1 00:00:00,030 --> 00:00:02,470 The following content is provided under a Creative 2 00:00:02,470 --> 00:00:04,000 Commons license. 3 00:00:04,000 --> 00:00:06,330 Your support will help MIT OpenCourseWare 4 00:00:06,330 --> 00:00:10,690 continue to offer high-quality educational resources for free. 5 00:00:10,690 --> 00:00:13,300 To make a donation or view additional materials 6 00:00:13,300 --> 00:00:17,025 from hundreds of MIT courses, visit MIT OpenCourseWare 7 00:00:17,025 --> 00:00:17,650 at ocw.mit.edu. 8 00:00:26,910 --> 00:00:29,266 LORNA GIBSON: So I should probably get started. 9 00:00:29,266 --> 00:00:31,640 So I just wanted to mention this Friday the libraries are 10 00:00:31,640 --> 00:00:33,110 having Furry Friday. 11 00:00:33,110 --> 00:00:35,870 So they have therapy dogs come, and if you like dogs, 12 00:00:35,870 --> 00:00:39,240 it's kind of fun to go get cuddled by the dog. 13 00:00:39,240 --> 00:00:42,430 The other thing I wanted to mention, last term, 14 00:00:42,430 --> 00:00:45,380 there was a student taking 3032 who was interested in art. 15 00:00:45,380 --> 00:00:48,300 And I kept trying to find art pictures for him, 16 00:00:48,300 --> 00:00:49,160 and he's not here. 17 00:00:49,160 --> 00:00:51,930 But I thought everybody else can like the art too. 18 00:00:51,930 --> 00:00:55,130 So I belong to the Peabody Essex Museum in Salem, Mass. 19 00:00:55,130 --> 00:00:57,370 And they have an exhibit right now 20 00:00:57,370 --> 00:01:01,590 on wood and on sort of using wood as a sculptural material. 21 00:01:01,590 --> 00:01:04,540 And this is one of their posters to advertise it. 22 00:01:04,540 --> 00:01:07,260 So this thing was carved out of a single piece of wood, 23 00:01:07,260 --> 00:01:08,130 I think. 24 00:01:08,130 --> 00:01:10,690 And they've got lots of other sort of sculptural wood. 25 00:01:10,690 --> 00:01:13,120 So I thought you might like to see that. 26 00:01:13,120 --> 00:01:16,171 If you wanted to go to Salem, there's a couple of options, 27 00:01:16,171 --> 00:01:17,170 if you don't have a car. 28 00:01:17,170 --> 00:01:19,260 You can take a commuter rail to Salem. 29 00:01:19,260 --> 00:01:20,840 You can also take the ferry. 30 00:01:20,840 --> 00:01:22,840 And if you take the ferry to Salem, 31 00:01:22,840 --> 00:01:25,424 it's like a five minute walk to where the ferry lets you off 32 00:01:25,424 --> 00:01:26,590 to get to the Peabody Essex. 33 00:01:26,590 --> 00:01:27,650 And it's a kind of neat museum. 34 00:01:27,650 --> 00:01:28,460 It's not too big. 35 00:01:28,460 --> 00:01:29,677 It's kind of small. 36 00:01:29,677 --> 00:01:32,260 But it's a beautiful building, and they have neat stuff there. 37 00:01:32,260 --> 00:01:34,997 So you could go to the Peabody Essex Museum. 38 00:01:34,997 --> 00:01:35,871 Hmm? 39 00:01:35,871 --> 00:01:36,310 STUDENT: It's very nice. 40 00:01:36,310 --> 00:01:37,893 LORNA GIBSON: Yeah, you've been there? 41 00:01:37,893 --> 00:01:39,390 Yeah, it's really nice. 42 00:01:39,390 --> 00:01:42,000 So I was going to talk about honeycomb-like materials 43 00:01:42,000 --> 00:01:43,670 in nature today. 44 00:01:43,670 --> 00:01:46,290 And I'm going to talk about wood today, 45 00:01:46,290 --> 00:01:48,470 and I might finish this today. 46 00:01:48,470 --> 00:01:48,990 I might not. 47 00:01:48,990 --> 00:01:50,880 And then I'm going to talk about cork 48 00:01:50,880 --> 00:01:52,820 for a little bit on Wednesday, and then we'll 49 00:01:52,820 --> 00:01:56,930 start talking about foams after that. 50 00:01:56,930 --> 00:01:59,290 So I have a couple of sort of cute little language 51 00:01:59,290 --> 00:02:00,680 historically things. 52 00:02:00,680 --> 00:02:02,400 And you know how I like that stuff too. 53 00:02:02,400 --> 00:02:08,684 So I have two things about words that are related to wood. 54 00:02:08,684 --> 00:02:10,350 So the word "materials--" you know where 55 00:02:10,350 --> 00:02:12,930 the word materials comes from? 56 00:02:12,930 --> 00:02:14,090 It comes from the Latin. 57 00:02:14,090 --> 00:02:16,510 So there's a Latin "materies materia." 58 00:02:16,510 --> 00:02:18,510 And materies materia means "wood" 59 00:02:18,510 --> 00:02:19,850 or "the trunk of a tree." 60 00:02:19,850 --> 00:02:23,920 So if you think of studying materials, in olden times 61 00:02:23,920 --> 00:02:25,796 that was like studying wood. 62 00:02:25,796 --> 00:02:29,060 And another cute thing that I found was that in old Irish 63 00:02:29,060 --> 00:02:32,040 the names of the first few letters of the alphabet 64 00:02:32,040 --> 00:02:33,800 are named after trees. 65 00:02:33,800 --> 00:02:37,120 So the letter A, that's called alem in old Irish, 66 00:02:37,120 --> 00:02:38,732 and alem is the word for elm. 67 00:02:38,732 --> 00:02:40,815 And B is-- I don't know if I'm saying these right. 68 00:02:40,815 --> 00:02:43,460 It's called beith, and that's the word for birch. 69 00:02:43,460 --> 00:02:44,470 And C is call. 70 00:02:44,470 --> 00:02:45,640 That's the word for hazel. 71 00:02:45,640 --> 00:02:47,840 And D is dair, and that's the word for oak. 72 00:02:47,840 --> 00:02:50,070 And so they sort of named the letters of the alphabet 73 00:02:50,070 --> 00:02:52,955 after different kinds of trees, different kinds of woods. 74 00:02:52,955 --> 00:02:54,330 So I just thought those were kind 75 00:02:54,330 --> 00:02:57,980 of interesting historical things. 76 00:02:57,980 --> 00:03:00,582 So I wanted to start by talking about wood structure. 77 00:03:00,582 --> 00:03:02,290 And then we're going to look at how would 78 00:03:02,290 --> 00:03:06,340 deforms and fails, and talk about the data 79 00:03:06,340 --> 00:03:08,060 that people have measured for the wood 80 00:03:08,060 --> 00:03:10,045 properties, things like stiffness and strength. 81 00:03:10,045 --> 00:03:12,670 And then we'll talk a little bit about how the honeycomb models 82 00:03:12,670 --> 00:03:15,150 can be applied to understanding the mechanical properties 83 00:03:15,150 --> 00:03:16,200 of woods. 84 00:03:16,200 --> 00:03:19,460 So this is kind of a generic trunk of the tree here. 85 00:03:19,460 --> 00:03:22,650 And we're defining three axes. 86 00:03:22,650 --> 00:03:25,650 The radial axis comes radially out of the tree. 87 00:03:25,650 --> 00:03:29,330 There's the tangential axis, so that's the x1 and the x2 axes. 88 00:03:29,330 --> 00:03:31,010 And then there's the longitudinal 89 00:03:31,010 --> 00:03:33,650 or the axial axis, x3. 90 00:03:33,650 --> 00:03:35,230 So if you think of the wood as being, 91 00:03:35,230 --> 00:03:38,220 in a very, very simple way, just like the honeycomb, 92 00:03:38,220 --> 00:03:39,650 the radial would be this way on. 93 00:03:39,650 --> 00:03:41,025 The tangent would be that way on. 94 00:03:41,025 --> 00:03:43,390 And that axial would be that way on. 95 00:03:43,390 --> 00:03:44,800 So it's like that. 96 00:03:44,800 --> 00:03:47,330 And if you neglect the growth rings, 97 00:03:47,330 --> 00:03:49,070 you can say that other woods orthotropic, 98 00:03:49,070 --> 00:03:50,440 and that's typically what people do. 99 00:03:50,440 --> 00:03:52,064 They neglect the growth rings, and they 100 00:03:52,064 --> 00:03:53,430 say that it's orthotropic. 101 00:03:53,430 --> 00:03:56,030 And the density of the woods, the relative density 102 00:03:56,030 --> 00:04:00,170 ranges from about 5% for balsa wood to about 80% 103 00:04:00,170 --> 00:04:01,170 for lignum vitae. 104 00:04:01,170 --> 00:04:02,810 So I brought in some pieces of wood. 105 00:04:02,810 --> 00:04:03,780 So this is balsa wood. 106 00:04:03,780 --> 00:04:05,780 You're probably familiar, making different kinds 107 00:04:05,780 --> 00:04:07,239 of models with balsa. 108 00:04:07,239 --> 00:04:08,155 So balsa's very light. 109 00:04:08,155 --> 00:04:09,780 It grows in Ecuador. 110 00:04:09,780 --> 00:04:11,660 And it's the lightest wood. 111 00:04:11,660 --> 00:04:12,730 And this is lignum vitae. 112 00:04:12,730 --> 00:04:14,480 You're probably not so familiar with that. 113 00:04:14,480 --> 00:04:17,500 This actually grows in Florida, and it's the densest wood. 114 00:04:17,500 --> 00:04:19,450 It has a relative density of 0.8. 115 00:04:19,450 --> 00:04:21,910 And it's so dense, that if you put it in water, it sinks. 116 00:04:21,910 --> 00:04:23,440 So it's a very dense wood. 117 00:04:26,160 --> 00:04:29,370 And the way the wood cells grow is 118 00:04:29,370 --> 00:04:33,380 that if you look at the sort of structure here of a tree, 119 00:04:33,380 --> 00:04:35,340 there's the bark on the outside here, 120 00:04:35,340 --> 00:04:38,140 and then there's the kind of wood cells inside the bark. 121 00:04:38,140 --> 00:04:40,770 And there's a layer of cells in between the bark 122 00:04:40,770 --> 00:04:43,080 and the wood called cambial layer. 123 00:04:43,080 --> 00:04:44,830 And that's really the layer of cells that 124 00:04:44,830 --> 00:04:46,480 are alive and are dividing. 125 00:04:46,480 --> 00:04:49,400 So if you think of the wood cells, 126 00:04:49,400 --> 00:04:52,890 they're living when they're in that little cambial layer 127 00:04:52,890 --> 00:04:53,700 there. 128 00:04:53,700 --> 00:04:54,930 And they're dividing. 129 00:04:54,930 --> 00:04:57,000 And that cambial layer, the cells 130 00:04:57,000 --> 00:05:00,750 have a plasma membrane and a protoplast. 131 00:05:00,750 --> 00:05:04,414 And then they sort of exude the plant cell wall. 132 00:05:04,414 --> 00:05:06,080 So a little like bone cells, like if you 133 00:05:06,080 --> 00:05:07,930 think of the bone in your body, there's 134 00:05:07,930 --> 00:05:11,450 osteoblasts and osteoclasis, different kinds of bone cells. 135 00:05:11,450 --> 00:05:15,090 But the bone cells secrete the sort of collagen 136 00:05:15,090 --> 00:05:17,000 and the calcium phosphate that are 137 00:05:17,000 --> 00:05:19,680 the sort of hard mineral part of the bone that you think about 138 00:05:19,680 --> 00:05:20,440 in the bone. 139 00:05:20,440 --> 00:05:21,690 And that's not a living thing. 140 00:05:21,690 --> 00:05:22,981 The cells are the living thing. 141 00:05:22,981 --> 00:05:25,002 That's like an extracellular matrix. 142 00:05:25,002 --> 00:05:26,710 In the trees, it's a little bit the same. 143 00:05:26,710 --> 00:05:29,890 So there's the living cells that are just under the bark, 144 00:05:29,890 --> 00:05:34,580 and they have this plasma membrane and the protoplasm. 145 00:05:34,580 --> 00:05:37,700 And over a few weeks they excrete the plant cell wall, 146 00:05:37,700 --> 00:05:38,620 and then they die. 147 00:05:38,620 --> 00:05:40,510 So the living cells die, and you're 148 00:05:40,510 --> 00:05:42,210 left with the plant cell walls. 149 00:05:42,210 --> 00:05:45,930 And then as the tree grows, you're 150 00:05:45,930 --> 00:05:48,250 always having a layer of these cambial cells, 151 00:05:48,250 --> 00:05:50,910 and it forms bark on the outside and wood on the inside. 152 00:05:50,910 --> 00:05:53,860 So there's sort of a layer of cells that are differentiated, 153 00:05:53,860 --> 00:05:56,010 such that on the outer layer they form the bark, 154 00:05:56,010 --> 00:05:57,920 and on the inner layer they form the wood. 155 00:05:57,920 --> 00:06:01,080 And as the tree grows, that cambial layer 156 00:06:01,080 --> 00:06:03,700 is kind of expanding out radially. 157 00:06:03,700 --> 00:06:06,422 So let me write some of these things down. 158 00:06:09,530 --> 00:06:10,286 Let's see. 159 00:06:13,320 --> 00:06:15,660 So let me just write down those two little word things 160 00:06:15,660 --> 00:06:16,868 because I think they're cute. 161 00:06:19,230 --> 00:06:33,615 So the word materials is from the Latin materies materia. 