MOMENTY I SIŁY BRZEGOWE
PRĘT LEWOSTRONNIE UTWIERDZONY
PRAWOSTRONNIE PODPARTY PRZEGUBOWO
M
EI =const
ij
M ij
V
M = 0
ji
V
ji
ij
Vij
L
Vji
M = − FLξ
ij
(1− ξ )(1− ξ / 2)
ξL
F
2
V = − Fξ
ji
(3 −ξ )/ 2
V = F
ij
(1−ξ )(1
2
+ ξ − ξ / 2)
M = −3 FL /16
ij
F
L/2
L/2
V = −5 F /16
ji
V = 11 F /16
ij
M = −3 FL
ij
(1 2
− ξ )/ 8
F
F
ξL
ξL
V = − F
ji
(5+ 3 2ξ)/8
V = F
ij
(11−3 2ξ)/8
M = − FL
−
ij
( n 1/ n)/8
F
F
F
L/n
L/n
L/n
L/n
V = − F
ji
(3 n +1/ n − 4)/8
V = F
ij
(5 n −1/ n − 4)/8
M = − FL
+
ij
( n 0.5/ n)/8
L F
F
F
F L
L/n
L/n
L/n
2n
2n
V = − F
−
ji
(3 n 0.5 / n)/8
V = F
+
ij
(5 n 0.5/ n)/8
M = FLξ
ij
(1 2
− ξ )/ 8
F
ξL
V = − Fξ
ji
(9 2
− ξ )
F
ξL
/ 8
V = − Fξ
ij
(9 2
− ξ )/ 8
M = M
ij
(−1+ 3ξ −3 2ξ /2)
ξL
M
V = −3 M ⋅ ξ − ξ
ji
(1
/ 2)/ L
V = −3 M ⋅ ξ − ξ
ij
(1
/ 2)/ L
M = M / 8
ij
M
L/2
L/2
V ji = −(9 / 8) M / L
Vij = −(9 / 8) M / L
M = M / 2
ij
M
V = −1.5 M L
V = −1.5 M L
ji
/
ij
/
M = −
+
ij
(8 q 7
1
q 2 ) 2
L /120
q1
q2
V = −
+
ji
(4 q 11
1
q 2 ) L / 40
V =
+
ij
(16 q 9
1
q 2 ) L / 40
2
M = − qL / 8
ij
q
V = −3 qL / 8
ji
V = 5 qL / 8
ij
2
M = − qL /15
q
ij
V = − qL /10
V = 2 qL / 5
ji
ij
M = −7
2
qL /120
ij
q
V = −11 qL / 40
V = 9 qL / 40
ji
ij
http://www.iil.pwr.wroc.pl/zukowski 1
M
EI =const
ij
M ij
M = 0
V
Vij
ji
V
ji
ij
L
Vji
2 2
M = − qL ξ
ij
(2 −ξ )2 /8
ξL
q
3
V = − qLξ
ji
(1−ξ / 2)/ 2
V = qLξ
ij
[1 2
− ξ (1−ξ / 4)/ 2]
M = 9 2
− qL /128
ij
L/2
= −
q
V
7 qL /128
ji
V = 57 qL /128
ij
2 2
M = − qL ξ
ij
(2 2
−ξ )/8
ξL
q
V = − qLξ
ji
[1−ξ(6 2
− ξ )/8]
2
V = qLξ
ij
(6 2
− ξ )/8
M = 7 2
− qL /128
ij
L/2
q
V = −41 qL /128
ji
V = 23 qL /128
ij
2
M = − qL ξ
ij
(3 2
− ξ )/16
γL
ξL
γL
q
V = − qLξ
ji
(5 2
+ ξ )/16
V = qLξ
ij
(11 2
− ξ )/16
2 2
M = − qL ξ
ij
[20−3ξ(5−ξ)]/120
q
ξL
3
V = − qLξ
ji
(5 −ξ)/ 40
V = qLξ
ij
[1/2 2
− ξ (5 −ξ )/ 40]
M = 53 2
− qL /1720
ij
q
L/2
V = −9 qL / 640
