Ãëàâíàÿ
Çàäà÷à 1. Ðàñ÷åò ñòàòè÷åñêè íåîïðåäåëèìûõ
íåðàçðåçíûõ áàëîê
Äëÿ ñòàòè÷åñêè
íåîïðåäåëèìîé íåðàçðåçíîé áàëêè (ðèñ.1),
ñîîòâåòñòâóþùåé âàðèàíòó çàäàíèÿ,
ñ ðàçìåðàìè è íàãðóçêîé,
âûáðàííûìè ïî øèôðó èç òàáë.1,
òðåáóåòñÿ ìåòîäîì ñèë ïîñòðîèòü
ýïþðû Ì è Q.
Òàáëèöà 1
|
Íîìåð còðîêè |
Íîìåð ñõåìû ïî ðèñ.11.1 |
q, êÍ/ì |
à, ì |
b, ì |
l, ì |
|
01 |
1 |
5 |
1 |
2 |
2 |
|
02 |
2 |
4 |
2 |
2 |
3 |
|
03 |
3 |
6 |
3 |
2 |
4 |
|
04 |
4 |
2 |
2 |
3 |
2 |
|
05 |
5 |
4 |
1 |
3 |
5 |
|
06 |
6 |
2 |
3 |
1 |
6 |
|
07 |
7 |
3 |
2 |
2 |
3 |
|
08 |
8 |
6 |
1 |
2 |
2 |
|
09 |
9 |
5 |
2 |
1 |
4 |
|
10 |
10 |
6 |
1 |
3 |
3 |
|
11 |
11 |
6 |
1 |
2 |
5 |
|
12 |
12 |
2 |
3 |
3 |
1 |
|
13 |
13 |
4 |
2 |
3 |
2 |
|
14 |
14 |
2 |
1 |
1 |
4 |
|
15 |
15 |
3 |
2 |
2 |
5 |
|
16 |
16 |
6 |
1 |
2 |
3 |
|
17 |
17 |
5 |
2 |
1 |
2 |
|
18 |
18 |
6 |
3 |
2 |
5 |
|
19 |
19 |
2 |
2 |
2 |
3 |
|
20 |
20 |
4 |
1 |
3 |
2 |
|
21 |
21 |
2 |
3 |
3 |
1 |
|
22 |
22 |
3 |
2 |
1 |
3 |
|
23 |
23 |
6 |
1 |
2 |
4 |
|
24 |
24 |
5 |
1 |
2 |
5 |
|
25 |
25 |
6 |
3 |
1 |
3 |
|
26 |
26 |
6 |
2 |
3 |
2 |
|
27 |
27 |
2 |
1 |
2 |
1 |
|
28 |
28 |
4 |
2 |
3 |
3 |
|
29 |
29 |
2 |
1 |
3 |
5 |
|
30 |
30 |
3 |
2 |
1 |
4 |
|
31 |
31 |
6 |
3 |
2 |
2 |
|
32 |
32 |
5 |
2 |
2 |
1 |
|
33 |
33 |
6 |
1 |
1 |
3 |
|
34 |
34 |
2 |
3 |
3 |
6 |
|
35 |
35 |
4 |
2 |
2 |
4 |
|
36 |
36 |
3 |
1 |
2 |
3 |
|
|
á |
ã |
â |
à |
ã |
1 ñõåìà 2 ñõåìà
3 ñõåìà 4 ñõåìà
5 ñõåìà 6 ñõåìà
7 ñõåìà 8 ñõåìà
9 ñõåìà 10 ñõåìà
11 ñõåìà 12 ñõåìà
13 ñõåìà 14 ñõåìà
15 ñõåìà 16 ñõåìà
17 ñõåìà 18 ñõåìà
19 ñõåìà 20 ñõåìà
21 ñõåìà 22 ñõåìà
23 ñõåìà 24 ñõåìà
25 ñõåìà 26 ñõåìà
27 ñõåìà 28 ñõåìà
29 ñõåìà 30 ñõåìà
31 ñõåìà 32 ñõåìà
33 ñõåìà 34 ñõåìà
35 ñõåìà 36 ñõåìà
Ðèñ.1
Çàäà÷à 2. Ðàñ÷åò íåðàçðåçíûõ áàëîê
Äëÿ íåðàçðåçíîé áàëêè (ðèñ.2) ñ âûáðàííûì ïî øèôðó èç òàáë. 2 ðàçìåðàìè è íàãðóçêîé,
òðåáóåòñÿ:
1) Íàéòè ñ ïîìîùüþ óðàâíåíèÿ òðåõ
ìîìåíòîâ îïîðíûå ìîìåíòû è ïîñòðîèòü ýïþðû Ì
è Q
îò ïîñòîÿííîé
íàãðóçêè q1, P1;
2) Íàéòè ôîêóñíûå îòíîøåíèÿ è
ïîñòðîèòü ýïþðû îò ïîñëåäîâàòåëüíîãî çàãðóæåíèÿ êàæäîãî ïðîëåòà è êîíñîëåé âðåìåííîé íàãðóçêîé q2, P2;
3) Ïîñòðîèòü îáúåìëþùóþ ýïþðó
ìîìåíòîâ äëÿ âòîðîãî ïðîëåòà (ñ÷èòàÿ
ñëåâà).
