3.3. Mechanical Properties of Reinforced Concrete
3.3.3. Concrete, under Plane Stress Condition
Finite element method (FEM) in the inelastic range became recently a popular and useful analytical tool for researchers of reinforced concrete. It was considered to be an effective method to fill up gaps between experimental data in the New RC project, as the number of laboratory test specimens had always to be limited because of financial reasons. As FEM was to be used extensively
in the New RC project, constitutive equations of high strength concrete under biaxial compression was vitally needed.
3.3.3.1. Biaxial Loading Test of Plain Concrete Plate
Tests were conducted using plain concrete plate of 200 mm square with 50 mm thickness, the same size as those tested by Kupfer et aL (Ref. 3.9). Concrete with compressive strength ranging from 60 to 65 MPa was used. Biaxial com- pression load was applied, as shown in Fig. 3.53, through three layers of t e l o n sheet and cup grease to avoid deformation confinement due to friction on the loading surface.
Figure 3.54 shows comparison of the failure criterion of 62 MPa concrete for various stress ratio 0*2/^l- Also shown in the figure is the failure criterion of 30 MPa concrete, expressed by the full line curves. For high strength con- crete, the ultimate strength for each stress ratio exceeded uniaxial compressive strength, and it became largest, 37.5 percent greater than uniaxial strength, for stress ratio between 0.2 and 0.52. When stress ratio a%l<J\ was equal to 1, on the other hand, strength increase over uniaxial strength was only 2.5 percent.
Thus the trend of strength increase due to biaxial compression for high strength concrete is different from that for normal strength concrete. A new equation for failure criterion of high strength concrete derived from the test is the following.
Fig. 3.53. Biaxial loading method for plain concrete plate.
-1.6 -1.4 -1.2 -1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2
Fig. 3.54. Failure criterion of high strength concrete under biaxial compression.
For - 0 . 8 3 ^cn/U^O
307!/7co)(<Tl/'fee + 1) - 2 ( < 71/ /c o + 1) = 0 . (3.27) For -1.025 S cri/fco < - 0 . 8 3
(ai/fco) + [ptlfco) + 2-041 = 0 (3.28) where <j\ and cr2 are principal stresses in compression under plane stress con-
dition and are interchangeable, and fco is the uniaxial compressive strength of the plate.
3.3.3.2. Tests of Reinforced Concrete Plate under In-plane Shear
Figure 3.55 shows a reinforced concrete plate specimen subjected to in-plane pure shear loading. Twelve specimens, 600 mm square and 80 mm thick, with doubly orthogonal reinforcement, were made using 40, 70 and 100 MPa con- crete, and tested under pure shear loading to examine the effect of concrete strength, reinforcement ratio, steel yield strength, and unequal steel amount in two directions, on the ultimate strength, cracking, stress-strain relationship and mode of failure.
Fig. 3.55. Specimen of reinforced concrete plate subjected to in-plane shear.
Cracking stress was approximately 0 . 3V/ O B where OB is compressive strength in MPa. With the increase of reinforcement the shear strength in- creased while deformation capacity was reduced. When the amount of re- inforcement exceeded certain value concrete started to crush, and ultimate strength increased more slowly with the increase of reinforcement. For higher strength concrete, the tension stiffening was decreased, and effective strength of concrete was also reduced, down to about 0.35 to 0.4 for 100 MPa concrete.
These test data are useful for the calibration of FEM softwares.
In the course of New RC project, standard formulation of constitutive equa- tions for high strength concrete and high strength steel, including confined concrete, was compiled as a guideline for FEM users. This guideline will be explained in Chapter 5 of this book.
References
3.1. Nagataki, S., Research on high strength concrete and its application (in Japanese), Proc. Japan Concrete Institute Annual Convention 10(1), 1988, pp. 61-68.
3.2. Fukuzawa, K., High strength concrete (in Japanese), Mod. Concrete Technol.
Ser., Sankaido, 8, 1987, p. 93.
3.3. Uchiyama, H., Toshisuke, H. and Daisuke, S., Evaluation of transition zone thickness of hardened mortar and concrete and relationship between transition
zone thickness and compressive strength (in Japanese), Trans. Japan Concrete Institute 4(2), 1993, pp. 1-8.
3.4. Morita, S. and Hitoshi, S., Development of high strength mild steel deformed bars for high performance reinforced concrete structural members, Proc, 11th
World Conference on Earthquake Engineering, Paper No. 1742, Acapulco, Mexico, 1996.
3.5. Design guidelines for earthquake resistant reinforced concrete buildings based on ultimate strength concept (in Japanese), Arch. Inst. Japan, November 1990, p. 340.
3.6. Sargin, M., Ghosh, S.K. and Handa, V.K., Effect of lateral reinforcement upon the strength and deformation properties of concrete, Mag. Concrete Res. 2 3 , June 1971, pp. 99-100.
3.7. Popovics, S., Numerical approach to complete stress-strain curve of concrete, Cement Concrete Res. 3, 1973, pp. 583-599.
3.8. Sun, Y. and Sakino, K., Flexural behavior of reinforced concrete columns con- fined in square steel tube, Proc. 10th World Conference on Earthquake Engi- neering, Madrid, Spain, 1992, pp. 4365-4370.
3.9. Kupfer, H. and Hilsdorf, H.K., Behavior of concrete under biaxial stresses, ACI J. 66(8), August 1969, pp. 656-666.
New R C Structural Elements
Takashi Kaminosono
Associate Director, Codes and Evaluation Research Center,
Building Research Institute, Ministry of Land, Infrastructure and Transport, 1 Tachihara, Tsukuba, ttarahi 305-0802, Japan
E-mail: kamino@kenken.go.jp