MOMENTY I SIŁY BRZEGOWE
PRĘT OBUSTRONNIE UTWIERDZONY
EI =const
M
M
M
ij
ji
ij
M
V
V
L
ji
ij
V ji
ij
Vji
M = − FLξ
ξL
F
M =
ξ 2
FL
ji
(1−ξ)
ij
( − )2
1 ξ
V = F
V = − ξ 2
F
ji
(3− ξ
2 )
ij
(1 + 2ξ )( − ξ )2
1
M = − FL / 8
F
ij
M =
/
FL 8
L/2
L/2
ji
V = F / 2
V = F
− /2
ij
ji
M = − FLξ
M = FLξ
ji
(1−ξ )
ij
(1−ξ )
F
F
ξL
ξL
V = F
V = − F
ij
ji
M = − FL −
M = FL −
ji
( n 1/ n) ij
( n 1/ n)/12
F
F
F
/12
L/n
L/n
L/n
L/n
V = F
V = − F
ji
( n − )
ij
( n − )1/ 2
1 / 2
M = − FL +
M =
+
ji
(
FL n
5
.
0 / n)/12
ij
( n 0.5/ n)/12
L F
F
F
F L
L/n
L/n
L/n
2n
2n
V = Fn / 2
ij
V = − Fn / 2
ji
M =
ξ
FL
F
F
M =
ξ
FL
ji
(1 2
−ξ )
ij
(1 2
−ξ )/4
/ 4
γ L
ξL
γ L
V = − ξ
F
V = − ξ
F
ji
(3 2
−ξ )/2
ij
(3 2
−ξ )/2
M = M
M = Mξ
ji
(2 − ξ
3 )
ij
(1−ξ )(3ξ − )1
ξL
M
V = −6 Mξ − ξ
V = − Mξ −ξ
ji
6
(1 )
ij
(1 )/ L
/ L
M = M / 4
=
ij
M
M
M / 4
ji
L/2
L/2
V = −1.5 M L
= −
ij
/
V
1.5 M L
ji
/
M = −
+
M =
+
ji
(2 q 3
1
2
q ) 2
L /60
ij
(3 q 2
1
2
q ) 2
L /60
q1
q2
V =
+
V = −
+
ji
(3 q 7
1
q 2 ) L / 20
ij
(7 q 3
1
q 2 ) L / 20
2
M = qL
−
/12
2
=
ij
q
M
qL /12
ji
V = /
qL 2
ij
V = − qL / 2
ji
2
M = qL
−
/20
q
2
=
ij
M
qL /30
ji
V = 7 qL / 20
V = −3 qL / 20
ij
ji
2 2
M = − qL ξ
2 3
M = qL ξ
ji
(4−3ξ)/12
ij
[6−ξ(8−3ξ)]/12
ξL
q
V =
ξ
qL
3
V = − ξ
qL
ji
(1−ξ / )2
ij
[1 2
−ξ (1−ξ / )
2 ]
M = 11 2
− qL /192
ij
L/2
M = 5 2
qL /192
ji
q
V = 13 qL / 32
= −
ij
V
3 qL / 32
ji
2
M = − qLξ
2
M = qLξ
ji
(3 2
−ξ )
ij
(3 2
−ξ )/24
γ L
ξL
γ L
/24
q
V = qLξ / 2
V = − qLξ / 2
ij
ji
http://www.iil.pwr.wroc.pl/zukowski 1
M
EI =const
M
ij
M
ji
ij
M
Vij
V
L
ji
V ji
ij
Vji
2 2
M = − qL ξ
2 3
M
= qL ξ
q
ξL
ji
(5 − 3ξ )/ 60
ij
[10 −ξ(10 − 3ξ )]/ 60
2
3
V = qLξ
ij
[1/2−ξ (5−2ξ)/20]
V = − qLξ
