Question

The limit of proportionality of a certain steel sample is 300 MPa in simple tension. It is subjected to principal stresses of 150 MPa (tensile), 60 MPa (tensile), and 30 MPa (tensile). According to the maximum principal stress theory, what will be the factor of safety in this case?

1. 10
2. 5
3. 4
4. 2
5.

Answer 1

Correct Answer - Option 4 : 2

Concept:

Maximum principal stress theory (Rankine Theory):

• As per this theory, for no failure maximum principal stress should be less than yield stress under uniaxial loading.
• i.e. σ_max < f_y
• For design, \({σ _{1}} \le \frac{{{σ_{y}}}}{{FOS}}\)
• This theory is most suitable for brittle materials, not applicable to ductile materials, not applicable to pure shear case because as per this theory τ should be less then f_y

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Calculation:

Given, 

Yield stress in simple tension for this material, σ_y = 300 MPa, 

Principal stresses are σ₁ = 150 MPa, σ₂ = 60 MPa, σ₃ = 30 MPa

According to the Maximum Principal Stress Theory,

\({σ _{1}} \leq \frac{{{\sigma_{y}}}}{{FOS}}\)

\(150 = \frac{{300}}{{FOS}} \Rightarrow FOS = 2\)

The factor of safety = 2.