Understanding Web Crippling and Load Dispersion

Web crippling is a localized buckling failure that can occur in the web of a steel beam or column, particularly under concentrated loads or reactions applied through a flange. This failure happens when the compressive stress in the web, directly under the point of load application (often a bearing plate), exceeds the web's capacity to resist local buckling.

A bearing plate is used to distribute the concentrated load over a larger area of the flange and the web directly beneath it. However, even with a bearing plate, the load has to be transferred through the web thickness. The stress from the concentrated load applied at the bearing plate spreads out as it travels down the web.

In the analysis of web crippling, it is necessary to determine the effective area of the web that is subjected to this concentrated compressive stress. This effective area depends on how the load disperses from the bearing plate into the web. Standards and design codes typically assume a certain angle for this load dispersion to simplify calculations and provide a safe estimate for the web's resistance.

Load Dispersion Angle in Web Crippling

For web crippling analysis, the load dispersion from the bearing plate is commonly assumed to take place at an angle. This angle represents the spread of the compressive force into the web depth away from the loaded flange.

Based on experimental observations and structural design codes, the dispersion of load from the bearing plate in case of web crippling is typically assumed to occur at an angle of \(30^\circ\). This angle is measured from the horizontal plane at the level of the bearing plate, spreading the load downwards into the web depth. This assumption helps in calculating the effective length of the web resisting crippling, which is the length of the bearing plate plus an area resulting from this \(30^\circ\) dispersion on both sides.

The effective length for crippling resistance calculation usually includes the length of the bearing \(N\) plus a portion of the web depth determined by the \(30^\circ\) dispersion angle. If the web thickness is \(t_w\) and the bearing length is \(N\), the effective length might be considered as \(N + 2 \times (\text{some value derived from } 30^\circ \text{ angle})\). Different codes might have slightly different formulations based on this angle.

Comparing Options

Let's look at the given options for the load dispersion angle:

• Option 1: \(30^\circ\)
• Option 2: \(60^\circ\)
• Option 3: \(45^\circ\)
• Option 4: \(10^\circ\)

As discussed, standard practice and design codes for analyzing web crippling assume a load dispersion angle of \(30^\circ\) from the horizontal at the bearing edge. Angles like \(60^\circ\), \(45^\circ\), or \(10^\circ\) are not typically used for web crippling dispersion calculations in standard design procedures. For instance, a \(45^\circ\) angle might sometimes be considered for general stress distribution or concrete bearing design, but not specifically for the effective area calculation in steel web crippling.

Therefore, the correct angle for load dispersion from the bearing plate in the case of web crippling is \(30^\circ\).

Revision Table: Key Concepts in Web Crippling

Additional Information: Web Crippling vs. Web Yielding

It is important to distinguish web crippling from web yielding, another failure mode under concentrated loads.

• Web Yielding: This is a yielding failure that occurs in the web under the bearing area. The stress distribution for yielding is often assumed to spread at a different rate (e.g., a 1:2.5 slope in some codes, which corresponds to an angle whose tangent is 1/2.5 or approx \(21.8^\circ\) from the vertical, or \(68.2^\circ\) from the horizontal). The calculation area for yielding is typically based on the bearing length plus a portion of the web thickness or depth related to this slope, extending into the root of the fillet. Web yielding resistance is checked against the yield strength of the web material.
• Web Crippling: This is a buckling failure. The resistance depends on the web's slenderness (height-to-thickness ratio), yield strength, and the effective length subjected to compression, which is influenced by the \(30^\circ\) dispersion angle. Web crippling is a local instability phenomenon rather than a simple crushing (yielding).

Both web yielding and web crippling must be checked when a concentrated load or reaction is applied to a steel beam's web. The load dispersion angle assumed is different for the two failure modes because they involve different failure mechanisms (yielding vs. buckling) and stress patterns.