Sfeliouras Xristou [Main]
Transcript of Sfeliouras Xristou [Main]
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Beam Engilab.
AutoCad 2007 AutoDesk.
00 == G
G
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12
BP=25KN
HA
VA
VB
1
..
KNVKNVVVVFy ABABA 5.12250550 ==+=+=
KNVVVM BBBA 5.1255.62055.2250 ===+=
B
q=5KN/m
-
13
HA
VA
M(x)N(x)
Q(x)
x
q=5KN/m
-
=0m =0, Q=-12.5KN, M=0KNm =1m =0, Q=-7.5KN, M=10KNm
I-I
=0m =5.30, Q=5.30KN, M=10KNm =3m =-5.30, Q=-5.30KN, M=10KNm
00 == NFx
05.122
50 =+= XXXM
055.120 =+= XQFy
XRXR == 55.7555.12
HA
VA
M(x)
N(x) Q(x)
x
q=5KN/m
XRQ == 54.330.5cos
XRN == 54.330.5sin
02
5)5.0(5)1(5.120 =++++= XXXXMM
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14
B
10KNm10KNm
10KNm
10KNm
+
+
+
I-I
=0m =0, Q=7.5KN, M=10KNm =1m =0, Q=12.5KN, M=0KNm
M, N, Q
(M)
HA
q=5KN/m
M(x)N(x)Q(x)
x
VA
KNNFx 00 ==
051555.120 =+= XQFy
02
5)5.1(15)5.3(5)4(5.120 =++++++= XXXXXMM
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15
(Q)
(N)
5
B++
-
-
-12.5KN -7.5KN-5.3KN
5.3KN7.5KN
12.5KN
B-
+
-5.3KN
5.3KN
B
P1=5KN P2=5KN
-
16
...
KNHFx A 00 ==
KNVVVFy ABA 50550 ==+=
KNVVM BBA 50103080 ===
-
B
P1=5KN P2=5KN
HA
VA VB
B
VB
x
N(x)Q(x)
M(x)
050 == XMM
KNQQFy 5050 ==+=
KNNFx 00 ==
-
17
=0m =0, Q=-5KN, M=0KNm =2m =0, Q=-5KN, M=10KNm
I-I
=0m =0, Q=0KN, M=10KNm =4m =0, Q=0KN, M=10KNm
I-II
B
P2=5KN
VB
N(x)
Q(x)
M(x)
x
05)2(50 =++= XXMM
KNQQFy 00550 ==+=
KNNFx 00 ==
B
P1=5KN P2=5KN
VB
N(x)Q(x)
M(x)
x 05)4(5)6(50 =++++= XXXMM
KNQQFy 505550 ==+=
KNNFx 00 ==
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18
=0m =0, Q=5KN, M=10KNm =2m =0, Q=5KN, M=0KNm
M, N, Q
(M)
(Q)
(N)
B10KNm 10KNm
+
B
5KN
-5KN-5KN
5KN+
-
B0
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19
B
VB
HA
VA
P=280KN
3
..
KNHFx A 00 ==
KNVVVFy ABA 8004700 ==+=
KNVVM BBA 2000547070 ===
q=70KN/m
B
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20
-
=0m =0, Q=-200KN, M=0KNm =4m =0, Q=80KN, M=240KNm
I-I
KNNFx 00 ==
=0m =0, Q=80KN, M=240KNm =3m =0, Q=80KN, M=0KNm
q=70KN/m
BN (x)
Q (x)M (x)
VBx
KNNFx 00 ==
02
702000 =+= XXXMM
0702000 =+= XQFy
q=70KN/m
B
VB
N(x)
Q(x)M(x)
x
KNQQFy 8004702000 ==+=
0)2(470)4(2000 =+++= XXMM
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21
M, N,Q
(M)
(Q)
(N)
B
240KNm
+
B
-200KN
80KN80KN+
-
B0
-
22
B
VB
HA
VA
P=16KN P=100KN
B
q=8KN/m q=20KN/m
4
..
KNHFx A 00 ==
KNVVVFy ABA 2.690520280 ==+=
KNVVM BBA 8.460285.25205 ==+=
-
23
B
q=20KN/m
VB
x
N(x)Q(x)M(x)
B
q=20KN/m
VB
HA
VA
q=8KN/m
N(x)Q(x)M(x)
x
-
=0m =0, Q=-46,8KN, M=0KNm =5m =0, Q=53,2KN, M=-16KNm
I-I
KNNFx 00 ==
082.695208.460 =++= XQFy0
282.69)5.2(520)5(8.460 =++++= XXXXXMM
=0m =0, Q=-16KN, M=-16KNm =2m =0, Q=0KN, M=0KNm
KNNFx 00 ==
0208.460 =+= XQFy
02
208.460 =+= XXXMM
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24
B00
M, N, Q
(M)
(Q)
()
B
0 0
-16KNm
-
+
B
-16KN
-46.8KN
53.2KN
0
+
-
-
-
25
q=20KN/m
B
B
P=240KN
HA
VA VB
N(x)Q(x)
M(x)
q=20KN/m
x
5
..