ji
(5 − 2ξ )/ 20
M = −23 2
qL / 960
=
ij
M
7 2
qL / 960
q
L/2
ji
V = 9 qL / 40
= −
ij
V
qL / 40
ji
2 2
M = − qLξ
2 3
M = qL ξ
ji
(5 − 4ξ )
ij
[10−ξ(15−6ξ)]/30
q
ξL
/ 20
2
3
V = qLξ
ij
[1/2−ξ (15−8ξ)/20]
V = − ξ
qL
ji
(15−8ξ)/20
2
M = qL
−
/30
M =3 2
qL /160
ij
L/2
q
ji
V = 29 qL /160
ij
V = −11 qL /160
ji
M = 5 2
− qL /96
=
ij
L/2
q
M
5 2
qL /96
ji
V = qL / 4
V = − qL / 4
ij
ji
2
M = qL
−
/32
2
M = qL /32
ij
q
L/2
q
ji
V = qL / 4
V = − qL / 4
ij
ji
2 2
M = − qLξ
2 2
M = qL ξ
ji
(4−3ξ)
ij
(4−3ξ)/12
ξL
ξ
/12
q
L
q
V = qLξ / 2
ij
V = − qLξ / 2
ji
2 2
M = − qL ξ
2 2
M = qL ξ
ji
(2−ξ)/12
ij
(2−ξ)/12
q
ξL
ξL
q
V = qLξ / 2
V = − qLξ
ij
/ 2
ji
2
M = − qL
2
M = qL
ji
[1 2
−ξ (2−ξ)]/12
ij
[1 2
−ξ (2−ξ)]/12
q
ξL
ξL
V = qL
V = − qL
ji
(1−ξ )
ij
(1−ξ )/ 2
/ 2
ϕ
M = 4 EIϕ / L
i
M = 2 EIϕ / L
ij
i
ji
i
2
V = 6
− EIϕ / L
2
V = 6
− EIϕ / L
ij
i
ϕ
ji
i
i
M = 2 EIϕ / L
ϕ
=
ϕ
ij
j
M
4 EI
/ L
j
ji
j
2
V = 6
− EIϕ / L
2
= −
ϕ
ij
j
ϕ
V
6 EI
/ L
j
ji
j
M = −6 EIψ L
= −
ψ
ij
/
M
6 EI
L
ji
/
ψ =∆/L
∆
2
2
V = 12 EIψ / L
V = 12 EIψ / L
ij
ji
M = − EIα ∆ − ∆
M
= EIα ∆ − ∆
ji
T ( t
t
d
g )
ij
T ( t
t
d
g )/ h
∆t
h
/ h
g
= 0
∆t
V =
ij
V
0
d
ji
M = 0
M = EIα ∆ − ∆
ji
T ( t
t
d
g )
ij
/ h
h ∆tg
V = − EIα ∆ − ∆
V = − EIα ∆ − ∆
ji
T ( t
t
d
g ) /( Lh) ij
T ( t
t
d
g )/( Lh)
∆td
2
http://www.iil.pwr.wroc.pl/zukowski
M
EI =const
M
ij
M
ji
ij
M
Vij
V
L
ji
V ji
ij
Vji
= 2 ⋅ 3
( ⋅ξ − )
2 ⋅ EI
M
⋅ ϕ
∆
= 2 ⋅ (3 ⋅ξ − )
1 ⋅ EI
M
⋅ ∆ϕ
ij
L
ξL
ji
L
=
EI
EI
V
6 ⋅ 1
( − 2 ⋅ξ ) ⋅
⋅ ∆ϕ
∆ϕ
V = 6 ⋅ 1
( − 2 ⋅ξ ) ⋅
⋅ ϕ
∆
ij
2
L
ji
2
L
EI
M = 6 ⋅
⋅ h
∆
EI
ij
M = 6 ⋅
⋅ ∆ h
L 2
ξL
ij
L 2
∆h
EI
EI
V = −12 ⋅
⋅ ∆ h
V = −12 ⋅
⋅ h
∆
ij
3
ji
L
L 3
http://www.iil.pwr.wroc.pl/zukowski 3