162 00:06:38,141 --> 00:06:44,960 And that means "wood" or the "trunk of a tree." 163 00:06:44,960 --> 00:06:48,257 And here's the little old Irish thing. 164 00:06:48,257 --> 00:06:50,090 It's not like I think-- I'm not going to put 165 00:06:50,090 --> 00:06:51,070 this on the test or something. 166 00:06:51,070 --> 00:06:52,195 I just thought it was cute. 167 00:06:57,390 --> 00:07:03,570 So the letter A is alem, which is elm. 168 00:07:03,570 --> 00:07:11,150 And letter B is beith, which is birch. 169 00:07:11,150 --> 00:07:14,240 Letter C is call. 170 00:07:14,240 --> 00:07:16,370 That's hazel. 171 00:07:16,370 --> 00:07:23,080 And D was dair, and that's oak. 172 00:07:23,080 --> 00:07:25,708 So that's just for general interest. 173 00:07:33,726 --> 00:07:36,810 So then the wood structure we can think of it as orthotropic, 174 00:07:36,810 --> 00:07:39,885 if we ignored the growth rings. 175 00:07:48,710 --> 00:07:51,960 And if you have a sort of large diameter tree 176 00:07:51,960 --> 00:07:55,320 and you take a piece of wood not from the very center, 177 00:07:55,320 --> 00:07:57,340 but from somewhere near the outside, 178 00:07:57,340 --> 00:08:00,320 then that's not a bad approximation. 179 00:08:00,320 --> 00:08:07,320 Now, the relative density of the woods 180 00:08:07,320 --> 00:08:14,610 ranges from about 0.05 for balsa to about 0.8 for lignum vitae. 181 00:08:19,540 --> 00:08:21,644 Any Latin scholars here? 182 00:08:21,644 --> 00:08:23,310 I took one year of Latin in high school. 183 00:08:23,310 --> 00:08:24,875 Anybody take Latin? 184 00:08:24,875 --> 00:08:25,570 No, no Latin. 185 00:08:25,570 --> 00:08:28,445 So I think lignum vitae I think is "tree of life." 186 00:08:28,445 --> 00:08:31,090 "Vitae" is the sort of life. 187 00:08:31,090 --> 00:08:34,559 And when it has this ending A-E it means "of life." 188 00:08:34,559 --> 00:08:38,419 So I think that's the "tree of life" is lignum vitae. 189 00:08:38,419 --> 00:08:41,679 So trees have cambial layer beneath the bark. 190 00:08:52,940 --> 00:08:55,640 And the cell division occurs in that cambial layer. 191 00:09:08,440 --> 00:09:11,135 So the new cells on the outer part turn into bark, 192 00:09:11,135 --> 00:09:13,760 and the new cells on the inner part turn into wood. 193 00:09:42,510 --> 00:09:51,300 And then we have the living plant cells 194 00:09:51,300 --> 00:09:55,420 that have the plasma membrane and the protoplast. 195 00:10:03,390 --> 00:10:10,530 And those cells then secret the plant cell wall, 196 00:10:10,530 --> 00:10:12,020 which sort of surrounds them. 197 00:10:44,910 --> 00:10:48,490 So in trees, the living cells lay down the plant cell wall 198 00:10:48,490 --> 00:10:50,380 over a period of a few weeks. 199 00:10:50,380 --> 00:10:52,720 And then the living cells die. 200 00:10:52,720 --> 00:10:53,780 Oops. 201 00:10:53,780 --> 00:10:54,280 Back. 202 00:10:54,280 --> 00:10:54,779 Here. 203 00:11:26,132 --> 00:11:28,340 Now you always retain a layer of those cambial cells. 204 00:11:32,054 --> 00:11:33,720 So you may have heard if you have a tree 205 00:11:33,720 --> 00:11:37,010 and you cut a ring around the tree through the bark, 206 00:11:37,010 --> 00:11:38,740 if you go into those cambial cells 207 00:11:38,740 --> 00:11:40,770 and you destroy them, you kill the tree, 208 00:11:40,770 --> 00:11:43,726 because you're killing that layer of living cells. 209 00:12:11,080 --> 00:12:14,740 So then we want to look at the cellular structure of the woods 210 00:12:14,740 --> 00:12:15,590 as well. 211 00:12:15,590 --> 00:12:17,290 And I've got a couple of slides here. 212 00:12:17,290 --> 00:12:20,060 This one is of softwoods. 213 00:12:20,060 --> 00:12:22,230 And softwoods have two types of cells. 214 00:12:22,230 --> 00:12:25,700 That have tracheids, which are the bulk of the cells here, 215 00:12:25,700 --> 00:12:28,480 and the tracheids provide structural support. 216 00:12:28,480 --> 00:12:30,410 And the tracheids also have little holes 217 00:12:30,410 --> 00:12:33,760 along the length of them at their ends called pits, 218 00:12:33,760 --> 00:12:37,620 and those pits allow fluid transport up and down the tree. 219 00:12:37,620 --> 00:12:40,060 And then the softwood also has these ray cells here. 220 00:12:40,060 --> 00:12:42,230 So those are examples of ray cells. 221 00:12:42,230 --> 00:12:43,600 So this is a transverse section. 222 00:12:43,600 --> 00:12:45,820 This is a longitudinal section here. 223 00:12:45,820 --> 00:12:49,060 And the rays are parenchyma cells which store sugars. 224 00:12:49,060 --> 00:12:51,820 So softwoods have tracheids and rays. 225 00:12:51,820 --> 00:12:54,950 And then hardwoods, here's an example of a hardwood oak. 226 00:12:54,950 --> 00:12:56,620 They have three types of cells. 227 00:12:56,620 --> 00:12:59,210 There's cells called fibers, so these guys all in here 228 00:12:59,210 --> 00:12:59,960 would be fibers. 229 00:12:59,960 --> 00:13:01,890 They provide the structural support. 230 00:13:01,890 --> 00:13:04,030 They have vessels, these really large cells 231 00:13:04,030 --> 00:13:06,600 that provide fluid transport up and down the tree. 232 00:13:06,600 --> 00:13:08,040 And they also have rays. 233 00:13:08,040 --> 00:13:09,770 So here are some rays here. 234 00:13:09,770 --> 00:13:11,890 And again, those rays are parenchyma cells 235 00:13:11,890 --> 00:13:14,250 that store sugars in the tree. 236 00:13:14,250 --> 00:13:18,380 So let me just write down what all these cells are. 237 00:13:18,380 --> 00:13:22,790 So in softwoods most of the cells 238 00:13:22,790 --> 00:13:24,930 are these tracheids, so they make up 239 00:13:24,930 --> 00:13:33,250 the bulk of the tree, something like 90% of the tree. 240 00:13:33,250 --> 00:13:34,900 And they provide structural support. 241 00:13:49,440 --> 00:13:52,453 They have holes in the cell wall for fluid transport, 242 00:13:52,453 --> 00:13:53,536 and those are called pits. 243 00:14:02,991 --> 00:14:04,990 And to give you some idea of what size they are, 244 00:14:04,990 --> 00:14:07,750 they're are a few millimeters long, so something like 2 245 00:14:07,750 --> 00:14:10,700 and 1/2 to seven millimeters long. 246 00:14:10,700 --> 00:14:13,970 And then they're tens of microns in the other two directions, 247 00:14:13,970 --> 00:14:19,430 so they're something like 20 to 80 microns across. 248 00:14:19,430 --> 00:14:23,840 And the cell wall thickness, t, is usually a few microns, 249 00:14:23,840 --> 00:14:27,820 so something between about two and seven microns. 250 00:14:27,820 --> 00:14:29,330 So typically, the denser the wood, 251 00:14:29,330 --> 00:14:31,610 the thicker the cell wall's going to be. 252 00:14:31,610 --> 00:14:34,810 Whoops, let's see if I can get the rays down here. 253 00:14:34,810 --> 00:14:36,054 Put it on the same board. 254 00:14:43,450 --> 00:14:45,893 So the rays are parenchyma cells that store sugar. 255 00:15:08,470 --> 00:15:10,680 And then the hardwoods have three types of cells. 256 00:15:10,680 --> 00:15:13,600 They have the fibers that provide the structural support. 257 00:15:22,480 --> 00:15:24,760 And the amount of cells that are fibers 258 00:15:24,760 --> 00:15:27,330 varies, depending on the species, 259 00:15:27,330 --> 00:15:30,315 but it's usually somewhere around 35% to 70% of the cells. 260 00:15:36,970 --> 00:15:40,251 And then they the vessels, which are the sap channels. 261 00:15:47,410 --> 00:15:49,318 That provides for the conduction of fluids. 262 00:15:54,160 --> 00:15:57,550 And that's between about 6% and 55% of the cells. 263 00:16:00,220 --> 00:16:09,385 And then, again, there's rays that store sugars, 264 00:16:09,385 --> 00:16:11,994 and they usually make a boat 10% to 30% of the cells. 265 00:16:20,160 --> 00:16:22,910 So there's the structure of this sort of cellular structure, 266 00:16:22,910 --> 00:16:27,536 at this kind of length scale of tens of microns. 267 00:16:27,536 --> 00:16:28,910 And then there's also a structure 268 00:16:28,910 --> 00:16:31,170 within the cell wall itself. 269 00:16:31,170 --> 00:16:37,120 And the cell wall itself is made up of cellulose fibrils 270 00:16:37,120 --> 00:16:40,540 in a matrix of lignin and something called hemicellulose. 271 00:16:40,540 --> 00:16:42,430 So if you look at the cellulose structure, 272 00:16:42,430 --> 00:16:46,070 the cellulose has a regular structure, 273 00:16:46,070 --> 00:16:47,980 a sort of periodic lattice. 274 00:16:47,980 --> 00:16:51,560 And it's crystalline for most of the length of the fibrils. 275 00:16:51,560 --> 00:16:55,100 So this is the structure of the cellulose here, 276 00:16:55,100 --> 00:16:58,690 and this is showing it at a slightly larger length scale. 277 00:16:58,690 --> 00:17:00,690 It might have a crystalline region here and then 278 00:17:00,690 --> 00:17:02,760 a non-crystalline region here. 279 00:17:02,760 --> 00:17:05,900 And these macro fibrils, which are made up 280 00:17:05,900 --> 00:17:11,210 of bundles of micro fibrils, are about 10 to 25 nanometers. 281 00:17:11,210 --> 00:17:12,740 And each one of the micro fibrils 282 00:17:12,740 --> 00:17:15,109 might be three to four nanometers across. 283 00:17:15,109 --> 00:17:17,420 So you have these cellulose fibers. 284 00:17:17,420 --> 00:17:20,520 And then the cell wall is made up of different layers. 285 00:17:20,520 --> 00:17:23,160 So there's what's called the primary wall here, 286 00:17:23,160 --> 00:17:27,410 which has a random arrangement of the cellulose fibrils. 287 00:17:27,410 --> 00:17:29,150 Then there's an outer layer here. 288 00:17:29,150 --> 00:17:30,910 These are all called secondary layers. 289 00:17:30,910 --> 00:17:35,160 This is S-- I think that's S1. 290 00:17:35,160 --> 00:17:36,220 Yeah, it's S1. 291 00:17:36,220 --> 00:17:39,880 And it has this arrangement of the fibrils. 292 00:17:39,880 --> 00:17:43,370 Then there's a layer called S2, and it's generally 293 00:17:43,370 --> 00:17:45,610 the thickest layer in the cell wall. 294 00:17:45,610 --> 00:17:49,670 And the cellulose fibrils are aligned not perfectly vertical, 295 00:17:49,670 --> 00:17:51,460 but a little off the vertical. 296 00:17:51,460 --> 00:17:52,880 And the angle between the vertical 297 00:17:52,880 --> 00:17:55,940 and the orientation of the cellulose fibers 298 00:17:55,940 --> 00:17:58,200 is called the microfibril angle. 299 00:17:58,200 --> 00:18:00,400 And then there's a third layer here, S3, 300 00:18:00,400 --> 00:18:02,790 with, again, a different winding of the fibers. 301 00:18:02,790 --> 00:18:05,930 So because S2 layer is the thickest layer 302 00:18:05,930 --> 00:18:09,910 and because the fibrils are closest to the vertical axis, 303 00:18:09,910 --> 00:18:11,790 the S2 layer actually contributes 304 00:18:11,790 --> 00:18:16,950 the most to the longitudinal modulus and stiffness 305 00:18:16,950 --> 00:18:19,550 and strength of the cell wall. 306 00:18:19,550 --> 00:18:23,830 So that's kind of the arrangement of the cell wall. 307 00:18:23,830 --> 00:18:26,062 And then so that one cell would have that. 308 00:18:26,062 --> 00:18:27,270 Another cell would have that. 309 00:18:27,270 --> 00:18:28,640 And in between the two, there's a layer 310 00:18:28,640 --> 00:18:31,226 called the middle lamella that kind of glues them together. 311 00:18:31,226 --> 00:18:32,850 So that's the arrangement of the cells. 312 00:18:35,190 --> 00:18:38,060 Let me scoot over here. 313 00:18:38,060 --> 00:18:42,800 So the cells are often modeled as a fiber reinforced composite 314 00:18:42,800 --> 00:18:46,110 that has four layers to it. 315 00:18:46,110 --> 00:18:48,380 And in each layer there's different volume fraction 316 00:18:48,380 --> 00:18:50,970 of the fibers and different orientation of the fibers. 