Presented at the XXIV Nordic Concrete Research Symposium in Stockholm, August 17-19, 2022.

1. Shear in Concrete Structural Elements
Subjected to Dynamic Loads
Johan Magnusson, Senior Advisor FORTV
Anders Ansell, Prof. KTH
Mikael Hallgren, Adj. Prof. KTH
Richard Malm, Researcher FOI (previously KTH) XXIV NCR Symposium 2022-08-17
Swedish Fortifications Agency

2. 2 (18)
Presentation
Doctoral thesis from 2019 at KTH Royal
Institute of Technology
Department of Civil and Architectural Engineering
Division of Concrete Structures
2

3. Overview
 Background: Explosions and shear failures
 Experimental programs
 Analyses of experiments
 Parametric study
 Conclusions & further research
3 (18)

4.  Increase the understanding of shear in concrete structural elements
subjected to explosions
 The loads simplified as uniformly distributed
 Beams and slabs analysed 1:2 scale
Aim and scope
4 (18)

5.  “Explosions can be both awesome and devastating” (Kinney & Graham, 1985)
 Explosions generate a shock wave (blast wave)
 The blast wave propagates at supersonic speed in all directions
Shock front
Ground surface
Explosions and shear failures
5 (18)

6.  The blast wave profile
 The blast load parameters:
- peak pressure
- duration
 An equivalent triangular blast wave in
design and parametric studies
Explosions and shear failures
6 (18)

7.  Explosions at close range high pressures
 Such loads can cause shear failures
Blast load
Explosions and shear failures
7 (18)

8.  Shear is a brittle failure
 Limited energy absorption capabilities
 Shear failures appear in regions with high shear stresses
Explosions and shear failures
a
d
F F
a a
F
(a) (b)
a
d
F F
a
F
a
F
a
8 (18)

9. General approach
1) Simulations (Abaqus/Explicit) with test results as reference
2) The evolution of shear failures analysed
3) A separate parametric study using Abaqus/Explicit
Experiments and analyses
9 (18)

10.  Experiments in a shock tube (FOI)
 High explosive charge
 Beam cross-section 290  160 mm2
 Measurements of load and
beam response
Experiments (1) – dynamic tests on beams
10 (18)

11.  Flexural shear failure
 Evolution of tensile damage (cracks)
 Initial flexural response
Analyses of experiments (1)
11 (18)

12.  Tests by Slawson (1984)
 Slab 1500  184 mm2
 Blast pressures across roof slab from high
explosives charges
 Measurements of loads and slab response
Experiments (2) – dynamic tests on slabs
12 (18)

13.  The roof slab separated from the
walls in several tests
Experiments (2) – dynamic tests on slabs
Failed slabs
13 (18)

14. Analyses of experiments (2)
 Direct shear failure
 Inclined compression struts at supports
 Crushing of the struts
 A ”straight” central part of the slab
14 (18)

15. Parametric study
 3 different beam depths –
260 mm, 160 mm and 84 mm
 2 different reinforcement ratios
 Simply supported; 1500 mm span
(a) B7(2) (b) B7(5)
(a) B12(2) (b) B12(5)
(a) B27(2) (b) B27(5)
Beam type h (m) d (m) L/d Reinforcement  (%)
B7(2)
0.260 0.228 6.6
216 0.59
B7(5) 516 1.47
B12(2)
0.160 0.128 11.7
212 0.59
B12(5) 512 1.47
B27(2)
0.084 0.056 26.8
28 0.60
B27(5) 58 1.50
15 (18)

16. Parametric study
 Somplified triangular load
 Uniformly distributed load
 Variations of peak pressure
and duration
Pressure
Time (ms)
p(t)
16 (18)

17. Conclusions
 Shear is controlled by
- peak pressure
- load duration
- structural stiffness
 Flexural shear flexural cracks shear cracks
 Indicates that the same calculation model as in static shear may be used
 Direct shear crushing/splitting of compression struts
 Indicates that strut-and-tie models can be used
 A size effect appears to exist in dynamic shear (similar to static shear) 17 (18)

18. Further research
 Extended simulations with varying
- span-to-depth ratios
- support conditions
- load levels and durations
- load distributions
- other material models for concrete
 Extended experimental program
 Further analyses and development of design tools
18 (18)

19. Acknowledgements
This research was financially supported by:
- Swedish Defence Research Agency (FOI)
- the Swedish Armed Forces Headquarters
- Fortifikationskåren
- KTH Royal Institute of Technology (Dept. of Civil and Architectural Eng., Div. of
Concrete Structures)
- Grontmij
- RISE Research Institutes of Sweden
- Swedish Fortifications Agency
Their support is greatfully acknowledged.

20. Doctoral thesis
The doctoral thesis can be found on the Department of Civil and Architectural
Engineering homepage:
https://www.byv.kth.se/en/publ/doktorsavhandlingar-1.758851
Magnussson, J. (2019). Shear in Concrete Structural Elements Subjected to
Dynamic Loads. PhD Thesis. Stockholm: KTH Royal Institute of Technology,
Sweden.

21. Thank you for your attention!
Questions?
XXIV NCR Symposium 2022-08-17
Swedish Fortifications Agency