Äàíî: EI=const.
Òàáëèöà 2
|
Íîìåð còðîêè |
Íîìåð ñõåìû áàëêè ïî ðèñ.2 |
q1, êÍ/ì |
q2, êÍ/ì |
P1, êÍ |
P2, êÍ |
l1, ì |
l2, ì |
l3, ì |
b, ì |
c, ì |
|
01 |
1 |
1,0 |
1,1 |
4 |
8 |
6 |
5 |
7 |
2 |
1 |
|
02 |
2 |
1,2 |
1,3 |
8 |
4 |
7 |
6 |
9 |
3 |
2 |
|
03 |
3 |
1,4 |
0,8 |
5 |
12 |
8 |
9 |
10 |
4 |
2 |
|
04 |
4 |
1,6 |
1,7 |
9 |
5 |
9 |
10 |
6 |
3 |
2 |
|
05 |
5 |
1,8 |
1,8 |
7 |
6 |
10 |
8 |
4 |
2 |
1 |
|
06 |
6 |
1,7 |
1,2 |
6 |
14 |
11 |
7 |
8 |
3 |
1 |
|
07 |
7 |
1,1 |
0,9 |
10 |
11 |
5 |
11 |
11 |
4 |
2 |
|
08 |
8 |
1,3 |
1,4 |
3 |
9 |
12 |
12 |
12 |
3 |
3 |
|
09 |
9 |
1,5 |
1,0 |
11 |
7 |
7,5 |
13 |
5 |
2 |
3 |
|
10 |
10 |
1,9 |
1,5 |
12 |
6 |
13 |
7,5 |
6 |
3 |
2 |
|
11 |
11 |
1,0 |
1,1 |
4 |
8 |
6 |
5 |
7 |
2 |
1 |
|
12 |
12 |
1,2 |
1,3 |
8 |
4 |
7 |
6 |
9 |
3 |
2 |
|
13 |
13 |
1,4 |
0,8 |
5 |
12 |
8 |
9 |
10 |
4 |
2 |
|
14 |
14 |
1,6 |
1,7 |
9 |
5 |
9 |
10 |
6 |
3 |
2 |
|
15 |
15 |
1,8 |
1,8 |
7 |
6 |
10 |
8 |
4 |
2 |
1 |
|
16 |
16 |
1,7 |
1,2 |
6 |
14 |
11 |
7 |
8 |
3 |
1 |
|
17 |
17 |
1,1 |
0,9 |
10 |
11 |
5 |
11 |
11 |
4 |
2 |
|
18 |
18 |
1,3 |
1,4 |
3 |
9 |
12 |
12 |
12 |
3 |
3 |
|
19 |
1 |
1,5 |
1,0 |
11 |
7 |
7,5 |
13 |
5 |
2 |
3 |
|
20 |
2 |
1,9 |
1,5 |
12 |
6 |
13 |
7,5 |
6 |
3 |
2 |
|
21 |
3 |
1,0 |
1,1 |
4 |
8 |
6 |
5 |
7 |
2 |
1 |
|
22 |
4 |
1,2 |
1,3 |
8 |
4 |
7 |
6 |
9 |
3 |
2 |
|
23 |
5 |
1,4 |
0,8 |
5 |
12 |
8 |
9 |
10 |
4 |
2 |
|
24 |
6 |
1,6 |
1,7 |
9 |
5 |
9 |
10 |
6 |
3 |
2 |
|
25 |
7 |
1,8 |
1,8 |
7 |
6 |
10 |
8 |
4 |
2 |
1 |
|
26 |
8 |
1,7 |
1,2 |
6 |
14 |
11 |
7 |
8 |
3 |
1 |
|
27 |
9 |
1,1 |
0,9 |
10 |
11 |
5 |
11 |
11 |
4 |
2 |
|
28 |
10 |
1,3 |
1,4 |
3 |
9 |
12 |
12 |
12 |
3 |
3 |
|
29 |
11 |
1,5 |
1,0 |
11 |
7 |
7,5 |
13 |
5 |
2 |
3 |
|
30 |
12 |
1,9 |
1,5 |
12 |
6 |
13 |
7,5 |
6 |
3 |
2 |
|
31 |
13 |
1,0 |
1,1 |
