Effect of Stress Amplitude on the Damping of Recycled Aggregate Concrete
Abstract
:1. Introduction
2. Theoretical Derivation
2.1. Material Damping Models
2.2. Member Model and Assumptions
- (1)
- The member is only loaded in the Y direction and bent in the XOY plane. The load types are arbitrary.
- (2)
- The cross section is symmetric about the Y-axis, and the bending stress is uniform along the Z-axis of the cross section. The cross section shape is arbitrary.
- (3)
- The transverse bending vibration is the member’s main vibration mode, and the influence of shear stress on damping is neglected.
- (4)
- The material is considered continuous and isotropic, and the bending stress amplitude is low.
2.3. Elastic Strain Energy of Member
2.4. Damping Energy of Member
2.5. Loss Factor of Member
Cross Section Forms | Values of |
---|---|
Rectangular Section | |
Circular Section | |
Symmetrical I-section | |
T-section |
Member’s Boundary Conditions | Load Types | Values of |
---|---|---|
Simply Supported | Concentrated Load at Mid-span | |
Simply Supported | Uniformly Distributed Load | |
Cantilever | Concentrated Load at Cantilever End | |
Cantilever | Uniformly Distributed Load | |
One End Clamped and Another End with Sliding Bearing | Concentrated Load at the End of Sliding Bearing |
2.6. Loss Tangent of Material
3. Experimental Investigation
3.1. Materials
3.1.1. Cement
SiO2 (%) | Al2O3 (%) | Fe2O3 (%) | CaO (%) | R2O (%) | Loss on Ignition (%) |
---|---|---|---|---|---|
18.73 | 5.88 | 3.37 | 61.89 | 0.54 | 3.03 |
3.1.2. Fine Aggregate
3.1.3. Coarse Aggregate
Types | Apparent Density (kg/m3) | Bulk Density (kg/m3) | Moisture Content (%) | Water Absorption (%) | Crushing Index (%) |
---|---|---|---|---|---|
NCA | 2561 | 1380 | 0.41 | 1.06 | 9.8 |
RCA | 2509 | 1253 | 2.19 | 5.48 | 15.6 |
3.1.4. Modified Materials
3.2. Specimen Preparation
- (1)
- The first group had three types of specimens, and it was used to study the effect of the RCA replacement ratio on the damping of concrete. Three RCA replacement ratios were considered, i.e., 0%, 30%, and 70%, and corresponding specimens were denoted as RCA-0, RCA-30, and RCA-70, respectively.
- (2)
- The second group also had three types of specimens, and it was used to study the effect of modified materials on the damping of concrete. The specimens were respectively modified by MSF + PF, RP + SF, and FA + US, and the corresponding specimens were denoted as RCA-MSF + PF, RCA-RP + SF, and RCA-FA + US, respectively.
Types | Cement | Water | Sand | NCA | RCA | Modifiers | AW | Water Reducer |
---|---|---|---|---|---|---|---|---|
RCA-0 | 410 | 205 | 625 | 1160 | 0 | 0 | 0 | 0 |
RCA-30 | 410 | 205 | 625 | 812 | 348 | 0 | 19 | 0 |
RCA-70 | 410 | 205 | 625 | 348 | 812 | 0 | 44 | 0 |
RCA-MSF + PF | 390 | 205 | 625 | 0 | 1160 | 20(MSF) + 1.2(PF) | 134 | 7.37 |
RCA-RP + SF | 410 | 205 | 575 | 0 | 1040 | 50(RP) + 120(SF) | 62 | 3.0 |
RCA-FA + US | 287 | 205 | 625 | 0 | 1160 | 82(FA) + 41(US) | 50 | 1.0 |
3.3. Testing Method
3.4. Experimental Results and Discussion
3.4.1. Compressive Strength and Split Tensile Strength
Specimens | RCA-0 | RCA-30 | RCA-70 | RCA-MSF + PF | RCA-RP + SF | RCA-FA + US |
---|---|---|---|---|---|---|
Compressive Strength/Standard deviation (MPa) | 50.4/1.6 | 48.8/1.8 | 47.0/0.4 | 30.4/1.5 | 24.9/1.1 | 36.6/1.4 |
Split Tensile Strength/Standard deviation (MPa) | 5.36/0.45 | 5.14/0.14 | 4.87/0.38 | 3.83/0.34 | 5.15/0.40 | 3.77/0.27 |
3.4.2. Loss Tangent and Elastic Modulus
Specimens | Loss Tangent (%) | Elastic Modulus (104 N/mm2) | ||||||
---|---|---|---|---|---|---|---|---|
50 N | 100 N | 150 N | 200 N | 50 N | 100 N | 150 N | 200 N | |
RCA-0 | 5.50 | 5.63 | 5.66 | 5.82 | 3.68 | 3.55 | 3.36 | 3.54 |
RCA-30 | 5.67 | 5.71 | 5.83 | 5.89 | 3.63 | 3.55 | 3.49 | 3.54 |
RCA-70 | 5.79 | 5.93 | 6.00 | 6.14 | 3.00 | 3.30 | 3.27 | 3.36 |
RAC-MSF + PF | 5.82 | 6.10 | 6.62 | 6.99 | 2.92 | 3.03 | 3.02 | 2.95 |
RAC-RP + SF | 8.58 | 9.31 | 9.72 | 9.95 | 2.77 | 2.87 | 2.75 | 2.97 |
RAC-FA + US | 7.55 | 7.88 | 8.28 | 8.58 | 3.59 | 3.08 | 3.29 | 3.06 |
3.4.3. Energy Coefficient and Exponent
Specimens | Damping Energy Coefficient J (×10−6 MPa−1) | Damping Energy Exponent n | Correlation Coefficient R2 |
---|---|---|---|
RCA-0 | 5.39 | 2.04 | 0.862 |
RCA-30 | 5.41 | 2.03 | 0.898 |
RCA-70 | 6.29 | 2.04 | 0.957 |
RCA-MSF + PF | 9.53 | 2.10 | 0.969 |
RCA-RP + SF | 13.04 | 2.14 | 0.996 |
RCA-FA + US | 8.73 | 2.14 | 0.937 |
4. Conclusions
Acknowledgments
Author Contributions
Conflicts of Interest
Notation
the cross section factor for the member’s loss factor | |
the length factor for the member’s loss factor | |
damping energy exponent | |
damping energy coefficient, MPa−1 | |
elastic modulus of material, MPa | |
the maximum stress of the member, MPa |
Appendix
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Liang, C.; Liu, T.; Xiao, J.; Zou, D.; Yang, Q. Effect of Stress Amplitude on the Damping of Recycled Aggregate Concrete. Materials 2015, 8, 5298-5312. https://doi.org/10.3390/ma8085242
Liang C, Liu T, Xiao J, Zou D, Yang Q. Effect of Stress Amplitude on the Damping of Recycled Aggregate Concrete. Materials. 2015; 8(8):5298-5312. https://doi.org/10.3390/ma8085242
Chicago/Turabian StyleLiang, Chaofeng, Tiejun Liu, Jianzhuang Xiao, Dujian Zou, and Qiuwei Yang. 2015. "Effect of Stress Amplitude on the Damping of Recycled Aggregate Concrete" Materials 8, no. 8: 5298-5312. https://doi.org/10.3390/ma8085242