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

1. EVALUATION OF DYNAMICALLY TESTED
CONCRETE BEAMS REINFORCED WITH
STIFF AND MILD STEEL QUALITIES
Viktor Peterson, PhD Student
Supervised by Anders Ansell and Mikael Hallgren

2. Background
2022-09-05
• Impulse-loaded structure must safely absorb the imposed energy
• For flexural failure modes this is mainly done by plastic straining of
the reinforcement
• The Swedish guidelines for protective concrete structures use data for
steel reinforcements used in the 1970s
• Modern steel reinforcement shows a smaller ultimate strength to yield
strength ratio, which was predicted to decrease the rotation capacity
• The effect of using modern reinforcement was tested experimentally
during dynamic and static testing
2

3. Energy absorption capacity of RC-members
2022-09-05
• The maximum work that may be done on the beam is:
• 𝑊
𝑚𝑎𝑥 = 𝐹𝑅𝑑
𝑢𝑒𝑙
2
+ 𝑢𝑅𝑑 − 𝑢𝑒𝑙 = 𝐹𝑅𝑑
𝑢𝑒𝑙
2
+ 𝑢𝑝𝑙
• During a flexural failure mode its either rupture of the reinforcement or crushing
of the concrete in the critical section that governs the displacement capacity 𝑢𝑅𝑑
• The significant part 𝑊
𝑚𝑎𝑥 is due to the plastic displacement 𝑢𝑝𝑙
3

4. Energy absorption capacity of RC-members
2022-09-05
• Eurocode 2 uses a simple model with a discrete plastic hinge
• where the maximum plastic displacement may be determined from the rotation
capacity: 𝑢𝑝𝑙,𝑚𝑎𝑥 = 𝑙0𝜃𝑝𝑙,𝑅𝑑
• However, the beam actually responds with a distributed yield
zone 𝑙𝑝𝑙 at the displacement capacity. This since the yielding
moment 𝑀𝑦 is reached for many sections
• Both the rotation capacity and accumulated plastic curvature along the yield zone are
therefore important for the maximum plastic displacement
4

5. Aims of the study
2022-09-05
• Study the plastic strain levels in the reinforcement during dynamic and
static loading
• Indication of the rotation capacity
• Study the plastic strain distribution in the reinforcement during dynamic
and static loading
• Indication of accumulated plastic curvature of several sections, and
therefore the plastic displacement level
5

6. Test series and tensile testing
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• B500BT type 1 shows a yield plateau (mild)
• Ps50 shows no yield plateau (stiff)
• Both qualities of reinforcement class C
𝑓𝑢
𝑓𝑦
≥ 1.15

7. Static test set-up
2022-09-05
• Four-point bending
• 300 x 150 mm rectangular cross-section (plate strip)
• Free length: 1500 mm
• 2ϕ8 tensile reinforcement used for the configurations compared
7

8. Static response of the beams
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• B500BT beam deformed to almost failure
• Ps50 beam deformed to reinforcement
rupture
• Maximum deflection under load
application (a third of length from support):
• B500BT: 33 mm
• Ps50: 14 mm

9. Dynamic test set-up
2022-09-05
• “Dynamic four-point bending”
• Steel mass of 300 kg dropped: Initial velocity = 2.0 m/s (assuming plastic collision)
• Drop height determined from static deformation capacity of plate strips with B500BT: 20
mm maximum displacement should be reached, i.e. close to failure (Protection class C)
• This resulted in a drop height of 400 mm
9
Equivalent to the initial velocity of the plate subjected to
airblast from the detonation of 100 kg TNT, 10 m from the wall
(small aerial bomb)

10. 2022-09-05
Dynamic response of the beam with B500BT
10
Measured signal,
vibration of the
displacement sensor
Integrated from
acceleration
signal
• Maximum displacement almost
20 mm!
• Has not reached failure

11. 2022-09-05
Plastic strain measurements after static test
11
• Marking every 50 mm of tensile reinforcement before testing. Elongation measured after
loading has been removed. Results are therefore average strain in each 50 mm span
• Max strain: N = 8 %, S = 8 %
• Sum. strain: N = 40.16 %, 45.19 %
• Max strain: N = 11 %, S = 11 %
• Sum. strain: N = 31 %, 23 %
• Rupture strain: N = 11 %, S = 11 %

12. 2022-09-05
Explanation for the static results
12
Johansson, M., Hallgren, M., Ansell, A., Leppänen, J. “Plastisk
deformationsförmåga och tvärkraftsrespons hos impulsebelastade
betongkonstruktioner”. Chalmers University of Technology, Göteborg,
Sweden, 2021
Softer!
Softer!
Stiffer!
• Moment is the same between the concentrated forces, but not curvature! Different steel
strain for each section
• This is due to tension stiffening and statistical effects (weak sections)
• Stiffening of mild steel (B500B) is favourable
• Allows propagation of a yield zone as the
sections stiffen

13. 2022-09-05
Explanation for the static results
13
• Both beams have similar yield loads
• To increase the load beyond the yield load a
lot of deformation is needed for the beam
containing mild steel
• This due to propagation of the yield zone
due to hardening of the steel (forming
plastic curvature at many sections)
• The beam containing stiff steel instead
increases in load instantaneously due to
forming a localized plastic hinge in the
softest section, with the largest
reinforcement strain

14. 2022-09-05
Plastic strain measurements after dynamic test
14
• Max strain: N = 10 %, S = 8 %
• Sum. strain: N = 27 %, 28 %
• Max strain: N = 10 %, S = 10 %
• Sum. strain: N = 24 %, 23 %
• Rupture strain: N = 10 %, S = 10 %
• Both tested at 400 mm drop height. Strain is now localized also using mild steel

15. 2022-09-05
Comparison dynamic and static response
15
• Mild steel beam responds similar to stiff steel beam during dynamic loading
Static loading: Dynamic loading:

16. 2022-09-05
Explanation for differences
16
Static loading:
Dynamic loading:
• The inertia forces result in a different moment distribution!
• Acceleration field assumed from a rigid-plastic model

17. 2022-09-05
Explanation for differences
17
• Wave propagation effects. All of the structure does not know of the load before it
changes
• Will be studied in a later project

18. 2022-09-05 18
Thanks for listening!