-
KNVVM BBA 1200424080 ===
KNVVVFy ABA 12002400 ==+=
00 == AHFx
02
200 =+= XXMM
0200 == XQFy
KNNFx 00 ==
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26
B
VB
q=20KN/m
N(x)Q(x)
M(x)
x
B
x
HA
VAVB
N(x)
Q(x)M(x)
q=20KN/m
=0m =0, Q=0KN, M=0KNm =2m =0, Q=40KN, M=-40KNm
I-I
=0m =0, Q=-80KN, M=-40KNm =8m =0, Q=80KN, M=-40KNm
I-I
KNNFx 00 ==
020160401201200 =++= XQFy
02
20)4(160)9(40)8(1201200 =++++++= XXXXXXMM
=0m =0, Q=-40KN, M=-40KNm =2m =0, Q=0KN, M=0KNm
02
20120)1(400 =+++= XXXXMM
XQXQFy +==+= 2080020401200
KNNFx 00 ==
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27
M, N, Q
()
(Q)
(N)
B+
-
--
-
-40KNm -40KNm
B++
-
-
-40KN-80KN
40KN80KN
B0 0 0
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28
A B
q=10KN /m
A B
P=120KN
HA
VA VB
6
...
KNHFx A 00 ==
KNVVVFy ABA 6001200 ==+=
KNVVM BBA 600412080 ===
-
29
N(x)
Q(x)M(x)
x
q=10KN/m
-
=0m =0, Q=0KN, M=0KNm =2m =0, Q=20KN, M=-20KNm
-
=0m =0, Q=-40KN, M=-20KNm =8m =0, Q=40KN, M=-20KNm
KNNFx 00 ==
02
100 === XXMM
0100 == XQFy
B
q=10KN/m
N(x)
Q(x)M(x)
x
VB
02
1060)1(200 =+++= XXXXMM
01020600 =+= XQFy
KNNFx 00 ==
-
30
A B
q=10KN/m
N(x)
Q(x)M(x) HA
VAVB
x
-
KNNFx 00 ==
010802060600 =++= XQFy
02
10)4(80)9(20)8(60600 =++++++= XXXXXXMM
=0m =0, Q=-20KN, M=-20KNm =2m =0, Q=0KN, M=0KNm
M, N, Q
(M)
(M)
A B
20KNm
+
20KNm
-- -
-
-
31
A B
q1=5KN/m
q2=5KN/mq2=3KN/m
(Q)
(N)
7
A B
++
-
-
20KN
-40KN
40KN
-20KN
00
A B0 0 0
-
32
A BHA
VA VB
P=60KNP=6KN P=6KN..
KNHFx A 00 ==
KNVVVFy ABA 36085)28(20 ==+= KNVVM BBA 36092592348512512380 ==++=
-
KNNFx 00 ==
0530 == XXQFy
280 XXMM ==
=0m =0, Q=0KN, M=0KNm =2m =0, Q=16KN, M=-16KNm
q 1=5KN /m
q 2=3KN/m
N (x)Q (x)M (x) x
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33
B
q1=5KN/m
q2=3KN/m
x
VB
N(x)Q(x)M(x)
A B
q1=5KN/m
q2=3KN/mq2=3KN/m
HA
VA VB
N(x)Q(x)M(x)
x
I-I
=0m =0, Q=-20KN, M=-16KNm =8m =0, Q=20KN, M=-16KNm
II-II
KNNFx 00 ==
02885836360 =++= XQFy
02
52
3)4(40)9(10)9(6)8(36360 =+++++++++= XXXXXXXXXMM
=0m =0, Q=-16KN, M=-16KNm =2m =0, Q=0KN, M=0KNm
KNNFx 00 ==
0)1(6)1(102
5360 =+++++= XXXXXMM
023525360 =+= XQFy
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34
M, N, Q
(M)
(Q)
(N)
A B+
-16KNm -16KNm
--
- -0 0
A B
0 0+ +--
20KN
-16KN
16KN
-20KN
A B0 0 0
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35
A
A
VA
HAMA
A
VA
HAMAM(x)N(x)
Q(x)
8
...
KNHFx A 00 ==
KNVFy A 00 ==
MMMMM AA === 00
TOMH I-I
-
36P
A
M, N, Q
(M)
(Q)
(N)
9
A
M ..KNm
+
A 0
A0
-
37
P
A
VA
HAMA
A
VA
HAMAM(x)N(x)
Q(x)
...
