k12 for timber designers' manuel by me.xls

8/14/2019 K12 For Timber Designers' Manuel By me.xls

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It follows : 17.2 TIMBER STRESS GRADES FOR GLULAM COLUMNS

E = EMEAN X K20

= 10800 X 1.07 = 11556

c,par = grade x K3 X K17

= 7.9 X 1 X 1.04 = 8.216

= 7.9 X 1.25 X 1.04 = 10.27

= 7.9 X 1.5 X 1.04 = 12.324

= 7.9 X 1.75 X 1.04 = 14.378

E/c,par = 11556 / 8.22 = 1407

= 11556 / 10.3 = 1125

= 11556 / 12.3 = 937.7

= 11556 / 14.4 = 803.7

FOR SERVICE CLASS 3

E = EMEAN X K2 X K20

= 10800 X 0.8 X 1.07 = 9244.8

c,par = grade x K2 X K3 X K17

= 7.9 X 0.6 X 1 X 1.04 = 4.9296

= 7.9 X 0.6 X 1.25 X 1.04 = 6.162

= 7.9 X 0.6 X 1.5 X 1.04 = 7.3944

= 7.9 X 0.6 X 1.75 X 1.04 = 8.6268

E/c,par = 9244.8 / 4.93 = 1875

= 9244.8 / 6.16 = 1500


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= 9244.8 / 7.39 = 1250

= 9244.8 / 8.63 = 1072


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TABLE 15.1 DETAMINATION OF E/ FOR SERVICES CLASSES 1 AND 2 AND 3

E c//g E/c//g c//g E/c//g c//g E/c//g c//g

C14 4600 5.2 885 6.5 708 7.8 590 9.1

C16 5800 6.8 853 8.5 682 10.2 569 11.9

C18 6000 7.1 845 8.875 676 10.65 563 12.425

C22 6500 7.5 867 9.375 693 11.25 578 13.125

C24 7200 7.9 911 9.875 729 11.85 608 13.825

TR26 7400 8.2 902 10.25 722 12.3 602 14.35

C27 8200 8.2 1000 10.25 800 12.3 667 14.35

Kempas 16000 19.4 825 24.25 660 29.1 550 33.95

Teak 7400 13.4 552 16.75 442 20.1 368 23.45

E c//g E/c//g c//g E/c//g c//g E/c//g c//g

C14 3680 3.12 1179 3.9 944 4.68 786 5.46

C16 4640 4.08 1137 5.1 910 6.12 758 7.14

C18 4800 4.26 1127 5.325 901 6.39 751 7.455

C22 5200 4.5 1156 5.625 924 6.75 770 7.875

C24 5760 4.74 1215 5.925 972 7.11 810 8.295

TR26 5920 4.92 1203 6.15 963 7.38 802 8.61

C27 6560 4.92 1333 6.15 1067 7.38 889 8.61

Kempas 12800 11.64 1100 14.55 880 17.46 733 20.37

Teak 5920 8.04 736 10.05 589 12.06 491 14.07

SERVICE CLASSES 1 AND 2

SERVICE CLASSES 1 AND 3

Long Medium Short Very

Long Medium Short Very


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E/c//g

505

487

483

495

521

516

571

471

316

E/c//g

674

650

644

660

694

688

762

628

421

Short

Short


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Long Medium Short Very Short Long Medium

(N/mm2)

5 0.976 0.976 0.976 0.975 4566 0.976 0.976

10 0.952 0.952 0.952 0.952 1141 0.952 0.952

15 0.929 0.928 0.928 0.928 507 0.929 0.929

20 0.906 0.905 0.904 0.903 285 0.907 0.906

25 0.883 0.881 0.879 0.878 183 0.884 0.883

30 0.859 0.857 0.854 0.851 127 0.862 0.860

35 0.836 0.831 0.827 0.822 93 0.840 0.837

40 0.811 0.805 0.799 0.792 71 0.817 0.813

45 0.786 0.778 0.769 0.759 56 0.794 0.788

50 0.761 0.749 0.737 0.725 46 0.771 0.763

55 0.734 0.720 0.704 0.688 38 0.748 0.738

60 0.707 0.689 0.670 0.650 32 0.724 0.71265 0.680 0.658 0.635 0.612 27 0.701 0.685

70 0.652 0.626 0.600 0.573 23 0.676 0.658

75 0.624 0.594 0.564 0.535 20 0.652 0.631

80 0.595 0.562 0.530 0.498 18 0.628 0.604

85 0.567 0.531 0.496 0.464 16 0.604 0.576

90 0.540 0.501 0.465 0.431 14 0.579 0.550

95 0.513 0.472 0.434 0.400 13 0.556 0.523

100 0.487 0.445 0.406 0.372 11 0.532 0.498

105 0.462 0.418 0.380 0.346 10 0.509 0.473

110 0.438 0.394 0.355 0.323 9 0.487 0.450

115 0.415 0.371 0.333 0.301 9 0.466 0.427

120 0.393 0.349 0.312 0.281 8 0.445 0.405

125 0.373 0.329 0.293 0.263 7 0.425 0.385

130 0.353 0.310 0.275 0.247 7 0.406 0.366

135 0.335 0.293 0.259 0.231 6 0.388 0.347

140 0.318 0.277 0.244 0.217 6 0.370 0.330

145 0.302 0.262 0.230 0.205 5 0.354 0.314

150 0.287 0.248 0.217 0.193 5 0.338 0.299

155 0.273 0.235 0.205 0.182 5 0.324 0.284

160 0.260 0.223 0.195 0.172 4 0.309 0.271

165 0.248 0.212 0.184 0.163 4 0.296 0.259170 0.236 0.201 0.175 0.155 4 0.284 0.247

