400:
254:
263:, Hankinson's equation has been found to be remarkably accurate for many other types of wood. A generalized form of the Hankinson formula has also been used for predicting the uniaxial tensile strength of wood at an angle to the grain. This formula has the form
564:
269:
123:
712:
95:
68:
641:
446:
115:
621:
594:
454:
423:
27:) is a mathematical relationship for predicting the off-axis uniaxial compressive strength of wood. The formula can also be used to compute the fiber
1261:
97:
perpendicular to the grain, Hankinson's equation predicts that the uniaxial compressive strength of the wood in a direction at an angle
395:{\displaystyle \sigma _{\alpha }={\cfrac {\sigma _{0}~\sigma _{90}}{\sigma _{0}~\sin ^{n}\alpha +\sigma _{90}~\cos ^{n}\alpha }}}
249:{\displaystyle \sigma _{\alpha }={\cfrac {\sigma _{0}~\sigma _{90}}{\sigma _{0}~\sin ^{2}\alpha +\sigma _{90}~\cos ^{2}\alpha }}}
1254:
668:
1227:
928:
765:
1247:
968:
854:
923:
832:
715:
1353:
1315:
839:
1358:
1134:
1129:
918:
911:
744:
73:
1275:
1197:
1192:
861:
46:
749:
559:{\displaystyle V(\alpha )={\frac {V_{0}V_{90}}{V_{0}\sin ^{2}\alpha +V_{90}\cos ^{2}\alpha }}}
1172:
790:
626:
431:
100:
599:
1290:
1010:
827:
807:
795:
739:
572:
8:
1295:
1212:
1060:
953:
659:
1363:
1232:
866:
822:
817:
448:
to the grain at the elastic limit can similarly be obtained from the
Hankinson formula
408:
1280:
849:
800:
1187:
1162:
1075:
1050:
1045:
1000:
32:
28:
1177:
1101:
1065:
1015:
946:
935:
880:
782:
1285:
1182:
1040:
1005:
906:
812:
1347:
1222:
1055:
1207:
1202:
1167:
899:
1217:
1120:
1316:
Investigation of crushing strength of spruce at varying angles of grain
1139:
1035:
36:
1111:
1106:
940:
1090:
995:
975:
961:
1334:
844:
985:
260:
889:
1335:
The Tsai-Wu strength theory for
Douglas fir laminated veneer
40:
259:
Even though the original relation was based on studies of
43:. For a wood that has uniaxial compressive strengths of
1025:
321:
289:
175:
143:
324:
292:
178:
146:
671:
629:
602:
575:
457:
434:
411:
272:
126:
103:
76:
49:
35:
wave velocity at the elastic limit as a function of
1338:, M. S. Thesis, The University of British Columbia.
706:
635:
615:
588:
558:
440:
417:
394:
248:
109:
89:
62:
1345:
623:is the velocity perpendicular to the grain and
1255:
707:{\displaystyle J=-D{\frac {d\varphi }{dx}}}
1262:
1248:
596:is the velocity parallel to the grain,
1346:
1321:Air Force Information Circular No. 259
425:can take values between 1.5 and 2.
13:
428:The stress wave velocity at angle
14:
1375:
1326:
1307:
467:
461:
1:
1301:
90:{\displaystyle \sigma _{90}}
7:
646:
63:{\displaystyle \sigma _{0}}
10:
1380:
70:parallel to the grain and
117:to the grain is given by
1313:Hankinson, R. L., 1921,
766:Clausius–Duhem (entropy)
716:Fick's laws of diffusion
1276:Material failure theory
924:Navier–Stokes equations
862:Material failure theory
636:{\displaystyle \alpha }
441:{\displaystyle \alpha }
110:{\displaystyle \alpha }
708:
637:
617:
616:{\displaystyle V_{90}}
590:
560:
442:
419:
396:
250:
111:
91:
64:
919:Bernoulli's principle
912:Archimedes' principle
709:
638:
618:
591:
589:{\displaystyle V_{0}}
561:
443:
420:
397:
251:
112:
92:
65:
25:Hankinson's criterion
1332:Clouston, P., 1995,
1323:, U. S. Air Service.