KNHFx A 00 ==
PVPVFy AA ==+= 00
LPMLPMM AA === 00
-
M, N, Q
-
38
A
M ..KNm
+
A +P ..KN
A 0
q
A
()
(Q)
()
10
-
39
A P
VA
HAMA
A
VA
HAMAM(x)N(x)
Q(x)
...
KNHFx A 00 ==
AA VLqLqVFy ==+= 00
20
20
2LqMLLqMM AA ===
-
M, N, Q
-
40
A
M ..KNm
+
A+
P ..KN
A 0
P=15KN
q=6KN/m
A
()
(Q)
()
11
-
41
P=15KN
A
P=9KN
VA
HAMA
...
-
KNmMMM AAA 75.36021575.05.160 ==++=
KNVVFy AA 2405.16150 ===
KNHFx A 00 ==
-
42
=0m =0, Q=15KN, M=0KNm =0,5m =0, Q=15KN, M=-7,5KNm
-
=0m =0, Q=15KN, M=-7,5KNm =1,5m =0, Q=24KN, M=-36,75KNm
P=15KN
N(x)
Q(x)M(x)
x
0150 =+= XMM
KNQFy 150 ==
KNNFx 00 ==
P=15KN
x
N(x)
Q(x)M(x)
q=6KN/m
0)5.0(152
60 =+++= XXXMM
06150 == XQFy
KNNFx 00 ==
-
43
q2=3KN/m
P2=20KN
P1=15KN
M, N, Q
(M)
(Q)
(N)
A
-
-
-36.75KNm
-7.5KNm
A+ +
24KN15KN
A 0
-
44
P2=20KN
P1=15KN
A
B
C
P1=4.5KN
P2=4.5KN
M=3.375KNm
M=3.375KNm
VA
MA
HA
12
..
I-I
KNHHFx AA 150150 ===
KNVVFy AA 2905.45.4200 ===
KNmMMM 5.6705.4150 ===
-
45
A
BP1=4.5KN
M=3.375KNm
VA
MA
HA
N(x)Q(x)
M(x)
KNQQFx 150150 ===
KNNNFy 290290 ==+=
KNmMMM 5.6705.670 ==+=
II-II
=0m =-24.5, Q=15KN, M=48.375KNm =1.5m =-24.5, Q=15KN, M=25.875KNm
III-III
A
VA
MA
HA
N(x)Q(x)
M(x)
x
KNQQFx 150150 ===
KNNNFy 5.2405.4290 ==+=
0)5.1(15775.35.670 =++= XMM
-
46
=0m =-20, Q=15KN, M=22.5KNm =1.5m =-20, Q=15KN, M=0KNm
M, N, Q
(M)
x
A
B
C
P1=4.5KN
P2=4.5KN
M=3.375KNm
M=3.375KNm
VA
MA
HA
N(x)Q(x)
M(x)KNQQFx 150150 ===
KNNNFy 200295.45.40 ==+=
05.67375.3375.3)3(150 =+++= XMM
A
B
C-
-
-
-
-
-3.375KNm
0
-22.5KNm-25.875KNm
-48.375KNm
-67.5KNm
-3.375KNm
-67.5KNm
-
47
P2=5KN P2=5KNq=20KN/m
B C D
(Q)
(N)
13
A
B
C
+
+
+
15KN
15KN
15KN
15KN
-
-
-4.5KN
-4.5KN
A
B
C
-
-
-
-20KN
-20KN-24.5KN
-24.5KN-29KN
-29KN
-
48
P2=5KN P2=5KNP=1200KN
A
B C D
HA
VAMA
N(x)Q(x)
M(x)
...
KNHFx A 00 ==
KNVVFy AA 121001200550 ===
KNmMMHVM AAB 0060530602080300 ==+=
I-I
-
49
KNQFx 00 ==
KNNNFy 1210012100 ==+=
II-II III-III ( )
KNNFx 00 ==
0206050 =+= XQFy
02
206050 =+= XXXMM
=0m =0, Q=-605KN, M=0KNm =30m =0, Q=-5KN, M=9150KNm
M, N, Q
= 0 [ M =O KNm
A
C
HA
VAMA
q=20KN/m
N(x)Q(x)M(x)
x
-
50
A
B C D
- -
-9150KNm
A
B C D
- -
-605KN
-5KN -5KN
A
B C D
-1210KN
-1210KN
-
P=15KNq=30KN/m
AC
()
(Q)
()
14
-
51
P=15KN
A
B
C
P=3600KN
HA
VA
VB
...