V = 151 qL / 640
ji
ij
2 2
M = − qLξ
ij
[40−3ξ(15−4ξ)]/120
q
ξL
3
V = − qLξ
ji
(15 − 4ξ )/ 40
V =
ξ
qL
ij
[1/2 2
−ξ (15− 4ξ )/ ]
40
M = 41 2
− qL / 960
ij
L/2
q
V = −13 qL / 320
ji
V = 67 qL / 320
ij
2 2
M = − qL ξ
ij
(10−3 2ξ)/120
ξL
q
V = − ξ
qL
ji
[1/2−ξ(10 2
−ξ )/ ]
40
2
V = − qLξ
ij
(10 2
−ξ )/ 40
M = 17 2
− qL / 960
ij
L/2
q
V = −121 qL / 640
ji
V = 39 qL / 640
ij
2 2
M = − qL ξ
ij
(5−3 2ξ)/30
ξL
q
V = − qLξ
ji
[1/2−ξ(5 2
−ξ )/10]
2
V = − qLξ
ij
(5 2
− ξ )/10
M = 17 2
− qL / 480
ij
q
L/2
V = −21 qL /160
ji
V = 19 qL /160
ij
2
http://www.iil.pwr.wroc.pl/zukowski
M
EI =const
ij
M ij
M = 0
V
Vij
ji
ji
Vij
L
Vji
M = 5 2
− qL / 64
ij
L/2
q
V = −11 qL / 64
ji
V = 21 qL / 64
ij
M = 3 2
− qL / 64
ij
q
L/2
q
V = −13 qL / 64
ji
V = 19 qL / 64
ij
2 2
M = − qL ξ
ij
(4 − 3ξ )/8
ξL
ξL
q
q
V = − qLξ
ji
[4 −ξ(4 − 3ξ )]/8
V = − qLξ
ij
[4 +ξ(4 − 3ξ )]/8
2 2
M = − qL ξ
ij
(2 −ξ )/8
q
ξL
ξL
q
V = − qLξ
ji
[1/ 2 −ξ(2 −ξ )/ ]8
V = qL
ij
[1/ 2 +ξ(2 −ξ )/ ]8
2
M = − qL
ij
[1 2
−ξ (2 −ξ )]/8
q
ξL
ξL
V = − qL
ji
[8−4 2
ξ + ξ (2 −ξ )]/8
V = qL
ij
[5−4 2
ξ −ξ (4 −ξ )]/8
ϕ
M = 3 EIϕ / L
i
ij
i
2
V = 3
− EIϕ / L
ji
i
2
V = 3
− EIϕ / L
ϕ
ij
i
i
M = −3 EIψ L
ij
/
ψ =∆/L
2
∆
V = 3 EIψ / L
ji
2
V = 3 EIψ / L
ij
M = −1.5 EIα ∆ − ∆
ij
T ( t
t
d
g )/ h
∆t
h
g
V = 1.5 EIα ∆ − ∆
ji
T ( t
t
d
g )/( Lh)
V = 1.5 EIα ∆ − ∆
ij
T ( t
t
d
g )/( Lh)
∆td
M = − EIα ∆ − ∆
ij
T ( t
t
d
g )/ h
∆t
h
g
V = EIα ∆ − ∆
ji
T ( t
t
d
g )/( Lh)
V = EIα ∆ − ∆
ij
T ( t
t
d
g )/( Lh)
∆td
M = −0.5 EIα ∆ − ∆
ij
T ( t
t
d
g )/ h
h ∆tg
V = 0.5 EIα ∆ − ∆
ji
T ( t
t
d
g )/( Lh)
∆t
V = 0.5 EIα ∆ − ∆
ij
T ( t
t
d
g )/( Lh)
d
= − EI
M
3
⋅
ξL
ij
(1−ξ)⋅ ϕ
∆
L
= EI
V
3
⋅
ji
(1−ξ)⋅ ϕ
∆
2
= EI
∆ϕ
L
V
3
⋅
ij
(1−ξ)⋅ ϕ
∆
2
L
EI
M = 3
⋅ h
∆
ξL
ij
L 2
EI
∆h
V = −3
⋅ h
∆
EI
ji
L 3
V = −3
⋅ h
∆
ij
L 3
http://www.iil.pwr.wroc.pl/zukowski 3