GTSTRUDL Users Group Annual Meeting, June 2010, page-1 Stability Analysis of 400 Ton Lifting Truss Luis M. Moreschi Hongchun Liu Peter J. Carrato Bechtel Power Corp.

GTSTRUDL Users Group Annual Meeting, June 2010, page-2 Outline  Background: Heavy Load Lifting in Power Plant Construction  Lifting Truss Buckling Problem  Stability Evaluation of the Original Lifting Truss  Root Cause and Proposed Solution  Stability Evaluation of the Retrofitted Lifting Truss  Conclusion

GTSTRUDL Users Group Annual Meeting, June 2010, page-3 Heavy Lifting in Power Plant Construction  Wall panels are assembled at ground to reduce # of components being lifted  Heavy wall panel assembly weights up to 400 Tons  Strand jacks are provided on the structure  Lifting beam / truss is used to spread the load evenly to multiple lifting points  An approved Rigging Plan is required for critical heavy lifts

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GTSTRUDL Users Group Annual Meeting, June 2010, page-9 Lifting Truss Buckling Problem  Lifting truss was tested to 125% of the design capacity  The truss exhibited out-of-plane deflections during testing  Home office engineering was consulted for retrofit solution

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GTSTRUDL Users Group Annual Meeting, June 2010, page-11 FEA Model

GTSTRUDL Users Group Annual Meeting, June 2010, page-12 Test Lifting Load (792kips)

GTSTRUDL Users Group Annual Meeting, June 2010, page-13 Linear Buckling Analysis (Engenvalue) … >Stiffness analysis >Perform buckling analysis >Eigen parameters >Shift 1.0 $ Required to find the realistic buckling mode shape for $ this application. Try-and-error needed to find the $ lowest positive buckling multiplier > End parameters >Perform buckling analysis …

GTSTRUDL Users Group Annual Meeting, June 2010, page-14 Fundamental Buckling Shape Buckling Multiplier (FOS against buckling) = 1.32

GTSTRUDL Users Group Annual Meeting, June 2010, page-15 Fundamental Buckling Shape Buckling Multiplier (FOS against buckling) = 1.32

GTSTRUDL Users Group Annual Meeting, June 2010, page-16 Further Analysis – Pushover Analysis Linear Buckling Analysis predicts the classical ‘Euler’ load, which cannot be directly used in real-life. Pushover Analysis is an automated nonlinear incremental load analysis that searches for structural instability or collapse load. Geometric nonlinearity was considered for the truss Small out-of-plane loads were applied at selected joints to Initiate the desired buckling shape

GTSTRUDL Users Group Annual Meeting, June 2010, page-17 Small out-of-plane loads applied to initiate the desired buckling shape Pushover Analysis

GTSTRUDL Users Group Annual Meeting, June 2010, page-18 Pushover Analysis Commands … >NONLINEAR EFFECT >GEOMETRY MEMBER EXISTING >PUSHOVER ANALYSIS DATA CONSTANT LOAD ‘2’$ 0.1kips load at selected lifting point INCREMENTAL LOAD ‘1’$ 88kips lifting load at each lifting point MAXIMUM NUMBER OF LOAD INCREMENTS 200 MAXIMUM NUMBER OF TRIALS 20 LOADING RATE 0.2 CONVERGENCE RATE CONVERGENCE TOLERANCE COLLAPSE MAXIMUM NUMBER OF CYCLES 50 >END >PERFORM PUSHOVER ANALYSIS …

GTSTRUDL Users Group Annual Meeting, June 2010, page-19 Pushover Analysis – Original Lifting Truss Buckling Load at JNT_12 = 88kips 792kips Total Buckling Load = 88 x 9 = 792kips FOS against Buckling = 792/792 = 1.0

GTSTRUDL Users Group Annual Meeting, June 2010, page-20 Root Cause and Proposed Solution  Both linear and nonlinear analyses indicated that the buckling load is very close to the actual test load (792kips).  Original design did not consider the unbraced length correctly for top and bottom chords. KL/r = 419 for bottom chord!  Out-of-plane stiffness shall be significantly increased to eliminate out-of-plane buckling.

GTSTRUDL Users Group Annual Meeting, June 2010, page-21 Reinforced Top & Bottom Chords

GTSTRUDL Users Group Annual Meeting, June 2010, page-22 Reinforced Top & Bottom Chords Reinforced Cross Section

GTSTRUDL Users Group Annual Meeting, June 2010, page-23 Pushover Analysis - Retrofitted Lifting Truss Selected Buckling Load at JNT_12 = 2,024 kips Total Buckling Load = 2,024 x 9 = 18,216kips FOS Against Buckling = 18,216 / 792 = 23

GTSTRUDL Users Group Annual Meeting, June 2010, page-24 Comparison: FOS Against Buckling Linear Buckling Analysis Pushover Analysis (Geometric nonlinearity) Original Lifting Truss 1.32  1.00  Retrofitted Lifting Truss Practically, a FOS in the magnitude of 10~20 should be used to account for imperfections, out-of-plane loads, residual stresses, and etc. Remember: Buckling is a wild beast to deal with. Be cautious!

GTSTRUDL Users Group Annual Meeting, June 2010, page-25 Conclusions  Buckling could occur if lifting devices are not properly designed for heavy lifts  Linear Elastic Buckling Analysis is just a starting point for buckling evaluation  Pushover Analysis should be performed to further investigate the situation  FOS against buckling should be set high (10~20) for real-life applications

GTSTRUDL Users Group Annual Meeting, June 2010, page-26 Questions or Comments?