4 |
8 |
6 |
5 |
7 |
2 |
1 |
|
32 |
14 |
1,2 |
1,3 |
8 |
4 |
7 |
6 |
9 |
3 |
2 |
|
33 |
15 |
1,4 |
0,8 |
5 |
12 |
8 |
9 |
10 |
4 |
2 |
|
34 |
16 |
1,6 |
1,7 |
9 |
5 |
9 |
10 |
6 |
3 |
2 |
|
35 |
17 |
1,8 |
1,8 |
7 |
6 |
10 |
8 |
4 |
2 |
1 |
|
36 |
18 |
1,7 |
1,2 |
6 |
14 |
11 |
7 |
8 |
3 |
1 |
|
|
á |
ã |
â |
à |
ã |
á |
ã |
â |
à |
ã |
1 ñõåìà 2 ñõåìà
3 ñõåìà 4 ñõåìà
5 ñõåìà 6 ñõåìà
7 ñõåìà 8 ñõåìà
9 ñõåìà 10 ñõåìà
11 ñõåìà 12 ñõåìà
13 ñõåìà 14 ñõåìà
15 ñõåìà 16 ñõåìà
17 ñõåìà 18 ñõåìà
Ðèñ.2
Ïîÿñíåíèÿ
ê ðåøåíèþ çàäà÷è
Ïðè ðåøåíèè çàäà÷è ïîä çàäàííîé áàëêîé
íåîáõîäèìî ïîêàçàòü îñíîâíóþ ñèñòåìó è ýïþðû ìîìåíòîâ îò íàãðóçêè.
Ïðè ïîñòðîåíèè ýïþðû ìîìåíòîâ îðäèíàòû
ñëåäóåò îòêëàäûâàòü ñî ñòîðîíû ðàñòÿíóòûõ âîëîêîí, ò.å. ïîëîæèòåëüíûå âíèç.
Ñíà÷àëà íàäî îòëîæèòü çíà÷åíèÿ îïîðíûõ ìîìåíòîâ è ñîåäèíèòü êîíöû ïîëó÷åííûõ îðäèíàò
ïóíêòèðíîé ëèíèåé. Îò ïîëó÷åííîé ëèíèè îïîðíûõ ìîìåíòîâ îòêëàäûâàþòñÿ ýïþðû
ìîìåíòîâ, ïîñòðîåííûå äëÿ êàæäîãî ïðîëåòà â îñíîâíîé ñèñòåìå.
Äëÿ âòîðîãî ïðîëåòà, äëÿ êîòîðîãî òðåáóåòñÿ ñòðîèòü
îáúåìëþùóþ ýïþðó ìîìåíòîâ, íóæíî îïðåäåëÿòü îðäèíàòû îêîí÷àòåëüíîé ýïþðû â
òî÷êàõ ñ èíòåðâàëîì 0,25l2.
Îðäèíàòû îáúåìëþùåé ýïþðû ðåêîìåíäóåòñÿ îïðåäåëÿòü â òàáëè÷íîé ôîðìå.
Çàäà÷à 3. Ðàñ÷åò ñòàòè÷åñêè íåîïðåäåëèìûõ
íåðàçðåçíûõ áàëîê
Äëÿ áàëêè (ðèñ.3), ñîîòâåòñòâóþùåé âàðèàíòó
çàäàíèÿ, ñ ðàçìåðàìè è
íàãðóçêîé (ðèñ.4), âûáðàííûìè ïî
øèôðó èç òàáë.3,
òðåáóåòñÿ:
1)
Ñ ïîìîùüþ óðàâíåíèÿ òðåõ ìîìåíòîâ íàéòè îïîðíûå ìîìåíòû è ïîñòðîèòü ýïþðû
èçãèáàþùèõ ìîìåíòîâ Ì è ïîïåðå÷íûõ
ñèë Q îò ïîñòîÿííîé íàãðóçêè.
2)
Íàéòè ìîìåíòíûå ôîêóñíûå îòíîøåíèÿ è ïîñòðîèòü ýïþðû èçãèáàþùèõ ìîìåíòîâ M îò
ïîñëåäîâàòåëüíîãî çàãðóæåíèÿ êàæäîãî ïðîëåòà
âðåìåííîé íàãðóçêîé.
3)
Ïîñòðîèòü îáúåìëþùèå (îãèáàþùèå) ýïþðû.
4)
Ðàññ÷èòàòü óñèëèÿ â áàëêå íà ÝÂÌ îò äåéñòâèÿ ïîñòîÿííîé íàãðóçêè.