175 0.225 0.192 0.166 0.147 4 0.272 0.236

180 0.215 0.183 0.158 0.140 4 0.260 0.225

185 0.206 0.174 0.151 0.133 3 0.250 0.215

190 0.197 0.166 0.144 0.126 3 0.240 0.206

195 0.188 0.159 0.137 0.121 3 0.230 0.197

200 0.181 0.152 0.131 0.115 3 0.221 0.189

205 0.173 0.146 0.125 0.110 3 0.213 0.182

Service Classes 1 and 2 ServiceEuler

Stress

K12 and Euler Stress Value FOR C24 glulam

E/c,par1,407 1,125 938 804 1,875 1,500


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210 0.166 0.139 0.120 0.105 3 0.204 0.174

215 0.159 0.134 0.115 0.101 2 0.197 0.167

220 0.153 0.128 0.110 0.097 2 0.190 0.161

225 0.147 0.123 0.106 0.093 2 0.183 0.155

230 0.142 0.118 0.102 0.089 2 0.176 0.149

235 0.137 0.114 0.098 0.085 2 0.170 0.144

240 0.132 0.110 0.094 0.082 2 0.164 0.138245 0.127 0.106 0.090 0.079 2 0.158 0.134

250 0.122 0.102 0.087 0.076 2 0.153 0.129


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Short Very Short

(N/mm2)

0.976 0.976 3653

0.952 0.952 913

0.929 0.928 406

0.905 0.905 228

0.882 0.881 146

0.858 0.856 101

0.833 0.830 75

0.808 0.804 57

0.782 0.776 45

0.755 0.746 37

0.727 0.716 30

0.698 0.684 250.669 0.652 22

0.639 0.619 19

0.609 0.587 16

0.579 0.554 14

0.549 0.522 13

0.520 0.492 11

0.492 0.462 10

0.465 0.435 9

0.439 0.408 8

0.415 0.384 8

0.392 0.361 7

0.370 0.339 6

0.350 0.319 6

0.331 0.301 5

0.313 0.284 5

0.296 0.268 5

0.281 0.253 4

0.266 0.240 4

0.253 0.227 4

0.240 0.215 4

0.229 0.204 30.218 0.194 3

0.207 0.185 3

0.198 0.176 3

0.189 0.168 3

0.180 0.160 3

0.173 0.153 2

0.165 0.146 2

0.158 0.140 2

1,072

Classes 3Euler

Stress

1,250


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0.152 0.134 2

0.146 0.128 2

0.140 0.123 2

0.134 0.118 2

0.129 0.114 2

0.124 0.109 2

0.120 0.105 20.115 0.101 2

0.111 0.098 1


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(N/mm2)

5 0.976 0.975 0.975 0.975 6322 0.976 0.976

10 0.952 0.951 0.951 0.951 1580 0.952 0.952

15 0.928 0.927 0.926 0.926 702 0.928 0.928

20 0.903 0.902 0.900 0.898 395 0.905 0.904

25 0.878 0.875 0.872 0.868 253 0.881 0.879

30 0.851 0.846 0.841 0.835 176 0.856 0.853

35 0.823 0.815 0.806 0.797 129 0.831 0.825

40 0.793 0.781 0.768 0.754 99 0.804 0.796

45 0.761 0.744 0.725 0.706 78 0.777 0.765

50 0.727 0.704 0.680 0.654 63 0.748 0.732

55 0.691 0.662 0.632 0.601 52 0.718 0.698

60 0.654 0.619 0.583 0.548 44 0.687 0.66265 0.616 0.575 0.536 0.498 37 0.655 0.626

70 0.578 0.533 0.490 0.451 32 0.623 0.589

75 0.540 0.492 0.448 0.409 28 0.591 0.553

80 0.504 0.454 0.409 0.371 25 0.559 0.517

85 0.469 0.418 0.374 0.337 22 0.527 0.483

90 0.437 0.385 0.342 0.307 20 0.497 0.451

95 0.406 0.355 0.314 0.280 18 0.468 0.421

100 0.378 0.328 0.289 0.257 16 0.440 0.392

105 0.352 0.304 0.266 0.236 14 0.414 0.366

110 0.328 0.282 0.246 0.217 13 0.389 0.342

115 0.306 0.262 0.227 0.201 12 0.366 0.320

120 0.286 0.243 0.211 0.186 11 0.344 0.299

125 0.268 0.227 0.196 0.173 10 0.324 0.280

130 0.251 0.212 0.183 0.161 9 0.306 0.263

135 0.236 0.199 0.171 0.150 9 0.289 0.247

140 0.222 0.186 0.160 0.140 8 0.273 0.233

145 0.209 0.175 0.150 0.131 8 0.258 0.219

150 0.197 0.165 0.141 0.123 7 0.244 0.207

155 0.186 0.155 0.133 0.116 7 0.231 0.196

160 0.176 0.146 0.125 0.109 6 0.219 0.185

165 0.167 0.138 0.118 0.103 6 0.208 0.175170 0.158 0.131 0.112 0.098 5 0.198 0.166

