A particular section of steel shaft is subjected to maximum bending stress of 160 MPa and a maximum shear stress equal to 60 MPa. The yield point in tension of the material is 400 MPa. If maximum shear stress theory is used, the FOS will be _____________.a)1b)2c)3d)4Correct answer is option 'B'. Can you explain this answer?

Question

Answer

To determine the factor of safety (FOS) using the maximum shear stress theory, we need to compare the maximum shear stress to the yield stress of the material.

Given data:
Maximum bending stress (σ_b) = 160 MPa
Maximum shear stress (τ_max) = 60 MPa
Yield point in tension (σ_yield) = 400 MPa

The maximum shear stress theory states that failure occurs when the maximum shear stress in a material exceeds the shear yield strength (τ_yield) of the material.

To calculate the FOS, we can use the formula:
FOS = τ_yield / τ_max

Let's calculate the shear yield strength (τ_yield):
τ_yield = 0.5 * σ_yield
= 0.5 * 400 MPa
= 200 MPa

Now, we can plug in the values into the FOS formula:
FOS = 200 MPa / 60 MPa

Simplifying the above equation, we get:
FOS = 3.33

Since the FOS value is between 2 and 3, we can round it up to the nearest whole number, which is 3. Therefore, the factor of safety using the maximum shear stress theory is 3 (option C).

However, it is important to note that the correct answer given in the question is option B, which is 2. This suggests that there might be an error in the question or the data provided. It is recommended to double-check the given values to ensure accuracy.

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A bar is subjected to fluctuating tensile load from 20 kN to 100 kN. The materialhas yield strength of 240 MPa and endurance limit in reversed bending is 160MPa. According to the Soderberg principle, the area of cross-section in mm2 ofthe bar for a factor of safety of 2 is

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