317 00:19:17,520 --> 00:19:21,525 So the cell wall has this fiber-reinforced structure. 318 00:19:30,285 --> 00:19:36,210 Here's the cellulose fibers in a matrix 319 00:19:36,210 --> 00:19:37,440 of lignin and hemicellulose. 320 00:19:48,770 --> 00:19:50,805 And there's four layers, each with the fibers 321 00:19:50,805 --> 00:19:51,930 in a different orientation. 322 00:20:17,300 --> 00:20:19,826 And then there's the middle lemella between the two cells. 323 00:20:36,360 --> 00:20:39,632 So in doing the modeling of a material like wood, 324 00:20:39,632 --> 00:20:41,840 you need to know what the properties of the cell wall 325 00:20:41,840 --> 00:20:44,150 material are, because, obviously, the properties 326 00:20:44,150 --> 00:20:47,027 of the wood would depend on the cell wall properties. 327 00:20:47,027 --> 00:20:48,610 And it turns out that they're similar. 328 00:20:48,610 --> 00:20:50,318 They're not exactly the same, but they're 329 00:20:50,318 --> 00:20:52,500 similar in different species of wood, 330 00:20:52,500 --> 00:20:55,790 so we're going to call them more or less the same. 331 00:21:04,880 --> 00:21:08,940 So the density of the solid is 1,500 kilograms 332 00:21:08,940 --> 00:21:11,160 per cubic meter. 333 00:21:11,160 --> 00:21:15,330 The modulus of the solid in the axial direction 334 00:21:15,330 --> 00:21:19,180 is 35 gigapascals. 335 00:21:19,180 --> 00:21:22,930 The modulus in the tangential direction or transverse 336 00:21:22,930 --> 00:21:26,370 direction is 10 gigapascals. 337 00:21:26,370 --> 00:21:31,400 And the strength of the solid in the axial direction 338 00:21:31,400 --> 00:21:32,890 is 350 megapascals. 339 00:21:36,510 --> 00:21:38,870 And the strength of the transverse direction 340 00:21:38,870 --> 00:21:40,760 is about 135. 341 00:21:40,760 --> 00:21:48,606 So here A means Axial direction, and T is transverse. 342 00:21:57,490 --> 00:22:03,130 And just for comparison, if you just look at cellulose, 343 00:22:03,130 --> 00:22:05,690 cellulose has some pretty amazing properties. 344 00:22:05,690 --> 00:22:11,120 The modulus of cellulose is about 140 gigapascals, which 345 00:22:11,120 --> 00:22:13,040 is very high for a polymer. 346 00:22:13,040 --> 00:22:16,400 And the strength of cellulose fibers 347 00:22:16,400 --> 00:22:21,830 run between about 700 and 900 megapascals. 348 00:22:21,830 --> 00:22:24,300 So the cellulose fibers have very impressive properties. 349 00:22:24,300 --> 00:22:26,415 And that's one of the things that gives wood 350 00:22:26,415 --> 00:22:27,290 very good properties. 351 00:23:04,482 --> 00:23:05,940 So the next thing is I want to show 352 00:23:05,940 --> 00:23:07,792 you some stress-strain curves for wood. 353 00:23:07,792 --> 00:23:10,000 And you'll see how similar they are to the honeycombs 354 00:23:10,000 --> 00:23:11,500 that we looked at before. 355 00:23:11,500 --> 00:23:14,600 And then we'll look at how the cells are deforming 356 00:23:14,600 --> 00:23:15,950 as they're getting loaded. 357 00:23:15,950 --> 00:23:17,908 And from that, we're going to do some modeling. 358 00:23:20,940 --> 00:23:24,135 So let me just wait till people get caught up. 359 00:23:24,135 --> 00:23:26,540 Are we caught up? 360 00:23:26,540 --> 00:23:27,700 More or less? 361 00:23:27,700 --> 00:23:28,770 OK. 362 00:23:28,770 --> 00:23:30,310 So these are all compression curves, 363 00:23:30,310 --> 00:23:32,400 so I'm just going to talk about compression. 364 00:23:32,400 --> 00:23:34,980 So these are curves for different types of woos. 365 00:23:34,980 --> 00:23:36,790 And on the left, the wood is loaded 366 00:23:36,790 --> 00:23:39,680 in the tangential direction. 367 00:23:39,680 --> 00:23:43,290 So in terms of the sort of honeycomb model, 368 00:23:43,290 --> 00:23:46,840 it's loading at kind of this way on, like that. 369 00:23:46,840 --> 00:23:49,590 And on the right, are a set of curves for wood load 370 00:23:49,590 --> 00:23:51,070 it in axial compression. 371 00:23:51,070 --> 00:23:55,480 So in axial compression loading, we're loading it that way on. 372 00:23:55,480 --> 00:23:57,440 And we've got different species here. 373 00:23:57,440 --> 00:24:01,460 So the lowest density is balsa, around about 100 kilograms 374 00:24:01,460 --> 00:24:02,680 per cubic meter. 375 00:24:02,680 --> 00:24:04,630 The densest species on this plot is 376 00:24:04,630 --> 00:24:08,190 beech, which is around 700 kilograms per cubic meter. 377 00:24:08,190 --> 00:24:10,580 And then there's pine and willow, some other species in 378 00:24:10,580 --> 00:24:11,540 between here. 379 00:24:11,540 --> 00:24:16,090 So you can see the shapes of the curve look just like the curves 380 00:24:16,090 --> 00:24:17,540 that we had for the honeycombs. 381 00:24:17,540 --> 00:24:19,300 So here there's a linear elastic bit. 382 00:24:19,300 --> 00:24:20,600 There's a stress plateau. 383 00:24:20,600 --> 00:24:22,320 And there's a densification bit. 384 00:24:22,320 --> 00:24:25,380 And then, as the density goes up, it gets stiffer, 385 00:24:25,380 --> 00:24:28,290 and the strain at which the densification occurs 386 00:24:28,290 --> 00:24:31,680 gets smaller, and the strength gets higher. 387 00:24:31,680 --> 00:24:34,800 And if we look at the axial properties, 388 00:24:34,800 --> 00:24:36,490 the shape of the curve is similar. 389 00:24:36,490 --> 00:24:40,320 We get linear elastic stress plateau densification. 390 00:24:40,320 --> 00:24:41,910 But if you look at the scale here, 391 00:24:41,910 --> 00:24:44,870 this scale goes from 0 to 100, whereas that scale 392 00:24:44,870 --> 00:24:46,690 went from 0 to 20. 393 00:24:46,690 --> 00:24:49,660 And so the stiffness and the strength along the grain 394 00:24:49,660 --> 00:24:51,620 are much higher than they are across the grain. 395 00:24:51,620 --> 00:24:53,550 And you probably already know that. 396 00:24:53,550 --> 00:24:55,820 Wood is stronger and stiffer along the grain 397 00:24:55,820 --> 00:24:57,710 than across the grain. 398 00:24:57,710 --> 00:25:00,650 So that's what the stress-strain curves looked like. 399 00:25:00,650 --> 00:25:03,240 And the fact that we're getting the curves that 400 00:25:03,240 --> 00:25:04,700 look like that makes us think maybe 401 00:25:04,700 --> 00:25:06,440 the mechanisms of deformation and failure 402 00:25:06,440 --> 00:25:09,180 are similar to the honeycomb, too. 403 00:25:09,180 --> 00:25:12,460 So here's a set of curves for balsa 404 00:25:12,460 --> 00:25:14,730 all plotted on the same scale. 405 00:25:14,730 --> 00:25:18,789 And, again, you can see for loading across the grain, 406 00:25:18,789 --> 00:25:20,830 either in the radial or the tangential direction, 407 00:25:20,830 --> 00:25:22,205 the stiffness and the strength is 408 00:25:22,205 --> 00:25:25,120 a lot less than if you load it in the axial direction. 409 00:25:25,120 --> 00:25:28,230 So a number of years ago, we had a project on balsa. 410 00:25:28,230 --> 00:25:29,950 And the thing we were interested in doing 411 00:25:29,950 --> 00:25:32,760 was looking at how the cells deformed and failed. 412 00:25:32,760 --> 00:25:34,550 And because balsa's a low-density wood, 413 00:25:34,550 --> 00:25:37,090 it was easier to see the deformation in the cells, 414 00:25:37,090 --> 00:25:38,540 because the cells were thin. 415 00:25:38,540 --> 00:25:40,220 So that's why we chose balsa. 416 00:25:40,220 --> 00:25:42,770 I actually have a project on balsa right now. 417 00:25:42,770 --> 00:25:46,046 And [? Sardar ?], my postdoc, is doing more detailed kind 418 00:25:46,046 --> 00:25:48,170 of finite [INAUDIBLE] modeling, trying to represent 419 00:25:48,170 --> 00:25:49,372 the structure of balsa. 420 00:25:49,372 --> 00:25:50,830 And I think I mentioned, the reason 421 00:25:50,830 --> 00:25:52,371 we're interested in it is the balsa's 422 00:25:52,371 --> 00:25:57,230 used as a core in sandwich panels in wind turbine blades. 423 00:25:57,230 --> 00:25:59,370 It's actually the best material that they can find, 424 00:25:59,370 --> 00:26:01,720 it's better than any engineering material. 425 00:26:01,720 --> 00:26:06,160 So that's comparing the three curves for balsa. 426 00:26:06,160 --> 00:26:09,850 And then if you look at a specimen that's 427 00:26:09,850 --> 00:26:14,730 loaded in the [? SCM ?], with a loading stage, 428 00:26:14,730 --> 00:26:16,540 you can measure the stress-strain curve, 429 00:26:16,540 --> 00:26:18,550 and you can take photographs of what 430 00:26:18,550 --> 00:26:20,890 the cellular structure looks like at different stages 431 00:26:20,890 --> 00:26:21,800 of loading. 432 00:26:21,800 --> 00:26:24,750 So here, this picture one, is unloaded. 433 00:26:24,750 --> 00:26:27,180 And these four images here are looking 434 00:26:27,180 --> 00:26:30,580 at the same section of cells, the same area of cells. 435 00:26:30,580 --> 00:26:32,330 And you can see there's a big vessel here, 436 00:26:32,330 --> 00:26:34,030 and that's the same vessel there. 437 00:26:34,030 --> 00:26:36,680 So here, this image two, is at this point 438 00:26:36,680 --> 00:26:37,920 on the stress-strain curve. 439 00:26:37,920 --> 00:26:39,500 Here's three, at that point. 440 00:26:39,500 --> 00:26:41,900 And four is at that point. 441 00:26:41,900 --> 00:26:43,842 So if you look at this carefully-- 442 00:26:43,842 --> 00:26:46,050 and I've got another higher mag picture I'll show you 443 00:26:46,050 --> 00:26:48,360 in a second-- you can see that what's happening 444 00:26:48,360 --> 00:26:49,620 is the cell walls are bending. 445 00:26:49,620 --> 00:26:51,770 So it's kind of like taking my honeycomb like this, 446 00:26:51,770 --> 00:26:53,603 and I'm doing that to it, and the cell walls 447 00:26:53,603 --> 00:26:55,850 are bending, so just the same as the honeycomb. 448 00:26:55,850 --> 00:26:57,760 And then eventually, if I load it enough, 449 00:26:57,760 --> 00:26:59,710 you get to this sort of densified stage. 450 00:26:59,710 --> 00:27:02,100 And you're doing this, and the stress-strain curve 451 00:27:02,100 --> 00:27:03,660 increases sharply. 452 00:27:03,660 --> 00:27:06,620 So here you can see how the cells have densified over here. 453 00:27:06,620 --> 00:27:08,780 It kind of looks a lot like my honeycomb 454 00:27:08,780 --> 00:27:10,740 when I-- maybe I do it this way-- 455 00:27:10,740 --> 00:27:12,840 when I smush it up like that. 456 00:27:12,840 --> 00:27:14,890 It looks kind of similar. 457 00:27:14,890 --> 00:27:16,900 So if we look at the higher mag picture, 458 00:27:16,900 --> 00:27:20,270 again, these four images are the same area of the cells. 459 00:27:20,270 --> 00:27:23,530 And if you look at that a little bit of crud, 460 00:27:23,530 --> 00:27:25,410 it's the same on all four of them there. 461 00:27:25,410 --> 00:27:27,540 So this is the unloaded one. 462 00:27:27,540 --> 00:27:29,720 And these were loaded from top to bottom. 463 00:27:29,720 --> 00:27:33,310 And this is loaded to some extent/ that's loaded more, 464 00:27:33,310 --> 00:27:34,600 and that's loaded more. 465 00:27:34,600 --> 00:27:36,357 So if you look at this cell here, 466 00:27:36,357 --> 00:27:37,690 it's got this little tear on it. 467 00:27:37,690 --> 00:27:39,397 So you can sort of find it again. 468 00:27:39,397 --> 00:27:40,980 If you look at that cell there, that's 469 00:27:40,980 --> 00:27:42,510 what it looks like unloaded. 470 00:27:42,510 --> 00:27:44,780 And here you can see-- see that wall there? 