Two kinds of failure of reinforced-concrete beams concern the engineer: one, "the under-reinforced moment" failure, is preceded by large deflections which give warning of its imminence; the other, the "diagonal-tension or shear" failure, occurs suddenly and without warning, not permitting persons to remove the cause of the overload or to evacuate the structure.

A structure consultant has been retained to observe a suspect beam in a building. From the engineer's experience he estimates that about 5 percent of all beams proportioned according to the building code in use at the time the building was designed will fail owing to a weakness in the shear manner, if tested to failure, while the others will fail in the moment manner. From laboratory experience, however, the engineer knows that at some load prior to failure 8 of 10 beams destined to fail in the shear manner will exhibit small characteristic diagonal cracks near their ends. On the other hand, only 1 of 10 beams which finally fail in the moment manner shows similar cracks prior to failure.

Suppose that the relative consequences of the sudden shear failure versus warning-giving moment type of failure are such that the expensive replacement of the beam is justified only if a sudden failure is more likely than a moment failure. Then, if upon inspecting the beam, the engineer observes these characteristic diagonal cracks, should he demand the repairs or conclude that the risk is too small to justify the repairs ( without further study)?