Òàáëèöà 3
|
Íîìåð còðîêè |
Íîìåð ñõåìû áàëêè ïî ðèñ. 3 |
Íîìåð ñõåìû íàãðóçêè ïî ðèñ. 4 |
Âðåìåííàÿ íàãðóçêà, qâð, êÍ/ì |
q1, êÍ/ì |
q2, êÍ/ì |
P1, êÍ |
P2, êÍ |
m, êÍ∙ì |
J1 |
J2 |
J3 |
J4 |
l1 |
l2 |
l3=l4 |
c=a |
|
01 |
1 |
0 |
1,8 |
1,0 |
1,0 |
12,0 |
6,0 |
5 |
1,0 |
2,0 |
1,0 |
2,0 |
6,0 |
8,0 |
6,0 |
1,0 |
|
02 |
2 |
9 |
1,9 |
3,0 |
2,0 |
9,0 |
8,0 |
6 |
3,0 |
2,0 |
2,0 |
3,0 |
6,0 |
7,0 |
9,0 |
2,0 |
|
03 |
3 |
8 |
2,0 |
1,0 |
2,0 |
6,0 |
4,0 |
7 |
1,0 |
1,0 |
2,0 |
2,0 |
5,0 |
7,0 |
6,0 |
2,0 |
|
04 |
4 |
7 |
2,1 |
1,0 |
3,0 |
16,0 |
8,0 |
8 |
3,0 |
3,0 |
2,0 |
1,0 |
4,0 |
6,0 |
7,0 |
1,0 |
|
05 |
5 |
6 |
2,3 |
2,0 |
1,0 |
15,0 |
8,0 |
9 |
2,0 |
1,0 |
1,0 |
2,0 |
6,0 |
8,0 |
7,0 |
2,0 |
|
06 |
1 |
5 |
2,0 |
2,0 |
3,0 |
18,0 |
4,0 |
10 |
2,0 |
2,0 |
1,5 |
1,0 |
7,0 |
8,0 |
10,0 |
2,0 |
|
07 |
2 |
4 |
2,2 |
10,0 |
1,5 |
12,0 |
4,0 |
11 |
2,0 |
2,0 |
1,0 |
1,0 |
4,0 |
5,0 |
5,0 |
1,0 |
|
08 |
3 |
3 |
2,4 |
1,5 |
1,0 |
10,0 |
5,0 |
12 |
1,5 |
2,0 |
1,0 |
1,0 |
8,0 |
4,0 |
4,0 |
1,0 |
|
09 |
4 |
2 |
2,8 |
1,5 |
1,5 |
15,0 |
6,0 |
13 |
2,0 |
1,5 |
2,0 |
2,0 |
5,0 |
6,0 |
8,0 |
2,0 |
|
10 |
5 |
1 |
1,8 |
2,0 |
3,0 |
12,0 |
15,0 |
14 |
1,0 |
2,5 |
2,0 |
3,0 |
6,0 |
5,0 |
7,0 |
1,0 |
|
11 |
1 |
0 |
1,8 |
1,0 |
1,0 |
12,0 |
6,0 |
5 |
1,0 |
2,0 |
1,0 |
2,0 |
6,0 |
8,0 |
6,0 |
1,0 |
|
12 |
2 |
9 |
1,9 |
3,0 |
2,0 |
9,0 |
8,0 |
6 |
3,0 |
2,0 |
2,0 |
3,0 |
6,0 |
7,0 |
9,0 |
2,0 |
|
13 |
3 |
8 |
2,0 |
1,0 |
2,0 |
6,0 |
4,0 |
7 |
1,0 |
1,0 |
2,0 |
2,0 |
5,0 |
7,0 |
6,0 |
2,0 |
|
14 |
4 |
7 |
2,1 |
1,0 |
3,0 |
16,0 |
8,0 |
8 |
3,0 |
3,0 |
2,0 |
1,0 |
4,0 |
6,0 |
7,0 |
1,0 |
|
15 |
5 |
6 |
2,3 |
2,0 |
1,0 |
15,0 |
8,0 |
9 |
2,0 |
1,0 |
1,0 |
2,0 |
6,0 |
8,0 |
7,0 |
2,0 |
|
16 |
1 |
5 |
2,0 |
2,0 |
3,0 |
18,0 |
4,0 |
10 |
2,0 |
2,0 |
1,5 |
1,0 |
7,0 |
8,0 |
10,0 |
2,0 |
|
17 |
2 |
4 |
2,2 |
10,0 |
1,5 |
12,0 |
4,0 |
11 |
2,0 |
2,0 |
1,0 |
1,0 |
4,0 |
5,0 |
5,0 |
1,0 |
|
18 |
3 |
3 |
2,4 |
1,5 |
1,0 |
10,0 |
5,0 |
12 |
1,5 |
2,0 |
1,0 |
1,0 |
8,0 |
4,0 |
4,0 |
1,0 |
|
19 |
4 |
2 |
2,8 |
1,5 |
1,5 |
15,0 |
6,0 |
13 |
2,0 |
1,5 |
2,0 |
2,0 |
5,0 |
6,0 |
8,0 |
2,0 |
|
20 |
5 |
1 |
1,8 |
2,0 |
3,0 |
12,0 |
