WARUNKI BRZEGOWE

W1”=W1 W2”=W2 W3”=W3 W4”=W4 W5”=W5 W6”=W6 W11”=W11 W16”=W16 W22”=W22		W5’= -W5 W10’=-W10 W15’=-W15 W20’=-W20 W25’=-W25 W24’=-W24 W23’=-W23 W22’=-W22 W21’=-W21		WI =0 WII =0 WIII =0 WIV =0 WV =0 WVI =0 WVII =0 WVIII =0 WIX =0 WX =0 WXI =0 WXII =0		WXII =0 WXIV=0 WXV =0 WXVI=0 WXVII =0 WXVIII =0 WXIX =0 WXX =0 WXXI =0 WXXII=0 WXXIII =0

Obliczenie wyznaczników:

	W1	W2	W3	W4	W5	W6	W7	W8	W9	W10	W11	W12	W13	W14	W15	W16	W17	W18	W19	W20	W21	W22	W23	W24	W25
1	22	-8	1	0	0	-8	2	0	0	0	1	0	0	0	0	0	0	0	0	0	0	0	0	0	0
2	-8	21	-8	1	0	2	-8	2	0	0	0	1	0	0	0	0	0	0	0	0	0	0	0	0	0
3	1	-8	21	-8	1	0	2	-8	2	0	0	0	1	0	0	0	0	0	0	0	0	0	0	0	0
4	0	1	-8	21	-8	0	0	2	-8	2	0	0	0	1	0	0	0	0	0	0	0	0	0	0	0
5	0	0	1	-8	20	0	0	0	2	-8	0	0	0	0	1	0	0	0	0	0	0	0	0	0	0
6	-8	2	0	0	0	21	-8	1	0	0	-8	2	0	0	0	1	0	0	0	0	0	0	0	0	0
7	2	-8	2	0	0	-8	20	-8	1	0	2	-8	2	0	0	0	1	0	0	0	0	0	0	0	0
8	0	2	-8	2	0	1	-8	20	-8	1	0	2	-8	2	0	0	0	1	0	0	0	0	0	0	0
9	0	0	2	-8	2	0	1	-8	20	-8	0	0	2	-8	2	0	0	0	1	0	0	0	0	0	0
10	0	0	0	2	-8	0	0	1	-8	19	0	0	0	2	-8	0	0	0	0	1	0	0	0	0	0
11	1	0	0	0	0	-8	2	0	0	0	21	-8	1	0	0	-8	2	0	0	0	1	0	0	0	0
12	0	1	0	0	0	2	-8	2	0	0	-8	20	-8	1	0	2	-8	2	0	0	0	1	0	0	0
13	0	0	1	0	0	0	2	-8	2	0	1	-8	20	-8	1	0	2	-8	2	0	0	0	1	0	0
14	0	0	0	1	0	0	0	2	-8	2	0	1	-8	20	-8	0	0	2	-8	2	0	0	0	1	0
15	0	0	0	0	1	0	0	0	2	-8	0	0	1	-8	19	0	0	0	2	-8	0	0	0	0	1
16	0	0	0	0	0	1	0	0	0	0	-8	2	0	0	0	21	-8	1	0	0	-8	2	0	0	0
17	0	0	0	0	0	0	1	0	0	0	2	-8	2	0	0	-8	20	-8	1	0	2	-8	2	0	0
18	0	0	0	0	0	0	0	1	0	0	0	2	-8	2	0	1	-8	20	-8	1	0	2	-8	2	0
19	0	0	0	0	0	0	0	0	1	0	0	0	2	-8	2	0	1	-8	20	-8	0	0	2	-8	2
20	0	0	0	0	0	0	0	0	0	1	0	0	0	2	-8	0	0	1	-8	19	0	0	0	2	-8
21	0	0	0	0	0	0	0	0	0	0	1	0	0	0	0	-8	2	0	0	0	20	-8	1	0	0
22	0	0	0	0	0	0	0	0	0	0	0	1	0	0	0	2	-8	2	0	0	-8	19	-8	1	0
23	0	0	0	0	0	0	0	0	0	0	0	0	1	0	0	0	2	-8	2	0	1	-8	19	-8	1
24	0	0	0	0	0	0	0	0	0	0	0	0	0	1	0	0	0	2	-8	2	0	1	-8	19	-8
25	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1	0	0	0	2	-8	0	0	1	-8	18

$$\frac{px^{4}}{D} = \frac{40 \bullet 1^{4}}{20571,43} = 0,00188\ m$$

p = 40 kN/m²

x = 1 m

$$D = \frac{Eh^{3}}{12(1 - \upsilon^{2})} = \frac{31 \bullet 10^{6} \bullet {0,2}^{3}}{12\left( 1 - \frac{1}{6}^{2} \right)} = 21257,14\ \text{kNm}$$

	m	mm
W1	0,0007	0,72
W2	0,0016	1,55
W3	0,0020	1,99
W4	0,0019	1,90
W5	0,0012	1,21
W6	0,0016	1,55
W7	0,0034	3,39
W8	0,0044	4,39
W9	0,0042	4,16
W10	0,0026	2,61
W11	0,0020	1,99
W12	0,0044	4,39
W13	0,0057	5,70
W14	0,0054	5,38
W15	0,0034	3,35
W16	0,0019	1,90
W17	0,0042	4,16
W18	0,0054	5,38
W19	0,0051	5,07
W20	0,0032	3,16
W21	0,0012	1,21
W22	0,0026	2,61
W23	0,0034	3,35
W24	0,0032	3,16
W25	0,0020	1,98

