( , , , , , , ) 1
augment K11 K12 K13 K14 K15 K16 K17
K :=
( , , , , , , ) 2
augment K12 K22 K23 K24 K25 K26 K27
K :=
( , , , , , , ) 3
augment K13 K23 K33 K34 K35 K36 K37
K :=
( , , , , , , ) 4
augment K14 K24 K34 K44 K45 K46 K47
K :=
( , , , , , , ) 5
augment K15 K25 K35 K45 K55 K56 K57
K :=
( , , , , , , ) 6
augment K16 K26 K36 K46 K56 K66 K67
K :=
( , , , , , , ) 7
augment K17 K27 K37 K47 K57 K67 K77
K := stack(K ,
,
,
,
,
,
)
1 K2 K3 K4 K5 K6 K7
b) Macierz sztywności kratownicy 1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
1
669.687
338.469
-374.35
-449.221
-295.336
110.751
0
0
0
0
0
0
0
0
2
338.469
1.7710 3
-449.221
-539.065
110.751
-41.532
0
0
0
0
0
-1.18910 3
0
0
3
-374.35
-449.221
1.50510 3
223.624
-75.199
225.597
-479.7
0
0
0
-575.64
0
0
0
4
-449.221
-539.065
223.624
1.21610 3
225.597
-676.791
0
0
0
0
0
0
0
0
5
-295.336
110.751
-75.199
225.597
741.07 1.86310
-14
-75.199
-225.597
-295.336
-110.751
0
0
0
0
6
110.751
-41.532
225.597
-676.791 1.86310
-14
1.43710 3
-225.597
-676.791
-110.751
-41.532
0
0
0
0
kN
K = 7
0
0
-479.7
0
-75.199
-225.597
1.50510 3
-223.624
-374.35
449.221
0
0
-575.64
0
cm
8
0
0
0
0
-225.597
-676.791
-223.624
1.21610 3
449.221
-539.065
0
0
0
0
9
0
0
0
0
-295.336
-110.751
-374.35
449.221
669.687
-338.469
0
0
0
0
10
0
0
0
0
-110.751
-41.532
449.221
-539.065
-338.469
1.7710 3
0
0
0
-1.18910 3
11
0
0
-575.64
0
0
0
0
0
0
0
575.64
0
0
0
12
0
-1.18910 3
0
0
0
0
0
0
0
0
0
1.18910 3
0
0
13
0
0
0
0
0
0
-575.64
0
0
0
0
0
575.64
0
14
0
0
0
0
0
0
0
0
0
-1.18910 3
0
0
0
1.18910 3
K
:=
m
K
i := 1 .. 14
K
:= 0
K
:= 0
K
:=
m
m
m
0
2, i
10 , i
9, i
K
:= 0
K
:= 0
K
:=
m
m
m
0
i, 2
i, 10
i, 9
kN
kN
kN
K
:= 1⋅
K
:= 1⋅
K
:= ⋅
m
m
m
1
2, 2
cm
9, 9
cm
10 , 10
cm
c) Macierz sztywności kratownicy z uwzględnieniem warunków brzegowych 1
2
3
4
5
6
7
8
9
10
11
12
13
14
1
669.687
0
-374.35
-449.221
-295.336
110.751
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
-374.35
0
1.50510 3
223.624
-75.199
225.597
-479.7
0
0
0
-575.64
0
0
0
4
-449.221
0
223.624
1.21610 3
225.597
-676.791
0
0
0
0
0
0
0
0
5
-295.336
0
-75.199
225.597
741.07 1.86310
-14
-75.199
-225.597
0
0
0
0
0
0
6
110.751
0
225.597
-676.791 1.86310
-14
1.43710 3
-225.597
-676.791
0
0
0
0
0
0
kN
K
=
m
7
0
0
-479.7
0
-75.199
-225.597
1.50510 3
-223.624
0
0
0
0
-575.64
0
cm
8
0
0
0
0
-225.597
-676.791
-223.624
1.21610 3
0
0
0
0
0
0
9
0
0
0
0
0
0
0
0
1
0
0
0
0
0
10
0
0
0
0
0
0
0
0
0
1
0
0
0
0
11
0
0
-575.64
0
0
0
0
0
0
0
575.64
0
0
0
12
0
0
0
0
0
0
0
0
0
0
0
1.18910 3
0
0
13
0
0
0
0
0
0
-575.64
0
0
0
0
0
575.64
0
14
0
0
0
0
0
0
0
0
0
0
0
0
0
1.18910 3
0
0
0
1
1
150
−
1
-0.1256
1
0
2
0
0
2
90.625
3
0.0337
0
3
7.96510
-15
4
-0.2608
0
:=
⋅
4
-150
P
kN
5
0.0138
m
− 1
40
d := K
⋅P
5
1.12410
-15
m
m
6
-0.1479
0
=
6
-0
d
7
-0.03
cm
0
P := K⋅d
P = 7 -6.84810
-15
kN
8
-0.0524
0
8
40
9
0
0
9 -4.89910
-15
10
0
10
19.375
0
11
0.0337
11
0
0
12
0
12
0
13
-0.03
13
0
14
0
d :=
(
( , , , ,
, ( , , , ,
14
0
1
stack sb d 1 2 1 1) sb d 3 4 1 1)) d :=
(
( , , , ,
, ( , , , ,
2
stack sb d 1 2 1 1) sb d 5 6 1 1)) d :=
(
( , , , ,
, ( , , , ,
3
stack sb d 5 6 1 1) sb d 3 4 1 1)) d :=
(
( , , , ,
, ( , , , ,
4
stack sb d 3 4 1 1) sb d 7 8 1 1)) d :=
(
( , , , ,
, ( , , , ,
5
stack sb d 5 6 1 1) sb d 7 8 1 1)) d :=
(
( , , , ,
, ( , ,
, ,
6
stack sb d 5 6 1 1) sb d 9 10 1 1)) d :=
(
( , ,
, , , ( , , , , 7
stack sb d 9 10 1 1) sb d 7 8 1 1)) d :=
(
( , , , ,
, ( ,
,
, ,
8
stack sb d 1 2 1 1) sb d 11 12 1 1)) d :=
(
( ,
,
, , , ( , , , , 9
stack sb d 11 12 1 1) sb d 3 4 1 1)) d
:=
(
( , , , ,
, ( ,
,
, ,
10
stack sb d 7 8 1 1) sb d 13 14 1 1)) d
:=
(
( , ,
, , , ( ,
,
, ,
11
stack sb d 9 10 1 1) sb d 13 14 1 1))