15,0 |
14 |
1,0 |
2,5 |
2,0 |
3,0 |
6,0 |
5,0 |
7,0 |
1,0 |
|
21 |
1 |
0 |
1,8 |
1,0 |
1,0 |
12,0 |
6,0 |
5 |
1,0 |
2,0 |
1,0 |
2,0 |
6,0 |
8,0 |
6,0 |
1,0 |
|
22 |
2 |
9 |
1,9 |
3,0 |
2,0 |
9,0 |
8,0 |
6 |
3,0 |
2,0 |
2,0 |
3,0 |
6,0 |
7,0 |
9,0 |
2,0 |
|
23 |
3 |
8 |
2,0 |
1,0 |
2,0 |
6,0 |
4,0 |
7 |
1,0 |
1,0 |
2,0 |
2,0 |
5,0 |
7,0 |
6,0 |
2,0 |
|
24 |
4 |
7 |
2,1 |
1,0 |
3,0 |
16,0 |
8,0 |
8 |
3,0 |
3,0 |
2,0 |
1,0 |
4,0 |
6,0 |
7,0 |
1,0 |
|
25 |
5 |
6 |
2,3 |
2,0 |
1,0 |
15,0 |
8,0 |
9 |
2,0 |
1,0 |
1,0 |
2,0 |
6,0 |
8,0 |
7,0 |
2,0 |
|
26 |
1 |
5 |
2,0 |
2,0 |
3,0 |
18,0 |
4,0 |
10 |
2,0 |
2,0 |
1,5 |
1,0 |
7,0 |
8,0 |
10,0 |
2,0 |
|
27 |
2 |
4 |
2,2 |
10,0 |
1,5 |
12,0 |
4,0 |
11 |
2,0 |
2,0 |
1,0 |
1,0 |
4,0 |
5,0 |
5,0 |
1,0 |
|
28 |
3 |
3 |
2,4 |
1,5 |
1,0 |
10,0 |
5,0 |
12 |
1,5 |
2,0 |
1,0 |
1,0 |
8,0 |
4,0 |
4,0 |
1,0 |
|
29 |
4 |
2 |
2,8 |
1,5 |
1,5 |
15,0 |
6,0 |
13 |
2,0 |
1,5 |
2,0 |
2,0 |
5,0 |
6,0 |
8,0 |
2,0 |
|
30 |
5 |
1 |
1,8 |
2,0 |
3,0 |
12,0 |
15,0 |
14 |
1,0 |
2,5 |
2,0 |
3,0 |
6,0 |
5,0 |
7,0 |
1,0 |
|
31 |
1 |
0 |
1,8 |
1,0 |
1,0 |
12,0 |
6,0 |
5 |
1,0 |
2,0 |
1,0 |
2,0 |
6,0 |
8,0 |
6,0 |
1,0 |
|
32 |
2 |
9 |
1,9 |
3,0 |
2,0 |
9,0 |
8,0 |
6 |
3,0 |
2,0 |
2,0 |
3,0 |
6,0 |
7,0 |
9,0 |
2,0 |
|
33 |
3 |
8 |
2,0 |
1,0 |
2,0 |
6,0 |
4,0 |
7 |
1,0 |
1,0 |
2,0 |
2,0 |
5,0 |
7,0 |
6,0 |
2,0 |
|
34 |
4 |
7 |
2,1 |
1,0 |
3,0 |
16,0 |
8,0 |
8 |
3,0 |
3,0 |
2,0 |
1,0 |
4,0 |
6,0 |
7,0 |
1,0 |
|
35 |
5 |
6 |
2,3 |
2,0 |
1,0 |
15,0 |
8,0 |
9 |
2,0 |
1,0 |
1,0 |
2,0 |
6,0 |
8,0 |
7,0 |
2,0 |
|
36 |
1 |
5 |
2,0 |
2,0 |
3,0 |
18,0 |
4,0 |
10 |
2,0 |
2,0 |
1,5 |
1,0 |
7,0 |
8,0 |
10,0 |
2,0 |
|
|
á |
à |
â |
ã |
â |
à |
ã |
á |
ã |
á |
à |
â |
á |
ã |
â |
à |
Ðèñ. 3. Ñõåìû áàëîê
Ðèñ. 4. Ñõåìû
íàãðóçîê
Ïîÿñíåíèÿ
ê ðåøåíèþ çàäà÷è
Íåðàçðåçíîé íàçûâàåòñÿ ñòàòè÷åñêè íåîïðåäåëèìàÿ
ñïëîøíàÿ áàëêà, èìåþùàÿ áîëåå äâóõ âåðòèêàëüíûõ îïîð è, ñëåäîâàòåëüíî,
ïåðåêðûâàþùàÿ áîëåå äâóõ ïðîëåòîâ. Åñëè ñâîèìè êîíöàìè îíà îïèðàåòñÿ íà øàðíèðíûå
îïîðû, ýòî ïðîñòàÿ íåðàçðåçíàÿ áàëêà;
åñëè èìååò êîíñîëè – êîíñîëüíî-íåðàçðåçíàÿ; åñëè èìååò ïî êîíöàì çàùåìëåíèÿ –
íåðàçðåçíàÿ ñ îäíèì èëè äâóìÿ çàùåìëåíèÿìè.
