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3U]\NáDG8NáDGEHONRZRNUDWRZ\
:\]QDF]\üUHDNFMH
80 kN
30 kN/m
3.0 m
5,0 m
4,0 m
4.0 m
5,0 m
5R]ZL ]DQLH
8ZDOQLDP\XNáDG]ZL ]yZZSURZDG]DM FLFKZáDFLZHUHDNFMHLRWU]\PXMHP\XNáDGVLá
przedstawiony na rysunku.
80 kN
M A
30 kN/m
H A
B
H B
M B
A
1
2
V B
V A
1LH]QDQ\FK MHVWVNáDGRZ\FKRSLVXMF\FKUHDNFMHSRGSyU:FHOX LFKZ\]QDF]HQLD
SRG]LHOP\ NRQVWUXNFMZ\MFLRZ QD F]FLZ WHQ VSRVyE DE\Z\G]LHOLü XNáDG
WUyMSU]HJXERZ\&]ü,Z\G]LHORQDSU]HJXEDPLLVWDQRZLWDNLXNáDG
80 kN
I
II
3
R 1
2
R 2
III
1
30 kN/m
M A
R 2
H A
B
H B
M B
R 1
A
V A
V B
=DXZD*P\*HGRNáDGQLHMPDP\WXGRF]\QLHQLD]XNáDGHPSUWyZSURVW\FKREFL*RQ\FK
W\ONRQDNRFDFKLSRáF]RQ\FKSU]HJXEHPF]\OL]NUDWRZQLFRMHGQ\PZ(OH0R*HP\
]DWHPXVWDOLüNLHUXQNLZ]DMHPQHJRRGG]LDá\ZDQLDZSU]HJXEDFKLLGRSROLF]HQLD
RGG]LDá\ZDZHZQWU]Q\FK5
1 i R 2 Z\NRU]\VWDüUyZQDQLDUyZQRZDJLZ]áD
y
I
80 kN
a
a
x
R 1
R 2
=SRGDQ\FKRGOHJáRFLZ\QLND*HGODR]QDF]RQHJRQDU\VXQNXNWD
a
:
= 4/5 ,
cos(90-
a
) = sin
a
=3/5.
cos
a
89765959.005.png 89765959.006.png 89765959.007.png
5yZQDQLDUyZQRZDJLZ]áD
å
P
I
ix
=
0
i
å
P
I
iy
=
0
SU]\MPXMSRVWDü
i
i
R 1 cos
a
+ 80 kN – R 2 cos
a
= 0 i R 1 cos(90-
a
) + R 2 cos(90-
a
) = 0,
1 = - 50 kN, R 2 = 50 kN.
:GDOV]HMF]FLUR]ZL]DQLDXZ]JOGQLRQ\EG]LHU]HF]\ZLVW\]ZURWUHDNFML5
LVWG5
1 .
:\NRU]\VWDP\REOLF]RQHZLHONRFL5
1 i R 2 GRZ\]QDF]HQLDUHDNFMLSRGSRURZ\FKUR]ZD*DMF
UyZQRZDJF]FL,,L,,,
II
y
y
III
M A
30 kN/m
50 kN
50 kN
M B
H B
H A
a
a
x
x
V B
V A
=DSLVXMFNROHMQRUyZQDQLD
0
P
II
ix
=
Þ
H A + 4/5(50 kN) = 0
i
å
P
II
iy
=
0
Þ
V A + 3/5(50 kN) – 30 kN/m ÂP
i
å
M
II
iA
=
0
Þ
M A +3/5(50kN) ÂP±N1PÂPÂP
i
RWU]\PDP\ZDUWRFL
H A = - 40 kN , V A = 120 kN , M A = 225 kNm.
$QDORJLF]QLHGODF]FL,,,PDP\UyZQDQLD
0
P
III
ix
=
Þ
-H B + 4/5(50 kN) = 0
i
å
P
III
iy
=
0
Þ
V B – 3/5(50 kN) = 0
i
å
M
III
iB
=
0
Þ
-M B +3/5(50kN) ÂP
i
]NWyU\FKRWU]\PXMHP\ZDUWRFL
H B = 40 kN , V B = 30 kN , M B = 150 kNm.
2VWDWHF]QLHUR]ZL]DQLHPDSRVWDü
80 kN
30 kN/m
40 kN
40 kN
3.0 m
1
2
120 kN
30 kN
225 kNm
150 kNm
5,0 m
4,0 m
4.0 m
5,0 m
2
å
å
89765959.008.png 89765959.001.png 89765959.002.png 89765959.003.png 89765959.004.png

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