323:
202:
537:
423:
30:
The first moment of area of a shape, about a certain axis, equals the sum over all the infinitesimal parts of the shape of the area of that part times its distance from the axis .
632:
207:
89:
654:
483:
369:
24:
604:
328:
728:
723:
683:
678:
587:
668:– the thickness of a particular web section of the cross-section at the point being measured
639:
8:
27:. It is a measure of the spatial distribution of a shape in relation to an axis.
688:
318:{\displaystyle S_{y}=A{\bar {x}}=\sum _{i=1}^{n}{x_{i}\,dA_{i}}=\int _{A}x\,dA.}
477:
339:(m). In the American Engineering and Gravitational systems the unit is a cubic
197:{\displaystyle S_{x}=A{\bar {y}}=\sum _{i=1}^{n}{y_{i}\,dA_{i}}=\int _{A}y\,dA}
717:
340:
74:
be the distances (coordinates) to each elemental area measured from a given
598:
363:
656:– the shear stress through a particular web section of the cross-section
473:
662:– the shear flow through a particular web section of the cross-section
545:– the shear flow through a particular web section of the cross-section
362:, is a property of a shape that is used to predict its resistance to
34:
443:
axis of the entire body (not the neutral axis of the area "j");
467:
336:
344:
707:
Shigley's
Mechanical Engineering Design, 9th Ed. (Page 96)
455:– the perpendicular distance to the centroid of element
33:
First moment of area is commonly used to determine the
476:
in a particular web section of the cross-section of a
642:
607:
486:
372:
210:
92:
601:
may now be calculated using the following equation:
556:– the shear force perpendicular to the neutral axis
648:
626:
571:– the first moment of area about the neutral axis
531:
417:
317:
196:
575:for a particular web section of the cross-section
439:– the first moment of area "j" about the neutral
715:
49:, of any shape, and division of that area into
532:{\displaystyle q={\frac {V_{y}S_{x}}{I_{x}}}}
78:axis. Now, the first moment of area in the
16:Measurement of a shape about a certain axis
468:Shear stress in a semi-monocoque structure
405:
305:
274:
187:
156:
418:{\displaystyle Q_{j,x}=\int y_{i}\,dA,}
86:directions are respectively given by:
53:number of very small, elemental areas (
23:is based on the mathematical construct
716:
627:{\displaystyle \tau ={\frac {q}{t}}}
13:
14:
740:
560:through the entire cross-section
449:– an elemental area of area "j";
358:, usually denoted by the symbol
701:
233:
115:
1:
694:
40:
594:for the entire cross-section
7:
672:
10:
745:
25:moments in metric spaces
684:Polar moment of inertia
590:about the neutral axis
356:statical moment of area
650:
628:
533:
459:from the neutral axis
419:
343:(ft) or more commonly
319:
262:
198:
144:
679:Second moment of area
651:
649:{\displaystyle \tau }
629:
588:second moment of area
534:
420:
320:
242:
199:
124:
640:
605:
484:
370:
333:first moment of area
208:
90:
21:first moment of area
646:
624:
529:
415:
366:. By definition:
315:
194:
622:
527:
472:The equation for
236:
118:
736:
729:Moment (physics)
708:
705:
655:
653:
652:
647:
633:
631:
630:
625:
623:
615:
538:
536:
535:
530:
528:
526:
525:
516:
515:
514:
505:
504:
494:
424:
422:
421:
416:
404:
403:
388:
387:
