X
Vigas con Momento Puro Simplemente apoyada Empotrada Empotrada con apoyo simple Doblemente empotrada
RA=ML
RC=−ML
RA=0 M A=M RA=3M
2 L3( L2−b2 ) RC=
−3M2L3
(L2−b2 )
M A=M
2 L2(L2−3b2 )
RA=6Mab
L3RC=
−6MabL3
M A=Mb
L2(2a−b )MC=
−MaL2
(2b−a)
V ( x )=RA0<x<L
V ( x )=00<x<L V ( x )=RA0<x<L V ( x )=RA0<x<L
M (x )=R A x−M
Mmáx=MaLxMmax=a
�
�( x )=M A−M
Mmáx=M 0< xMmáx<aM (x )=R A x−M A−M
Mmáx1=M
2 L3(2a3+3a2b+2b3 )
Mmáx2=−3Mab2 L3
(L+b)
M (x )=R A x−M A−M
Mmax1=Mb
L3(4 a2−ab+b2)
Mmax2=−MaL3
(a2−ab+4 b2)
EIθ ( x )=RA2x2−M ⟨ x−a ⟩− M
6 L(L2−3b2 )
EIθmáx=M6 L
(2 L2−6ab )xθmáx=a
EIθ ( x )=M A x−M ⟨ x−a ⟩
EIθmáx=Maa<xθmáx<L
EIθ ( x )=RA2x2−M A x−M ⟨ x−a ⟩
EIθmáx=Ma
4 L3(a3+4b3 ) xθmax=a
EIθ ( x )=RA2x2−M A x−M ⟨ x−a ⟩
EIθmax=Mab
L3(L2−3ab ) xθmax=a
Flores Moreno Antonio de Jesús 4am1
RA RC
M(X)
a b
MAMCY
X
RA
M(X)
a b
Y
X
MA M(X)
a b
Y
X
RA RC
MA M(X)
a b
Y
RA RCL=a+b a>b L=a+b a>b L=a+b a>b L=a+b a>b
EIY ( x )=R A6x3−M
2⟨ x−a ⟩2− M
6 L(L2−3b2 ) x
EIY máx=M (L−30 ) (102−3b2 )3 /2
180√3 L
xYmáx=√ (L2−3b2 )3
0<xYmax<L2
EIY ( x )=MA
2x2−M
2⟨ x−a ⟩2
Y máx=M2
(L2−b2 )
xYmáx=L
EIY ( x )=R A6x3−
M A
2x2−M
2⟨ x−a ⟩2
EIYmax=−M (L2−3b2 )3
27a2 (L+b )2
xYmax=2L (L2−3b2 )3a (L+b )
0<xYmax<L2
EIY ( x )=R A6x3−
M A
2x2−M
2⟨ x−a ⟩2
EIYmax=−Mb (2a−b )3
54a2
xYmax=(2a−b )L3a
0<xYmax<L2
Flores Moreno Antonio de Jesús 4am1