A New Generation of Simplified Models for Steel and Composite Structures under Blast Loading Bassam A. Izzuddin* and Bassam A. Burgan† (*) Computational Structural Mechanics Group Department of Civil and Environmental Engineering Imperial College London, U.K. www.imperial.ac.uk/csm (†) The Steel Construction Institute, U.K. 12th International Conference on Shock & Impact Loads on Structures Singapore, 14-16 June 2017

Overview Introduction SDOF Models for Steel Beams Generalised supports and catenary action Rate-sensitivity General loading configurations SDOF Composite Floor Model MDOF Building Model Conclusions

Introduction Blast assessment for structural safety http://www.geograph.org.uk/photo/1248657 http://static3.businessinsider.com/image/4ba5e8c27f8b9ae82a560600-1190-625/natural-gas-is-now-blowing-up-in-australia.jpg https://www.rt.com/files/opinionpost/21/3d/20/00/ira-3.jpg Accidental vs intentional blast Blast can also arise from terrorist activity, but concern here is with blast loading is reasonably predictable

Introduction Detailed Nonlinear Finite Element Analysis General applicability Modelling complexity Black box Computational demand More complexity leads to models that are error prone

Introduction Simplified Modelling for Blast Assessment Problem-specific, hence restricted applicability Capture of cause-and-effect Computational efficiency Practical application for parametric investigations Cross-checking of detailed finite element models Attractive provided accuracy not significantly compromised

Introduction New Generation of Simplified Blast Models Address shortcomings of Biggs’ SDOF approach for steel members Extend application to composite floors under blast uplift Simplified modelling of steel-framed buildings under global blast

SDOF Models for Steel Beams Addressing Shortcoming of Biggs’ Models (1964) Generalised supports and catenary action Rate-sensitivity General loading configurations

SDOF Models for Steel Beams Generalised Supports and Catenary Action Generalised Supports Stiffness and strength Rotational and axial Catenary Action Development of tensile axial force at large displacement Depends on axial support stiffness and strength Other Assumptions Elastic perfectly-plastic beam UDL blast

SDOF Models for Steel Beams Generalised Supports and Catenary Action SDOF Discretisation F(x): incremental static mode shape (dependent on response stage)

SDOF Models for Steel Beams Generalised Supports and Catenary Action Static Response Stages Up to 3 elasto-plastic response segments Order of plastic hinges: 3 generic and 3 derived cases Plastic bending followed by transient and final catenary stages Start of catenary stages determined by plastic interaction radius

SDOF Models for Steel Beams Generalised Supports and Catenary Action Order of Plastic Hinges Generic (and derived) cases identified by simple conditions

SDOF Models for Steel Beams Generalised Supports and Catenary Action Static/Dynamic Response Parameters Table extract for generic case B1

SDOF Models for Steel Beams Generalised Supports and Catenary Action Example: Set (1) Boundary Conditions I-beam: L=5m Left end: semi-rigid Right end: pinned No axial restraint

SDOF Models for Steel Beams Generalised Supports and Catenary Action Example: Set (1) Boundary Conditions Generic Case B3 governs: midspan→left plastic hinges Favourable comparison of static resistance against ADAPTIC

SDOF Models for Steel Beams Generalised Supports and Catenary Action Example: Set (2) Boundary Conditions I-beam: L=5m Left/right ends: pinned Semi-rigid partial-strength axial restraint

SDOF Models for Steel Beams Generalised Supports and Catenary Action Example: Set (2) Boundary Conditions Favourable comparison of static resistance against ADAPTIC Good prediction of plastic bending and catenary action

SDOF Models for Steel Beams Generalised Supports and Catenary Action Example: Set (2) Boundary Conditions Response under blast load: peak 2000kN, duration 100msec Good prediction of displacements and reactions Importance of catenary action

SDOF Models for Steel Beams Rate-Sensitivity Cowper-Symonds Model at Material Level Increased ‘dynamic’ yield strength at high strain-rates

