Design Strength of Tension Members

The design strength of a structural member under axial tension needs to be calculated based on different potential failure modes. One important failure mode is the yielding of the gross section of the member. This mode considers the strength of the entire cross-sectional area before any holes for connections are accounted for.

According to structural design codes, the design strength due to yielding of the gross section is determined by taking the yield strength of the material over the gross area and dividing it by a partial safety factor. The yield strength of the gross section is the product of the gross cross-sectional area ($A_g$) and the yield stress ($f_y$) of the steel material.

Yielding of Gross Section Formula

The formula for the design strength ($T_{dg}$) of a tension member based on the yielding of the gross section is given by:

$$ T_{dg} = \frac{A_g \times f_y}{\gamma_{mo}} $$

Where:

• $T_{dg}$ is the design strength of the member under axial tension due to yielding of the gross section.
• $A_g$ is the gross cross-sectional area of the member.
• $f_y$ is the yield stress of the steel material.
• $\gamma_{mo}$ is the partial safety factor for failure in tension by yielding. This factor accounts for uncertainties in material properties and resistance.

This formula ensures that the design strength is less than the yield strength by a safety margin defined by $\gamma_{mo}$.

Identifying the Correct Expression

Comparing the derived formula with the given options:

• Option 1: $T_{dg} = A_g f_y / \gamma_{mo}$
• Option 2: $T_{dg} = A_g / f_y \gamma_{mo}$
• Option 3: $T_{dg} = \gamma_{mo} / A_g f_y$
• Option 4: $T_{dg} = f_y / \gamma_{mo} A_g$

The expression that correctly represents the design strength due to yielding of the gross section is $T_{dg} = \frac{A_g f_y}{\gamma_{mo}}$.