Estos ejercicios son como ventanas a un mundo de conocimientos que te ayudarán a comprender mejor cómo se comportan los materiales y las estructuras en situaciones reales. Cada ejercicio viene con una explicación detallada y paso a paso de cómo abordar y resolver los desafíos, lo que te permit...
Dado un continuo donde el estado tensional es conocido en un punto y es
representado por el tensor de tensiones de Cauchy en coordenadas cartesianas
1 1 0
σij = 1 1 0 P a
0 0 2
a) Encontrar las tensiones principales (eigenvalues).
b) Las direcciones principales.
c) Las invariantes fundamentales.
a)- Encontrar las tensiones principales (eigenvalues)
1 1 0
[σ] = 1 1 0 P a
0 0 2
Una direccion principal ya esta dada por n̂(3) = ê3 y el strees principal en
esa direccion es de 2.
por lo tanto
1 1
[σ] = (σ − λ1)V⃗ = 0
1 1
las direcciones principales
1−λ 1
det(σ − λ1) = 0 =0
1 1−λ
(1 − λ)2 − 1 = 0
(1 − λ + 1)(1 − λ − 1) = 0
−λ + 2 = 0, λ=0
λ1 = 2 λ2 = 0
el tensor de tensiones principales es:
2 0 0
[σ] = 0 0 0 P a
0 0 2
b)- Las direcciones principales.
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