PSI - Issue 81

Olena Romashko-Maistruk et al. / Procedia Structural Integrity 81 (2026) 310–315

314

1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8

1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8

a)

b)

Relative valuesM d /M, DIF c , DIF y

Relative valuesM d /M, DIF c , DIF y

DIFc DIFy Md/M

DIFc DIFy Md/M

-8

-6

-4

-2

0

2

4

-8

-6

-4

-2

0

2

4

log έ

log έ

Fig. 2. The influence of the dynamic increase factors of tensioned reinforcement DIF y according to CEB Bulletin 187 (1988) (a) and according to Malvar (1998) (b), together with the dynamic increase factor of compressed concrete DIF c according to expression (7), on the relative strength M d /M of heavily reinforced (A s =2520 mm 2 ) elements subjected to bending at different strain rates. Similar calculations of these same bending elements were performed under dynamic loads according to fib (2012). Their results, as well as the results according to the above-developed express methodology, are included in Table 1.

Table 1. Relative bending strength of elements M d /Mat strain rate   =10 3 s -1

Relative strength M d /Mat DIF y values 1.14 1.23

Reinforcement ratioµ s

DIF c

Method

0.006 0.033

1.15 1.22 1.29 1.18 1.41 1.66

1.24 1.29 1.34 1.27 1.52 1.78

authors'

1.74

0.05

0.006 0.033

fib (2012)

3.89

0.05

Analysis of these results shows that the DIF y of reinforcement has a decisive influence on the change in the strength of reinforced concrete elements under the action of dynamic loads. It was also established that at the strain rate 1 30 −  c c   the fib (2012) method significantly overestimates the relative strength of reinforced concrete elements, and at the strain rate 1 30 −  c c   , on the contrary, it significantly underestimates it. The reason for this is the insufficiency of experimental and the absence of any analytical substantiation of the dependences of the DIF c of concrete. In addition, the rejection of the dependences of the DIF c of concrete on the CEB-FIP (1991) completely eliminated the influence of plastic deformations (class) of concrete on the change in the strength of reinforced concrete elements under the action of dynamic loads. This is absolutely inconsistent with the publicly available results of experimental studies. Also, the fib (2012) method requires numerous iterative operations, which prevents its application in approximate express methods. Therefore, it is better to implement it using the finite element method (Mathern and Yang (2021), Kononchuк et al. (2022) ). But without sufficient experimental and analytical substantiation of the dependences of the DIF of materials (concrete and reinforcement), even this will not allow for proper prediction of the stress-strain state of reinforced concrete elements under the action of dynamic loads. The main advantage of the method proposed by the authors is that, by supplementing the system of equations (2) with additional dependencies (3) - (10), it can be implemented using the simplest engineering programs and methods even without iterations. This is facilitated by analytically derived dependences for the DIF c and other deformation characteristics of concrete. 4. Conclusions The degree of increase in the strength of flexural reinforced concrete elements under dynamic (explosive) loads, M d /M depends to a greater extent on the dynamic increase factor of the reinforcement DIF y, than on the dynamic increase factor of the concrete DIF c . The influence of the dynamic increase factor of the concrete DIF c on the increase in the strength of flexural reinforced concrete elements under dynamic loads M d /M increases with an increase in the reinforcement ratio µ s . If the relationship between the dynamic increase factor of the concrete DIF c and the deformation rate is nonlinear, then the relationship between the dynamic