KNHFx A 00 ==
KNVVVFy BBA 3630015120300 ==+=
KNVVM AAB 1506015600 ===
I-I
-
52
KNQFx 00 ==
KNNFy 36300 ==
KNmMM 00 ==
II-II
KNNFx 00 ==
030)15(0 =+= XQFy
02
30)15(0 =+= XXXMM
=0m =0, Q=-15KN, M=0KNm =60m =0, Q=-1815KN, M=54900KNm
III-III
B
HA
VB
N(x)Q(x)
M(x)
x
A
VA
q=30KN/m
M(x)N(x)
Q(x)
x
-
53
=0m =0, Q=1815KN, M=0KNm =60m =0, Q=15KN, M=-54900KNm
M, N, Q
(M)
KNNFx 00 ==
03018150 =+= XQFy
B
C
HA
VB
q=30KN/m
M(x)N(x)
Q(x)x
02
3018150 =+= XXXMM
A
B
C
-54900KNm
00
- -
-
54
(Q)
(N)
A
B
C
-15KN -15KN
-1815KN
- -
A
B
C
-3630KN
-
-3630KN
-
55
q=10KN/m q=5KN/m P1=15KN P2=10KN P3=20KN
B C D E
BC
CB
P=15KN
VB
HB
VC
HC
CE
P1=15KN P2=10KN
D E
P3=20KN
HC
VDVE
VC
P3X*COS45
P3*SIN45
HD
15
CBCB HHHHFx === 00
KNVVVFy BCB 5.70150 ==+=
KNVVM CCB 5.7035.1150 ==+=
-
56
014.140 == DC HHFx
KNVVVVFy DEDC 94.20014.1410150 ==++=
KNVVVM EECD 70.2505.914.1486102155.20 ==+=
TOMH I-I
=0m =-14,14, Q=14,14KN, M=0KNm =1.5m =-14,14, Q=14,14KN, M=-21,21KNm
I-I
KNNNFx 14.14014.140 ==+=
014.140 =+= XMM
E
P3=20KN
P3X*COS45N(x)
Q(x)M(x)
x
P3*SIN45
VE KNQQFy 56.11014.1470.250 ==+=
KNNNFx 14.14014.140 ==+=
070.25)5.1(14.140 =++= XXMM
P3=20KN
P3*COS45
P3*SIN45
N(x)
Q(x)M(x)
x
KNQQFy 14.14014.140 ===
-
57
=0m =-14,14, Q=-11,56KN, M=-21,21KNm =2m =-14,14, Q=-11,56KN, M=1,91KNm
I-I
KNNNFx 14.14014.140 ==+=
KNQQFy 56.1014.1470.25100 ==+= 010)2(70.25)5.3(14.140 =++++= XXXMM
=0m =-14,14, Q=-1,56KN, M=1,91KNm =4m =-14,14, Q=-1,56KN, M=8,15KNm
P2=10KN
E
P3=20KN
VE
P3X*COS45
P3*SIN45
N(x)
Q(x)M(x)x
-
58
P1=15KN P2=10KN
E
P3=20KN
VE
P3X*COS45
P3*SIN45
N(x)
Q(x)M(x)
x
P1=15KN P2=10KN
D E
P3=20KN
VDVE
P3X*COS45
P3*SIN45
HD
N(x)
Q(x)M(x)
x
V-IV
KNNNFx 14.14014.140 ==+=
KNQQFy 44.13014.1470.2510150 ==+=
015)4(10)6(70.25)5.7(14.140 =++++++= XXXXMM
=0m =-14,14, Q=13,44KN, M=8,15KNm =2m =-14,14, Q=13,44KN, M=-18,73KNm
V-V
KNNNFx 14.14014.140 ==+=
KNQQFy 5.7014.1470.25101594.200 ==++=
094.20)2(15)6(10)8(70.25)5..9(14.140 =+++++++= XXXXXMM
-
59
C
VC
HCN(x)
Q(x)M(x)
q=5KN/m
x
N(x)
Q(x)M(x)
VA
HA
MA
q=10KN/m
x
=0m =-14,14, Q=-7,5KN, M=-18,73KNm =2,5m =-14,14, Q=-7,5KN, M=0KNm
V-V
=0m =0, Q=-7,5KN, M=0KNm =3m =0, Q=-7,5KN, M=0KNm
V-V
=0m =0, Q=57,5KN, M=-162,5KNm =5m =0, Q=7,5KN, M=0KNm
KNNFx 00 ==
02
55.70 =+= XXXMM
055.70 =+= XQFy
05.57100 =+= XQFy
KNNFx 00 ==
02
105.575.1620 =++= XXXMM
-
60
P=10KNq=2KN/m q=4KN/m
A BC D
E FG
H
P=10KN
A BC D
E FG
H
P=35KNP=14KN
CD
P=10KN
VD
HD
VC
HC
16
...
