BRACING
12.1 Introduction
Stability bracing requirements first appeared in the early 1900s related to the design of lacing in the built-up members of trusses (Waddell, 1916). Numerous railroad truss failures prompted the development of the 2% rule-the lacing shear force equals 2% of the force in the column. The lacing rule was most likely simply extended by structural engineers to all stability bracing situations, primarily as a result of steel design specifications in the United States not containing general bracing requirements until 1999. In the 1970s, the New York City building code contained the 2% rule for stability bracing but no stiffness requirements. Timoshenko's 1936 book, Theory of Elastic Stability, contained solutions for columns with flexible supports (brace points). He showed that if the flexible supports had a certain minimum stiffness, a straight column would behave as if the supports were rigid (no movement). Making the brace stiffness greater than the minimum did not affect the column strength. He also gave a simple technique for determining the minimum (later called ideal ) stiffness for column bracing. Winter (1960) extended Timoshenko's solution to columns with initial crookedness (real columns) and to beams. Winter introduced the concept that stability bracing strength and stiffness requirements are interconnected. He showed that the design stiffness needed to be twice the ideal stiffness to keep brace forces small. The recommendations found in this chapter follow and expand on Winter's concept. An adequate brace system requires both strength and stiffness (Winter, 1960). A simple brace design formulation, such as designing the brace for 2% of the member compressive force, addresses only the strength criterion. The magnitude of the initial out-of-straightness of the members to be braced has a direct effect on the bracing force. The brace stiffness also affects the brace force. Many published solutions provide stiffness recommendations only for perfectly straight structural systems. Such recommendations should not be used directly in design because very large brace forces may result, as will be shown subsequently.