175 0.150 0.124 0.106 0.092 5 0.188 0.158

180 0.143 0.118 0.101 0.088 5 0.179 0.150

185 0.136 0.112 0.095 0.083 5 0.171 0.143

190 0.129 0.107 0.091 0.079 4 0.163 0.136

195 0.123 0.102 0.086 0.075 4 0.156 0.130

200 0.118 0.097 0.082 0.072 4 0.149 0.124

205 0.112 0.093 0.079 0.068 4 0.143 0.119

K12 FOR KEMPUS

E/c,par825 660 550 471 1,100 880

Service Classes 1 and 2Euler

Stress

Service


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210 0.108 0.088 0.075 0.065 4 0.137 0.114

215 0.103 0.085 0.072 0.062 3 0.131 0.109

220 0.099 0.081 0.069 0.060 3 0.126 0.104

225 0.095 0.078 0.066 0.057 3 0.121 0.100

230 0.091 0.075 0.063 0.055 3 0.116 0.096

235 0.087 0.072 0.061 0.053 3 0.112 0.092

240 0.084 0.069 0.058 0.050 3 0.108 0.089245 0.081 0.066 0.056 0.048 3 0.104 0.085

250 0.078 0.064 0.054 0.047 3 0.100 0.082

320.1 0.049 0.040 0.033 0.029 2 0.063 0.052

121.9 0.279 0.237 0.205 0.181 11 0.336 0.292

130.8 0.249 0.210 0.181 0.159 9 0.303 0.261

178.1 0.145 0.120 0.103 0.089 5 0.183 0.153

346.5 0.042 0.034 0.029 0.025 1 0.054 0.044

166.3 0.164 0.137 0.117 0.102 6 0.206 0.173

436 0.027 0.022 0.018 0.016 1 0.035 0.029


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Short Very Short

(N/mm2)

0.975 0.975 5057

0.951 0.951 1264

0.927 0.927 562

0.902 0.901 316

0.876 0.874 202

0.849 0.845 140

0.819 0.813 103

0.787 0.778 79

0.753 0.739 62

0.716 0.698 51

0.677 0.655 42

0.637 0.610 350.596 0.565 30

0.555 0.522 26

0.516 0.480 22

0.478 0.442 20

0.443 0.406 17

0.410 0.374 16

0.380 0.344 14

0.352 0.318 13

0.326 0.293 11

0.303 0.272 10

0.282 0.252 10

0.263 0.235 9

0.246 0.219 8

0.230 0.204 7

0.216 0.191 7

0.203 0.179 6

0.190 0.168 6

0.179 0.158 6

0.169 0.149 5

0.160 0.140 5

0.151 0.133 50.143 0.126 4

0.136 0.119 4

0.129 0.113 4

0.123 0.107 4

0.117 0.102 4

0.111 0.097 3

0.106 0.093 3

0.102 0.089 3

Euler

Stress

733 628

Classes 3


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0.097 0.085 3

0.093 0.081 3

0.089 0.078 3

0.085 0.074 2

0.082 0.071 2

0.079 0.068 2

0.076 0.066 20.073 0.063 2

0.070 0.061 2

0.044 0.038 1

0.256 0.228 9

0.228 0.202 7

0.132 0.115 4

0.037 0.032 1

0.149 0.131 5

0.024 0.021 1


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(N/mm2)

5 0.975 0.975 0.975 0.975 4566 0.975 0.975

10 0.951 0.951 0.951 0.950 1141 0.951 0.951

15 0.926 0.925 0.924 0.923 507 0.927 0.927

20 0.900 0.898 0.895 0.892 285 0.902 0.901

25 0.872 0.867 0.862 0.856 183 0.876 0.873

30 0.841 0.832 0.822 0.812 127 0.849 0.843

35 0.806 0.792 0.776 0.759 93 0.819 0.810

40 0.768 0.747 0.723 0.698 71 0.787 0.773

45 0.726 0.696 0.664 0.631 56 0.753 0.733

50 0.680 0.642 0.602 0.563 46 0.716 0.690

55 0.633 0.587 0.541 0.499 38 0.677 0.644

60 0.584 0.532 0.484 0.441 32 0.637 0.59865 0.537 0.481 0.432 0.390 27 0.596 0.551