1291:Orthotropic material
1011:Cohesion (chemistry)
833:Infinitesimal strain
669:
643:is the grain angle.
627:
600:
573:
455:
432:
409:
270:
124:
101:
74:
47:
17:Hankinson's equation
1296:Transverse isotropy
929:Poiseuille equation
660:Continuum mechanics
654:Part of a series on
405:where the exponent
323:
291:
177:
145:
21:Hankinson's formula
1135:Magnetorheological
1130:Electrorheological
867:Fracture mechanics
704:
633:
613:
586:
556:
438:
415:
392:
388:
318:
246:
242:
172:
107:
87:
60:
1354:Materials science
1281:Linear elasticity
1272:
1271:
1147:
1146:
1081:
1080:
850:Contact mechanics
773:
772:
702:
554:
418:{\displaystyle n}
390:
370:
338:
322:
306:
290:
244:
224:
192:
176:
160:
144:
1371:
1339:
1330:
1324:
1311:
1264:
1257:
1250:
1096:
1095:
1061:Gay-Lussac's law
1051:Combined gas law
1001:Capillary action
886:
885:
729:
728:
713:
711:
710:
705:
703:
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685:
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66:
61:
59:
58:
1379:
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1374:
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1359:Solid mechanics
1344:
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1331:
1327:
1312:
1308:
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1268:
1239:
1238:
1237:
1157:
1149:
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1102:Viscoelasticity
1093:
1083:
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1016:Surface tension
980:
883:
881:Fluid mechanics
873:
872:
871:
785:
783:Solid mechanics
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81:
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54:
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12:
11:
5:
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1038:
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1021:
1019:
1018:
1013:
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1006:Chromatography
1003:
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815:
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747:
742:
734:
733:
727:
724:
723:
720:
719:
714:
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697:
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689:
683:
680:
677:
674:
663:
662:
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632:
610:
606:
583:
579:
567:
566:
552:
549:
544:
540:
534:
530:
526:
523:
520:
515:
511:
505:
501:
493:
489:
483:
479:
472:
469:
466:
463:
460:
437:
414:
403:
402:
386:
383:
378:
374:
365:
361:
357:
354:
351:
346:
342:
333:
329:
314:
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285:
280:
276:
257:
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240:
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196:
187:
183:
168:
164:
155:
151:
139:
134:
130:
106:
84:
80:
57:
53:
9:
6:
4:
3:
2:
1376:
1365:
1362:
1360:
1357:
1355:
1352:
1351:
1349:
1337:
1336:
1329:
1322:
1318:
1317:
1310:
1306:
1297:
1294:
1292:
1289:
1287:
1284:
1282:
1279:
1277:
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1260:
1258:
1253:
1251:
1246:
1245:
1243:
1242:
1234:
1231:
1229:
1226:
1224:
1221:
1219:
1216:
1214:
1211:
1209:
1206:
1204:
1201:
1199:
1196:
1194:
1191:
1189:
1186:
1184:
