Question

A linear elastic structure under plane stress condition is subjected to two sets of loading, I and II. The resulting states of stress at a point corresponding to these two loadings are as shown in the figure below. If these two sets of loading are applied simultaneously, then the net normal component of stress Οƒxx is ________.

Options :

  1. 3𝜎/2

  2. 𝜎(1 + 1/√2)

  3. 𝜎/2

  4. 𝜎(1 - 1/√2)

Show Answer

Answer :

𝜎/2

Solution :

Οƒx1 = 0, Οƒy1 = Οƒ, Ο„x1, y1 = 0, ΞΈ = 45Β°

Οƒx Οƒ x 1 + Οƒ x 2 2 + Οƒ x 1 βˆ’ Οƒ x 2 2   c o s   ( 2 ΞΈ ) + Ο„ x y   s i n   ( 2 ΞΈ )

Οƒx = Οƒ/2

Net normal stress

Οƒxx = Οƒ + Οƒx = Οƒ + Οƒ/2

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