70 0.491 0.434 0.386 0.346 23 0.556 0.507

75 0.449 0.392 0.346 0.308 20 0.517 0.465

80 0.410 0.355 0.311 0.275 18 0.479 0.426

85 0.375 0.322 0.280 0.247 16 0.444 0.391

90 0.343 0.292 0.254 0.223 14 0.411 0.358

95 0.315 0.267 0.230 0.202 13 0.381 0.329

100 0.290 0.244 0.210 0.184 11 0.353 0.303

105 0.267 0.224 0.192 0.168 10 0.327 0.280

110 0.246 0.206 0.177 0.154 9 0.304 0.259

115 0.228 0.190 0.163 0.142 9 0.283 0.240

120 0.212 0.176 0.150 0.131 8 0.264 0.223

125 0.197 0.163 0.139 0.121 7 0.247 0.208

130 0.184 0.152 0.130 0.113 7 0.231 0.194

135 0.172 0.142 0.121 0.105 6 0.216 0.181

140 0.161 0.133 0.113 0.098 6 0.203 0.170

145 0.151 0.124 0.105 0.092 5 0.191 0.159

150 0.142 0.117 0.099 0.086 5 0.180 0.150

155 0.133 0.110 0.093 0.081 5 0.170 0.141

160 0.126 0.103 0.087 0.076 4 0.160 0.133

165 0.119 0.097 0.082 0.071 4 0.152 0.126170 0.112 0.092 0.078 0.067 4 0.144 0.119

175 0.106 0.087 0.074 0.064 4 0.136 0.113

180 0.101 0.083 0.070 0.060 4 0.130 0.107

185 0.096 0.078 0.066 0.057 3 0.123 0.101

190 0.091 0.074 0.063 0.054 3 0.117 0.097

195 0.087 0.071 0.060 0.052 3 0.112 0.092

200 0.083 0.067 0.057 0.049 3 0.107 0.088

205 0.079 0.064 0.054 0.047 3 0.102 0.084

K12 FOR TEAK

E/c,par552 442 368 316 736 589

Service Classes 1 and 2Euler

Stress

Service


14/68

210 0.075 0.061 0.052 0.045 3 0.097 0.080

215 0.072 0.059 0.050 0.043 2 0.093 0.076

220 0.069 0.056 0.047 0.041 2 0.089 0.073

225 0.066 0.054 0.045 0.039 2 0.086 0.070

230 0.063 0.052 0.043 0.038 2 0.082 0.067

235 0.061 0.049 0.042 0.036 2 0.079 0.065

240 0.058 0.047 0.040 0.035 2 0.076 0.062245 0.056 0.046 0.038 0.033 2 0.073 0.060

250 0.054 0.044 0.037 0.032 2 0.070 0.057


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Short Very Short

(N/mm2)