DCDC HHHHFx === 00
KNVVVFy CDC 50100 ==+=
KNVVM DDC 5035.1100 ==+=
-
61
GH
GH
P=12KN
VHVG
HG
KNHFx G 00 ==
KNVVVFy GHG 60120 ==+=
KNVVM HHG 6035.1120 ==+=
GD HHFx == 0
KNVVVVVFy FGFED 8.2105.740 ==++=
KNVVVVM EGEDE 2.1965.51455.25475.05.145.10 ++=
DG
VE VF
HG
VD
HD
VG
D E F G
q=4KN/m
-
62
CA HHFx == 0
KNVVVFy ABA 3.805140 ==++=
KNVVVM BDB 7.1005.655.2521220 ==+=
-
KNNFx 00 ==
0460 =+= XQFy
062
40 =+= XXXMM
=0m =0, Q=-6KN, M=0KNm =3m =0, Q=6KN, M=0KNm
-D
q=2KN/m
A
VE VB
HDHG
VG
B C
q=4KN/m
HN(x)Q(x)M(x)
x
VH
-
63
F HG
VG
N(x)Q(x)M(x)
x
VF
q=4KN/m
I-I
KNNFx 00 ==
0460 == XQFy
062
40 =++= XXXMM
=0m =0, Q=6KN, M=0KNm =1m =0, Q=10KN, M=-8KNm
II-II
KNNFx 00 ==
06)1(48.210 =++= XQFy
0)1(68.21)5.0(42
40 =+++++= XXXXXMM
=0m =0, Q=0KN, M=-8KNm =5m =0, Q=0KN, M=1KNm
G
x
HG
VGq=4KN/m
N(x)Q(x)M(x)
-
64
D E F G
x
N(x)Q(x)M(x)
VFVE
HG
VGq=4KN/m
IV-IV
KNNFx 00 ==
0420468.212.190 =++= XQFy
0)6(6)5.5(4)5(8.21)5.2(542.192
40 =++++++++= XXXXXXXMM
=0m =0, Q=-11KN, M=-8KNm =1.5m =0, Q=-5KN, M=1KNm
V-V
KNNFx 00 ==
KNQQFy 5050 ==+=
050 == XMM
=0m =0, Q=-5KN, M=0KNm =1.5m =0, Q=-5KN, M=7.5KNm
VDHDD
N(x)Q(x)M(x)
x
-
65
VI-VI
KNNFx 00 ==
KNQQFy 501050 ==+=
0)5.1(5100 =++= XXMM
=0m =0, Q=5KN, M=7.5KNm =1.5m =0, Q=5KN, M=-7.5KNm
VII-VII
KNNFx 00 ==
KNQFy 50 ==
050 =+= XMM
=0m =0, Q=5KN, M=0KNm =1.5m =0, Q=5KN, M=-7.5KNm
VDHDD
N(x)Q(x)M(x)
x
P=10KN
VC
HCCN(x)
Q(x)M(x)
x
-
66
VIII-VIII
KNNFx 00 ==
027.1050 =+= XQFy
0)5.1(57.102
20 =+++= XXXXMM
=0m =0, Q=-5.7KN, M=-7.5KNm =5m =0, Q=4.3KN, M=-4KNm
IX-IX
KNNFx 00 ==
025257.103.80 =++= XQFy
0)5.6(5)5(7.10)5.2(5.23.82
20 =++++++= XXXXXXMM
=0m =0, Q=-4KN, M=-4KNm =2m =0, Q=0KN, M=0KNm
q=2KN/m
B C
x
VB
VC
HCN(x)
Q(x)M(x)
q=3KN/m
A B C
VC
HCN(x)
Q(x)M(x)
x
VA VB
-
67
A BC D
E FG
H
--
--
----
+ ++ + +
-8KNm
0-1KNm
7.5KNm
-7.5KNm-4KNm
0 00
A B C D E F G H+ + +
+ + +
-
-
-
-
--
-6KN
6KN10KN8.2KN
5KN
-5.7KN -5KN -5KN
-11KN
-4KN
4.3KN
11.8KN
5KN5KN
A BC D
E FG
H
0 0 0 0 0 00
q=5KN/m
C DBA
M, N, Q
17
-
68
C DBA
P=35KN
CE
C D
q=5KN/m
VC VD
VB
HBHC
..
