Understanding Net Effective Area for Steel Angle Tension Members

When a steel angle section is used as a tension member and is connected by only one leg (e.g., bolted or welded to a gusset plate), the entire cross-sectional area is not fully effective in resisting the tensile force. This is due to a phenomenon called shear lag.

What is Shear Lag?

Shear lag occurs because the tensile force is introduced through only one part of the cross-section (the connected leg). This causes the stress distribution to be uneven across the member's cross-section, particularly in the outstanding leg. The part of the outstanding leg furthest from the connection may not be stressed to the same level as the connected leg, making it less effective in carrying the load. Therefore, a reduced effective area is used for design calculations instead of the full gross or net area.

Calculating the Net Effective Area

Different structural design codes provide formulas to calculate the net effective area \(A_{net,eff}\) considering shear lag. These formulas typically involve the area of the connected part and a reduced area of the outstanding part.

Given the areas of the connecting leg as \(a\) and the outstanding leg as \(b\), the question provides options that suggest a specific formula structure relating these areas to the net effective area. The general idea is that the effective area is the area of the connected leg plus some effective portion of the outstanding leg.

Let's examine the structure of the plausible options (B and D), which add a term involving \(b\) to \(a\):

• Option B: \(a+\frac{b}{1+0.35\times\frac{b}{a}}\)
• Option D: \(a+\frac{b}{1+0.20\times\frac{b}{a}}\)

This structure implies that the effective area is the area of the connected leg (\(a\)) plus the area of the outstanding leg (\(b\)) multiplied by a reduction factor. The reduction factor is represented by \(\frac{1}{1+C\times\frac{b}{a}}\), where \(C\) is a constant (0.35 or 0.20). Since \(b/a\) is positive, the denominator is greater than 1, making the reduction factor less than 1. This confirms that only a fraction of the outstanding leg's area is considered effective.

Based on common formulas used in structural design for angles connected by one leg, a formula similar in structure to Option B is often adopted, where a constant related to shear lag is used. The formula provided in Option B: \[A_{net,eff} = a + \frac{b}{1+0.35\times\frac{b}{a}}\] represents a method to calculate the net effective area of the angle in tension, where \(a\) is the area of the connected leg and \(b\) is the area of the outstanding leg. The term \(\frac{b}{1+0.35\times\frac{b}{a}}\) represents the effective area contributed by the outstanding leg after accounting for shear lag.

Options A and C involve subtracting a value from the connected leg area \(a\), which does not align with the principle that the effective area is generally the connected area plus a reduced portion of the outstanding area. Options B and D follow the correct principle of adding a reduced outstanding leg area. The specific constant 0.35 in Option B is consistent with certain forms of shear lag calculation formulas.

Therefore, the net effective area of the angle is given by the formula: \[a+\frac{b}{1+0.35\times\frac{b}{a}}\]

Revision Table: Key Concepts

Additional Information on Shear Lag in Tension Members

Shear lag is a crucial factor in the design of tension members, especially those with plate or angle elements connected eccentrically or through only a portion of their cross-section. The effective area is always less than or equal to the net area and sometimes less than the gross area, depending on the connection details and material properties.

Factors influencing shear lag include:

• The ratio of the length of the connection to the width of the connected element. Longer connections distribute stress more evenly, reducing shear lag.
• The geometry of the member (e.g., angle, channel, plate). Angles connected by one leg are particularly susceptible.
• The type of connection (bolted or welded). The arrangement of bolts or the length of welds affects stress distribution.
• The ratio of yield strength to ultimate tensile strength of the steel.

Design codes provide specific provisions and formulas for calculating the effective area for various types of tension members and connections to ensure safe and economical designs. The formula given in option B is an example of such a formula, simplifying the calculation based on the areas of the individual legs.