My understanding is approvale of requests for variance from building codes follow the lines of this draft proposal for the city of chicago.
Review Criteria 1. Pursuant to Section 13-8-032(a) of the Municipal Code, The Department may approve an alternative method for complying with any requirement of the building code for individual cases where:
a. Specifically authorized by a provision of the building code;
b. There are practical difficulties in carrying out the strict requirements of the building code, specific individual reasons make the strict application of the building code impractical, the alternative to be approved will comply with the intent and purpose of the building code, and the alternative to be approved will provide equivalent or greater health protection, accessibility, life and fire safety, and structural performance; or
c. A material, design, or method of construction not specifically allowed by the building code complies with the intent of the building code and will, in the specific application, result in a building or structure providing equal or greater quality, strength, effectiveness, fire resistance, durability, and safety as one meeting the strict requirements of the building code.
If it does not meet one of these criteria they won't even consider your request (unless it is accompanied by a wad of cash, it being Chicago).