471 00:27:44,780 --> 00:27:46,110 You can see how it's bent up. 472 00:27:46,110 --> 00:27:48,280 So it's bent like the honeycomb walls. 473 00:27:48,280 --> 00:27:50,720 And here it's bent even more. 474 00:27:50,720 --> 00:27:54,590 And eventually, it has this sort of a shape here, 475 00:27:54,590 --> 00:27:57,154 and it's deformed permanently. 476 00:27:57,154 --> 00:27:58,820 It's formed one of these plastic hinges. 477 00:27:58,820 --> 00:28:00,830 So it's like the aluminum honeycombs almost, 478 00:28:00,830 --> 00:28:02,430 that it's filled like that. 479 00:28:02,430 --> 00:28:04,930 So in the balsa wood, when we load it 480 00:28:04,930 --> 00:28:06,840 in the tangential direction, we're 481 00:28:06,840 --> 00:28:09,070 getting bending of the cell walls and then yielding 482 00:28:09,070 --> 00:28:11,030 and plastic hinges forming, just the same as we 483 00:28:11,030 --> 00:28:13,500 would in an aluminum honeycomb. 484 00:28:13,500 --> 00:28:14,420 Are we good with that? 485 00:28:14,420 --> 00:28:16,211 Well, I'll go through all three directions. 486 00:28:16,211 --> 00:28:19,310 And then I'll write down the notes. 487 00:28:19,310 --> 00:28:22,890 So this is loading the balsa in the radial direction. 488 00:28:22,890 --> 00:28:24,930 And these things here are the rays. 489 00:28:24,930 --> 00:28:27,410 So we're loading it in that direction. 490 00:28:27,410 --> 00:28:30,900 And here you see this also bending occurs, 491 00:28:30,900 --> 00:28:33,840 but the rays act a little bit like fiber reinforcement. 492 00:28:33,840 --> 00:28:35,590 So the rays are a little bit stiffer, 493 00:28:35,590 --> 00:28:37,770 and they sort of reinforce the thing a bit. 494 00:28:37,770 --> 00:28:39,480 And this is the loading platten here, 495 00:28:39,480 --> 00:28:42,690 and you can kind of see that the failure starts at the loading 496 00:28:42,690 --> 00:28:44,650 platten, and as you sort of load up more, 497 00:28:44,650 --> 00:28:47,490 it progresses in from the loading platten. 498 00:28:47,490 --> 00:28:49,420 So we're going to look at the modeling 499 00:28:49,420 --> 00:28:51,630 of the balsa in the radial direction, 500 00:28:51,630 --> 00:28:55,090 and we're going to count for the rays, at least in a crude way. 501 00:28:55,090 --> 00:28:58,174 And then when you load them balsa in the axial direction, 502 00:28:58,174 --> 00:29:00,090 initially you don't really see much happening. 503 00:29:00,090 --> 00:29:02,480 So if one is unloaded, one's down here. 504 00:29:02,480 --> 00:29:05,010 And two is at this peak stress up here. 505 00:29:05,010 --> 00:29:07,130 And really, if you look between one and two, 506 00:29:07,130 --> 00:29:08,700 you just don't see an awful lot of difference. 507 00:29:08,700 --> 00:29:11,283 And that's because what you're doing is you're taking the wood 508 00:29:11,283 --> 00:29:12,910 and you're loading it this way on. 509 00:29:12,910 --> 00:29:15,410 And it's so stiff, you just don't see much deformation. 510 00:29:15,410 --> 00:29:17,080 So there's not really much to see. 511 00:29:17,080 --> 00:29:19,890 But then eventually, something starts to fail. 512 00:29:19,890 --> 00:29:22,110 And in this case, what fails are the end caps. 513 00:29:22,110 --> 00:29:24,485 So the balsa wood has these long cells here. 514 00:29:24,485 --> 00:29:25,860 But then at the end of the cells, 515 00:29:25,860 --> 00:29:27,750 there's little caps on the ends. 516 00:29:27,750 --> 00:29:29,770 And the cells kind of fit together like that. 517 00:29:29,770 --> 00:29:32,130 So that eventually, if you keep smushing it, 518 00:29:32,130 --> 00:29:33,670 those end caps start to fail. 519 00:29:36,250 --> 00:29:38,220 Here you can see how bright it gets, 520 00:29:38,220 --> 00:29:41,430 and the cells are starting to crush together and kind of fail 521 00:29:41,430 --> 00:29:42,372 those end caps. 522 00:29:42,372 --> 00:29:44,330 And in fact, each one of these serrations here, 523 00:29:44,330 --> 00:29:46,130 if you look at, say, from that peak 524 00:29:46,130 --> 00:29:48,640 up to that peak, that corresponds 525 00:29:48,640 --> 00:29:51,370 to a length of about the length of the cell, 526 00:29:51,370 --> 00:29:55,260 or the length of the cell between the end caps. 527 00:29:55,260 --> 00:29:57,600 So in axial deformation you're just 528 00:29:57,600 --> 00:30:01,350 actually deforming the cells until you break those end caps. 529 00:30:01,350 --> 00:30:03,940 If you look at denser words, they 530 00:30:03,940 --> 00:30:05,340 fail in slightly different ways. 531 00:30:05,340 --> 00:30:08,150 This is a Douglas fir, which is much denser. 532 00:30:08,150 --> 00:30:10,100 This particular specimen, the whole thing 533 00:30:10,100 --> 00:30:11,590 is kind of buckled over. 534 00:30:11,590 --> 00:30:13,210 So it's not really so representative 535 00:30:13,210 --> 00:30:15,870 of the structure itself. 536 00:30:15,870 --> 00:30:17,986 This is Douglas fir in radial compression. 537 00:30:17,986 --> 00:30:19,610 You can see this picture, it looks just 538 00:30:19,610 --> 00:30:21,776 like what I showed you for the balsa wood, that sort 539 00:30:21,776 --> 00:30:24,455 of propagation of the failure. 540 00:30:24,455 --> 00:30:27,380 These long things here are the rays. 541 00:30:27,380 --> 00:30:29,930 And this is a Norway spruce in axial compression. 542 00:30:29,930 --> 00:30:33,280 And this is fairly common in denser words. 543 00:30:33,280 --> 00:30:35,640 You get this buckling formation. 544 00:30:35,640 --> 00:30:37,310 And what happens is, I think, you 545 00:30:37,310 --> 00:30:40,420 get some yielding of the cell walls initially, 546 00:30:40,420 --> 00:30:44,000 but that leads to buckling, like a plastic buckling. 547 00:30:44,000 --> 00:30:46,390 And you can see on this higher mag picture down here, 548 00:30:46,390 --> 00:30:49,500 you get these really small wavelength buckles 549 00:30:49,500 --> 00:30:50,570 in the cell wall. 550 00:30:50,570 --> 00:30:52,860 And the two-- you get a plane that kind 551 00:30:52,860 --> 00:30:53,990 of shears over itself. 552 00:30:53,990 --> 00:30:55,970 And you can see in the top image, 553 00:30:55,970 --> 00:30:59,960 this top half has shared over relative to the bottom half. 554 00:30:59,960 --> 00:31:02,400 And all the deformation is in this little band here. 555 00:31:02,400 --> 00:31:08,680 So this stuff here is all going on in that band up there. 556 00:31:08,680 --> 00:31:11,130 So let me write down some notes about how 557 00:31:11,130 --> 00:31:13,160 these things to form and fail. 558 00:31:13,160 --> 00:31:17,957 And then we'll get to the modeling in little bit. 559 00:31:17,957 --> 00:31:19,540 So we can say the stress-strain curves 560 00:31:19,540 --> 00:31:20,955 resemble those for honeycombs. 561 00:31:36,190 --> 00:31:40,240 And I'll say the mechanisms of deformation and failure 562 00:31:40,240 --> 00:31:42,970 are most easily identified in low density balsa wood. 563 00:32:12,360 --> 00:32:17,730 So for balsa, if we look at the tangential loading, 564 00:32:17,730 --> 00:32:20,728 we see bending of the cell walls and then eventually plastic 565 00:32:20,728 --> 00:32:21,228 yielding. 566 00:32:45,730 --> 00:32:48,885 And for radial loading, the rays act as reinforcing. 567 00:33:36,008 --> 00:33:40,510 And for axial loading, you get axial deformation and then 568 00:33:40,510 --> 00:33:41,950 the failure of the end caps. 569 00:34:01,270 --> 00:34:03,290 And I'll just say failure by plastic buckling 570 00:34:03,290 --> 00:34:06,740 is also observed, say, in the denser woods. 571 00:35:20,641 --> 00:35:21,140 [INAUDIBLE] 572 00:35:29,740 --> 00:35:33,790 So then we can look at some data for the properties of woods. 573 00:35:33,790 --> 00:35:38,080 And these charts plot relative Young's modulus and relative 574 00:35:38,080 --> 00:35:40,334 strength against relative density. 575 00:35:40,334 --> 00:35:41,750 So here the modulus of the wood is 576 00:35:41,750 --> 00:35:45,640 divided by the modulus of the solid cell wall material. 577 00:35:45,640 --> 00:35:47,800 And here we've normalized everything 578 00:35:47,800 --> 00:35:49,780 by the modulus of the solid cell wall 579 00:35:49,780 --> 00:35:52,100 material in the axial direction, because the cell 580 00:35:52,100 --> 00:35:54,190 wall itself is anisotropic. 581 00:35:54,190 --> 00:35:55,867 And so here's the relative modulus, 582 00:35:55,867 --> 00:35:57,200 and here's the relative density. 583 00:35:57,200 --> 00:35:59,010 These are log-log plots. 584 00:35:59,010 --> 00:36:02,890 And we see that when we load the wood in the axial direction, 585 00:36:02,890 --> 00:36:05,600 the moduli is just linearly related to the density. 586 00:36:05,600 --> 00:36:07,620 And when we load it across the grain, 587 00:36:07,620 --> 00:36:10,012 it varies with the cube of the relative density. 588 00:36:10,012 --> 00:36:11,970 So do you remember our little honeycomb models? 589 00:36:11,970 --> 00:36:14,011 If I took the honeycomb and I loaded it this way, 590 00:36:14,011 --> 00:36:18,040 it went as the cube of T over L. And that's because the bending. 591 00:36:18,040 --> 00:36:21,270 And so the wood doesn't lie perfectly on that cube line, 592 00:36:21,270 --> 00:36:22,927 but it's fairly close. 593 00:36:22,927 --> 00:36:24,760 And then similarly, if we took the honeycomb 594 00:36:24,760 --> 00:36:27,320 and we loaded it this way on, it deformed axially. 595 00:36:27,320 --> 00:36:31,290 The modulus depended linearly on the density. 596 00:36:31,290 --> 00:36:34,010 So you get the same kind of relationships there. 597 00:36:34,010 --> 00:36:36,270 And then if you look at the strength, 598 00:36:36,270 --> 00:36:38,780 the strength along the grain goes linearly, 599 00:36:38,780 --> 00:36:41,870 and the strength across the grain goes with the square. 600 00:36:41,870 --> 00:36:46,290 And we'll see when we get to the modeling in a minute, 601 00:36:46,290 --> 00:36:50,130 that if we loaded, say, an aluminum honeycomb this way on, 602 00:36:50,130 --> 00:36:52,180 the strength would go linearly with the density, 603 00:36:52,180 --> 00:36:54,210 if we're just yielding the cell walls. 604 00:36:54,210 --> 00:36:56,780 And if we loaded it this way on, it went as the square of T 605 00:36:56,780 --> 00:36:59,302 over L. So these things kind of correspond. 606 00:36:59,302 --> 00:37:01,010 And you can see the structure of the wood 607 00:37:01,010 --> 00:37:04,280 is a lot more complicated than just a simple honeycomb. 608 00:37:04,280 --> 00:37:06,630 And so these models are sort of first order, 609 00:37:06,630 --> 00:37:07,700 and they're fairly crude. 610 00:37:07,700 --> 00:37:10,950 They don't try to capture every detail of the wood structure. 611 00:37:10,950 --> 00:37:14,100 But they can give you a sense of where the wood properties are 612 00:37:14,100 --> 00:37:15,500 coming from. 613 00:37:15,500 --> 00:37:19,090 So let me just write down some of these observations. 614 00:37:26,190 --> 00:37:34,000 So the data for the wood-- the modulus along the grain 615 00:37:34,000 --> 00:37:36,570 goes linearly with density. 616 00:37:48,950 --> 00:37:51,480 It goes more or less as the cube for loading 617 00:37:51,480 --> 00:37:52,880 in the tangential direction. 618 00:37:52,880 --> 00:37:55,550 And the radial direction is somewhat stiffer different 619 00:37:55,550 --> 00:37:56,050 than that. 620 00:38:03,720 --> 00:38:07,390 The strength in the axial direction 621 00:38:07,390 --> 00:38:08,880 goes linearly with the density. 622 00:38:14,200 --> 00:38:19,940 And the strength across the grain 623 00:38:19,940 --> 00:38:21,440 goes with the square of the density. 