0.975 0.975 3653

0.951 0.951 913

0.926 0.925 406

0.899 0.897 228

0.869 0.866 146

0.836 0.830 101

0.799 0.788 75

0.758 0.741 57

0.711 0.688 45

0.661 0.632 37

0.610 0.575 30

0.558 0.520 250.508 0.468 22

0.462 0.421 19

0.419 0.380 16

0.381 0.343 14

0.347 0.310 13

0.316 0.282 11

0.289 0.257 10

0.265 0.235 9

0.244 0.215 8

0.225 0.198 8

0.208 0.183 7

0.192 0.169 6

0.179 0.157 6

0.166 0.146 5

0.155 0.136 5

0.145 0.127 5

0.136 0.119 4

0.128 0.112 4

0.120 0.105 4

0.113 0.099 4

0.107 0.093 30.101 0.088 3

0.096 0.083 3

0.091 0.079 3

0.086 0.075 3

0.082 0.071 3

0.078 0.068 2

0.074 0.064 2

0.071 0.062 2

Euler

Stress

491 421

Classes 3


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0.068 0.059 2

0.065 0.056 2

0.062 0.054 2

0.059 0.051 2

0.057 0.049 2

0.055 0.047 2

0.052 0.045 20.050 0.044 2

0.048 0.042 1


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UDL on Member = 0.44 kN/m

Axial Loading on Member

= 3453.262384

Length of Member = 4.62 m

Moment on Member = 1.173942 kN m

Trail section = 50 x 125

Z = 1.30E+05

m,a = 9.02E+00

c,a = 0.552521981

x = 320.0829892

y = 128.0331957

= 320.0829892

K12 = 0.03960829 For Medium

K3 = 1.25

c,g = 19.4

c,adm = 0.960501021

Check for very short term condition

K3 = 1.75

K12 = 0.028850779 320.083

c,adm = 0.979483934

c,a = 0.552521981

K7 = 1.10109106

For =


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m,g = 19.3

m,adm = 37.18935056

m,a = 9.02E+00

Euler Critical Stress

e = 2 N/mm2

Euler Co-efficient Keu = 0.984499194

Interaction Formula = 0.246248674 + 0.575244

= 0.821492187


19/68



= 2065.0652




Z = 1.30E+05

m,a = 1.31E+00

c,a = 0.330410432

x = 121.9363769

y = 48.77455074

= 121.9363769

K12 = 0.236904042 For Medium

K3 = 1.25

c,g = 19.4

c,adm = 5.74492303


K3 = 1.75

K12 = 0.180663873 121.9364

c,adm = 6.133538499

For =


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c,a = 0.330410432

K7 = 1.10109106

m,g = 19.3

m,adm = 37.18935056

m,a = 1.31E+00


e = 11 N/mm2



= 0.09299518


21/68



= 3453.262384




Z = 1.30E+05

m,a = 9.02E+00

c,a = 0.552521981

x = 320.0829892

y = 128.0331957

= 320.0829892

K12 = 0.03960829 For Medium

K3 = 1.25

c,g = 19.4

c,adm = 0.960501021


K3 = 1.75

K12 = 0.028850779 320.083

c,adm = 0.979483934

For =


22/68

c,a = 0.552521981

K7 = 1.10109106

m,g = 19.3

m,adm = 37.18935056

m,a = 9.02E+00


e = 2 N/mm2



= 0.821492187


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Lets check deflection

2470 mm length Span Continuation of Cantilever Portion of 1820 mm is considered

1 Geomatric Properties

= 1.82 m

= 0.4 m

Raft Dimension

= 50 mm= 125 mm

= b x h

= mm2

= 1/12 x b x h3

= mm4

2 Loading

= 0.6 kNm-2

= 0.5 kNm-2

= (DL+IL) x JS xLe

= 0.8008 kN

3 K-Factors

= 1

= 1 for longterm

= 1

= 1 for notch fro

= 1

= (300 mm /h)0.11

K7 = 1.10109106

= 1

4 Grade Stress

Strength Class

= 19.3 Nmm-2

= 4.3 Nmm-2

no wa

= 2.3 Nmm-2

Reference was made to Ex 5.15 on page No:249 Analysis of Structures Vol-1 By Prof V.N. Vazirani, Dr M.

Dr S.K.Duggal

It is illustrated that Bending Moment of Inclind member could be written as in the form of

member

Reference was made to Example 4.2 Design of Main Beam from from Structural Timber Design By Abdy Ke

BS 5268: Part 2, Tables 14

Kempas Grade HS

Bending parallel to grain m.g.//

Compression perpenidcular to grain c.g.pp

Shear parallel to grain g.//

Bearing : assume 50 mm, but located>75 mm

from the end of the member (K4, Table 18)

Notch end effect (K5,Clause 2.10.4)

Form factor K6 (K6, Clause 2.10.5)

Depth factor (K7 Clause 2.10.6)

No Load sharing(K8, Clause 2.9) K8

Effective span Le

Spacing of Rafters, JS

Breadth of Section, bDepth of section, h

Dead Load, DL

Imposed Load, IL

Cross-sectional area, A

Second moment of area Ixx

8.1E+06

6.25E+03

Total Load, W

Load Duration(K#, Table 17) K3

Service class 1 (K2, Table 16) K2


24/68

= Nmm-2

5 Bending stress

= W.Le/2

= 0.728728 kN-m

= bh2/6

= mm3

= M/ Zprovided

= Nm-2

= 19.3 x K2.K3.K6.K

21.25105746 Nm-2

6 Lateral stability

= 2.5End held in position for h/b=3, No Leteral Support for h/b = 2

7 Shear stress

= W(N+L)2/2Le

N=1290 mm Cantilever portion N = 1820 mm

L= Span length following Cantilever 1750 mm Span L = 2470 mm

W = 0.44 kN/m =N/mm

= W(N+L)2/2Le

= 1639.231579 N

3 Fv

2 b .

= 0.393415579 Nmm-2

= 2.3 x K2.K3.K5.K

= 2.3

8 Bearing stress

= W(N+L)2/2Le

( Ref:Example 5.8 pages (233-237) and page 1317 of APPENDIX from Analysis of structure Vol-1 by ProfDr M.M. Ratwani,Dr. S.K.Duggal )

( Ref:Example 5.8 pages (233-237) and page 1317 of APPENDIX from Analysis of structure Vol-1 by Prof

Dr M.M. Ratwani,Dr. S.K.Duggal )

=

Section modulus Zprovided

Applied bending stress

BS 5268; Part 2, Clause 2.10.8, and Table 19

Maximum depth to breadth ratio, h/b

Applied shear force from shear force diagram

Applied shear force Fv

Applied bending moment

Mean modulus of elasticity, load sharing Emean

1.E+05

5.60

Applied Load from shear force diagram

Permissible shear stress, no notch

Applied shear force Fv

19100

Applied shear stress a

Permissible bending stress


25/68

1639.231579 N

Assume bearing width, bw, of 100 mm either side

bw = 100

= Fv/(b .bw)

= 3.E-03

= 4.3 x K2.K3.K4.K

= 4.3

= Fv/(b . c.a.pp)

9 Deflection

w = (DL+IL) x JS kN/m

= 0.44

L = 2570.019 mm

= 2.570019 m

N = 1820

1.82 m

I = Ixx

= 8138020.833 x 1.E+05

n = N/L

= 0.708165971

= WLe3N

24E I

OR

( Ref: pages (232-233) along with figure 12.16 of Timber Designers' Manuel 3rd Ed by E.C.Ozalton )

= 7.55 mm

= (1.2/Gbd)wx.dx

Shear Modulus =Shear stress/Shear strain i.e. say G=(/)

Poissson's ratio ( ) = Lateral strain /Longitudinal strain

( Ref:Example 5.8 pages (233-237) and page 1317 of APPENDIX from Analysis of structure Vol-1 by Prof

Dr M.M. Ratwani,Dr. S.K.Duggal )

( Ref:page 451 of Analysis of structure Vol-1 by Prof V.N.Vaziani, Dr M.M. Ratwani,Dr. S.K.Duggal )

( Ref:page 272 of Strength of Materials for Civil Engineers 2nd Ed by T.H.G.Megson )

Permissible bearing stress c.a.pp

Minimum required bearing width

Applied bearing stress c.a.pp

Defelection due to Bending m

Defelection due to Shearing

Defelection due to Bending m

(3n

3

+4n

2

-1)


