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

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