324:
322:
321:
316:
301:
300:
288:
287:
286:
273:
272:
261:
256:
238:
237:
229:
220:
219:
203:
201:
200:
195:
183:
182:
170:
169:
168:
155:
154:
143:
138:
120:
119:
111:
102:
101:
744:
743:
739:
738:
737:
735:
734:
733:
724:Solid mechanics
714:
713:
712:
711:
706:
702:
697:
689:Section modulus
675:
641:
638:
637:
614:
606:
603:
602:
585:
570:
555:
521:
517:
510:
506:
500:
496:
495:
493:
485:
482:
481:
470:
438:
399:
395:
377:
373:
371:
368:
367:
296:
292:
282:
278:
268:
264:
263:
257:
246:
228:
227:
215:
211:
209:
206:
205:
178:
174:
164:
160:
150:
146:
145:
139:
128:
110:
109:
97:
93:
91:
88:
87:
72:
65:
58:
45:Given an area,
43:
17:
12:
11:
5:
742:
732:
731:
726:
710:
709:
699:
698:
696:
693:
692:
691:
686:
681:
674:
671:
670:
669:
663:
657:
645:
621:
618:
613:
610:
596:
595:
581:
576:
566:
561:
551:
546:
524:
520:
513:
509:
503:
499:
492:
489:
480:structure is:
478:semi-monocoque
469:
466:
465:
464:
450:
444:
434:
414:
411:
408:
402:
398:
394:
391:
386:
383:
380:
376:
314:
311:
308:
304:
299:
295:
291:
285:
281:
277:
271:
267:
260:
255:
252:
249:
245:
241:
235:
232:
226:
223:
218:
214:
193:
190:
186:
181:
177:
173:
167:
163:
159:
153:
149:
142:
137:
134:
131:
127:
123:
117:
114:
108:
105:
100:
96:
70:
63:
56:
42:
39:
15:
9:
6:
4:
3:
2:
741:
730:
727:
725:
722:
721:
719:
704:
700:
690:
687:
685:
682:
680:
677:
676:
667:
664:
661:
658:
643:
636:
635:
634:
619:
616:
611:
608:
600:
593:
589:
584:
580:
577:
574:
569:
565:
562:
559:
554:
550:
547:
544:
541:
540:
539:
522:
518:
511:
507:
501:
497:
490:
487:
479:
475:
462:
458:
454:
451:
448:
445:
442:
437:
433:
430:
429:
428:
425:
412:
409:
406:
400:
396:
392:
389:
384:
381:
378:
374:
365:
361:
357:
353:
348:
346:
342:
338:
334:
330:
325:
312:
309:
306:
302:
297:
293:
289:
283:
279:
275:
269:
265:
258:
253:
250:
247:
243:
239:
230:
224:
221:
216:
212:
191:
188:
184:
179:
175:
171:
165:
161:
157:
151:
147:
140:
135:
132:
129:
125:
121:
112:
106:
103:
98:
94:
85:
81:
77:
73:
66:
59:
52:
48:
38:
36:
31:
28:
26:
22:
703:
665:
659:
599:Shear stress
597:
591:
582:
578:
572:
567:
563:
557:
552:
548:
542:
471:
460:
456:
452:
446:
440:
435:
431:
426:
364:shear stress
359:
355:
351:
349:
332:
326:
83:
79:
75:
68:
61:
54:
50:
46:
44:
37:of an area.
32:
29:
20:
18:
335:is a cubic
718:Categories
695:References
474:shear flow
41:Definition
644:τ
609:τ
393:∫
331:unit for
294:∫
244:∑
234:¯
176:∫
126:∑
116:¯
673:See also
35:centroid
60:). Let
586:– the
427:where
352:static
337:metre
204:and
350:The
345:inch
341:foot
327:The
82:and
67:and
19:The
436:j,x
354:or
76:x-y
720::
457:dA
447:dA
347:.
329:SI
55:dA
666:t
660:q
620:t
617:q
612:=
592:x
583:x
579:I
573:x
568:x
564:S
558:x
553:y
549:V
543:q
523:x
519:I
512:x
508:S
502:y
498:V
491:=
488:q
463:.
461:x
453:y
441:x
432:Q
413:,
410:A
407:d
401:i
397:y
390:=
385:x
382:,
379:j
375:Q
360:Q
313:.
310:A
307:d
303:x
298:A
290:=
284:i
280:A
276:d
270:i
266:x
259:n
254:1
251:=
248:i
240:=
231:x
225:A
222:=
217:y
213:S
192:A
189:d
185:y
180:A
172:=
166:i
162:A
158:d
152:i
148:y
141:n
136:1
133:=
130:i
122:=
113:y
107:A
104:=
99:x
95:S
84:y
80:x
71:i
69:y
64:i
62:x
57:i
51:n
47:A
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.