Obliczenie momentów:

$$\left( \text{mx} \right)_{i,k} = \frac{- D}{\lambda^{2}}\left\lbrack \left( W_{i + 1,k} - 2W_{i,k} + W_{i - 1,k} \right) + \upsilon\left( W_{i,\ k + 1} - 2W_{i,k} + W_{i,k - 1} \right) \right\rbrack$$

$$\left( \text{my} \right)_{i,k} = \frac{- D}{\lambda^{2}}\left\lbrack \left( W_{i,k + 1} - 2W_{i,k} + W_{i,k - 1} \right) + \upsilon\left( W_{i + 1,\ k} - 2W_{i,k} + W_{i - 1,k} \right) \right\rbrack$$

mx1	-2,55
mx2	7,17
mx3	10,02
mx4	11,23
mx5	10,61
mx6	-4,75
mx7	20,85
mx8	30,10
mx9	31,55
mx10	24,86
mx11	-6,65
mx12	27,54
mx13	40,32
mx14	41,71
mx15	31,55
mx16	-5,56
mx17	26,63
mx18	38,60
mx19	39,78
mx20	30,02
mx21	-1,97
mx22	17,57
mx23	24,67
mx24	25,43
mx25	19,70

my1	-2,55
my2	-4,75
my3	-6,65
my4	-5,56
my5	-1,97
my6	7,17
my7	20,85
my8	27,54
my9	26,63
my10	17,57
my11	10,02
my12	30,10
my13	40,32
my14	38,60
my15	24,67
my16	11,23
my17	31,55
my18	41,71
my19	39,78
my20	25,43
my21	10,61
my22	24,86
my23	31,55
my24	30,02
my25	19,70

Obliczenie momentów skręcających:

$$\left( \mathrm{\text{mxy}} \right)_{\mathrm{i,k}}\mathrm{=}\left( \mathrm{\text{myx}} \right)_{\mathrm{i,k}}\mathrm{=}\frac{\mathrm{1 - \upsilon}}{\mathrm{4}\mathrm{\lambda}^{\mathrm{2}}}\mathrm{D}\left\lbrack \mathrm{W}_{\mathrm{i - 1,k - 1}}\mathrm{+}\mathrm{W}_{\mathrm{i + 1,k + 1}}\mathrm{-}\mathrm{W}_{\mathrm{i - 1,k + 1}}\mathrm{-}\mathrm{W}_{\mathrm{i - 1,k + 1}}\mathrm{-}\mathrm{W}_{\mathrm{i + 1,k - 1}} \right\rbrack$$

mxy =myx	kNm
mxy1 =myx1	-15,02
mxy2 =myx2	-12,57
mxy3 =myx3	-3,38
mxy4 =myx4	7,89
mxy5 =myx5	18,40
mxy6 =myx6	-12,57
mxy7 =myx7	-10,78
mxy8 =myx8	-2,84
mxy9 =myx9	6,93
mxy10 =myx10	15,42
mxy11 =myx11	-3,38
mxy12 =myx12	-2,84
mxy13 =myx13	-0,67
mxy14 =myx14	1,94
mxy15 =myx15	4,05
mxy16 =myx16	7,89
mxy17 =myx17	6,93
mxy18 =myx18	1,94
mxy19 =myx19	-4,29
mxy20 =myx20	-9,83
mxy21 =myx21	18,40
mxy22 =myx22	15,42
mxy23 =myx23	4,05
mxy24 =myx24	-9,83
mxy25 =myx25	-22,46

