1. 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.
(†) The Steel Construction Institute, U.K.
12th International Conference on
Shock & Impact Loads on Structures
Singapore, June 2017

2. 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

3. Introduction Blast assessment for structural safety
Accidental vs intentional blast
Blast can also arise from terrorist activity, but concern here is with blast loading is reasonably predictable

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

5. 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

6. 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

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

8. 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

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

10. 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

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

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

13. 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

14. 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

15. 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

16. 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

17. 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

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

19. 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

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

21. 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

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

23. 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

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

25. 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

26. 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

27. 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

28. 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

29. 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

30. 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

31. 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

32. 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

33. 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

34. 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.
(†) The Steel Construction Institute, U.K.
12th International Conference on
Shock & Impact Loads on Structures
Singapore, June 2017