SDOF Models for Steel Beams Rate-Sensitivity Transformation to Cross-Sectional Level Increased ‘dynamic’ plastic moment and axial force capacities in terms of rates of plastic curvature and centroidal axial strain

SDOF Models for Steel Beams Rate-Sensitivity Transformation to Member Level Increased ‘dynamic’ plastic moment and axial force capacities in terms of displacement rate

SDOF Models for Steel Beams Rate-Sensitivity Example: Set (2) Boundary Conditions Cowper-Symonds parameters: D=40sec-1, n=5 Good comparison against ADAPTIC Significance of material rate-sensitivity

SDOF Models for Steel Beams General Loading Configurations UDL, PT and 2PT Loading Initial static loads combined with dynamic blast load

SDOF Models for Steel Beams General Loading Configurations Example Initial static: UDL + PT[-L/6] Dynamic: 2PT Left/right ends: pinned Semi-rigid partial-strength axial restraint

SDOF Models for Steel Beams General Loading Configurations Example Good comparison against ADAPTIC Significance of catenary action

SDOF Composite Floor Model Composite Floor System under Blast Uplift Vulnerability to uplift Relevance to building response to global blast Secondary beams with simple connections Composite beam response Two-way action allowing for transverse slab contribution Not addressed by Biggs

SDOF Composite Floor Model Idealisation of Floor System Two typical floor systems Assumption of rigid support on boundary Uniformly distributed mass over floor area and secondary beam length Deformed configuration governed by secondary beam

SDOF Composite Floor Model Idealisation of Secondary Beam Simple connection offering moment resistance via axial spring Steel beam with effective slab width Effective axial restraint at centre of slab Pre- and post-cracking response, plastic bending resistance and catenary action

SDOF Composite Floor Model Example: Composite Secondary Beam (L=9m) Static response and dynamic response under UDL blast uplift: peak load = 900 kN, duration = 100 msec Good comparison of static and dynamic response against ADAPTIC

SDOF Composite Floor Model Example: Composite Floor System (II) Static response and dynamic response under UDL blast uplift: peak load = 1800 kN, duration = 100 msec Good comparison of static and dynamic response against ADAPTIC

MDOF Building Model Steel-Framed Building under Global Blast Response dominated by lateral displacements Allowance for rigid lateral resistance system(s) at specific longitudinal locations Beam deformations localised in connections Diaphragm action for floors and semi-rigid lateral resistance system Aggregate response of columns and connections over building depth Not addressed by Biggs

MDOF Building Model MDOF Grillage Representation Stiffness and strength for columns, connections and diaphragms P-D effects from gravity loading Transformation of MDOF model to interactive SDOF models via explicit time-integration Determination of lateral displacements at grillage nodes Efficient static condensation of nodal rotations to facilitate transformation to SDOF Evaluation of internal forces and reactions Not addressed by Biggs

MDOF Building Model Example: 3-Storey 4-Bay Building Global blast with duration of 100msec Excellent comparisons against similar grillage model using ADAPTIC Not addressed by Biggs

Conclusions New Generation of Simplified Structural Blast Models Combining efficiency and good accuracy SDOF Models for Steel Beams Addressing shortcomings of original Biggs models: i) generalised supports and catenary action, ii) rate-sensitivity, and iii) general loading Composite Floor (SDOF) and Building (MDOF) Models Incorporation in FABIG Technical Notes, SATEL Software and Recent Design Guidance Facilitating application in preliminary structural design and retrofitting for blast loading

A New Generation of Simplified Models for Steel and Composite Structures under Blast Loading Bassam A. Izzuddin* and Bassam A. Burgan† (*) Computational Structural Mechanics Group Department of Civil and Environmental Engineering Imperial College London, U.K. www.imperial.ac.uk/csm (†) The Steel Construction Institute, U.K. 12th International Conference on Shock & Impact Loads on Structures Singapore, 14-16 June 2017