algo

TORSIÓN: RESUMEN DE FÓRMULAS
Rueda dentada: Mt = P . cos α . R

Momento torsor: Polea y correa: Mt = (T2-T1 ).R
Ec. de equivalencia: ∫ ρ ⋅τ ⋅ dF = Mt = 0 [6]
F

Sección circular maciza : τ =Mt
⋅ ρ [13]
Io

τ max =

Mt
[15]
Wt

π ⋅ d 3 [14´]
π ⋅ d 4 [10]
Io =
W0 =
16
32
Mt
Mt
ϕ=
[17]
⋅ L [16] θ =

I
W = W0 = o = [14]
t
d/2

Mt
⋅ dz
G ⋅ Io
G ⋅ Io
Seccióncircular hueca (anular)
di
π ⋅d 4
1 − η 4 [18] η =
Io =
32
d
dϕ =

(

)

G ⋅ Io

[19] Wo =

Dimensionado: por resistencia Wo =
°
°
con θ adm[ ° / m] : θ adm = θ adm ⋅

Mt

τ adm(

π ⋅ d3
1 −η 4
16

)

[20]

[15´] por deformación I o =

π
 rad 
[21]
⋅
18000  cm 


°
θ adm = θ adm ⋅

ó

Mt
[17´]
G ⋅ θ adm

π  rad 
[22]
⋅
180  m 


Capacidad de carga: p/resistencia: Mt = Wo ⋅τ adm [23] p/deformación: Mt = G ⋅ I o ⋅ θ adm [24]
Evaluación del momento torsor Mt en función de potencia N y velocidad de giro n.
N [CV ]
[25]n[rpm]
N [W ]
Si N[W], n[rps] ó [Hz]: Mt [N .m] =
[27]
2π ⋅ n[ Hz ]

Si N[CV], n[rpm]: Mt [kgf ⋅ cm ] = 71620 ⋅

Si N[HP]: Mt [kgf ⋅ cm ] = 72575 ⋅

N [HP ]
[26]
n[rpm]

Sección no circulartubular de pared delgada (Bredt)

τ ⋅ t = q = cte [28] τ = Mt [30]
2⋅ A⋅ t

El máximo “ τ ” ocurre para el mínimo valor de “t”

Mt ⋅ L S dS
Mt ⋅ L ⋅ S
Espesor constante: ϕ =
[45]
2 ∫0 t[44]
4⋅G⋅ A
4 ⋅ G ⋅ A2 ⋅ t
Mt ⋅ L n Si
Espesor constante por tramos: ϕ =
∑ [46]
4 ⋅ G ⋅ A 2 i =1 ti
Espesor variable continuo:ϕ =

Barras de sección rectangular: (a>b)

τ máx =

Mt
Mt [31]ó τ máx = β ⋅ G ⋅ θ ⋅ b [32]
=
α
α ⋅ a ⋅ b 2 Wt

Wt = α ⋅ a ⋅ b 2
a/b

α
β
a/b

α
β
a/b
δ

1,1

1,2

1,25

Mt
Mt [33]
=
3
G ⋅ β ⋅ a ⋅b
C

Inercia ficticia I f = β ⋅ a ⋅b 3

C = G ⋅ β ⋅ a ⋅b3 = G ⋅ I f
1

siendo:θ =

1,3

1,4

1,5

1,6

1,7

τ ´máx = δ ⋅τ máx
1,75

1,8

0,208 0,214 0,219

0,221 0,223 0,227

0,231 0,234 0,237

0,239...