Rupture Strength of Tension Members

The design strength of a tension member is determined by considering several failure modes, including yielding of the gross section, rupture of the net section, and block shear failure. The question focuses on the rupture strength of the net section as per IS 800-2007.

Net Section Rupture Strength

According to IS 800-2007, the design strength of a tension member due to rupture of the net section is generally given by the formula:

\(T_{dn} = \frac{0.9 A_{net} f_u}{\gamma_{m1}}\)

Where:

• \(T_{dn}\) is the design strength due to rupture of the net section.
• \(A_{net}\) is the net effective area of the total cross-section.
• \(f_u\) is the ultimate tensile strength of the steel.
• \(\gamma_{m1}\) is the partial safety factor for failure in tension by rupture (usually 1.25).

This formula applies typically to plates or members connected over their full width/cross-section.

Shear Lag and Preliminary Sizing

When a tension member, such as an angle section or a tee section, is connected to a gusset plate or other member by only one leg or one element, the stress distribution across the entire cross-section at the connection is not uniform. This phenomenon is known as shear lag. The connected element is subjected to higher stress than the outstanding element. IS 800-2007 provides detailed methods to account for shear lag, particularly for angle sections connected by one leg (Clause 6.3.3.1). The formula involves the net area of the connected leg (\(A_{nc}\)) and the gross area of the outstanding leg (\(A_{go}\)) along with a factor \(\beta\). The question, however, provides a simplified equation for "preliminary sizing":

\(T_{dn} = \alpha \frac{A_n f_u}{\gamma_{ml}}\)

Here, \(A_n\) is referred to as the net section area (likely the net area of the entire cross-section accounting for bolt holes) and \(\alpha\) is a factor accounting for the efficiency reduction due to the connection method, primarily shear lag.

α Value for Bolted or Welded Connections

The question asks for the value of \(\alpha\) when the connection involves "one or two bolts along the length in the end connection or equivalent weld length". This specific condition is related to the degree of shear lag. A connection with fewer fasteners along the length results in greater shear lag and thus a lower efficiency factor. While the detailed IS 800-2007 clause uses a more complex formula, for simplified preliminary sizing, specific values of \(\alpha\) are sometimes used based on the number of bolts or length of the weld. For a single angle or similar member connected by one leg:

• For connections with one bolt along the length, shear lag is significant.
• For connections with two bolts along the length, shear lag is reduced compared to one bolt but is still present.
• For connections with more bolts or longer welds, shear lag effect decreases further.

Based on common simplified practices for preliminary calculations and in the context of the provided options, the value of \(\alpha\) for connections with one or two bolts along the length in the end connection or equivalent weld length is often taken as 0.6. This value is particularly relevant for single-bolt connections where shear lag is maximum, and it can also be a conservative value used for connections with up to two bolts in some simplified approaches for preliminary sizing. The value of \(\alpha\) for the specified condition (one or two bolts along the length in the end connection or equivalent weld length) as per the preliminary sizing equation given is 0.6. The final answer is 0.6.