MOMENTY I SIA
Y BRZEGOWE
PR
T LEWOSTRONNIE UTWIERDZONY
PRAWOSTRONNIE PODPARTY PRZEGUBOWO
EI =const
M M
ij
ij
V
Mji ji
= 0
Vij
Vij L Vji
M = -FL¾ (1 - ¾ )(1 - ¾ / 2)
F
ij
2
¾L
V = -F¾ (3 - ¾ )/ 2
ji
2
Vij = F(1 - ¾ )(1 + ¾ - ¾ / 2)
M = -3FL /16
F
ij
L/2 L/2
V = -5F /16
ji
Vij = 11F /16
2
M = -3FL(1 - ¾ )/ 8
ij F F
¾L 2
¾L
V = -F(5 + 3¾ )/ 8
ji
2
Vij = F(11 - 3¾ )/ 8
M = -FL(n - 1/ n)/ 8
ij
F F F
L/n L/n L/n L/n
V = -F(3n + 1/ n - 4)/ 8
ji
Vij = F(5n - 1/ n - 4)/ 8
M = -FL(n + 0.5 / n)/ 8 L F F F F L
ij
L/n L/n L/n
V = -F(3n - 0.5 / n)/ 8
2n 2n
ji
Vij = F(5n + 0.5 / n)/ 8
2
M = FL¾(1 - ¾ )/ 8
ij
F
2
¾L
¾L
V = -F¾(9 - ¾ )/ 8
F
ji
2
Vij = -F¾(9 - ¾ )/ 8
2
M = M (- 1 + 3¾ - 3¾ / 2)
ij
M
¾L
V = -3M Å" ¾(1 - ¾ / 2)/ L
ji
Vij = -3M Å"¾(1 - ¾ / 2)/ L
M = M / 8
ij M
L/2 L/2
V = -(9 / 8)M / L
ji
Vij = -(9 / 8)M / L
M = M / 2
ij M
V = -1.5M / L
ji
Vij = -1.5M / L
q1
q2
M = -(8q1 + 7q2 )L2 /120
ij
V = -(4q1 + 11q2 )L / 40
ji
Vij = (16q1 + 9q2 )L / 40
M = -qL2 / 8
ij
q
V = -3qL / 8
ji
Vij = 5qL / 8
M = -qL2 /15 q
ij
V = -qL /10
ji
Vij = 2qL / 5
M = -7qL2 /120
q
ij
V = -11qL / 40
ji
Vij = 9qL / 40
http://www.iil.pwr.wroc.pl/zukowski 1
EI =const
M
M
ij
ij
Mji V
= 0
ji
Vij Vij L Vji
2
2
M = -qL2¾ (2 - ¾ ) / 8
¾L
ij
3
q V = -qL¾ (1- ¾ / 2)/ 2
ji
2
Vij = qL¾[1-¾ (1- ¾ / 4)/ 2]
M = -9qL2 /128
ij
L/2
V = -7qL /128
ji
q
Vij = 57qL /128
2 2
M = -qL2¾ (2 -¾ )/ 8
ij ¾L
2
q V = -qL¾[1- ¾(6 - ¾ )/ 8]
ji
2 2
Vij = qL¾ (6 - ¾ )/ 8
M = -7qL2 /128
ij
L/2
V = -41qL /128
ji
q
Vij = 23qL /128
2
M = -qL2¾(3 - ¾ )/16
ij Å‚L ¾L Å‚L
2
q V = -qL¾(5 + ¾ )/16
ji
2
Vij = qL¾(11-¾ )/16
Mij = -qL2¾2[20-3¾(5-¾)]/120
¾L
q
3
V = -qL¾ (5 -¾ )/ 40
ji
2
Vij = qL¾[1/ 2 - ¾ (5 -¾ )/ 40]
M = -53qL2 /1720
ij
L/2
q
V = -9qL / 640
ji
Vij = 151qL / 640
Mij =-qL2¾2[40-3¾(15-4¾)]/120
¾L
q
3
V = -qL¾ (15 - 4¾ )/ 40
ji
2
Vij = qL¾[1/ 2 -¾ (15- 4¾)/ 40]
M = -41qL2 / 960
ij
L/2
q
V = -13qL / 320
ji
Vij = 67qL / 320
2 2
M = -qL2¾ (10 - 3¾ )/120
ij
¾L
q
2
Vji = -qL¾[1/ 2 -¾(10-¾ )/ 40]
2 2
Vij = -qL¾ (10 -¾ )/ 40
M = -17qL2 / 960
ij
L/2
q
V = -121qL / 640
ji
Vij = 39qL / 640
2 2
M = -qL2¾ (5 - 3¾ )/ 30
ij
¾L
q 2
V = -qL¾[1/ 2 -¾(5 -¾ )/10]
ji
2 2
Vij = -qL¾ (5 - ¾ )/10
Mij = -17qL2 / 480
L/2
q
V = -21qL /160
ji
Vij = 19qL /160
2 http://www.iil.pwr.wroc.pl/zukowski
EI =const
M
M
ij
ij
M
V
ji
Vij L
Vji ji= 0
Vij
Mij = -5qL2 / 64 q
L/2
V = -11qL / 64
ji
Vij = 21qL / 64
M = -3qL2 / 64
ij
q
L/2
q
V = -13qL / 64
ji
Vij = 19qL / 64
2
Mij = -qL2¾ (4 - 3¾ )/ 8
¾L ¾L
q q
V = -qL¾[4 - ¾(4 - 3¾ )]/ 8
ji
Vij = -qL¾[4 + ¾(4 - 3¾ )]/ 8
2
M = -qL2¾ (2 -¾ )/ 8 q
¾L ¾L
q
ij
V = -qL¾[1/ 2 - ¾(2 - ¾ )/ 8]
ji
Vij = qL[1/ 2 + ¾(2 - ¾ )/ 8]
2
q
M = -qL2[1-¾ (2 -¾)]/ 8
¾L ¾L
ij
2
V = -qL[8 - 4¾ + ¾ (2 -¾ )]/ 8
ji
2
Vij = qL[5 - 4¾ -¾ (4 - ¾)]/ 8
Õi
M = 3EIÕi / L
ij
V = -3EIÕi / L2
ji
Õi
Vij = -3EIÕi / L2
M = -3EIÈ / L
ij
È ="/L
V = 3EIÈ / L2
ji
Vij = 3EIÈ / L2
M = -1.5EIÄ…T ("td - "tg )/ h
ij
"tg
V = 1.5EIÄ…T ("td - "tg )/(Lh)
ji
"td
Vij = 1.5EIÄ…T ("td - "tg )/(Lh)
M = -EIÄ…T ("td - "tg )/ h
ij "tg
V = EIÄ…T ("td - "tg )/(Lh)
ji
"td
Vij = EIÄ…T ("td - "tg )/(Lh)
M = -0.5EIÄ…T ("td - "tg )/ h
"tg
ij
V = 0.5EIÄ…T ("td - "tg )/(Lh)
"td ji
Vij = 0.5EIÄ…T ("td - "tg )/(Lh)
EI
¾L
Mij = -3 Å"(1-¾)Å" "Õ
EI
L
Vji = 3 Å"(1-¾)Å" "Õ
EI L2
"Õ
Vij = 3 Å"(1-¾)Å" "Õ
L2
EI
¾L
M = 3 Å" "h
ij
EI
L2
Vji = -3 Å" "h
"h
EI L3
Vij = -3 Å" "h
L3
http://www.iil.pwr.wroc.pl/zukowski 3
"
h
h
h