26/68

E=2G(1+)

Also G=Emean/16

(19.2/Ebd)wx.dx

= 0.117206933

= 7.67 mm

OR

= Le/180

= 10.11 mm

Lets Check with Interaction Formula



= 512.4862134 N

Horizontal Length of Member X2 = 2.47 m

Horizontal Length of Cantilever X1 = 1.82 m

Inclined Length of Member l = 2.570019

Inclined Length of Cantilever a = 1.887432



Z = 1.30E+05

m,a = 0.538358161

c,a = 0.081997794

( Ref:page 18: 2.5.7 Additional Properties of Structural Timber Design by ABDY KERMANI )

( Ref:Deflection Limit from page 68 of Structural Engineer's Pocket Book by FIONA COBB )

( Ref:4th line of 1st pargraph from page 232 of Timber Designers' Manuel 3rd Ed by E.C.Ozalton

( Ref:page 249-251 of Analysis of structure Vol-1 by Prof V.N.Vaziani, Dr M.M. Ratwani,Dr. S.K.Dug

Defelection due to Shear s

Total Defelection due to Bending plus Shear T

Permissible deflection for Cantilevers adm

=

= ( 19 .2) .( M )

( b . h ) . E


27/68


28/68

k5=he/h

fig 2(b) of the code

ne

.Ratwani,

Horizontal

ramani


29/68

.K8

.N.Vaziani,

.N.Vaziani,


30/68

mm3

.N.Vaziani,


31/68

al )


32/68

O.k

130.7651

O.k


33/68



= 512.4862134 N

Horizontal Length of Member X2 = 2.47 m

Horizontal Length of Cantilever X1 = 1.82 m

Inclined Length of Member l = 2.570019

Inclined Length of Cantilever a = 1.887432



Z = 1.30E+05

m,a = 0.538358161

c,a = 0.081997794

x = 178.0561394

y = 71.22245575

= 178.0561394

K12 = 0.120349401 For Medium

K3 = 1.25

c,g = 19.4

c,adm = 2.918472963 > 0.081998

K3 = 1.75

K12 = 0.089337591 For =



34/68

c,adm = 3.033011216

c,a = 0.081997794

K7 = 1.10109106

m,g = 19.3

m,adm = 37.18935056

m,a = 5.38E-01


e = 5 N/mm2



= 0.042604248 < 1


It follows : Example 4.2 Design of Main Beam from Structural Timber Design By Abdy Keramani

2470 mm length Span Continuation of Cantilever Portion


= 2.47 m

= 0.4 m

Raft Dimension

= 50 mm

= 125 mm

= b x h

= 6.25 x 1.E+03

= 1/12 x b x h3

= mm4

2 Loading

= 0.6 kNm-2

= 0.5 kNm-2

= (DL+IL) x JS xLe

= 1.0868 kN

3 K-Factors

= 1

8.1E+06

Effective span

Breadth of Section, b

Depth of section, h




Dead Load, DL

Imposed Load, IL

Total Load, W



35/68

= 1 for longterm


from the end of the member (K4, Table 18) = 1

= 1 for no notch

= 1

= (300 mm /h)0.11

K7 = 1.10109106

= 1.1

4 Grade Stress


Kempas Grade HS Strength Class

= 19.3 Nmm-2

= 4.3 Nmm-2

no wa

= 2.3 Nmm-2

= Nmm-2

5 Bending stress( Ref:Example 5.8 pages (233-237) and page 1317 of APPENDIX from Analysis of structure Vol-1 by

= W x (L2-a

2)2

8.L2

L = 2470 mm

= 2.47 m

a = 1820 mm

1.82 m

= W x (L2-a

2)2

8.L2

= 0.070098719 kN-m

= bh2/6

= mm3

= M/ Zprovided

= Nm-2

= 19.3 x K2.K3.K6.K

23.37616321 Nm-2

6 Lateral stability

= 2.5

End held in position and compression edge held in line as by direct connection of sheating,

19100

1.30E+05

5.38.E-01





Load sharing appies with Purlin(K8, Clause 2.9)K8













36/68


37/68

= 0.01 mm

= -0.11 mm


= Le/330 Or 14 mm

= 7.484848485 mm

= ( 19 .2) .( M )

( b . h ) . EDefelection due toShear s

Total Defelection due toShear plus Bending T

Permissible deflection adm


38/68

O.k

178.0561


39/68

O.k

mm2


40/68

ne

rof V.N.Vaziani, Dr M.M. Ratwani,Dr. S.K.Duggal )

.K8

deck or joist


41/68


2.47 m

1.82 m

0.564474 m

0.44 kN/m=N/mm


42/68


43/68





= 4.81 m= 0.4 m

Raft Dimension

= 50 mm

= 150 mm

= b x h

= 7.5 x 1.E+03 mm2

= 1/12 x b x h3

= mm4

2 Loading

= 0.6 kNm-2

= 0.5 kNm-2

= (DL+IL) x JS xLe

= 2.1164 kN

3 K-Factors

= 1

= 1 for longterm



= 1 for no notch

= 1

= (300 mm /h)0.11

K7 = 1.079228237

= 1.1

4 Grade Stress



= 19.3 Nmm-2

= 4.3 Nmm-2

no wane

= 2.3 Nmm-2

= Nmm-2

5 Bending stress

( Ref:Example 5.8 pages (233-237) and page 1317 of APPENDIX from Analysis of structure Vol-1 by Prof V.N.V