1
A
q=5KN/m
VB
HB
VA
KNHFx B 00 ==
KNVVVFy ABA 100250 ==+=
KNVVM BBA 005.01515.0150 ==+=
-
69
q=5KN/m
D
N(x)Q(x)M(x)
x
VD
KNHFx B 00 ==
KNVVVFy CDC 84.20035250 ==+=
KNVVM DDC 16.4035.1351250 ==+=
I-I
=0m =0, Q=-4.16KN, M=0KNm =3m =0, Q=10.84KN, M=-10.02KNm
II-II
KNNFx 00 ==
KNNFx 00 ==
0516.40 =+= XQFy
02
516.40 =+= XXXMM
q=5KN/m
C D
x
N(x)Q(x)M(x)
VDVC
-
70
053516.484.200 =++= XQFy
02
584.20)5.1(15)3(16.40 =++++= XXXXXMM
=0m =0, Q=-10KN, M=-10.02KNm =2m =0, Q=0KN, M=0KNm
III-III
KNNFx 00 ==
050 == XQFy
02
50 =+= XXMM
=0m =0, Q=0KN, M=0KNm =1m =0, Q=5KN, M=-2.5KNm
IV-IV
VB
HB
q=5KN/m
N(x)Q(x)M(x)
x
-
71
=0m =0, Q=-5KN, M=-2.5KNm =1m =0, Q=0KN, M=0KNm
M, N, Q
()
A
VA
q=5KN/m
N(x)Q(x)M(x)
VB
HB
x
KNNFx 00 ==
0)5.0(52
5100 =+++= XXXXMM
0105150 =+= XQFy
C DBA
-2.5KNm
-10.02KNm
00 - -- -
+
-
72
q=20KN/m
C
P2=15KN
P3=20KN
P1=10KN
BA
(Q)
(N)
18
C DBA
10KN
-4.16KN-10KN
5KN
-5KN-
--
+ +
C DBA
0 0 0
-
73
C
P2=15KN
P3=20KN
P1=10KN
BA
P=100KN
...
KNHHFx BB 200200 ===
KNVVVFy CCB 35015100 ==+=
KNVVM BBC 10041521040 ==+=
2
C
P2=15KN
P3=20KN
P1=10KN
VC
HB
VB
-
74
1
A
q=20KN/m
VA
H AM A
VB
HB
KNHHHFx ABA 2000 ===
KNVVVFy ABA 9005200 ==+=
KNmMMM 20005105.25200 ==+=
I-I
KNNFx 200 ==
KNQFy 150 ==
0150 =+= XMM
=0m =-20, Q=15KN, M=0KNm =4m =-20, Q=15KN, M=-60KNm
P2=15KN
P3=20KNN(x)
Q(x)M(x)
x
-
75
C
P2=15KN
P3=20KN
P1=10KN
x
N(x)Q(x)M(x)
VC
II-II
KNNFx 200 ==
KNQQFy 20015350 ==+=
0)4(15350 =++= XXMM
=0m =-20, Q=20KN, M=-60KNm =2m =-20, Q=20KN, M=-20KNm
III-III
KNNFx 200 ==
KNQQFy 1001535100 ==+=
0)6(15)2(35100 =++++= XXXMM
=0m =-20, Q=-10KN, M=-20KNm =2m =-20, Q=-10KN, M=0KNm
C
P2=15KN
P3=20KN
x
VC
N(x)Q(x)M(x)
-
76
IV-IV
KNNFx 200 ==
020100 =+= XQFy
0102
200 =+= XXXMM
=0m =-20, Q=-10KN, M=0KNm =5m =-20, Q=90KN, M=200KNm
M, N, Q
(M)
(Q)
q=20KN/m
VB
HB
x
N(x)Q(x)M(x)
CBA
-
-
+
-
0
-60KNm
-20KNm
-200KNm
CBA-
--
+ +
-20KN-20KN-10KN
-10KN
90KN
15KN 15KN
-
77
(N)
CBA-
- - -
-20KN-20KN-20KN-20KN-20KN
-
78
4.
,
.
, .
.
, 3 .
[],[Q],[], (x), Q(x), M(x), . x, .
,
.
.
(x) , Q(x). (x): , .
Q(x): ,
.
(x): , .
.
l-x Q(x), M(x) -. ,
.
.
( , Q, M ), , .
-
79
,
, 3 , ,
. 3 .
-
,
.
.
, 3 4 .
G ,
:
3 4 .
.
[] , .
[, [] [Q] .
Beam Engilab.
AutoCad 2007 AutoDesk
00 == G
G
-
80
P1=15KN
P2=5KN
B
E
DC
P1=15KN
M=20KNm
M=30KNm
HA
VA VB
P=90KN
1
P1=15KN
P2=5KN
q=10KN/m q=15KN/m
B
E
DC
...