624 00:38:31,330 --> 00:38:35,569 And then there's data for the Poisson's ratios too. 625 00:38:35,569 --> 00:38:36,860 So let me just write them down. 626 00:39:41,370 --> 00:39:43,090 So the modeling based on the honeycomb 627 00:39:43,090 --> 00:39:49,410 is sort of a simplified model that 628 00:39:49,410 --> 00:39:53,300 gives you kind of a first-order description of the behavior. 629 00:39:53,300 --> 00:39:55,560 And it doesn't really attempt to capture 630 00:39:55,560 --> 00:39:59,250 all the details of the softwood and hardwood structure. 631 00:40:24,152 --> 00:40:26,360 And in the equations, I'm going to take the cell wall 632 00:40:26,360 --> 00:40:32,728 properties along the grain, or along the axial direction. 633 00:40:38,224 --> 00:40:40,640 And we're going to have a bunch of constants that describe 634 00:40:40,640 --> 00:40:43,100 the cell geometry, and those constants 635 00:40:43,100 --> 00:40:48,590 are also going to reflect the cell wall anisotropy. 636 00:42:09,480 --> 00:42:10,954 So we can model the wood structure 637 00:42:10,954 --> 00:42:13,370 as something that's a bit more of a simplified thing, just 638 00:42:13,370 --> 00:42:14,240 like this. 639 00:42:14,240 --> 00:42:16,980 And we say we've got cells that are roughly hexagonal, 640 00:42:16,980 --> 00:42:18,890 and then we've got some cells that 641 00:42:18,890 --> 00:42:21,715 are more or less rectangular that are the ray cells. 642 00:42:21,715 --> 00:42:23,340 And if you look at lots of micrographs, 643 00:42:23,340 --> 00:42:26,150 you can get some idea what the dimensions of the cells are. 644 00:42:26,150 --> 00:42:27,570 And these dimensions were measured 645 00:42:27,570 --> 00:42:30,125 for a particular density of balsa wood. 646 00:42:42,910 --> 00:42:46,150 So if we look at the linear elastic moduli, 647 00:42:46,150 --> 00:42:48,085 we can start off with a tangential loading. 648 00:42:53,660 --> 00:42:56,120 And if we have the tangential loading, 649 00:42:56,120 --> 00:42:58,440 we can model it as a honeycomb loaded in the plane, 650 00:42:58,440 --> 00:42:59,653 and we get cell wall bending. 651 00:43:27,025 --> 00:43:29,380 And from the cell wall bending in the honeycomb model, 652 00:43:29,380 --> 00:43:32,470 you would get that the tangential modulus varies 653 00:43:32,470 --> 00:43:35,120 with the relative density cubed. 654 00:43:35,120 --> 00:43:37,210 And the structure's not quite that simple. 655 00:43:37,210 --> 00:43:38,260 There's ray cells. 656 00:43:38,260 --> 00:43:39,180 There's end caps. 657 00:43:39,180 --> 00:43:41,040 And they act to stiffen it a little bit. 658 00:43:41,040 --> 00:43:43,055 And the data lie a little bit above this line. 659 00:44:19,380 --> 00:44:21,650 Then if we look at the radial loading, 660 00:44:21,650 --> 00:44:25,450 the rays kind of line up with the radial direction, 661 00:44:25,450 --> 00:44:28,125 and the rays act as reinforcing plates. 662 00:44:28,125 --> 00:44:31,690 And so you can just use kind of an upper-bound composites idea 663 00:44:31,690 --> 00:44:32,520 to get the modulus. 664 00:44:46,356 --> 00:44:48,564 And the rays tend to be a bit denser than the fibers. 665 00:44:57,510 --> 00:45:06,170 So if I say a Vr is the volume fraction of rays, 666 00:45:06,170 --> 00:45:08,550 and R is the ratio of the relative density 667 00:45:08,550 --> 00:45:11,210 of the rays compared to the fibers, 668 00:45:11,210 --> 00:45:17,680 so it's rho over rho S for the rays divided by rho over rho 669 00:45:17,680 --> 00:45:22,270 S for the fibers. 670 00:45:22,270 --> 00:45:26,690 And that varies a little bit from what one species 671 00:45:26,690 --> 00:45:28,190 to another, one specimen to another. 672 00:45:28,190 --> 00:45:31,750 But it's something a little over 1, something between 1 and 2. 673 00:45:31,750 --> 00:45:36,010 Then I can say the modulus in the radial direction 674 00:45:36,010 --> 00:45:39,230 is the volume fraction of the rays times 675 00:45:39,230 --> 00:45:44,760 R cubed times the tangential modulus plus 1 676 00:45:44,760 --> 00:45:48,270 minus the volume fraction of rays 677 00:45:48,270 --> 00:45:50,520 times the tangential modulus. 678 00:45:50,520 --> 00:45:52,490 And that works out to be about 1.5 679 00:45:52,490 --> 00:45:56,010 times the tangential modulus. 680 00:45:56,010 --> 00:45:57,510 I wanted to work this out in terms 681 00:45:57,510 --> 00:45:59,510 of the tangential modululs, so I've 682 00:45:59,510 --> 00:46:01,900 put this in terms of the tangential modules 683 00:46:01,900 --> 00:46:02,900 in the first term there. 684 00:46:05,560 --> 00:46:07,150 So we get that the radial modulus 685 00:46:07,150 --> 00:46:09,460 is slightly larger than the tangential, 686 00:46:09,460 --> 00:46:11,660 but also goes roughly as the cube of the density. 687 00:46:39,795 --> 00:46:41,420 And then for the axial loading, we just 688 00:46:41,420 --> 00:46:43,900 have axial deformation in the cell wall. 689 00:46:43,900 --> 00:46:46,407 And the Young's modulus just varies linearly 690 00:46:46,407 --> 00:46:47,115 with the density. 691 00:47:09,300 --> 00:47:10,950 So these are kind of simple models, 692 00:47:10,950 --> 00:47:13,290 but they kind of explain to first order 693 00:47:13,290 --> 00:47:16,660 the density dependence of the wood moduli and the anisotropy. 694 00:47:41,274 --> 00:47:43,690 So it's kind of nice because they're fairly simple models, 695 00:47:43,690 --> 00:47:45,520 and it gives you kind of a big picture. 696 00:47:45,520 --> 00:47:48,120 So if you wanted to know the modulus of a particular piece 697 00:47:48,120 --> 00:47:51,050 of wood, this probably isn't the best way to figure it out. 698 00:47:51,050 --> 00:47:52,920 But if you wanted to kind of compare 699 00:47:52,920 --> 00:47:56,130 how do woods behave in general and how does the density affect 700 00:47:56,130 --> 00:47:59,020 the properties and why are they anisotropic, 701 00:47:59,020 --> 00:48:00,710 this is a pretty good way to do it. 702 00:48:49,340 --> 00:48:51,310 We could also look at the Poisson's ratios. 703 00:48:51,310 --> 00:48:53,643 And just because I didn't want to write them down again, 704 00:48:53,643 --> 00:48:56,120 I've just left on what the data were down here. 705 00:48:56,120 --> 00:49:00,250 But let me just write what the model would give us 706 00:49:00,250 --> 00:49:05,760 for nu RT and nu TR, the model would give us one 707 00:49:05,760 --> 00:49:08,410 if we had regular hexagonal cells. 708 00:49:08,410 --> 00:49:10,240 And these are the values we get here. 709 00:49:10,240 --> 00:49:13,970 This might be 0.6, 0.7 would be a typical value, somewhere 710 00:49:13,970 --> 00:49:17,160 around 0.4 in there, so they're not quite one, 711 00:49:17,160 --> 00:49:18,930 but they're close to it. 712 00:49:18,930 --> 00:49:20,870 And I think the reason they're a little less 713 00:49:20,870 --> 00:49:24,540 is because the rays in the end caps provide some constraint. 714 00:49:24,540 --> 00:49:27,460 If you have the honeycomb, if I just had these cells, 715 00:49:27,460 --> 00:49:30,050 and I squeeze it like this, these guys can move out. 716 00:49:30,050 --> 00:49:32,120 If it's a regular hexagonal honeycomb, 717 00:49:32,120 --> 00:49:34,590 the strain that I'm applying here 718 00:49:34,590 --> 00:49:36,900 is equal to the strain going out that way. 719 00:49:36,900 --> 00:49:40,080 But if I have rays this way that sort of constrain it or end 720 00:49:40,080 --> 00:49:42,490 caps, it means that the Poisson's ratio is 721 00:49:42,490 --> 00:49:45,010 going to be a little bit less. 722 00:49:45,010 --> 00:49:48,010 So I'll just say constraining effect of the end caps 723 00:49:48,010 --> 00:49:50,105 and rays-- constraining. 724 00:50:00,250 --> 00:50:09,080 Then for nu RA and nu TA, the model 725 00:50:09,080 --> 00:50:12,852 says the value we would get would be zero. 726 00:50:12,852 --> 00:50:14,310 And these are pretty close to zero. 727 00:50:14,310 --> 00:50:17,690 They're not quite zero, but pretty close. 728 00:50:17,690 --> 00:50:25,680 And then the last pair nu AR and nu AT, 729 00:50:25,680 --> 00:50:28,842 the model says that we would get nu of the solid. 730 00:50:35,010 --> 00:50:38,880 And the data's close to 0.4, which we might expect 731 00:50:38,880 --> 00:50:40,635 would be about the nu of the solid. 732 00:50:40,635 --> 00:50:42,010 So, again, there's some variation 733 00:50:42,010 --> 00:50:43,010 in the Poisson's ratios. 734 00:50:43,010 --> 00:50:44,860 They're not all just one number. 735 00:50:44,860 --> 00:50:49,100 But you can see these ones here are about zero, 736 00:50:49,100 --> 00:50:51,380 and that's roughly what the model says. 737 00:50:51,380 --> 00:50:53,890 These ones here are closer to 1. 738 00:50:53,890 --> 00:50:55,440 And then these ones here are closer 739 00:50:55,440 --> 00:50:57,500 to what you might expect for a solid material. 740 00:50:57,500 --> 00:51:01,210 So it gives you the kind of general idea. 741 00:51:01,210 --> 00:51:02,798 Are we good? 742 00:51:02,798 --> 00:51:03,506 We're good, yeah? 743 00:51:15,760 --> 00:51:18,332 So we can do a similar thing for the compressive strength. 744 00:51:24,070 --> 00:51:27,600 So for tangential loading, we get plastic hinges forming 745 00:51:27,600 --> 00:51:37,970 and the bent cell walls, just like in an aluminum honeycomb. 746 00:51:45,400 --> 00:51:52,370 Then we get that the strength over the cell wall strength 747 00:51:52,370 --> 00:51:54,500 goes as the relative density squared, 748 00:51:54,500 --> 00:51:56,470 so just like the honeycomb. 749 00:51:56,470 --> 00:51:58,890 the radial loading, we can do the composites thing again. 750 00:52:05,220 --> 00:52:08,570 So we can say the strengths in the radial direction 751 00:52:08,570 --> 00:52:11,780 is about equal to the volume fraction of rays 752 00:52:11,780 --> 00:52:17,860 times R squared times the tangential strength plus 1 753 00:52:17,860 --> 00:52:20,440 minus the volume fraction of rays 754 00:52:20,440 --> 00:52:22,790 times the tangential strength. 755 00:52:22,790 --> 00:52:26,870 And for balsa, I have some values here. 756 00:52:26,870 --> 00:52:31,070 VR is about equal to 0.14. 757 00:52:31,070 --> 00:52:33,520 R is about equal to 2. 758 00:52:33,520 --> 00:52:37,810 And so the radial strength is about equal to 1.4 759 00:52:37,810 --> 00:52:40,970 times the tangential. 760 00:52:40,970 --> 00:52:43,380 And in higher density woods, the value of R 761 00:52:43,380 --> 00:52:47,480 is a little bit smaller, and in general, the radial strength 762 00:52:47,480 --> 00:52:49,750 is a bit larger than the tangential, 763 00:52:49,750 --> 00:53:20,700 and both depend on the density squared 764 00:53:20,700 --> 00:53:25,240 And then for axial loading, if the failure's 765 00:53:25,240 --> 00:53:27,340 initiated by yielding in the cell walls, 766 00:53:27,340 --> 00:53:30,580 then the axial strength's just going to depend linearly 767 00:53:30,580 --> 00:53:31,667 on the density. 768 00:53:57,850 --> 00:53:59,470 So the idea with these models isn't 769 00:53:59,470 --> 00:54:05,460 that they kind of describe a particular piece of wood 770 00:54:05,460 --> 00:54:06,070 exactly. 771 00:54:06,070 --> 00:54:08,740 It's more that it gives you a general picture of how 772 00:54:08,740 --> 00:54:11,270 the cells are deforming and failing, 773 00:54:11,270 --> 00:54:13,459 and how the properties scale with density 774 00:54:13,459 --> 00:54:14,750 and why the wood's anisotropic. 