Steel Allowable Tensile Strength Calculation

When designing structures, it is crucial to determine the maximum allowable stress that a material can safely withstand. This stress is typically derived from the material's yield strength by applying a suitable factor of safety. This ensures that the structure remains elastic and does not deform permanently under working loads.

Yield Strength Explained

Yield strength (\(f_y\)) is a critical mechanical property of a material, especially steel. It represents the stress at which the material begins to deform plastically (permanently). Beyond the yield point, even if the load is removed, the material will not return to its original shape. For structural design, it's essential to keep stresses below this point to maintain the structural integrity and prevent permanent deformation. In this question, the steel has a yield strength of 450 MPa.

Allowable Tensile Strength Determination

The term maximum allowable tensile strength refers to the permissible stress that a material can be subjected to under tension without exceeding its elastic limit and with an adequate margin of safety. This is generally calculated by dividing the material's yield strength by a factor of safety (FOS). The factor of safety accounts for uncertainties in material properties, loading conditions, and analysis methods.

For steel structures designed using the Working Stress Method (also known as the Allowable Stress Design method), a common factor of safety for yield strength in tension is 1.67. This factor helps ensure that the actual stresses in the structure are well below the yield strength, providing a safe and serviceable design.

Step-by-Step Calculation

To find the maximum allowable tensile strength, we use the following formula:

\[ \text{Allowable Tensile Strength} = \frac{\text{Yield Strength}}{\text{Factor of Safety}} \]

Given values:

• Steel Yield Strength (\(f_y\)) = 450 MPa
• Factor of Safety (FOS) = 1.67 (a standard value for steel in working stress design for yielding in tension)

Applying the formula:

\[ \text{Allowable Tensile Strength} = \frac{450 \text{ MPa}}{1.67} \]

\[ \text{Allowable Tensile Strength} \approx 269.461 \text{ MPa} \]

Rounding this value to two decimal places, we get 269.46 MPa.

Comparing with Options

Let's compare our calculated value for the maximum allowable tensile strength with the given options:

Based on our calculation, the maximum allowable tensile strength for steel with a yield strength of 450 MPa is 269.46 MPa.