In plate girders and thin-webbed beams, web crippling is most likely to occur at which location or loading condition?

Introduction / Context:
Web crippling is a local failure mode of thin webs under concentrated bearing loads at supports or under point loads from cross-beams, wheel loads, or jacks. It involves localized compression and buckling of the web, sometimes with flange participation, and is distinct from global bending or shear yielding.

Given Data / Assumptions:

• Consider a plate girder or a rolled section subjected to support reactions or point loads.
• Web thickness is relatively small compared with depth.

Concept / Approach:
Concentrated loads introduce high local compressive stresses in the web under the load patch or at supports. If bearing stiffeners, adequate web thickness, or load dispersion plates are not provided, the web may locally crush and buckle—this is web crippling. It does not necessarily coincide with locations of maximum global bending moment or maximum deflection, which are broader structural behaviors.

Step-by-Step Solution:
Identify the local load introduction points (supports, point loads). Recognize that local compressive bearing on thin webs governs here. Conclude web crippling risk is highest at concentrated load locations unless stiffened.

Verification / Alternative check:
Design provisions require bearing stiffeners or checking web bearing/crippling capacity under reactions and point loads; this confirms the mode is associated with concentrated loads rather than spanwise global effects.

Why Other Options Are Wrong:

• Maximum moment/deflection: Relate to global bending, not local bearing failure.
• Minimum shear: Unrelated to the local compressive mechanism of crippling.
• All the above: Overbroad; only concentrated loads are primarily responsible.

Common Pitfalls:

• Neglecting bearing checks when adding heavy point loads even if overall bending/shear capacities are adequate.
• Omitting stiffeners under concentrated loads due to space constraints.

Final Answer:
Where concentrated (bearing) loads act, such as under point loads or reactions.