775 00:54:49,500 --> 00:54:50,480 Are we good? 776 00:54:50,480 --> 00:54:51,170 Yeah? 777 00:54:51,170 --> 00:54:52,632 Caught up. 778 00:54:52,632 --> 00:54:54,840 So there are a couple more sort of interesting things 779 00:54:54,840 --> 00:54:58,384 we can do with looking at the wood properties. 780 00:54:58,384 --> 00:55:00,050 So we've been talking about how to model 781 00:55:00,050 --> 00:55:01,644 the cellular structure. 782 00:55:01,644 --> 00:55:03,810 But people have also looked at how to model the cell 783 00:55:03,810 --> 00:55:05,820 wall as a fiber composite. 784 00:55:05,820 --> 00:55:08,120 And this plot and the next one kind of show you 785 00:55:08,120 --> 00:55:11,300 how you can combine all of that together. 786 00:55:11,300 --> 00:55:13,770 So remember, I said the modulus of the cellulose 787 00:55:13,770 --> 00:55:15,610 was around 140 gigapascals. 788 00:55:15,610 --> 00:55:19,246 So here's the modulus of the cellulose, at least 789 00:55:19,246 --> 00:55:21,120 the crystalline part of the cellulose plotted 790 00:55:21,120 --> 00:55:22,850 in that little envelope there. 791 00:55:22,850 --> 00:55:26,620 The lignin and the hemicellulose have a modulus around 2 or 3 792 00:55:26,620 --> 00:55:28,740 gigapascals, so it's down there. 793 00:55:28,740 --> 00:55:31,750 And if you made composites with cellulose fibers 794 00:55:31,750 --> 00:55:34,150 in lignin and hemicellulose matrix, 795 00:55:34,150 --> 00:55:36,710 those composites would have a modulus that 796 00:55:36,710 --> 00:55:38,290 fell in this envelope here. 797 00:55:38,290 --> 00:55:40,681 They've got to be in between those two limits, right? 798 00:55:40,681 --> 00:55:42,680 The modulus have to be between those two limits. 799 00:55:42,680 --> 00:55:45,290 The density have to be within the densities 800 00:55:45,290 --> 00:55:47,610 of the constituents. 801 00:55:47,610 --> 00:55:49,870 And if you look at the modulus of the wood cell wall, 802 00:55:49,870 --> 00:55:51,780 it lies in this envelope here. 803 00:55:51,780 --> 00:55:54,240 Along the grain it'd be here, and then across the grain 804 00:55:54,240 --> 00:55:55,710 is further down here. 805 00:55:55,710 --> 00:55:58,552 So the cell wall modulus is in here. 806 00:55:58,552 --> 00:56:00,010 And then if you take that cell wall 807 00:56:00,010 --> 00:56:02,230 and you make it into the honeycomb-type material 808 00:56:02,230 --> 00:56:05,490 that wood is, if you load it along the grain, 809 00:56:05,490 --> 00:56:09,110 you're going to get this linear dependence of modulus 810 00:56:09,110 --> 00:56:09,700 on density. 811 00:56:09,700 --> 00:56:11,210 And if you load it across the grain 812 00:56:11,210 --> 00:56:13,390 in the radial or the tangential direction, 813 00:56:13,390 --> 00:56:15,920 you're going to get this cubed dependence here. 814 00:56:15,920 --> 00:56:18,240 So here's a set of data for different woods 815 00:56:18,240 --> 00:56:19,670 of different densities. 816 00:56:19,670 --> 00:56:24,410 And that envelope kind of encompasses all of them. 817 00:56:24,410 --> 00:56:26,580 But if you look at the slope of that data, 818 00:56:26,580 --> 00:56:28,510 it's roughly equal to a slope of 1. 819 00:56:28,510 --> 00:56:32,100 And so it corresponds to that equation there. 820 00:56:32,100 --> 00:56:34,100 And similarly, here's a set of data 821 00:56:34,100 --> 00:56:37,640 for different species of woods of different densities loaded 822 00:56:37,640 --> 00:56:39,440 perpendicular to the grain. 823 00:56:39,440 --> 00:56:43,410 And they lie on a line that has more or less a slope of 3. 824 00:56:43,410 --> 00:56:46,070 And this set of data here along the grain 825 00:56:46,070 --> 00:56:48,700 intersects the wood cell wall towards the top 826 00:56:48,700 --> 00:56:50,570 of that envelope, and this set of data 827 00:56:50,570 --> 00:56:54,280 here intersects closer to the bottom of that envelope 828 00:56:54,280 --> 00:56:55,770 for the cell wall material. 829 00:56:55,770 --> 00:56:58,353 So this gives you a way of sort of putting everything together 830 00:56:58,353 --> 00:57:01,190 on one plot-- the cell wall as well as the cellular structure. 831 00:57:01,190 --> 00:57:03,380 So that plot does it for the modulus. 832 00:57:03,380 --> 00:57:06,050 And you can do the same kind of thing for the strength. 833 00:57:06,050 --> 00:57:07,710 Here's the cellulose up here. 834 00:57:07,710 --> 00:57:09,350 Here's the lignin down there. 835 00:57:09,350 --> 00:57:12,860 Here's the wood cell wall, the composite made from those two. 836 00:57:12,860 --> 00:57:14,860 And then here's data for different kinds 837 00:57:14,860 --> 00:57:19,000 of woods loaded along the grain and for load across the grain. 838 00:57:19,000 --> 00:57:22,220 So it gives you a way of putting all this modeling 839 00:57:22,220 --> 00:57:24,734 into one set of plots. 840 00:57:24,734 --> 00:57:27,150 So let me just write a couple of little things about that. 841 00:57:48,427 --> 00:57:50,760 So we could say you could model the cell wall as a fiber 842 00:57:50,760 --> 00:57:51,260 composite. 843 00:58:05,860 --> 00:58:10,260 And you can use the composition upper and lower bounds 844 00:58:10,260 --> 00:58:11,103 to give an envelope. 845 00:58:34,660 --> 00:58:38,880 And then you can also show the cellular solids models 846 00:58:38,880 --> 00:58:39,825 on the same plot. 847 00:58:51,720 --> 00:58:55,130 So overall, it shows you how the hierarchical structure fits 848 00:58:55,130 --> 00:58:56,990 together and can be modeled. 849 00:59:18,070 --> 00:59:20,136 Now there's some more cute things we can see. 850 00:59:54,749 --> 00:59:56,290 So another thing I want to talk about 851 00:59:56,290 --> 00:59:58,200 is material selection, because it turns out 852 00:59:58,200 --> 01:00:00,620 wood is very good compared to other materials 853 01:00:00,620 --> 01:00:02,027 in certain applications. 854 01:00:02,027 --> 01:00:03,610 So we're going to look at, say, having 855 01:00:03,610 --> 01:00:06,340 a beam of a given stiffness at a given span, 856 01:00:06,340 --> 01:00:09,410 and say it's just a square cross-section beam 857 01:00:09,410 --> 01:00:11,660 of edge length T. And the question 858 01:00:11,660 --> 01:00:15,010 is, what material would minimize the mass of the beam? 859 01:00:15,010 --> 01:00:17,310 So say we have some span we have to have. 860 01:00:17,310 --> 01:00:20,550 It's got to have some rectangular cross-section, 861 01:00:20,550 --> 01:00:21,964 some given stiffness. 862 01:00:21,964 --> 01:00:23,630 And the question is, what's the material 863 01:00:23,630 --> 01:00:24,900 that minimizes the mass? 864 01:00:24,900 --> 01:00:26,730 So there's a little short calculation 865 01:00:26,730 --> 01:00:28,216 we can do to figure that out. 866 01:00:28,216 --> 01:00:29,840 And then I've got another plot, and you 867 01:00:29,840 --> 01:00:32,500 can compare different materials on this other plot. 868 01:00:32,500 --> 01:00:35,060 Then you'll see how good wood is compared to other materials. 869 01:00:42,910 --> 01:00:53,150 So from beam of a given stiffness and given span, 870 01:00:53,150 --> 01:01:05,470 and say it's a square cross-section, 871 01:01:05,470 --> 01:01:07,020 then the question is, what material 872 01:01:07,020 --> 01:01:08,680 minimizes the mass of the beam? 873 01:01:28,060 --> 01:01:30,260 So the mass is just going to be the density 874 01:01:30,260 --> 01:01:33,900 times t squared times l And if it's 875 01:01:33,900 --> 01:01:37,650 a beam, say it's got some central load on it, 876 01:01:37,650 --> 01:01:39,890 a concentrated load, the deflection's going 877 01:01:39,890 --> 01:01:44,820 to go as pl cubed divided by some constant 878 01:01:44,820 --> 01:01:46,940 and divided by the Young's modulus and the moment 879 01:01:46,940 --> 01:01:50,520 of inertia I. 880 01:01:50,520 --> 01:01:53,210 So the stiffness, if I just rearrange this, the stiffness, 881 01:01:53,210 --> 01:02:00,304 p over delta, that's going to go as p over delta CEI, 882 01:02:00,304 --> 01:02:06,500 and I's going to go as t to the fourth over l cubed. 883 01:02:06,500 --> 01:02:08,360 And then I can solve that for t squared. 884 01:02:08,360 --> 01:02:10,610 And I want t squared because I'm going to plug it back 885 01:02:10,610 --> 01:02:12,830 into the equation for the mass. 886 01:02:12,830 --> 01:02:15,870 So if I solve this for t squared, 887 01:02:15,870 --> 01:02:18,670 I've got my stiffness p over delta. 888 01:02:18,670 --> 01:02:23,440 I've got l cubed divided by CE. 889 01:02:23,440 --> 01:02:27,920 And then I take that whole thing to the 1/2 power like that. 890 01:02:27,920 --> 01:02:29,350 And then I plug the t squared back 891 01:02:29,350 --> 01:02:31,150 into the little equation for the mass. 892 01:02:34,180 --> 01:02:42,910 So I've got density minus p over delta times l cubed over CE. 893 01:02:42,910 --> 01:02:46,770 And we'll take that whole thing to the 1/2 power-- [INAUDIBLE] 894 01:02:46,770 --> 01:02:48,450 another l. 895 01:02:48,450 --> 01:02:50,370 And so to minimize the mass, you want 896 01:02:50,370 --> 01:02:52,306 to look at the material properties. 897 01:02:52,306 --> 01:02:53,680 And here, the material properties 898 01:02:53,680 --> 01:02:56,530 are the density and the Young's modulus. 899 01:02:56,530 --> 01:02:59,370 And to minimize the mass, you want to minimize rho 900 01:02:59,370 --> 01:03:00,850 over E the 1/2 power. 901 01:03:14,430 --> 01:03:18,676 Or conversely, you want to maximize E to the 1/2 over rho. 902 01:03:24,570 --> 01:03:28,610 So if you just had a bar that you were just pulling on, 903 01:03:28,610 --> 01:03:30,410 you would just want to maximize E over rho. 904 01:03:30,410 --> 01:03:32,240 But if it's a beam and bending, it 905 01:03:32,240 --> 01:03:35,940 works out that you want to maximize E to the 1/2 over rho. 906 01:03:35,940 --> 01:03:39,820 And if we look at the next slide, this next slide then 907 01:03:39,820 --> 01:03:44,280 plots on a log-log scale, it plots the modulus 908 01:03:44,280 --> 01:03:47,240 on this axis and the density on that axis. 909 01:03:47,240 --> 01:03:52,030 And here this plotted data for lots of different materials. 910 01:03:52,030 --> 01:03:53,850 So there's engineering alloys. 911 01:03:53,850 --> 01:03:55,370 Metals are up here. 912 01:03:55,370 --> 01:03:57,320 Engineering ceramics are here. 913 01:03:57,320 --> 01:03:59,100 Composites are here. 914 01:03:59,100 --> 01:04:00,660 Polymers are down here. 915 01:04:00,660 --> 01:04:02,600 Elastomer is way down here. 916 01:04:02,600 --> 01:04:04,370 Foamy things, down here. 917 01:04:04,370 --> 01:04:06,720 And this envelope here is woods. 918 01:04:06,720 --> 01:04:09,140 And notice log scale here. 919 01:04:09,140 --> 01:04:14,140 The lowest stiffness polymer foams here are 0.1 gigapascal, 920 01:04:14,140 --> 01:04:16,840 and diamond is up here at 1,000 gigapascal. 921 01:04:16,840 --> 01:04:19,570 So there's like five orders of magnitude difference 922 01:04:19,570 --> 01:04:22,000 in the modulus here. 923 01:04:22,000 --> 01:04:24,470 So then, if you look at the bottom right corner here, 924 01:04:24,470 --> 01:04:26,350 there's a bunch of old dashed lines. 