Проектирование и расчет балочной клетки (шаг колонн в продольном направлении - 18 м, шаг колонн в поперечном направлении - 6 м, тип сечения колонн - сплошная)

Содержание.

1.Исходные данные                                                                           стр.1  

2.Выбор схемы балочной клетки                                                     стр.1

3. Расчет и конструирование главной балки                                  стр.9

4. Проектирование и расчет колонн                                                стр.21

5. Список используемой литературы                                              стр.26

1.  Исходные данные.

Шаг колонн в продольном направлении А, м	18 м.
Шаг колонн в поперечном направлении В, м	6 м.
Габариты площадки в плане	3А ´ 3В
Отметка верха настила, м	7,5 м
Строительная высота перекрытия, м	-
Временная равномерно распределенная нагрузка, кН/м2	20 кН/м2
Материал конструкции настила - сталь	С235
Материал балок настила и вспомогательных - сталь	С235
Материал главных балок - сталь	С255
Материал колонн - сталь	С235
Материал фундаментов – бетон класса	В 12,5
Допустимый относительный прогиб настила	1/150
Тип сечения колонны	Сплошная

2.  Выбор схемы балочной клетки.

Расчет настила.

Дано:

Р = 20 кН/м²; g_f = 1,2 – коэффициент надежности по нагрузке.

Материал настила – сталь С235. Согласно СНиП II-23-81 R_y = 23 кН/см² – расчетное сопротивление фасонного проката при t £ 20мм.

Норма прогиба для настила n = 150.

Коэффициент условия работы g_с = 1.

Несущий настил состоит из стального листа, уложенного на балки и приваренного к ним. Для расчета такого настила мысленно вырежем из него полоску единичной ширины, закрепленную по концам неподвижными шарнирами. Тогда отношение наибольшего пролета настила к его толщине из условия заданного предельного прогиба можно приближенно вычислить по формуле:

 где

кН/см² ,

Принимаем для сравнения две толщины настила t_н.

1.  Примем t_н =8 мм, тогда

см.

Определим число балок настила в пролете L = 18 м

 шага – округляем до 20 шагов.                 

Принимаем , тогда расстояние между балками настила:

см.                

Расчетная схема настила.

Расчетная схема балок настила.

Определяем распределенную нагрузку от веса настила зная, что 1м² стального листа толщиной 8 мм весит 78,5 кг:

кг/м² = 0,628 кН/м²

Нормативная нагрузка на балку настила:

кН/м.                  

Расчетная нагрузка на балку настила:

кН/м.                 

Расчетный изгибающий момент (пролет балки В = 6м):

кНм.               

Требуемый момент сопротивления сечения:

см³, где

С_х = 1,1 – коэффициент, для расчета на прочность с учетом развития пластических деформаций, принимаемый по таблице 66 СНиП 2-23-81*  

По сортаменту принимаем двутавр № 30: W_x = 472 см³; I_x = 7080 см⁴; g = 36,5 кг/м.

Проверка прогиба балки:

см < [] = =0,004

Принятое сечение балки удовлетворяет условиям прочности и прогиба. Проверку касательных напряжений в прокатных балках обычно не производят из-за относительно большой толщины стенок балок.

Общую устойчивость балок настила проверять не надо, поскольку их сжатые пояса надежно закреплены в горизонтальном направлении приваренным к ним настилом.

Определяем расход металла на 1 м² перекрытия:

настил кг/м²;

балки настила кг/м².

Всего расход составит: 62,8 + 40,5 = 103,35 кг/м².

2.  Примем t_н = 10 мм, тогда

см.

Определим число балок настила в пролете L = 18 м

 шага – округляем до 17 шагов.                

Принимаем , тогда расстояние между балками настила:

см.                

.Определяем распределенную нагрузку от веса настила зная, что 1м² стального листа толщиной 10 мм весит 78,5 кг:

кг/м² = 0,785 кН/м²

Нормативная нагрузка на балку настила:

кН/м.                  

Расчетная нагрузка на балку настила:

кН/м.                 

Расчетный изгибающий момент (пролет балки В = 6м):

кНм.               

Требуемый момент сопротивления сечения:

см³, где

С_х = 1,1 – коэффициент, для расчета на прочность с учетом развития пластических деформаций, принимаемый по таблице 66 СНиП 2-23-81*  

По сортаменту принимаем двутавр № 33: W_x = 597 см³; I_x = 9840 см⁴; g = 42,2 кг/м.

Проверка прогиба балки:

см < [] = =0,004

Принятое сечение балки удовлетворяет условиям прочности и прогиба. Проверку касательных напряжений в прокатных балках обычно не производят из-за относительно большой толщины стенок балок.

Общую устойчивость балок настила проверять не надо, поскольку их сжатые пояса надежно закреплены в горизонтальном направлении приваренным к ним настилом.