19100







Imposed Load, IL

Total Load, W





Effective spanSpacing of Rafters, JS


Depth of section, h



1.4E+07

Dead Load, DL


44/68

= W x (L2-a

2)

2

8.L2

L = 4810 mm

= 4.81 m

a = 0 mm

0 m

= W x (L2-a

2)

2

8.L2

= 1.2724855 kN-m

= bh2/6

= mm3

= M/ Zprovided

= Nm-2

= 19.3 x K2.K3.K6.K7.K8

22.91201546 Nm-2

6 Lateral stability

= 3

End held in position and compression edge held in line as by direct connection of sheating, deck or joi

7 Shear stress

= W(N+L)2/2Le kN

W = 0.44 kN/m =N/mm

= W(N+L)2/2Le

= 5212.730769 N

= 3 Fv

2 b .

= 1.042546154

= 2.3 x K2.K3.K5.K8

L=9'-9" Span following Cantilever


Applied shear force


Applied shear stress


6.79.E+00





N=6'-0" Cantilever portion




1.88E+05



45/68

= 2.53

8 Bearing stress

= 5.213 kN


bw = 100

= Fv/(b .bw)

= 1.042546154

= 4.3 x K2.K3.K4.K8

= 4.73

=

9 Deflection

= Emean


l = 4.81

a= 0

= (l2-a

2)/2l x= 2.405

= 0.5 w= 0.44

= 0

= wl4(m

4-2m

3(1-n

2)+m(1-2n

2))

24EI

= 11.42 mm

= 0.17 mm

= 11.59 mm


= Le/330 Or 14 mm

= 14.57575758 mm

( b . h ) . E



x

m=x/l

n=a/l

m

Defelection due toShear s =

Permissible shearing stress


Load Sharing system E

Max Defelection due to Bending at x=(l2-a2)/2l m =

( 19 .2) .( M )

Applied Load from shear force



46/68

Lets Check with Interaction FormulaUDL on Member = 0.44 kN/m

= 0.55756767 N

= 4.81 m

= 0 m

= 5.0013

= 0

= 1.2724855 kN m

= 50 x 150

Z = 1.88E+05

m,a = 6.786589333

c,a = 7.43424E-05

x = 346.5002282

y = 115.5000761

= 346.5002282

K12 = 0.0339821 For Medium

K3 = 1.25

c,g = 19.4

c,adm = 0.824065919 > 7.43E-05 O.k

Trail section


Horizontal Length of Member X2

Horizontal Length of Cantilever X1

Inclined Length of Member l

Inclined Length of Cantilever a

Moment on Member



47/68

K3 = 1.75

K12 = 0.089337591 346.5002

c,adm = 3.033011216

c,a = 7.43424E-05

K7 = 1.079228237

m,g = 19.3

m,adm = 36.45093369

m,a = 6.79E+00


e = 1 N/mm2


Interaction Formula = 0.186185648 + 9.02E-05

= 0.186275862 < 1 O.k

For =


48/68

ziani, Dr M.M. Ratwani,Dr. S.K.Duggal )


49/68

t


50/68


m

m

m

kN/m=N/mm


51/68





= 2.31 m= 0.4 m

Raft Dimension

= 50 mm

= 150 mm

= b x h

= 7.5 x 1.E+03 mm2

= 1/12 x b x h3

= mm4

2 Loading

= 0.6 kNm-2

= 0.5 kNm-2

= (DL+IL) x JS xLe

= 1.0164 kN

3 K-Factors

= 1

= 1 for longterm



= 1 for no notch

= 1

= (300 mm /h)0.11

K7 = 1.079228237

= 1.1

4 Grade Stress



= 19.3 Nmm-2

= 4.3 Nmm-2

no wane

= 2.3 Nmm-2

= Nmm-2

5 Bending stress


Mean modulus of elasticity, load sharing Emean 19100







Dead Load, DL

Imposed Load, IL

Total Load, W




Effective spanSpacing of Rafters, JS


Depth of section, h



1.4E+07


52/68

= W x (L2-a

2)

2

8.L2

L = 2310 mm

= 2.31 m

a = 0 mm

0 m

= W x (L2-a

2)

2

8.L2

= 0.2934855 kN-m

= bh2/6

= mm3

= M/ Zprovided

= Nm-2

= 19.3 x K2.K3.K6.K7.K8

22.91201546 Nm-2

6 Lateral stability

= 3

End held in position and compression edge held in line as by direct connection of sheating, deck or joi

7 Shear stress

= W(N+L)2/2Le kN

W = 0.44 kN/m =N/mm

= W(N+L)2/2Le

= 5212.730769 N

= 3 Fv

2 b .

