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Обратите, пожалуйста, внимание на правила портала :
Я предлагаю Вам уменьшить стоимость данной консультации до минимальной, а оставшиеся денежные средства потратить на отправку ещё трёх заявок на консультацию, по одному вопросу в каждой.
С уважением.
Об авторе:
Facta loquuntur.
Неизвестный
05.12.2011, 19:04
общий
05.12.2011, 19:05
Адресаты:
Меня просто попросили выложить, т.к. вы мне уже помогли с подобным заданием.
Воспользуйтесь, пожалуйста, опцией мои файлы (слева на странице) и сохраните нужный рисунок на сервере портала. Дайте ссылку для визуализации изображения, которая заменит имеющуюся.
Из симметрии рассматриваемого сечения ясно, что его центр тяжести находится на оси z и вторая координата равна нулю.
Ответ: центр тяжести сечения находится на оси z на расстоянии 2,1a от точки касания кругов справа от неё.
Задача 2
Рассматриваемое сечение представляет собой совокупность двух прямоугольников. Больший из них назовём внешним, меньший - внутренним. Из симметрии сечения следует, что его центр тяжести находится в точке пересечения диагоналей внешнего прямоугольника. Проведём через центр тяжести сечения ось z0, сонаправленно оси z.
1. Находим центробежный момент инерции Jy0z0 площади заданного сечения относительно осей y0 и z0. Оси z0 и y0 являются осями симметрии. Поэтому центробежный момент инерции площади сечения относительно этих осей Jy0z0 = 0.
2. Находим площадь A рассматриваемого сечения: A = 4a [$183$] 6a - 3a [$183$] a = 24a2 - 3a2 = 21a2.
3. Находим центробежный момент инерции Jyz площади заданного сечения относительно осей y и z. Расстояние от оси y0 до оси y составляет -2a (знак "минус" поставлен потому, что переходе от оси y0 к оси y увеличивается "отрицательная" площадь), а расстояние от оси z до оси z0 составляет 3a. Следовательно, Jyz = -2a [$183$] 3a [$183$] 21a2 = -126a4.
Ответ: -126a4.
Задача 3
1. Находим момент инерции Jy0 площади заданного сечения относительно оси y0. Он равен алгебраической сумме момента инерции (J1)y0 площади внешнего прямоугольника и момента инерции (J2)y0 площади внутренего прямоугольника (для их вычисления воспользуемся известными формулами): Jy0 = (J1)y0 - (J2)y0 = 6a(4a)3/12 - a(3a)3/12 = 384a4/12 - 27a4/12 = 357a4/12 = 119a4/4.
2. Находим радиус инерции iy0 сечения относительно оси y0: iy0 = [$8730$](Jy0/A) = [$8730$]((119a4/4)/(21a2)) = [$8730$](119a2/48) = a[$8730$](119/48).
3. Находим момент инерции Jz0 площади заданного сечения относительно оси z0. Он равен алгебраической сумме момента инерции (J1)z0 площади внешнего прямоугольника и момента инерции (J2)z0 площади внутренего прямоугольника (для их вычисления воспользуемся известными формулами): Jz0 = (J1)z0 - (J2)z0 = 4a(6a)3/12 - 3a(a)3/12 = 864a4/12 - 3a4/12 = 861a4/12 = 287a4/4.
4. Находим расстояние от оси z0 до наиболее удалённой точки сечения: ymax = 3a.
5. 4. Находим расстояние от оси y0 до наиболее удалённой точки сечения: zmax = 2a.
6. Находим момент сопротивления Wz0 сечения относительно оси z0: Wz0 = Jz0/ymax = (287a4/4)/(3a) = 287a3/12 = 14,875a3.
7. Находим момент сопротивления Wy0 сечения относительно оси y0: Wy0 = Jy0/zmax = (119a4/4)/(2a) = 119a3/8 [$8776$] 23,917a3.
Из полученных в пп. 6,7 результатов следует, что наименьший осевой момент сопротивления равен 14,875a3.
Ответ: a[$8730$](119/48); 14,875a3.
С уважением.
Об авторе:
Facta loquuntur.
Форма ответа
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