925 01:04:26,350 --> 01:04:29,030 And this red one here is E to the 1/2 over rho. 926 01:04:29,030 --> 01:04:31,190 So if it's log-log plot, E to the 1/2 over rho's 927 01:04:31,190 --> 01:04:33,380 going to show up as a straight line. 928 01:04:33,380 --> 01:04:36,610 And every point on that line has the same value of E 929 01:04:36,610 --> 01:04:39,050 to the 1/2 over rho. 930 01:04:39,050 --> 01:04:43,740 And the material that would be the best for a beam of a given 931 01:04:43,740 --> 01:04:46,470 stiffness would be the one that has the biggest value of E 932 01:04:46,470 --> 01:04:47,950 to the 1/2 over rho. 933 01:04:47,950 --> 01:04:51,270 And if I move the line up to the top left here, 934 01:04:51,270 --> 01:04:53,390 I'm increasing E. I'm decreasing rho. 935 01:04:53,390 --> 01:04:55,980 It's got the biggest value of E to the 1/2 over rho. 936 01:04:55,980 --> 01:04:58,620 So the materials that are on this line here, 937 01:04:58,620 --> 01:05:00,930 they all have the same value of E to the 1/2 over rho. 938 01:05:00,930 --> 01:05:03,055 And they've got the biggest value-- well, virtually 939 01:05:03,055 --> 01:05:04,121 the biggest value. 940 01:05:04,121 --> 01:05:05,870 So let's look at what those materials are. 941 01:05:05,870 --> 01:05:07,896 There's things like engineering ceramics, 942 01:05:07,896 --> 01:05:10,270 like diamond that maybe are not the most convenient thing 943 01:05:10,270 --> 01:05:11,830 to make our beam out of, and tend 944 01:05:11,830 --> 01:05:13,100 to be brittle and might break. 945 01:05:13,100 --> 01:05:15,050 So we have some issues. 946 01:05:15,050 --> 01:05:18,120 There's engineering composite, so things like carbon fiber 947 01:05:18,120 --> 01:05:19,660 reinforced plastics. 948 01:05:19,660 --> 01:05:21,770 And at this sort of tip of the composites, 949 01:05:21,770 --> 01:05:25,270 there'd be things like unidirectional fiber 950 01:05:25,270 --> 01:05:26,170 composites. 951 01:05:26,170 --> 01:05:28,130 And then here's other woods down here. 952 01:05:28,130 --> 01:05:31,380 So the woods have the same performance index, 953 01:05:31,380 --> 01:05:32,920 this is called, the same value of E 954 01:05:32,920 --> 01:05:36,470 to the 1/2 over rho as the best engineering composites. 955 01:05:36,470 --> 01:05:39,825 And so they have very good properties for their weight. 956 01:05:39,825 --> 01:05:41,200 And one of the interesting things 957 01:05:41,200 --> 01:05:44,270 is if you look at this performance index of E 958 01:05:44,270 --> 01:05:49,460 to the 1/2 over rho, this is the performance index for the wood. 959 01:05:49,460 --> 01:05:51,610 This is for the solid cell wall material 960 01:05:51,610 --> 01:05:55,460 that the wood's made from, so E to the 1/2 of the solid 961 01:05:55,460 --> 01:05:57,080 over rho for the solid. 962 01:05:57,080 --> 01:05:59,910 And from the modeling of the wood, 963 01:05:59,910 --> 01:06:01,950 just looking at the axial modulus, 964 01:06:01,950 --> 01:06:05,482 this thing here is equal to that times rho S over rho. 965 01:06:05,482 --> 01:06:07,690 So if you look at this, this is the performance index 966 01:06:07,690 --> 01:06:08,630 for the wood. 967 01:06:08,630 --> 01:06:10,380 This is the solid it's made from. 968 01:06:10,380 --> 01:06:12,152 This number here is bigger than 1, right? 969 01:06:12,152 --> 01:06:13,610 Because the density of the solid is 970 01:06:13,610 --> 01:06:15,206 bigger than the density of the wood, 971 01:06:15,206 --> 01:06:16,580 and so this is saying the wood is 972 01:06:16,580 --> 01:06:18,204 more efficient than the thing that it's 973 01:06:18,204 --> 01:06:20,700 made from, than the solid that it's made from. 974 01:06:20,700 --> 01:06:23,770 And so that's the sort of plot for the stiffness. 975 01:06:23,770 --> 01:06:25,720 And there's a similar plot for the strength. 976 01:06:25,720 --> 01:06:28,150 That if you do the same little kind of calculation, 977 01:06:28,150 --> 01:06:30,730 you find that the performance index for the strength 978 01:06:30,730 --> 01:06:34,490 is some failure strength raised to the 2/3 power over a rho. 979 01:06:34,490 --> 01:06:37,220 And again, here we're plotting strength versus density 980 01:06:37,220 --> 01:06:38,770 on a log-log plot. 981 01:06:38,770 --> 01:06:43,140 And this red line here is the strength of the 2/3 over rho. 982 01:06:43,140 --> 01:06:46,610 And again, if we scoot over here so we have a parallel line, 983 01:06:46,610 --> 01:06:51,230 every point on that line has the same value of the strength 984 01:06:51,230 --> 01:06:53,330 to the 2/3 power over the density. 985 01:06:53,330 --> 01:06:55,980 And these are the materials that have the highest values. 986 01:06:55,980 --> 01:06:58,470 And again, here's engineering composites. 987 01:06:58,470 --> 01:06:59,380 These are ceramics. 988 01:06:59,380 --> 01:07:01,774 But the ceramics, they have a high compressive strength, 989 01:07:01,774 --> 01:07:02,940 but they tend to be brittle. 990 01:07:02,940 --> 01:07:05,820 So it's not really a practical strength. 991 01:07:05,820 --> 01:07:07,100 These are metals in here. 992 01:07:07,100 --> 01:07:08,392 And here's the woods down here. 993 01:07:08,392 --> 01:07:10,641 So it's kind interesting just to see that the wood has 994 01:07:10,641 --> 01:07:11,710 such a good property. 995 01:07:11,710 --> 01:07:13,590 Yes? 996 01:07:13,590 --> 01:07:18,765 STUDENT: So I realize why this is valuable setting up 997 01:07:18,765 --> 01:07:19,640 the problem this way. 998 01:07:19,640 --> 01:07:23,220 But if you're actually trying to design something, why would 999 01:07:23,220 --> 01:07:25,260 you want to fix your cross-section? 1000 01:07:25,260 --> 01:07:29,340 You could change your material and change your cross-section. 1001 01:07:29,340 --> 01:07:31,990 LORNA GIBSON: So this is the starter version 1002 01:07:31,990 --> 01:07:32,980 of this problem. 1003 01:07:32,980 --> 01:07:35,270 And there's another part two of the problem 1004 01:07:35,270 --> 01:07:36,590 is to change the shape. 1005 01:07:36,590 --> 01:07:38,530 And you could look at what shape's efficient. 1006 01:07:38,530 --> 01:07:40,363 There's something called a shape factor that 1007 01:07:40,363 --> 01:07:41,740 gives you the efficient shapes. 1008 01:07:41,740 --> 01:07:43,630 So you could take the material and turn it 1009 01:07:43,630 --> 01:07:45,430 into a different shape and have a more efficient thing 1010 01:07:45,430 --> 01:07:46,940 because it was a different shape. 1011 01:07:46,940 --> 01:07:48,890 So you can account for that. 1012 01:07:48,890 --> 01:07:50,603 STUDENT: So then if you varied, like 1013 01:07:50,603 --> 01:07:52,580 let's say you made your cross-section smaller, 1014 01:07:52,580 --> 01:07:54,310 like even if it was still square, 1015 01:07:54,310 --> 01:07:56,150 you could just still make it smaller. 1016 01:07:56,150 --> 01:07:56,340 LORNA GIBSON: Yeah. 1017 01:07:56,340 --> 01:07:58,190 I'm saying we've got a given stiffness. 1018 01:07:58,190 --> 01:08:01,410 So if we're given a certain stiffness and a certain span, 1019 01:08:01,410 --> 01:08:03,072 we would need a certain cross-section 1020 01:08:03,072 --> 01:08:04,113 to get to that stiffness. 1021 01:08:08,340 --> 01:08:09,830 Are we happy? 1022 01:08:09,830 --> 01:08:11,220 OK. 1023 01:08:11,220 --> 01:08:13,310 So that's one thing. 1024 01:08:13,310 --> 01:08:14,146 Let's see here. 1025 01:08:14,146 --> 01:08:16,479 So let me just write a few more notes about the material 1026 01:08:16,479 --> 01:08:18,630 selection, and then there's one more thing I wanted 1027 01:08:18,630 --> 01:08:19,796 to show you about the woods. 1028 01:08:23,319 --> 01:08:24,830 Hmm? 1029 01:08:24,830 --> 01:08:26,620 C is just a constant. 1030 01:08:26,620 --> 01:08:28,930 So it's just a number. 1031 01:08:28,930 --> 01:08:31,359 So if you had a beam in three-point bending, 1032 01:08:31,359 --> 01:08:32,470 then C would be three. 1033 01:08:32,470 --> 01:08:33,960 If you had a beam that was simply 1034 01:08:33,960 --> 01:08:37,069 supported with a central load, C would be 48. 1035 01:08:37,069 --> 01:08:37,910 C is just a number. 1036 01:08:42,217 --> 01:08:43,342 STUDENT: One more question. 1037 01:08:43,342 --> 01:08:47,772 So follow your line there, and the choice 1038 01:08:47,772 --> 01:08:51,577 is really just about cost. 1039 01:08:51,577 --> 01:08:53,160 LORNA GIBSON: No, it's not about cost. 1040 01:08:53,160 --> 01:08:55,059 There's nothing on cost here. 1041 01:08:55,059 --> 01:08:56,600 It's all really about the properties. 1042 01:08:56,600 --> 01:08:58,529 What's the best combination of properties 1043 01:08:58,529 --> 01:09:00,930 to minimize the mass, and then which material has 1044 01:09:00,930 --> 01:09:02,380 that combination of properties. 1045 01:09:02,380 --> 01:09:06,140 You can do charts like this that include cost. 1046 01:09:06,140 --> 01:09:08,670 You can make these charts with whatever property. 1047 01:09:08,670 --> 01:09:11,089 STUDENT: [INAUDIBLE]. 1048 01:09:11,089 --> 01:09:18,760 I guess maybe there's a difference off two or so 1049 01:09:18,760 --> 01:09:21,890 of strength. 1050 01:09:21,890 --> 01:09:24,029 LORNA GIBSON: Between pine and balsa? 1051 01:09:24,029 --> 01:09:25,390 Yeah, maybe more than that. 1052 01:09:25,390 --> 01:09:28,200 I think-- I can't quite see where-- pine's close to 100, 1053 01:09:28,200 --> 01:09:30,514 and balsa's, I don't know, 20 or something. 1054 01:09:30,514 --> 01:09:33,063 STUDENT: [INAUDIBLE] 1055 01:09:33,063 --> 01:09:35,229 LORNA GIBSON: Yeah, and it's not-- the point of this 1056 01:09:35,229 --> 01:09:38,310 isn't so much looking at the absolute value of a strength. 1057 01:09:38,310 --> 01:09:42,050 It's looking at the value of this performance index. 1058 01:09:42,050 --> 01:09:45,210 And what you want to do is maximize that index 1059 01:09:45,210 --> 01:09:49,080 to get the material that's going to minimize the mass. 1060 01:09:49,080 --> 01:09:51,540 So let me just read a couple notes about this. 1061 01:09:51,540 --> 01:09:53,790 So we have these-- these are called material selection 1062 01:09:53,790 --> 01:09:54,290 charts. 1063 01:10:05,870 --> 01:10:08,760 So you plot the log of one property versus the log 1064 01:10:08,760 --> 01:10:10,397 of some other property. 1065 01:10:14,960 --> 01:10:21,458 And then we have a line of constant E to the 1/2 over rho. 1066 01:10:21,458 --> 01:10:23,457 I'll just say it's shown in red because you're 1067 01:10:23,457 --> 01:10:24,540 going have the same plots. 1068 01:10:28,600 --> 01:10:32,620 And the materials with the largest values 1069 01:10:32,620 --> 01:10:33,670 are in the upper left. 1070 01:10:53,540 --> 01:10:56,160 So the woods have similar values to engineering composites. 1071 01:11:05,510 --> 01:11:07,798 And you can do a similar thing for strength. 1072 01:11:18,040 --> 01:11:19,365 So I have a few more minutes. 1073 01:11:36,194 --> 01:11:38,610 So I have a few minutes, and I want to talk about a couple 1074 01:11:38,610 --> 01:11:40,380 of uses of woods. 1075 01:11:40,380 --> 01:11:41,997 So one is in old ships. 1076 01:11:41,997 --> 01:11:44,080 So I don't know if you know Professor Lechtman has 1077 01:11:44,080 --> 01:11:46,570 this course Materials and the Human Experience, 1078 01:11:46,570 --> 01:11:49,170 and they talk about sort of ancient uses of materials. 1079 01:11:49,170 --> 01:11:52,010 And I did a section, a module, on woods 1080 01:11:52,010 --> 01:11:54,170 and the use of woods in old colonial ships, 1081 01:11:54,170 --> 01:11:56,440 like The Constitution that's in Boston Harbor. 1082 01:11:56,440 --> 01:12:00,530 So this is kind of a schematic of an old ship. 1083 01:12:00,530 --> 01:12:02,030 And the thing that was interesting 1084 01:12:02,030 --> 01:12:03,840 and the thing I talked about in this module 1085 01:12:03,840 --> 01:12:07,170 was that people chose particular species for particular parts 1086 01:12:07,170 --> 01:12:07,720 of the boat. 1087 01:12:07,720 --> 01:12:10,240 And they would choose a particular species 1088 01:12:10,240 --> 01:12:12,070 depending on its properties. 