3U]\NáDG8NáDGEHONRZRNUDWRZ\
:\]QDF]\üUHDNFMH
30 kN/m
80 kN
5,0 m
4,0 m
4.0 m
5,0 m
3.0 m
5R]ZL]DQLH
8ZDOQLDP\ XNáDG ] ZL]yZ ZSURZDG]DMF LFK ZáDFLZH UHDNFMH L RWU]\PXMHP\ XNáDG VLá
przedstawiony na rysunku.
30 kN/m
80 kN
H
A
V
A
H
B
V
B
M
B
M
A
A
B
1
2
1LH]QDQ\FK MHVW VNáDGRZ\FK RSLVXMF\FK UHDNFMH SRGSyU : FHOX LFK Z\]QDF]HQLD
SRG]LHOP\ NRQVWUXNFM Z\MFLRZ QD F]FL Z WHQ VSRVyE DE\ Z\G]LHOLü XNáDG
WUyMSU]HJXERZ\&]ü,Z\G]LHORQDSU]HJXEDPLLVWDQRZLWDNLXNáDG
30 kN/m
80 kN
H
A
V
A
H
B
V
B
M
B
M
A
A
B
1
2
R
1
R
1
R
2
R
2
3
I
II
III
=DXZD*P\ *H GRNáDGQLHM PDP\ WX GR F]\QLHQLD ] XNáDGHP SUWyZ SURVW\FK REFL*RQ\FK
W\ONR QD NRFDFK L SRáF]RQ\FK SU]HJXEHP F]\OL ] NUDWRZQLF R MHGQ\P Z(OH 0R*HP\
]DWHP XVWDOLü NLHUXQNL Z]DMHPQHJR RGG]LDá\ZDQLD Z SU]HJXEDFK L L GR SROLF]HQLD
RGG]LDá\ZDZHZQWU]Q\FK5
1
i R
2
Z\NRU]\VWDüUyZQDQLDUyZQRZDJLZ]áD
80 kN
y
R
1
R
2
x
α
α
I
=SRGDQ\FKRGOHJáRFLZ\QLND*HGODR]QDF]RQHJRQDU\VXQNXNWD
α
:
cos
α
= 4/5 ,
cos(90-
α
) = sin
α
=3/5.
2
5yZQDQLDUyZQRZDJLZ]áD
0
P
i
I
ix
=
∑
i
0
P
i
I
iy
=
∑
SU]\MPXMSRVWDü
R
1
cos
α
+ 80 kN – R
2
cos
α
= 0 i R
1
cos(90-
α
) + R
2
cos(90-
α
) = 0,
LVWG5
1
= - 50 kN, R
2
= 50 kN.
:GDOV]HMF]FLUR]ZL]DQLDXZ]JOGQLRQ\EG]LHU]HF]\ZLVW\]ZURWUHDNFML5
1
.
:\NRU]\VWDP\REOLF]RQHZLHONRFL5
1
i R
2
GRZ\]QDF]HQLDUHDNFMLSRGSRURZ\FKUR]ZD*DMF
UyZQRZDJF]FL,,L,,,
30 kN/m
H
A
V
A
M
A
II
50 kN
x
y
α
H
B
V
B
M
B
x
α
50 kN
y
III
=DSLVXMFNROHMQRUyZQDQLD
0
P
i
II
ix
=
∑
⇒
H
A
+ 4/5(50 kN) = 0
0
P
i
II
iy
=
∑
⇒
V
A
+ 3/5(50 kN) – 30 kN/m
ÂP
0
M
i
II
iA
=
∑
⇒
M
A
+3/5(50kN)
ÂP±N1PÂPÂP
RWU]\PDP\ZDUWRFL
H
A
= - 40 kN, V
A
= 120 kN, M
A
= 225 kNm.
$QDORJLF]QLHGODF]FL,,,PDP\UyZQDQLD
0
P
i
III
ix
=
∑
⇒
-H
B
+ 4/5(50 kN) = 0
0
P
i
III
iy
=
∑
⇒
V
B
– 3/5(50 kN) = 0
0
M
i
III
iB
=
∑
⇒
-M
B
+3/5(50kN)
ÂP
]NWyU\FKRWU]\PXMHP\ZDUWRFL
H
B
= 40 kN, V
B
= 30 kN, M
B
= 150 kNm.
2VWDWHF]QLHUR]ZL]DQLHPDSRVWDü
5,0 m
4,0 m
5,0 m
30 kN/m
80 kN
40 kN
120 kN
40 kN
30 kN
150 kNm
225 kNm
1
2
4.0 m
3.0 m