==
50F
KNVVVF ABAy 58.6401590100 ==+=
KNVVM BBA 42.6002036156155.153060 ==++=
-
81
B
VB
N(x)Q(x)
M(x)
x
P1=15KN
P2=5KN
B
E
M=30KNm
VB
x
N(x)Q(x)
M(x)
I-I
I-I
=0m =-45,42, Q=5KN, M=-30KNm =1,5m =-45,42, Q=5KN, M=-37,5KNm
I-I
KNQFx 00 ==
KNNFy 42.600 ==
KNmMM 00 ==
KNQFx 50 ==
KNNNFy 42.4501542.600 ==+=
015300 =+= XMM
-
82
P1=15KN
P2=5KN
B
E
DC
P1=15KN
M=20KNm
M=30KNm
VB
M(x)
Q(x)N(x)
x
KNNFx 50 ==
=0m =-5, Q=-45,42KN, M=-37,5KNm =6m =-5, Q=44,58KN, M=-34,98KNm
I-I
=0m =-64,58, Q=-5KN, M=-15KNm =6m =-64,58, Q=-5KN, M=0KNm
P1=15KN
P2=5KN
B
E
D
M=30KNm
q=15KN/m
N(x)Q(x)M(x)
x
VB
0151542.600 =+= XQFy0
215151553042.600 =++++= XXXXMM
KNQFx 50 ==
KNNXNFy 58.64042.601515200 ==+++=
05642.60306153615200 =+++= XMM
-
83
M, N, Q
()
(Q)
(N)
B
E
DC-37.5KNm
-30KNm
-30KNm
-37.5KNm-34.98KNm
-20KNm
-15KNm +
-
-
-
-
-
-
B
E
DC
44.58KN
-20KN
-5KN
15KN5KN
-45.42KN
-
+
++
-
-
15KN
B
E
DC
-45.42KN-60.42KN
-64.58KN
-5KN-5KN
-5KN
-5KN
-60.42KN
-64.58KN
-
-
-
-
-
-
84
B
C
P=200KN
2
...
KNHFx A 00 ==
KNVVVFy ABA 100010200 ==+=
KNVVM BB 100051020100 ===
-
85
-( )
KNQA 1001100cos100 === KNN A 1001100sin100 ===
KNmMMM CCC 25002552051000 ===
M, N, Q
(M)
q=20K N /m
N (x)
Q (x)M (x)
x
B
C
250KNm
+
250KNm
+
-
86
P1=15KN
P1=15KN
C B
(Q)
(N)
3
B
C
100KN+100KN +
B
C
-100KN
-
-
-100KN
-
87
P1=15KN
P1=15KN
C B
HA
VA
VB
...
KNHHFx AA 100100 ==+=
KNVVVFy AAB 56.00100 ==+=
KNVVM BBA 44.905.31051090 ===
-
KNNFx 00 ==
KNQFy 44.90 ==
XMM == 44.90
=0m =0, Q=-9,44KN, M=0KNm =4m =0, Q=-9,44KN, M=37,76KNm
B
VB
x
N(x)Q(x)M(x)
-
88
I-I
=0m =0, Q=0,56KN, M=37,76KNm =5m =0, Q=0,56KN, M=34,96KNm
I-I
KNQFx 00 ==
P1=15KN
B
VB
x
N(x)
Q(x)M(x)
KNNFx 00 ==
KNQQFy 56.001044.90 ==+=
010)4(44.90 =++= XXMM
P1=15KN
C B
VB
x
N(x)
Q(x)
M(x)
KNNNFy 56.0044.9100 ==+=
KNmMMM 96.340944.95100 ==+=
-
89
V-IV
=0m =-0.56, Q=0,56KN, M=34.96KNm =3.5m =-0.56, Q=0,56KN, M=0KNm
M, N, Q
(M)
P1=15KN
P1=15KN
C B
VB
N(x)
Q(x)
M(x)
x
KNQFx 100 ==
0944.9510100 =++= XMM
KNNNFy 56.0044.9100 ==+=
C B
34.96KNm
34.96KNm
0
37.76KNm
0
+
+
-
90
(Q)
(N)
C B
-9.44KN-9.44KN
0.56KN
10KN
10KN
+
+
-
0.56KN0
C B-0.56KN
-0.56KN
-
0
-
91
P=10KNq=10KN/m
A B
DC
P=10KN
A B
DC
P=40KN
HA
VA VB
4
...
KNHHFx AA 4004100 ==+=
KNVVVFy ABA 42.60100 ==+=
KNVVM BBA 42.16024105.31070 ===
-
92
-
KNQFx 00 ==
KNNFy 42.160 ==
KNmMM 00 ==
-
KNNFx 00 ==
KNQFy 42.160 ==
042.160 == XMM
=0m =0, Q=-16.42KN, M=0KNm =3.5m =0, Q=-16.42KN, M=57.5KNm
B
VB
N(x)Q(x)
M(x)
x
B
D
VB
N(x)
Q(x)M(x)
x
-
93
I-I
=0 =0, Q=-6.42KN, M=57.5KNm =3.5 =0, Q=-6.42KN, M=79.94KNm
V-V
P=10KN
B
D
VB
x
N(x)
Q(x)M(x)
0)5.3(42.16100 =++= XXMM
KNQQFy 42.601042.160 ==+=
KNNFx 00 ==
P=10KN
B
DC
VB
x
N(x)Q(x)
M(x)
q=10KN/m
-
94
0100 == XQFx
KNNNFy 42.6042.16100 ==+=
0742.165.3102
100 =++= XXMM
=0m =6.42, Q=0KN, M=79.94KNm =4m =6.42, Q=40KN, M=0KNm
M, N, Q
(M)
(Q)
A B
DC+
79.94KNm
79.94KNm 57.5KNm
0
00
+
+
A
B
D
C
40KN
0-6.42KN
-16.42KN
-6.42KN
-16.42KN-
0
-
+
-
95
C DG
P = 1 0 K N
q = 5 0 K N /m
(N)
5
AB
DC6.42KN
6.42KN
-16.42KN
-16.42KN
-
+
-
96
C DG
P = 1 0 K N
P = 3 0 0 K N
H A
V A
H B
V B
DG
V B
H B
q = 5 0 K N /mH G
H G
...
