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A structural element is subjected to pure shear of 80 N/mm2, as shown in the figure. The yield stresses both in tension and in compression are 240 N/mm2. According to the maximum normal stress theory, the factors of safety in tension and compression are, respectively,

A structural element is subjected to pure shear of 80 N/mm2, as shown in the figure. The yield stresses both in tension and in compression are 240 N/mm2. According to the maximum normal stress theory, the factors of safety in tension and compression are, respectively, Correct Answer 3 and 3

When an element is subjected to pure shear, then the magnitude of maximum/minimum normal stresses induced in a material are equal to the magnitude of shear stress itself i.e.

Maximum normal stress, σ1 = +τ = 80 N/mm2

Minimum normal stress, σ2 = -τ = -80 N/mm2

Here, the negative sign means compression.

As per maximum normal stress theory:

Maximum normal stress in tensile or Compression ≤  maximum design tensile or compression stress when the material is subjected to yielding only.

For tension

σ1  ≤  σyt/FOS (σyt = Yield stresses  in tension)

80 ≤ 240/FOS

⇒ FOS in tension = 3 

For Compression

σ1  ≤  σyc/FOS (σyc = Yield stresses  in tension)

80 ≤  240/FOS

⇒ FOS in Compression = 3  

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