124.065

1025.600

SOS_279

50

0.07

3.5

2.5

63

121.883

847.963

SOS_280

50

0.08

4

2.5

52

119.524

732.504

SOS_281

55

0.05

2.75

2.5

125

134.400

1924.592

SOS_282

55

0.06

3.3

2.5

90

135.901

1470.268

SOS_283

55

0.07

3.85

2.5

70

135.019

1208.618

SOS_284

55

0.08

4.4

2.5

58

131.648

1055.674

SOS_285

60

0.05

3

2.5

137

148.667

2614.447

SOS_286

60

0.06

3.6

2.5

100

147.853

2041.760

SOS_287

60

0.07

4.2

2.5

77

148.252

1671.572

SOS_288

60

0.08

4.8

2.5

62

149.088

1422.732

SOS_289

65

0.05

3.25

2.5

151

160.712

3519.779

SOS_290

65

0.06

3.9

2.5

109

161.452

2735.082

SOS_291

65

0.07

4.55

2.5

85

159.537

2283.188

SOS_292

65

0.08

5.2

2.5

68

161.458

1940.176

SOS_293

70

0.05

3.5

2.5

165

172.814

4636.124

SOS_294

70

0.06

4.2

2.5

120

172.029

3653.131

SOS_295

70

0.07

4.9

2.5

92

172.976

3010.595

SOS_296

70

0.08

5.6

2.5

75

171.491

2623.297

SOS_297

75

0.05

3.75

2.5

180

183.900

6027.961

SOS_298

75

0.06

4.5

2.5

130

184.234

4741.146

SOS_299

75

0.07

5.25

2.5

100

184.529

3939.481

SOS_300

75

0.08

6

2.5

80

186.745

3377.248

SOS_301

80

0.05

4

2.5

195

195.068

7704.673

SOS_302

80

0.06

4.8

2.5

140

196.511

6052.255

SOS_303

80

0.07

5.6

2.5

110

192.454

5164.348

SOS_304

80

0.08

6.4

2.5

87

197.183

4390.837

SOS_305

85

0.05

4.25

2.5

205

211.487

9464.216

SOS_306

85

0.06

5.1

2.5

150

208.859

7614.699

SOS_307

85

0.07

5.95

2.5

115

209.970

6354.599

SOS_308

85

0.08

6.8

2.5

93

210.274

5549.085

SOS_309

90

0.05

4.5

2.5

220

222.684

11782.512

SOS_310

90

0.06

5.4

2.5

158

224.187

9335.555

SOS_311

90

0.07

6.3

2.5

122

223.816

7874.508

SOS_312

90

0.08

7.2

2.5

99

223.526

6920.898

SOS_313

95

0.05

4.75

2.5

235

233.949

14495.484

SOS_314

95

0.06

5.7

2.5

170

233.761

11614.910

SOS_315

95

0.07

6.65

2.5

130

235.850

9729.005



Journal of Structural Engineering Vol. 40, No. 3, August - september 2013

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Table 5 Input and Output of DLG for Group IV by Software (STAAD 2005) Input to the STAAD Name

Grid Length (m)

Output from STAAD

Aspect

Height

Ratio=h/L

h =A.R.*L (m)

Module Size

A1 = A2 = A3 Central Weight (kN) (mm2) Deflection (mm) From STAAD

SOS_316

95

0.08

7.6

2.5

105

236.940

8530.880

SOS_317

100

0.05

5

2.5

248

247.304

17500.335

SOS_318

100

0.06

6

2.5

178

249.179

13955.233

SOS_319

100

0.07

7

2.5

138

248.012

11890.011

SOS_320

100

0.08

8

2.5

112

248.150

10504.067

Some problems (From SOS_129 to SOS_192) are solved by STAAD were not feasible to consider for the training the Neural network, so they are neglected here. Software Output

18000

ANN Output

16000

Weight in kN

14000 12000

ANN Analysis

10000 8000 6000 4000 2000

0

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Unknown Problems

Fig. 5 Variation in Weight by Software (STAAD 2005) and ANN for Unknown Problems

Conclusion In present work the Double Layer Grid (DLG) is analyzed and designed based on the linear analysis performed using Software5. The Artificial Neural Network (ANN) is designed in MATLAB. Present work is arrived at the following conclusions. SOFTWARE Analysis

1.

Deflection of DLG decreases with increase in h/L or Aspect Ratio. 2. Weight of DLG decreases with increasing h/L or Aspect Ratio. 3. Deflection of DLG decreases with increase in area of the member. 4. Weight of DLG increases with increasing area of the member. 226

5. For permissible displacement criteria of IS: 8001984, i.e. span/325, minimum weight given by SOS (Square on Square offset) pattern is 0.4 kN/m2.

Journal of Structural Engineering Vol. 40, No. 3, August - september 2013

1. Training time decreases with increase in No. of hidden layers. 2. Training time decreases with increase in No. of neurons in each hidden layer. 3. Training time decreases with Radial Basis transfer Function than Logarithmic sigmoid transfer function. 4. The performance obtained by ANN technology for preliminary design of DLG structures shows the acceptance of the results. The only effect on the computation time stems from the fact that each training pass requires the presentation of more points, i.e., the training set becomes larger. This problem can be tackled by considering either parallel implementations, or implementations on a neuroprocessor that can be embedded in a conventional machine and provide considerably better execution times. Such an implementation on neural hardware is one of our near future objectives, since it will permit the treatment of many difficult real-world problems. References 1. Chilton J., “Space grid structures” (First Edition), Architectural press, 2000. 2. West F.E.S., “A study of the efficiency of double-

layer grid structures”, M. Phil Thesis, University of Surrey, UK, 1967. 3. Makowski, Z. S., “Analysis, Design and Construction of Double Layer Grids”, Applied Science Publishers/Halstead Press, New York and Toronto, 1981. 4. Ahmed E-S, “Configurations of Double Layer Space Trusses”, Struct. Engg. and Mech., Vol. 6, No. 5, 1998, pp 543–554 5. STAAD Pro (2005) , Bentley. 6. Nooshin, “Configuration Classification in Struct. Engg.”, Elsevier, London, 1984. 7. Code of Practice for general construction in steel IS: 800, 1984. 8. Harty N., and Danaher M., “A Knowledge-Based approach to preliminary design of Buildings”, Proc. of the Institution of Civil Engrs., Structs.



and Build., Vol.104, No-1, 1994, pp 135–144. 9. Mukherjee A., and Deshpande J. M., “Modeling Initial Design Process Using Artificial Neural Networks”, Jl. of Computing in Civil Engg., Vol.9, No.3, 1995, pp 194–200. 10. MATLAB V.6.5, help radbas, The MathWorks, Inc. Software, 2002. 11. Ballal T., Sher W., and Neale R., “Conceptual Structural Design: A Neural Network Approach”, The 13th Inter-Schools Conf. on Design Dev., The University of Huddersfield, UK, 1996. 12. Ballal T. and Sher W. , “Improving the Quality of Structural Design:A Neural Network Approach”, RICS research, pp 1–10.

(Discussion on this article must reach the editor before November 31, 2013)

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