1181:
1179:
1176:
1174:
1171:
1169:
1166:
1164:
1161:
1160:
1153:
1152:
1141:
1138:
1136:
1133:
1131:
1128:
1127:
1126:
1125:
1122:
1119:
1118:
1113:
1110:
1108:
1105:
1103:
1100:
1099:
1098:
1097:
1092:
1087:
1086:
1077:
1074:
1073:
1067:
1064:
1062:
1059:
1057:
1054:
1052:
1049:
1047:
1046:Charles's law
1044:
1042:
1039:
1037:
1034:
1033:
1031:
1030:
1027:
1024:
1023:
1017:
1014:
1012:
1009:
1007:
1004:
1002:
999:
997:
994:
993:
991:
990:
987:
984:
983:
977:
974:
970:
967:
963:
960:
955:
954:non-Newtonian
952:
948:
944:
943:
942:
939:
937:
934:
930:
927:
925:
922:
920:
917:
913:
910:
908:
905:
901:
898:
897:
895:
894:
891:
888:
887:
882:
877:
876:
868:
865:
863:
860:
856:
853:
852:
851:
848:
846:
843:
841:
840:Compatibility
838:
834:
831:
829:
828:Finite strain
826:
825:
824:
821:
819:
816:
814:
811:
809:
806:
802:
799:
798:
797:
794:
792:
789:
788:
784:
779:
778:
767:
764:
763:
762:
761:
757:
756:
751:
748:
746:
743:
741:
738:
737:
736:
735:
732:Conservations
731:
730:
722:
721:
717:
698:
695:
690:
687:
681:
678:
675:
672:
665:
664:
661:
658:
657:
653:
652:
644:
630:
608:
604:
581:
577:
550:
547:
542:
538:
532:
528:
524:
521:
518:
513:
509:
503:
499:
491:
487:
481:
477:
470:
464:
458:
451:
450:
449:
435:
426:
412:
384:
381:
376:
372:
363:
359:
355:
352:
349:
344:
340:
331:
327:
312:
308:
299:
295:
283:
278:
274:
266:
265:
264:
262:
238:
235:
230:
226:
217:
213:
209:
206:
203:
198:
194:
185:
181:
166:
162:
153:
149:
137:
132:
128:
120:
119:
118:
104:
82:
78:
55:
51:
42:
38:
34:
30:
26:
22:
19:(also called
18:
1333:
1328:
1320:
1314:
1309:
1121:Smart fluids
1066:Graham's law
972:
965:
950:
936:Pascal's law
932:
915:
903:
758:Inequalities
568:
427:
404:
258:
24:
20:
16:
15:
1286:Hooke's law
1140:Ferrofluids
1041:Boyle's law
813:Hooke's law
791:Deformation
1348:Categories
1302:References
1193:Gay-Lussac
1156:Scientists
1056:Fick's law
1036:Atmosphere
855:frictional
808:Plasticity
796:Elasticity
1364:Equations
1233:Truesdell
1163:Bernoulli
1112:Rheometer
1107:Rheometry
947:Newtonian
941:Viscosity
691:φ
679:−
631:α
551:α
548:
522:α
519:
465:α
436:α
385:α
382:
360:σ
353:α
350:
328:σ
309:σ
296:σ
279:α
275:σ
239:α
236:
214:σ
207:α
204:
182:σ
163:σ
150:σ
133:α
129:σ
105:α
79:σ
52:σ
39:angle in
1091:Rheology
996:Adhesion
976:Pressure
962:Buoyancy
907:Dynamics
745:Momentum
647:See also
1178:Charles
986:Liquids
900:Statics
845:Bending
31:or the
1228:Stokes
1223:Pascal
1213:Navier
1208:Newton
1198:Graham
1173:Cauchy
1076:Plasma
971:
969:Mixing
964:
949:
931:
914:
902:
890:Fluids
823:Strain
818:Stress
801:linear
750:Energy
569:where
369:
337:
305:
261:spruce
223:
191:
159:
33:stress
29:stress
1203:Hooke
1183:Euler
1168:Boyle
1026:Gases
37:grain
1218:Noll
1188:Fick
740:Mass
725:Laws
41:wood
539:cos
510:sin
373:cos
341:sin
227:cos
195:sin
23:or
1350::
1319:,
609:90
533:90
492:90
364:90
313:90
218:90
167:90
83:90
1263:e
1256:t
1249:v
973:·
966:·
956:)
951:·
945:(
933:·
916:·
904:·
699:x
696:d
688:d
682:D
676:=
673:J
605:V
582:0
578:V
543:2
529:V
525:+
514:2
504:0
500:V
488:V
482:0
478:V
471:=
468:)
462:(
459:V
413:n
377:n
356:+
345:n
332:0
300:0
284:=
231:2
210:+
199:2
186:0
154:0
138:=
56:0
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