Obliczenie sił tnących:

$$\left( \mathrm{\text{qx}} \right)_{\mathrm{i,k}}\mathrm{= -}\frac{\mathrm{D}}{\mathrm{2}\mathrm{\lambda}^{\mathrm{3}}}\left\lbrack \mathrm{-}\mathrm{W}_{\mathrm{i - 1,k}}\mathrm{+}\mathrm{W}_{\mathrm{i + 2,k}}\mathrm{-}\mathrm{W}_{\mathrm{i - 1,k - 1}}\mathrm{+}\mathrm{W}_{\mathrm{i + 1,k - 1}}\mathrm{-}\mathrm{W}_{\mathrm{i - 1,k + 1}}\mathrm{+}\mathrm{W}_{\mathrm{i + 1,k + 1}}\mathrm{- 4}\left( \mathrm{W}_{\mathrm{i + 1,k}}\mathrm{-}\mathrm{W}_{\mathrm{i - 1,k}} \right) \right\rbrack$$

$$\left( \mathrm{\text{qy}} \right)_{\mathrm{i,k}}\mathrm{= -}\frac{\mathrm{D}}{\mathrm{2}\mathrm{\lambda}^{\mathrm{3}}}\left\lbrack \mathrm{-}\mathrm{W}_{\mathrm{i,\ k - 2}}\mathrm{+}\mathrm{W}_{\mathrm{i,k + 2}}\mathrm{-}\mathrm{W}_{\mathrm{i - 1,k - 1}}\mathrm{+}\mathrm{W}_{\mathrm{i + 1,k - 1}}\mathrm{-}\mathrm{W}_{\mathrm{i + 1,k - 1}}\mathrm{+}\mathrm{W}_{\mathrm{i + 1,k + 1}}\mathrm{- 4}\left( \mathrm{W}_{\mathrm{i,k + 1}}\mathrm{-}\mathrm{W}_{\mathrm{i,k - 1}} \right) \right\rbrack$$

qx	kN		qy	kN
qx1	16,44		qy1	-16,44
qx2	3,63		qy2	-50,86
qx3	1,40		qy3	-67,09
qx4	2,26		qy4	-65,28
qx5	-2,43		qy5	-43,98
qx6	50,86		qy6	-3,63
qx7	23,67		qy7	-23,67
qx8	7,07		qy8	-33,12
qx9	-6,52		qy9	-31,99
qx10	-24,93		qy10	-20,39
qx11	67,09		qy11	-1,40
qx12	33,12		qy12	-7,07
qx13	9,72		qy13	-9,72
qx14	-10,47		qy14	-9,16
qx15	-34,42		qy15	-5,58
qx16	65,28		qy16	-2,26
qx17	31,99		qy17	6,52
qx18	9,16		qy18	10,47
qx19	-10,65		qy19	10,65
qx20	-34,09		qy20	7,21
qx21	43,98		qy21	2,43
qx22	20,39		qy22	24,93
qx23	5,58		qy23	34,42
qx24	-7,21		qy24	34,09
qx25	-23,77		qy25	23,77

Obliczenia brzegowe:

$$\left( \overset{\overline{}}{\mathrm{\text{qx}}} \right)_{\mathrm{i,k}}\mathrm{= -}\frac{\mathrm{D}}{\mathrm{\lambda}^{\mathrm{3}}}\left\lbrack \mathrm{-}\mathrm{W}_{\mathrm{i - 2,k}}\mathrm{+ 2}\mathrm{W}_{\mathrm{i - 1,k - 1}}\mathrm{+ 2}\mathrm{W}_{\mathrm{i + 1,k}}\mathrm{+}\mathrm{W}_{\mathrm{i + 2,k}}\mathrm{+}\left( \mathrm{2 - \upsilon} \right)\left( \mathrm{-}\mathrm{W}_{\mathrm{i - 1,k - 1}}\mathrm{+ 2}\mathrm{W}_{\mathrm{i - 1,k}}\mathrm{-}\mathrm{W}_{\mathrm{i - 1,k + 1}}\mathrm{+}\mathrm{W}_{\mathrm{i + 1,k - 1}}\mathrm{- 2}\mathrm{W}_{\mathrm{i + 1,k}}\mathrm{+}\mathrm{W}_{\mathrm{i + 1,k + 1}} \right) \right\rbrack$$

$$\left( \overset{\overline{}}{\mathrm{\text{qy}}} \right)_{\mathrm{i,k}}\mathrm{= -}\frac{\mathrm{D}}{\mathrm{\lambda}^{\mathrm{3}}}\left\lbrack \mathrm{-}\mathrm{W}_{\mathrm{i,k - 2}}\mathrm{+ 2}\mathrm{W}_{\mathrm{i,k - 1}}\mathrm{+ 2}\mathrm{W}_{\mathrm{i1,k + 1}}\mathrm{+}\mathrm{W}_{\mathrm{i,k + 2}}\mathrm{+}\left( \mathrm{2 - \upsilon} \right)\left( \mathrm{-}\mathrm{W}_{\mathrm{i - 1,k - 1}}\mathrm{+ 2}\mathrm{W}_{\mathrm{i,k + 1}}\mathrm{-}\mathrm{W}_{\mathrm{i + 1,k - 2}}\mathrm{+}\mathrm{W}_{\mathrm{i - 1,k + 1}}\mathrm{- 2}\mathrm{W}_{\mathrm{i,k + 1}}\mathrm{+}\mathrm{W}_{\mathrm{i + 1,k + 1}} \right) \right\rbrack$$