Определяем расход металла на 1 м² перекрытия:

настил кг/м²;

балки настила кг/м².

Всего расход составит: 78,5 + 42,2 = 120,7 кг/м².

Окончательно принимаем первый вариант, как более экономичный:

t_н = 8мм; балки настила I 30; шаг балок настила а = 0,9м.

Расчет усложненной балочной клетки.

Принимаем шаг вспомогательных балок l = 4,5м.

а = 83.2;  Þ  - принимаем m = 8.

Поэтому см.

2.2.1 Расчет балки настила.

Нормативная нагрузка составит:

 кН/м.

Расчетная нагрузка составит:

 кН/м.

Расчетный изгибающий момент:

 кНм.

Требуемый момент сопротивления:

 см³.

Принимаем двутавр I 22 по ГОСТ 8239-89, имеющий:

W_x = 232см³; g = 24 кг/м; I_х =2550 см⁴.

Проверим прочность:

Проверяем прогиб:

[] = =0,004

Принятое сечение балки удовлетворяет условиям прочности и прогиба.

2.2.2 Расчет второстепенной балки

Если шагов балки настила m ≥ 5, то нагрузка представляется в виде равномерно- распределенных сил.

Нормативная нагрузка составит:

 кН/м.

g = 24 кг/м Þ кг/м².

Расчетная нагрузка составит:

 кН/м.

Расчетный изгибающий момент:

 кНм.

Требуемый момент сопротивления:

 см³.

Принимаем двутавр I 55 по ГОСТ 8239-89, имеющий:

W_x = 2035см³; g = 92.6 кг/м; I_х =55962 см⁴; b_f = 18см; l_ef = 75см; t_f = 1.65см; h = 55см.

Определяем отношение (l₀ / b_п):

 

; t_f = 1.65см; h = 55см.

Проверяем прогиб:

[] = =0,004

Проверяем прочность:

кН/см².

Принятое сечение удовлетворяет условиям прочности и прогиба.

Определяем расход металла на 1 м² перекрытия:

настил –  кг/м²;

балки настила -  кг/м²;

вспомогательные балки -  кг/м².

Всего расход металла составит: 62.8 + 32+ 20,6 = 130,6 кг/м².

Как наиболее экономичный вариант принимаем нормальный тип балочной клетки с толщиной настила t =8 мм.  

3.  Расчет и конструирование главной балки.

Исходные данные:

Р = 20 кН/м²; L = 18м; t_н = 8мм = 0,8см; g_p = 1,2; g_c = 1; g_н = 0,628 кН/м².

Балка настила: I 30 g₁ = 36,5 кг/м Þ  кН/м².

Для стали С255 при t 4÷ 20мм R_y = 24 кН/см²; R_s = 0.58R_y = 13,9 кН/см².

3.1 Определение высоты главной балки

Определяем нормативную нагрузку:

 кН/м.

Определяем расчетную нагрузку:

 кН/м.

Определяем расчетный изгибающий момент в середине пролета:

 кНм = 621756 кНсм.

Определяем поперечную силу на опоре:

 кН.

Определяем момент сопротивления:

 см³.

Определяем высоту балки:

, где -гибкость стенки принимаем равным 130

 см.

Определяем  h_min  балки из условия жесткости:

см.

Практикой проектирования установлено, что полученная оптимальная высота является наиболее рациональной, т.к. отступление в ту или другую сторону от высоты h_опт  вызовет увеличение расхода металла на балку. Поэтому принимаем высоту балки кратной 10 см = 100мм исходя из h_опт:

h = 180 см = 1,8м.

Принимаем предварительно t=20мм

t_ст должно удовлетворять двум условиям:

1.  из условия среза;

2.  из условия обеспечения  устойчивости стенки без постановки продольного ребра жесткости.

h=h-2t=180-2∙2=176cм

Пренебрегаем работой поясов

1.   см.                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       

2.   см.

Принимаем   t=12мм

Определяем требуемый момент инерции сечения балки:

см⁴ = I_n + I_ст.

Определяем требуемый момент инерции поясов:

см⁴.

см⁴.

Определим требуемую площадь сечения поясов:

см².

Принимаем пояса из листа 600×20мм

А=120см

==≤

3.2 Проверка несущей способности главной балки

Исходные данные:

h_o = 178см; h_ст = 176см;

h = 180см;

t_ст = 12мм; t_п = 20мм; b_св = 294мм; I_ст = 545178см⁴; A_п = 60 × 2 = 120 см².

Проверяем      местную устойчивость сжатого пояса:

Эту проверку производим в месте возникновения максимальных нормальных напряжений – в середине пролета главной балки. По СНиП  табл.30 будем иметь наибольшее отношение (где b_св – свес полки) при которых происходит потеря устойчивости полки. Эта величина будет различна при расчетах в пределах упругих