1089 01:12:12,070 --> 01:12:14,160 And a lot of the hull was made of oak. 1090 01:12:14,160 --> 01:12:16,600 So oak's a very dense wood. 1091 01:12:16,600 --> 01:12:18,870 But they would get something they called straight oak, 1092 01:12:18,870 --> 01:12:21,097 and they would get something they called compass oak. 1093 01:12:21,097 --> 01:12:22,930 And you can see this little thing down here, 1094 01:12:22,930 --> 01:12:25,840 this little kind of schematic here, this little sketch. 1095 01:12:25,840 --> 01:12:28,280 This is straight oak, just a straight trunk. 1096 01:12:28,280 --> 01:12:30,445 And this thing here would be the compass oak. 1097 01:12:30,445 --> 01:12:32,820 And what they would do is they would use the straight oak 1098 01:12:32,820 --> 01:12:35,260 for straight parts of the boat, so something 1099 01:12:35,260 --> 01:12:36,826 like this, these pieces here. 1100 01:12:36,826 --> 01:12:38,200 And then they would actually look 1101 01:12:38,200 --> 01:12:41,310 for trees that had the curve of the branches 1102 01:12:41,310 --> 01:12:44,130 to match some part of the boat that they were looking for. 1103 01:12:44,130 --> 01:12:47,690 So, for instance, if you have the hull out here and the deck 1104 01:12:47,690 --> 01:12:49,240 here and they had their cannons here, 1105 01:12:49,240 --> 01:12:50,460 there's something called a knee, which 1106 01:12:50,460 --> 01:12:52,120 is sort of a bracing piece that goes 1107 01:12:52,120 --> 01:12:54,150 between the deck and the hull. 1108 01:12:54,150 --> 01:12:55,900 And that bracing piece is curved. 1109 01:12:55,900 --> 01:12:57,770 And they would actually look for trees 1110 01:12:57,770 --> 01:13:01,520 in which the branches curved at the same kind of curvature 1111 01:13:01,520 --> 01:13:03,281 as they were looking for in that piece. 1112 01:13:03,281 --> 01:13:05,030 And then they would use it for that piece. 1113 01:13:05,030 --> 01:13:06,821 And the advantage of this is they basically 1114 01:13:06,821 --> 01:13:09,280 had the grain running along the curve, 1115 01:13:09,280 --> 01:13:11,890 and so they got the best properties out of the wood 1116 01:13:11,890 --> 01:13:12,910 by doing that. 1117 01:13:12,910 --> 01:13:15,110 So they had this straight oak and compass oak, 1118 01:13:15,110 --> 01:13:16,970 and that was one cute thing. 1119 01:13:16,970 --> 01:13:18,867 And often they used white oaks. 1120 01:13:18,867 --> 01:13:20,450 And I brought a piece of white oak in. 1121 01:13:20,450 --> 01:13:22,200 You can see how dense it is. 1122 01:13:22,200 --> 01:13:26,360 And the US Navy often used something called live oak. 1123 01:13:26,360 --> 01:13:27,700 Live Oak grows in the South. 1124 01:13:27,700 --> 01:13:28,810 Anybody from the South? 1125 01:13:28,810 --> 01:13:30,870 You see these big trees with huge sort 1126 01:13:30,870 --> 01:13:31,900 of spreading branches. 1127 01:13:31,900 --> 01:13:32,900 Those are the live oaks. 1128 01:13:32,900 --> 01:13:35,010 And apparently, the US Navy, I read somewhere, 1129 01:13:35,010 --> 01:13:37,970 still has a forest somewhere with live oak 1130 01:13:37,970 --> 01:13:40,390 for doing things like repairing The Constitution. 1131 01:13:40,390 --> 01:13:42,250 So let me just pass those guys around. 1132 01:13:42,250 --> 01:13:44,760 So those are a couple of oaks they would use for the hull. 1133 01:13:44,760 --> 01:13:47,621 Then they would use white pine for the masts. 1134 01:13:47,621 --> 01:13:49,620 And the reason they used white pine for the mast 1135 01:13:49,620 --> 01:13:51,953 is because the white pine grows very, very tall and very 1136 01:13:51,953 --> 01:13:52,840 straight. 1137 01:13:52,840 --> 01:13:56,280 And white pine was actually like a strategic resource 1138 01:13:56,280 --> 01:13:58,640 in the 1600s, the 1700s. 1139 01:13:58,640 --> 01:14:02,990 And it turns out that when the British Royal Navy was doing 1140 01:14:02,990 --> 01:14:06,190 all that colonial stuff in the 1600 and 1700s, 1141 01:14:06,190 --> 01:14:09,230 Britain actually ran out of trees for masts for boats, 1142 01:14:09,230 --> 01:14:12,780 and they would actually import masts from New England. 1143 01:14:12,780 --> 01:14:15,170 And there were these people called surveyors 1144 01:14:15,170 --> 01:14:16,010 who would go around and they would 1145 01:14:16,010 --> 01:14:17,551 mark certain trees that were supposed 1146 01:14:17,551 --> 01:14:20,560 to be saved for these masts for the British Royal Navy. 1147 01:14:20,560 --> 01:14:23,219 And the thing was that the size of the boat 1148 01:14:23,219 --> 01:14:25,510 and how many cannons you could put on the boat depended 1149 01:14:25,510 --> 01:14:27,290 on how big the mast was. 1150 01:14:27,290 --> 01:14:30,250 So the size of the boat depended on the mast, 1151 01:14:30,250 --> 01:14:35,260 because the mast height controlled how much sail area 1152 01:14:35,260 --> 01:14:36,190 you could get. 1153 01:14:36,190 --> 01:14:38,410 So the taller the mast, the more sail/ the more sail, 1154 01:14:38,410 --> 01:14:39,243 the bigger the ship. 1155 01:14:39,243 --> 01:14:41,000 The bigger the ship, the more cannons. 1156 01:14:41,000 --> 01:14:43,820 And so having these tall Eastern white pines 1157 01:14:43,820 --> 01:14:45,396 was a sort of a strategic resource. 1158 01:14:45,396 --> 01:14:46,770 And I have a piece of white pine. 1159 01:14:46,770 --> 01:14:50,096 Unfortunately, my dog got to this one. 1160 01:14:50,096 --> 01:14:50,720 And be careful. 1161 01:14:50,720 --> 01:14:51,594 It's a bit splintery. 1162 01:14:51,594 --> 01:14:53,880 But you can see it's a lighter kind of wood. 1163 01:14:53,880 --> 01:14:55,287 And if you go around New England, 1164 01:14:55,287 --> 01:14:57,370 if you go to the arboretum, you can see white oak. 1165 01:14:57,370 --> 01:14:59,470 You can see Eastern white pine. 1166 01:14:59,470 --> 01:15:01,810 The other wood they used is lignum vitae, 1167 01:15:01,810 --> 01:15:04,390 that first dense one that I passed around. 1168 01:15:04,390 --> 01:15:07,160 And if you notice that lignum vitae has kind of a waxy 1169 01:15:07,160 --> 01:15:08,230 feel to it. 1170 01:15:08,230 --> 01:15:11,610 And they used that in the block and tackle, so like pulleys 1171 01:15:11,610 --> 01:15:12,690 and stuff like that. 1172 01:15:12,690 --> 01:15:14,920 And it was thought to be self-lubricating 1173 01:15:14,920 --> 01:15:16,810 because of that kind of waxy layer on it. 1174 01:15:16,810 --> 01:15:19,184 And because it's very dense, if you think of like a block 1175 01:15:19,184 --> 01:15:22,430 and tackle and you've got like a rope going over a pulley, 1176 01:15:22,430 --> 01:15:24,750 you've got a pressure from everything sort of fitting 1177 01:15:24,750 --> 01:15:26,874 together and the bits bearing against each other. 1178 01:15:26,874 --> 01:15:29,540 And the fact that was very dense made it very good for the block 1179 01:15:29,540 --> 01:15:30,600 and tackle. 1180 01:15:30,600 --> 01:15:33,900 And so they used the lignum vitae for that. 1181 01:15:33,900 --> 01:15:36,564 And there's one other cute story about lignum vitae. 1182 01:15:36,564 --> 01:15:37,980 I don't know if any of you've ever 1183 01:15:37,980 --> 01:15:40,610 read Dava Sobel's Longitude. 1184 01:15:40,610 --> 01:15:41,510 Anybody read that? 1185 01:15:41,510 --> 01:15:43,870 I'm a sucker for those history of science books. 1186 01:15:43,870 --> 01:15:47,057 So her book Longitude is about the development 1187 01:15:47,057 --> 01:15:48,640 of an instrument to measure longitude. 1188 01:15:51,160 --> 01:15:53,600 Originally, they could get the latitude from the stars, 1189 01:15:53,600 --> 01:15:56,015 but they were really bad at getting the longitude. 1190 01:15:56,015 --> 01:15:58,140 And so boats would go off, and they wouldn't really 1191 01:15:58,140 --> 01:16:00,330 be able to figure out where they were, 1192 01:16:00,330 --> 01:16:03,240 until they had a method to measure longitude. 1193 01:16:03,240 --> 01:16:06,340 And there was some British board of something or another. 1194 01:16:06,340 --> 01:16:08,800 They put forward a prize for somebody 1195 01:16:08,800 --> 01:16:12,460 who could produce a way of measuring longitude accurately. 1196 01:16:12,460 --> 01:16:15,180 And there was a guy called John Harrison, and he built a clock. 1197 01:16:15,180 --> 01:16:17,510 He built a very accurate chronometer. 1198 01:16:17,510 --> 01:16:20,790 And if you knew when sunrise was and sunset was, and you knew 1199 01:16:20,790 --> 01:16:23,582 the time and where you left, you could figure out where you-- 1200 01:16:23,582 --> 01:16:24,790 it's kind of like time zones. 1201 01:16:24,790 --> 01:16:26,910 You could figure out where you are today. 1202 01:16:26,910 --> 01:16:29,750 And he built a chronometer, and one version of his chronometer 1203 01:16:29,750 --> 01:16:31,530 used a lignum vitae for the same reason, 1204 01:16:31,530 --> 01:16:34,710 because it was very dense, and it was very stable. 1205 01:16:34,710 --> 01:16:37,520 And the clock that he eventually won the prize with 1206 01:16:37,520 --> 01:16:40,230 was in the 1700s, 1759. 1207 01:16:40,230 --> 01:16:42,090 I think they went on some trip with it. 1208 01:16:42,090 --> 01:16:46,250 It was 81 days at sea, and it lost five seconds over 81 days. 1209 01:16:46,250 --> 01:16:49,200 So that's pretty impressive for 250 years ago. 1210 01:16:49,200 --> 01:16:51,139 So that was the lignum vitae in the clock. 1211 01:16:51,139 --> 01:16:53,180 I have one more picture, and then I can finish up 1212 01:16:53,180 --> 01:16:53,930 the thing on wood. 1213 01:16:53,930 --> 01:16:55,450 And we'll start the cork next time. 1214 01:16:55,450 --> 01:16:57,540 So this is another example of using wood. 1215 01:16:57,540 --> 01:16:59,280 And this is sort of a more modern use. 1216 01:16:59,280 --> 01:17:03,060 So this bridge here is made with a glue-laminated wood. 1217 01:17:03,060 --> 01:17:05,260 So this big beam here, the big arch, 1218 01:17:05,260 --> 01:17:09,840 is made up of sections of wood which are glued together. 1219 01:17:09,840 --> 01:17:13,240 And you can glue the sections in a curved shape if you want. 1220 01:17:13,240 --> 01:17:14,887 They sort of have molds to do that. 1221 01:17:14,887 --> 01:17:16,720 And when they make this glue-laminated wood, 1222 01:17:16,720 --> 01:17:17,940 they cut the defects out. 1223 01:17:17,940 --> 01:17:20,620 So they cut knots out, and they control 1224 01:17:20,620 --> 01:17:22,960 the pieces of each laminate that they 1225 01:17:22,960 --> 01:17:25,360 use to get the best quality. 1226 01:17:25,360 --> 01:17:26,860 And the glue-laminated wood actually 1227 01:17:26,860 --> 01:17:29,540 has better properties than just two-by-fours 1228 01:17:29,540 --> 01:17:31,350 or whatever you would cut down, lumber 1229 01:17:31,350 --> 01:17:32,890 that you would cut from a tree. 1230 01:17:32,890 --> 01:17:36,567 So glue-laminated wood is kind of a nice kind of wood 1231 01:17:36,567 --> 01:17:37,650 structure that's used now. 1232 01:17:37,650 --> 01:17:41,250 And you see it all the time in things like ice rink arenas, 1233 01:17:41,250 --> 01:17:42,300 like large spans. 1234 01:17:42,300 --> 01:17:43,470 It's kind of beautiful. 1235 01:17:43,470 --> 01:17:45,844 You can see the wood grain in the curve in the wood grain 1236 01:17:45,844 --> 01:17:47,130 when they make these things. 1237 01:17:47,130 --> 01:17:48,480 So that's the wood lecture. 1238 01:17:48,480 --> 01:17:49,744 I'm going to stop there. 1239 01:17:49,744 --> 01:17:51,160 So next time I'll talk about cork. 1240 01:17:51,160 --> 01:17:52,960 I just have a little bit about cork. 1241 01:17:52,960 --> 01:17:55,985 And then we'll start talking about foams.