NUS July 12-14, 2005 Analysis and Design for Robustness of Offshore Structures NUS – Keppel Short Course 1 Resistance to Accidental Explosions General principles

NUS July 12-14, 2005 Analysis and Design for Robustness of Offshore Structures NUS – Keppel Short Course 2 Outline  Classification of explosion loads  Dynamic response based on SDOF analogy  Dynamic response charts  ISO-damage (pressure-impulse) diagram  Resistance curves for beams, girders and plates  Ductility limitations  Verification of simple design methods

NUS July 12-14, 2005 Analysis and Design for Robustness of Offshore Structures NUS – Keppel Short Course 3 Simple (SDOF) vs. advanced methods SDOF methods – Biggs’ (1964) (Elastic-plastic/rigid plastic methods, component analysis…) – Early Design – Screening of scenarios – Codes (NORSOK, IGN(UK)… Advanced Methods – NLFEA – Large-scale simulations feasible – Detail Engineering – Critical Scenarios – Quality of analysis? Iso-damage curve for blast loading

NUS July 12-14, 2005 Analysis and Design for Robustness of Offshore Structures NUS – Keppel Short Course 4  Impulsive domain- t d /T< 0.3 Response independent of load magnitude  Dynamic domain-0.3 < t d /T < 3  Quasi-static domain-3 < t d /T EXPLOSION Classification of response

NUS July 12-14, 2005 Analysis and Design for Robustness of Offshore Structures NUS – Keppel Short Course 5 Conservation of momentum EXPLOSION Impulsive domain- t d /T< 0.3 F eq (t) m eq k eq (y) Y(t d ) t F eq (t) y(t) tdtd R(y)= k eq (y)·y Conservation of energy

NUS July 12-14, 2005 Analysis and Design for Robustness of Offshore Structures NUS – Keppel Short Course 6 Rise time small (1) External work Strain energy EXPLOSION Quasi-static domain- t d /T> 3 F eq (t) m eq k eq (y) Y(t d ) t F eq (t) y(t) tdtd R(y)= k eq (y)·y Rise time large (2) Static solution t F eq (t) y(t) tdtd (1) (2) t rise

NUS July 12-14, 2005 Analysis and Design for Robustness of Offshore Structures NUS – Keppel Short Course 7 Explosion response -1 DOF analogy

NUS July 12-14, 2005 Analysis and Design for Robustness of Offshore Structures NUS – Keppel Short Course 8 Dynamic equilibrium- alternative formulation

NUS July 12-14, 2005 Analysis and Design for Robustness of Offshore Structures NUS – Keppel Short Course 9 EXPLOSION SDOF analogy – Biggs’ method f(t) t F eq (t) m eq k eq (y) y Dynamic equilibrium: y(t) t y max Load-mass transformation factor

NUS July 12-14, 2005 Analysis and Design for Robustness of Offshore Structures NUS – Keppel Short Course 10 Development of explosion response charts  Dynamic equilibrium  Explosion load history  Solve dynamic equation – numerical integration  Determine maximum deformation y max  Perform analysis for different duration and load amplitude F(t) tt F max R(y)R(y) y R el y el

NUS July 12-14, 2005 Analysis and Design for Robustness of Offshore Structures NUS – Keppel Short Course 11 EXPLOSION Classification of resistance curves RR R R wwww K1K1 K1K1 K1K1 K1K1 K3K3 K2K2 K2K2 K2K2 Elastic Elastic-plastic (determinate) Elastic-plastic (indeterminate) Elastic-plastic with membrane K 2 =0 K1K1 R K3K3 w R el W el or y el

NUS July 12-14, 2005 Analysis and Design for Robustness of Offshore Structures NUS – Keppel Short Course 12 Explosion response chart maximum displacement versus load duration Governing parameters:  Mechanisme resistance vs. maximum load R el /F max  Load duration vs. eigenperiod t d /T  Membrane stiffness, if any

NUS July 12-14, 2005 Analysis and Design for Robustness of Offshore Structures NUS – Keppel Short Course 13 EXPLOSION Dynamic response chart for pressure pulse- [J.M.Biggs] Triangular load - rise time = 0.3 t d

NUS July 12-14, 2005 Analysis and Design for Robustness of Offshore Structures NUS – Keppel Short Course 14 Development of ISO-damage curves from dynamic response charts for a given pressure pulse Example y allow /y el =10

NUS July 12-14, 2005 Analysis and Design for Robustness of Offshore Structures NUS – Keppel Short Course 15 Example y allow /y el =10 Pressure = F max Impulse =1/2F maxt t d Development of ISO-damage curves from dynamic response charts for a given pressure pulse

NUS July 12-14, 2005 Analysis and Design for Robustness of Offshore Structures NUS – Keppel Short Course 16 EXPLOSION Iso-damage curve for y allow / yelastic =10. [W.Baker] Inadmissible domain Admissible domain

NUS July 12-14, 2005 Analysis and Design for Robustness of Offshore Structures NUS – Keppel Short Course 17 EXPLOSION Resistance curves  Beams and girders Tabulated values for elastic-plastic behaviour Resistance curves based on plastic thory  Plates Elastic and plastic theory

NUS July 12-14, 2005 Analysis and Design for Robustness of Offshore Structures NUS – Keppel Short Course 18 Transformation factors for beams with various boundary and load conditions

NUS July 12-14, 2005 Analysis and Design for Robustness of Offshore Structures NUS – Keppel Short Course 19 Transformation factors for beams with various boundary and load conditions

NUS July 12-14, 2005 Analysis and Design for Robustness of Offshore Structures NUS – Keppel Short Course 20 New Revision II: Transformation factors for clamped beam with two concentrated loads

NUS July 12-14, 2005 Analysis and Design for Robustness of Offshore Structures NUS – Keppel Short Course 21 Transformation factors for beams with various boundary and load conditions

NUS July 12-14, 2005 Analysis and Design for Robustness of Offshore Structures NUS – Keppel Short Course 22 Ductility ratios ( Ref: Interim Guidance Notes)