Ñòåïåíü ñòàòè÷åñêîé íåîïðåäåëèìîñòè íåðàçðåçíîé áàëêè Ë
çàâèñèò îò âèäà îïîð è ìîæåò áûòü îïðåäåëåíà ïî ôîðìóëàì
(1)
ãäå 
– ÷èñëî
çàìêíóòûõ êîíòóðîâ ñèñòåìû;
– ÷èñëî ïðîñòûõ
øàðíèðîâ;
– ÷èñëî îïîðíûõ
ñâÿçåé (íå îïîð).
Ðàñ÷åò áàëêè ïî óðàâíåíèþ òðåõ ìîìåíòîâ
Ðàñ÷åò íóæíî íà÷èíàòü ñ âûáîðà
îñíîâíîé ñèñòåìû, êîòîðóþ ìîæíî ïîëó÷èòü èç çàäàííîé ïóòåì óäàëåíèÿ ëèøíèõ
ñâÿçåé, ïðåïÿòñòâóþùèõ âçàèìíîìó ïîâîðîòó ñìåæíûõ ñå÷åíèé áàëêè íàä åå îïîðàìè
(ò.å. ââåñòè âî âñåõ îïîðàõ øàðíèðû è îáîçíà÷èòü íàä íèìè íåèçâåñòíûå îïîðíûå
ìîìåíòû). Ïîñëå ýòîãî ñëåäóåò ïðèñòóïèòü
ê ñîñòàâëåíèþ ñèñòåìû óðàâíåíèé òðåõ ìîìåíòîâ. Â îáùåì âèäå óðàâíåíèå çàïèøåòñÿ
ñëåäóþùèì îáðàçîì:
ãäå 
– ïðîèçâîëüíûé
ìîìåíò èíåðöèè ñå÷åíèÿ, êîòîðûé äëÿ ðàñ÷åòà ìîæíî ïðèíÿòü ðàâíûì ìîìåíòó
èíåðöèè îäíîãî èç ó÷àñòêîâ;
– ïðèâåäåííàÿ
äëèíà n-ãî ïðîëåòà;
– ëåâàÿ
ôèêòèâíàÿ îïîðíàÿ ðåàêöèÿ îò çàãðóæåíèÿ ïðîëåòà 
çàäàííîé
íàãðóçêîé;
– ïðàâàÿ
ôèêòèâíàÿ îïîðíàÿ ðåàêöèÿ îò çàãðóæåíèÿ ïðîëåòà 
çàäàííîé
íàãðóçêîé.
Âåëè÷èíû
ôèêòèâíûõ îïîðíûõ ðåàêöèé îïðåäåëÿþòñÿ ñëåäóþùèì îáðàçîì:
ãäå 
, 
– ïëîùàäè ýïþð èçãèáàþùèõ ìîìåíòîâ íà ïðîëåòàõ è â
îñíîâíîé ñèñòåìå îò çàäàííîé íàãðóçêè;
– ðàññòîÿíèå
öåíòðà òÿæåñòè ýïþðû 
íà áàëêå äî îïîðû;
– ðàññòîÿíèå îò
öåíòðà òÿæåñòè ýïþðû íà áàëêå äî
îïîðû;
, 
– äëèíà ïðîëåòà.