1) :
BGX HHF == 0
( ) KNVmm
KNVVF GBGy 145.4202500 ==
+=
1003201250230 ==+= BBBBG HVVH (1)
94565.105.410365065,1 =+=+= BBB VHV
(2)
(1) (2) : KNV B 145.142= = 43.61BH
-
97
-
KNNFY 145.1420 ==
KNQFX 43.610 ==
== 43,610
=m =-142,145, Q=61,43, =0 m =3m =-142,145, Q=61,43, =-184,29 m
I-I
=0m =-61,43, Q=-142.145KN, M=-184.29KNm =2m =-61,43, Q=-42.145KN, M=0KNm
D
VB
HB
M(x)
N(x)Q(x)
x
DG
VB
HB
q=50KN/m
N(x)Q(x)M(x)
x
050145.1420 =+= XQFY
KNNFX 43.610 ==
0343,61145,1422
500 =++=
-
98
C
P=10KN
q=50KN/m
VG
HG
M
QN
x
I-II
KNNFX 00 ==
0145.42500 =+= XQFY
0145.422
500 =+= XXXMM
=0m =0, Q=-42.145KN, M=0KNm =4m =0, Q=157,86KN, M=231,42KNm
V-IV
=0m =-157,85, Q=10KN, M=-231,42KNm =4m =-157,85, Q=10KN, M=0KNm
q=50KN/m
VG
HGN
QM
x
KNQQFX 100100 ===
KNNNFY 85.1570145.424500 ==+=
04145.422450100 =++= X
-
99
M, N, Q
()
(Q)
C DG
-184.29KNm
-184.29KNm
-231.42KNm
-231.42KNm
-
--
+
-
C DG
61.43KN
+
+
-
-
-142.145KN
-42.145KN
-10.0KN
157.86KN
-
100
B
EC
D
q=10KN/m
q=20KN/m
B
EC
D
P=240KN
P=40KN
VA
HA
VB
(N)
6
...
C DG
-
-
-
-142.145KN
-61.43KN
-157.85KN
-
101
VA
HA
N(x)Q(x)
M(x)
x
q=10KN/m
C
HA
q=10KN/m
N(x)
Q(x)
M(x)
q=20KN/m
x
VA
KNHHF AAx 1004100 ==+= KNVVVF ABAy 34.113012200 ==+=
KNVVM BBA 66.12601262402400 ==+=
-
010400 =+= XQFx
KNNFy 34.1130 ==
02
10400 =+= XXXMM
=0m =-113,34, Q=40KN, M=0KNm =4m =-113,34, Q=0KN, M=80KNm
-
-
102
C
D
VA
HA
q=10KN/m
q=20KN/m
N(x) Q(x)M(x)
x
Tan=2/6=0,333 R=113.34-20*X
=18,43 R1=35.81-6.32*X => R1=N
sin=0.316 R2=107.45-18.96*X => R2=Q
cos=0,948
=0m =-35,81, Q=107,45KN =6m =2,11, Q=-6,31KN
02
2034.1130 =+= XXXMM
=0m M= 0KNm =6m M= 320KNm
-
R=113.34-120-20*X = -6,66-20* R1=-2,10-6.32*X => R1=N
R2=-6,31-18.96*X => R2=Q
-
103
=0m =-2,10, Q=-6,31KN =6m =-40,02, Q=-120,07KN
02
2012034.1130 =++= MM
=0m M= 320,04 KNm =6m M= 0 KNm
V-V
KNQFx 00 ==
KNNNFy 66.126034.1132400 ==+=
04040136014400 =++=
=0m =-126.66, Q=0KN, M=0KNm =4m =-126.66, Q=0KN, M=0KNm
EC
D
VA
HA
q=10KN/m
q=20KN/m
M(x)
Q(x)N(x)
x
-
104
B
EC
D
+
++
80KNm
320.04KNm320.04KNm
80KNm 80KNm
0
0
M, N, Q
()
(Q)
(N)
B
EC
D
40KN
0
107.45KN
-6.31KN-120.07KN
-
+
+
-
0
0
B
EC
D
-113.34KN
-
-113.34KN
-35.81KN 2.10KN-
+
-2.10KN
-40.02KN-
-126.66KN
-126.66KN
-
-
105
5.
1. . 2003
2. 2002
3. 1997
4. . 1980
5. .
6. . () , 1983