= 1.042546154

= 2.3 x K2.K3.K5.K8






Applied shear force



1.57.E+00








1.88E+05


53/68

= 2.53

8 Bearing stress

= 5.213 kN


bw = 100

= Fv/(b .bw)

= 1.042546154

= 4.3 x K2.K3.K4.K8

= 4.73

=

9 Deflection

= Emean


l = 2.31

a= 0

= (l2-a

2)/2l x= 1.155

= 0.5 w= 0.44

= 0

= wl4(m

4-2m

3(1-n

2)+m(1-2n

2))

24EI

= 0.61 mm

= 0.04 mm

= 0.65 mm


= Le/330 Or 14 mm

= 7 mm

( 19 .2) .( M )

( b . h ) . E


n=a/l


m

Defelection due toShear s =



x

m=x/l

Applied Load from shear force





54/68


= 0.267771584 N

= 2.31 m

= 0 m

= 2.399708

= 0

= 0.2934855 kN m

= 50 x 150

Z = 1.88E+05

m,a = 1.565256000

c,a

= 3.57029E-05

x = 166.2566472

y = 55.41888239

= 166.2566472

K12 = 0.136524546 For Medium

K3 = 1.25

c,g = 19.4

c,adm = 3.310720248 > 3.57E-05 O.k

Trail section






Moment on Member


55/68

K3 = 1.75

K12 = 0.101707005 166.2566

c,adm = 3.452952825

c,a = 3.57029E-05

K7 = 1.079228237

m,g = 19.3

m,adm = 36.45093369

m,a = 1.57E+00


e = 6 N/mm2


Interaction Formula = 0.042941492 + 1.08E-05

= 0.042952276 < 1 O.k


For =


56/68



57/68

t


58/68


m

m

m

kN/m=N/mm


59/68



6050 mm length Span Continuation of Cantilever Portion = 0.00 mm


= 6.05 m

= 0.4 m

Raft Dimension

= 50 mm

= 200 mm

= b x h

= 10 x 1.E+03

= 1/12 x b x h3

= mm4

2 Loading

= 0.6 kNm-2

= 0.5 kNm-2

= (DL+IL) x JS xLe

= 2.662 kN

3 K-Factors

= 1

= 1 for longterm



= 1 for no notch

= 1

= (300 mm /h)0.11

K7 = 1.045610747

= 1.1

4 Grade Stress



= 19.3 Nmm-2

= 4.3 Nmm-2

no wa

= 2.3 Nmm-2

= Nmm-2

5 Bending stress

( Ref:Example 5.8 pages (233-237) and page 1317 of APPENDIX from Analysis of structure Vol-1 by

= W x (L2-a

2)2

8.L2

L = 6050 mm






Mean modulus of elasticity, load sharing Emean 19100

Total Load, W






Depth of section, h



3.3E+07

Dead Load, DL

Imposed Load, IL

Effective span




60/68

= 6.05 m

a = 0 mm

0 m

= W x (L2-a

2)2

8.L2

= 2.0131375 kN-m

= bh2/6

= mm3

= M/ Zprovided

= Nm-2

= 19.3 x K2.K3.K6.K

22.19831617 Nm-2

6 Lateral stability

= 4

End held in position and compression edge held in line as by direct connection of sheating,

7 Shear stress

= W(N+L)2/2Le kN

W = 0.44 kN/m =N/mm

= W(N+L)2/2Le

= 5212.730769 N

= 3 Fv

2 b .

= 0.781909615

= 2.3 x K2.K3.K5.K

= 2.53

8 Bearing stress

= 5.213 kNApplied Load from shear force


Applied shear force












3.33E+05


6.04.E+00


61/68


bw = 100

= Fv/(b .bw)

= 1.042546154

= 4.3 x K2.K3.K4.K

= 4.73

=

9 Deflection

= Emean

( Ref:Example 5.8 pages (233-237) and page 1317 of APPENDIX from Analysis of structure Vol-1 by

l =

a=

= (l2-a

2)/2l x=

= 0.5 w=

= 0

= wl4(m

4-2m

3(1-n

2)+m(1-2n

2))

24EI

= 12.06 mm

= 0.20 mm

= 12.26 mm


= Le/330 Or 14 mm

= 18.33333333 mm


= 0.701306529 N


m

Defelection due toShear s = ( 19 .2) .( M )

( b . h ) . E



x

m=x/l

n=a/l







62/68

= 6.05 m

= 0 m

= 6.292487584

= 0

= 2.0131375 kN m

= 50 x 200

Z = 3.33E+05

m,a = 6.039412500

c,a = 7.01307E-05

x = 435.9563281

y = 108.989082

= 435.9563281

K12 = 0.021752194 For Medium

K3 = 1.25

c,g = 19.4

c,adm = 0.527490711 > 7.01E-05

K3 = 1.75

K12 = 0.015758838

c,adm = 0.535012561

c,a = 7.01307E-05

K7 = 1.045610747

Trail section


For =





Moment on Member


63/68

m,g = 19.3

m,adm = 35.31550299

m,a = 6.04E+00

Euler Critical Stress e = 1 N/mm2

= 0.999998006

= 0.171013409 + 0.000133

= 0.17114636 < 1

Euler Co-efficient Keu

Interaction Formula


64/68

mm2

ne



65/68

.K8

deck or joist


66/68


6.05 m

0 m

3.025 m

0.44 kN/m=N/mm


67/68

O.k

435.9563


68/68

O.k

k12 for timber designers' manuel by me.xls

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