Ïðè ñîñòàâëåíèè óðàâíåíèÿ òðåõ ìîìåíòîâ ñëåäóåò
ïîìíèòü, ÷òî:
1) åñëè áàëêà èìååò êîíñîëü, òî êîíñîëüíûå åå ÷àñòè â
îñíîâíîé ñèñòåìå îòáðàñûâàþòñÿ, à èõ äåéñòâèå çàìåíÿåòñÿ èçâåñòíûìè ìîìåíòàìè
è ïîïåðå÷íûìè ñèëàìè;
2) åñëè áàëêà èìååò çàäåëêè íà êðàéíèõ îïîðàõ èëè íà
îäíîé èç íèõ, òî â îñíîâíîé ñèñòåìå îíè óñëîâíî çàìåíÿþòñÿ äîïîëíèòåëüíûì
ïðîëåòîì áåñêîíå÷íî áîëüøîé æåñòêîñòè.
Òàêèì îáðàçîì, ïîëó÷èâ ñèñòåìó óðàâíåíèé òðåõ ìîìåíòîâ
è ðåøèâ åå, íàéäåì íåèçâåñòíûå îïîðíûå ìîìåíòû. Îïðåäåëèâ îïîðíûå ìîìåíòû,
ïðèñòóïàþò ê ïîñòðîåíèþ ýïþðû èçãèáàþùèõ ìîìåíòîâ M, ïîëüçóÿñü ñëåäóþùåé ôîðìóëîé:
ãäå 
– èçãèáàþùèé
ìîìåíò îò çàäàííîé íàãðóçêè â ïðîñòîé øàðíèðíî îïåðòîé áàëêå;
,
– îïîðíûå
ìîìåíòû, ïîëó÷åííûå ïðè ðåøåíèè ñèñòåìû óðàâíåíèé òðåõ ìîìåíòîâ;
–
ðàññòîÿíèå äî ðàññìàòðèâàåìîãî ñå÷åíèÿ.
Ïîñòðîèâ ýïþðó èçãèáàþùèõ
ìîìåíòîâ M, ñëåäóåò âûïîëíèòü åå ïðîâåðêó, èñïîëüçóÿ ôîðìóëó Ìîðà
èëè ïðàâèëî Âåðåùàãèíà
Ïîñëå ïðîâåðêè ïðàâèëüíîñòè
ïîñòðîåíèÿ ýïþð M ñòðîÿò ýïþðó ïîïåðå÷íûõ ñèë 
êàê è äëÿ
ñòàòè÷åñêè íåîïðåäåëèìûõ ðàì. Äëÿ
îïðåäåëåíèÿ ïîïåðå÷íîé ñèëû ñëåäóåò ïðèìåíèòü ôîðìóëó
ãäå 
– áàëî÷íàÿ
ïîïåðå÷íàÿ ñèëà â ñå÷åíèè x â
ñòàòè÷åñêè îïðåäåëèìîé áàëêå îò âíåøíåé íàãðóçêè;
Îïîðíûå ðåàêöèè îïðåäåëÿþòñÿ óæå ïî ïîñòðîåííîé ýïþðå
ïîïåðå÷íûõ ñèë. Âûäåëÿåòñÿ ôðàãìåíò ýïþðû ïîïåðå÷íûõ ñèë â ðàéîíå n-é îïîðû è
âûðåçàåòñÿ ýòîò óçåë. Ïîïåðå÷íûå ïîëîæèòåëüíûå ñèëû âðàùàþò óçåë ïî ÷àñîâîé
ñòðåëêå.
Ïðîâåðêà ïðàâèëüíîñòè ïîñòðîåíèÿ ýïþð 
è
îïîðíûõ ðåàêöèé ïðîâîäèòñÿ òàê æå, êàê è äëÿ ñòàòè÷åñêè íåîïðåäåëèìûõ ðàì.
Ðàñ÷åò áàëêè ìåòîäîì ìîìåíòíûõ ôîêóñîâ
Ïðè ïîñòðîåíèè ýïþðû èçãèáàþùèõ ìîìåíòîâ îò âðåìåííîé
íàãðóçêè ñëåäóåò âîñïîëüçîâàòüñÿ ìåòîäîì ìîìåíòíûõ ôîêóñíûõ îòíîøåíèé.
Çàãðóæàåòñÿ ïîñëåäîâàòåëüíî êàæäûé ïðîëåò è
âû÷èñëÿþòñÿ âåëè÷èíû èçãèáàþùèõ ìîìåíòîâ íà êîíöàõ êàæäîãî çàãðóæåííîãî ïðîëåòà,
äëÿ ýòîãî ïðåæäå âû÷èñëÿåòñÿ ëåâûå 
è ïðàâûå 
ôîêóñíûå
îòíîøåíèÿ ïî ôîðìóëàì.
