Disproportionate collapse analysis aims to assure that frames, a commonstructural system of buildings, can survive unforeseen local events and a central modelingtool of such abnormal deterioration is the concept of column loss. This paperformulates an appropriate computational model on the basis of mathematical optimization,using the collapse load analysis problem of steel frames with pre-existingdamage. A respective collapse load robustness measure is proposed. The model hasthe ability to consider both full and partial column/node removals. It renders to be alinear programming model, if the US steel design regulations are used. A practicalexample is presented and several aspects are discussed.