RISK OPTIMIZATION OF A STEEL FRAME COMMUNICATIONS TOWER SUBJECT TO TORNADO WINDS

Abstract

THE STRUCTURAL ENGINEERING COMMUNITY IN BRAZIL FACES NEW CHALLENGES WITH THE RECENT OCCURRENCE OF HIGH INTENSITY TORNADOS. SATELLITE SURVEILLANCE DATA SHOWS THAT THE AREA COVERING THE SOUTH-EAST OF BRAZIL, URUGUAY AND SOME OF ARGENTINA IS ONE OF THE WORLD MOST TORNADO- PRONE AREAS, SECOND ONLY TO THE INFAMOUS TORNADO ALLEY IN CENTRAL UNITED STATES. THE DESIGN OF STRUCTURES SUBJECT TO TORNADO WINDS IS A TYPICAL EXAMPLE OF DECISION MAKING IN THE PRESENCE OF UNCERTAINTY. STRUCTURAL DESIGN INVOLVES FINDING A GOOD BALANCE BETWEEN THE COMPETING GOALS OF SAFETY AND ECONOMY. THIS PAPER PRESENTS A METHODOLOGY TO FIND THE OPTIMUM BALANCE BETWEEN THESE GOALS IN THE PRESENCE OF UNCERTAINTY. IN THIS PAPER, RELIABILITY-BASED RISK OPTIMIZATION IS USED TO FIND THE OPTIMAL SAFETY COEFICIENT THAT MINIMIZES THE TOTAL EXPECTED COST OF A STEEL FRAME COMMUNICATIONS TOWER, SUBJECT TO EXTREME STORM AND TORNADO WIND LOADS. THE TECHNIQUE IS NOT NEW, BUT IT IS APPLIED TO A PRACTICAL PROBLEM OF INCREASING INTEREST TO BRAZILIAN STRUCTURAL ENGINEERS. THE PROBLEM IS FORMULATED IN THE PARTIAL SAFETY FACTOR FORMAT USED IN CURRENT DESIGN CODES, WITH AN ADDITIONAL PARTIAL FACTOR INTRODUCED TO SERVE AS OPTIMIZATION VARIABLE. THE EXPECTED COST OF FAILURE (OR RISK) IS DE¯NED AS THE PRODUCT OF A LIMIT STATE EXCEEDANCE PROBABILITY BY X LIMIT STATE EXCEEDANCE COST. THESE COSTS INCLUDE COSTS OF REPAIRING, REBUILDING, AND PAYING COMPENSATION FOR INJURY AND LOSS OF LIFE. THE TOTAL EXPECTED FAILURE COST IS THE SUM OF INDIVIDUAL EXPECTED COSTS OVER ALL FAILURE MODES. THE STEEL FRAME COMMUNICATIONS TOWER SUBJECT OF THIS STUDY HAS BECOME VERY COMMON IN BRAZIL DUE TO INCREASING MOBILE PHONE COVERAGE. THE STUDY SHOWS THAT OPTIMUM RELIABILITY IS STRONGLY DEPENDENT ON THE COST (OR CONSEQUENCES) OF FAILURE. SINCE FAILURE CONSEQUENCES DEPEND ON ACTUAL TOWER LOCATION, IT TURNS OUT THAT DIFFERENT OPTIMUM DESIGNS SHOULD BE USED IN DIFFERENT LOCATIONS. FAILURE CONSEQUENCES ARE ALSO DIFFERENT FOR THE DIFFERENT PARTIES INVOLVED IN THE DESIGN, CONSTRUCTION AND OPERATION OF THE TOWER. HENCE, IT IS IMPORTANT THAT RISK IS WELL UNDERSTOOD BY THE PARTIES INVOLVED, SO THAT PROPER CONTRACTS CAN BE MADE. THE INVESTIGATION SHOWS THAT WHEN NON-STRUCTURAL TERMS DOMINATE DESIGN COSTS (E.G., INRESIDENTIAL OR O±CE BUILDINGS) IT IS NOT TOO COSTLY TO OVER-DESIGN; THIS OBSERVATION IS IN AGREEMENT WITH THE OBSERVED PRACTICE FOR NON-OPTIMIZED STRUCTURAL SYSTEMS. IN THIS SITUATION, IT IS MUCH EASIER TO LOOSE MONEY BY UNDER-DESIGN. WHEN STRUCTURAL MATERIAL COST IS A SIGNI¯CANT PART OF DESIGN COST (E.G. CONCRETE DAM OR BRIDGE), ONE IS LIKELY TO LOSE SIGNIFICANT MONEY BY OVER-DESIGN. IN THIS SITUATION, A COST-RISK-BENEFIT OPTIMIZATION ANALYSIS IS HIGHLY RECOMMENDED. FINALLY, THE STUDY ALSO SHOWS THAT UNDER TIME-VARYING LOADS LIKE TORNADOS, THE OPTIMUM RELIABILITY IS STRONGLY DEPENDENT ON THE SELECTED DESIGN LIFE.