Ôîðìóëà äëÿ îïðåäåëåíèÿ ëåâûõ ìîìåíòíî-ôîêóñíûõ
îòíîøåíèé áàëêè
Ôîðìóëà
äëÿ îïðåäåëåíèÿ ïðàâûõ ìîìåíòíî-ôîêóñíûõ îòíîøåíèé áàëêè
Ôîðìóëû äëÿ îïðåäåëåíèÿ îïîðíûõ ìîìåíòîâ ïî êîíöàì
çàãðóæåííîãî ïðîëåòà
Ôîðìóëà äëÿ îïðåäåëåíèÿ îïîðíûõ ìîìåíòîâ íà îïîðàõ,
ðàñïîëîæåííûõ ëåâåå îïîðû 
çàãðóæåííîãî
ïðîëåòà,
Ôîðìóëà äëÿ îïðåäåëåíèÿ îïîðíûõ ìîìåíòîâ íà îïîðàõ,
ðàñïîëîæåííûõ ïðàâåå îïîðû çàãðóæåííîãî
ïðîëåòà,
çàâèñÿò îò
ñïîñîáà çàêðåïëåíèÿ áàëêè (òàáë. 4).
Òàáëèöà 4
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Âñå ýïþðû èçãèáàþùèõ ìîìåíòîâ îò âðåìåííîé íàãðóçêè
íåîáõîäèìî ïîñòðîèòü â òîì æå ìàñøòàáå, ÷òî è ýïþðà èçãèáàþùèõ ìîìåíòîâ îò
ïîñòîÿííîé íàãðóçêè. Îíè ñòðîÿòñÿ îäíà ïîä äðóãîé. Äëÿ ïîñòðîåíèÿ îãèáàþùåé
ýïþðû èçãèáàþùèõ ìîìåíòîâ íóæíî êàæäûé ïðîëåò ðàçáèòü íà òðè ÷àñòè è ïîäñ÷èòàòü
ñîîòâåòñòâóþùèå âåëè÷èíû îðäèíàò èçãèáàþùèõ ìîìåíòîâ. Äëÿ ïîëó÷åíèÿ âåëè÷èí
ìàêñèìàëüíûõ îðäèíàò èçãèáàþùèõ ìîìåíòîâ (
) â êàæäîì ñå÷åíèè ê ìîìåíòó îò ïîñòîÿííîé íàãðóçêè (
) ïðèáàâëÿåò âñå ïîëîæèòåëüíûå îðäèíàòû îò âðåìåííîé
íàãðóçêè, à äëÿ ïîëó÷åíèÿ âåëè÷èí ìèíèìàëüíûõ îðäèíàò èçãèáàþùèõ ìîìåíòîâ (
) â êàæäîì ñå÷åíèè ê ìîìåíòó îò ïîñòîÿííîé íàãðóçêè () – âñå îòðèöàòåëüíûå îðäèíàòû îò âðåìåííîé íàãðóçêè:
(13)
(14)
Àíàëîãè÷íî
ýòîìó íàõîäÿò 
è 
(15)
(16)
Îðäèíàòû è îïðåäåëÿþò
îáû÷íî â òàáëè÷íîé ôîðìå, ïîñòðîåíèå 
è 
ìîæåò áûòü âûïîëíåíî áåç òàáëèöû.
Ïðèìåð 1. Ðàñ÷åò áàëêè ìåòîäîì óðàâíåíèé òðåõ
ìîìåíòîâ
Ðàññ÷èòàòü è ïîñòðîèòü ýïþðû 
è äëÿ íåðàçðåçíîé
áàëêè (ðèñ. 5)
Îïðåäåëÿåì ñòåïåíü ñòàòè÷åñêîé íåîïðåäåëèìîñòè:
Âûáèðàåì îñíîâíóþ ñèñòåìó ñîãëàñíî ðèñ. 5,á. Ìîìåíò íà îïîðå 3 îïðåäåëÿåòñÿ
íàãðóçêîé íà êîíñîëè:
Âû÷èñëÿåì äëÿ õàðàêòåðíûõ ñå÷åíèé êàæäîãî ïðîëåòà êàê
äëÿ ïðîñòîé áàëêè èçãèáàþùèå ìîìåíòû 
Ïî âû÷èñëåííûì çíà÷åíèÿì ñòðîèì ýïþðó 
â îñíîâíîé
ñèñòåìå (ðèñ. 5,â).
Ïî ôîðìóëå (2) ñîñòàâëÿåì óðàâíåíèÿ òðåõ ìîìåíòîâ äëÿ
îïîð, ñîîòâåòñòâåííî ïðèíÿâ n=(0, 1, 2):
Ïðèíÿâ 
íàéäåì çíà÷åíèÿ
Äëÿ ïåðâîãî è òðåòüåãî ïðîëåòîâ îò ðàâíîìåðíî
ðàñïðåäåëåííîé íàãðóçêè, ïîëüçóÿñü ïðèëîæåíèåì, íàõîäèì:
