Time-Dependent Behavior of Reinforced Polymer Concrete Columns under Eccentric Axial Loading
Abstract
:1. Introduction
2. Mechanical Model
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- the generic plane cross-sections still lie within the plane after bending;
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- perfect adhesion exists between the polymer concrete and rods;
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- the external axial force, Next, and the bending moment, Mext, are constant over time;
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- there is no difference between the tensile and compressive stiffness/strength of a given material;
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- the behavior of the polymer concrete is linear-viscoelastic;
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- no cracks are present;
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- the behavior of the reinforcement bars is linear-elastic;
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- the internal reinforcing bars make no contribution to creep.
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- G* indicates the centroid of the transformed cross-section, assumed as the origin of the x and y axes (Figure 1);
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- and denote the instantaneous values of the axial strain in the polymer concrete and the reinforcing bars, respectively, according to the following relationships (Figure 1):
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- λ(t) and µ(t) are the axial strain at G* and the cross-sectional curvature, respectively;
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- is the ordinate of the centroid of the generic bars;
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- and are the elastic polymer concrete and bar strains, respectively; and
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- is the viscous contribution to the polymer concrete strain.
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- A* = Ac + nbAbc + nbAbt is the area of the transformed section;
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- I* = Ic + nbIbc + nbIbt is the moment of inertia about the x axis of the transformed section;
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- nb = Eb/Ec;
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- Ic, Ibc and Ibt are the moments of inertia about the x axis of the polymer concrete, the top reinforcement bars and the bottom reinforcement bars, respectively.
3. Numerical Analysis
Bar ID | Material | Φb (mm) | Eb (GPa) | fb (MPa) |
---|---|---|---|---|
SI | Steel | 8 | 210.00 | 450.00 |
SII | Steel | 10 | 210.00 | 450.00 |
SIII | Steel | 12 | 210.00 | 450.00 |
SIV | Steel | 16 | 210.00 | 450.00 |
CI | CFRP | 8 | 115.00 | 2000.00 |
CII | CFRP | 10 | 115.00 | 2000.00 |
CIII | CFRP | 12 | 115.00 | 2000.00 |
CIV | CFRP | 16 | 115.00 | 2000.00 |
GI | GFRP | 8 | 40.00 | 1000.00 |
GII | GFRP | 10 | 40.00 | 1000.00 |
GIII | GFRP | 12 | 40.00 | 1000.00 |
GIV | GFRP | 16 | 40.00 | 1000.00 |
Binder Type | Mix Fraction (% of aggregate to polymer binder) | Ec (GPa) | fc (MPa) |
---|---|---|---|
Alkali sodium silicate-activated coal, combustion fly ash and slag | 23% Fine natural dune sand 29% 9 mm greywacke 18% 14 mm greywacke | 10.00 | 41.50 |
E1 (GPa) | E2 (GPa) | E3 (GPa) | η1 (GPa d) | η2 (GPa d) | η3 (GPa d) |
---|---|---|---|---|---|
7.38 | 0 | 0 | 5.47 × 102 | 0 | 0 |
Bar ID | σcs(0) (MPa) | σcs(10000 d) (MPa) | ∆σcs/σcs(0) (%) | σcs(0) (MPa) | σcs(10000 d) (MPa) | ∆σcs/⎕σcs(0) (%) |
---|---|---|---|---|---|---|
SI | −0.93 | 0.38 | −140.57 | −0.14 | 0.77 | −643.20 |
SII | −0.90 | 0.38 | −141.90 | −0.16 | 0.75 | −579.62 |
SIII | −0.87 | 0.38 | −143.39 | −0.17 | 0.72 | −524.66 |
SIV | −0.79 | 0.38 | −146.65 | −0.19 | 0.66 | −441.15 |
CI | −0.96 | 0.38 | −139.43 | −0.13 | 0.80 | −714.37 |
CII | −0.94 | 0.38 | −140.21 | −0.14 | 0.78 | −663.48 |
CIII | −0.92 | 0.38 | −141.13 | −0.15 | 0.76 | −614.35 |
CIV | −0.87 | 0.38 | −143.27 | −0.17 | 0.72 | −528.72 |
GI | −0.99 | 0.37 | −137.13 | −0.12 | 0.80 | −779.79 |
GII | −0.98 | 0.38 | −138.64 | −0.12 | 0.1 | −764.35 |
GIII | −0.97 | 0.38 | −139.10 | −0.13 | 0.80 | −737.21 |
GIV | −0.95 | 0.38 | −139.98 | −0.14 | 0.78 | −677.76 |
Bar ID | σcs(0) (MPa) | σcs(10000 d) (MPa) | ∆σcs/σcs(0) (%) | σcs(0) (MPa) | σcs(10000 d) (MPa) | ∆σcs/σcs(0) (%) |
---|---|---|---|---|---|---|
SI | −6.30 | −414.47 | 6473.95 | −24.34 | −580.25 | 2284.10 |
SII | −6.54 | −265.26 | 3941.06 | −23.56 | −371.36 | 1476.37 |
SIII | −6.82 | −184.21 | 2602.65 | −22.69 | −257.89 | 1036.53 |
SIV | −7.23 | −103.62 | 1333.60 | −20.82 | −145.06 | 596.60 |
CI | −3.21 | −414.47 | 12401.80 | −13.70 | −580.25 | 4134.80 |
CII | −3.41 | −265.26 | 7676.02 | −13.44 | −371.36 | 2662.20 |
CIII | −3.51 | −184.21 | 5141.24 | −13.15 | −257.89 | 1861.59 |
CIV | −3.72 | −103.62 | 2684.02 | −12.47 | −145.06 | 1063.74 |
GI | −1.11 | −408.40 | 36703.60 | −4.88 | −574.19 | 11674.90 |
GII | −1.12 | −264.93 | 23483.60 | −4.84 | −371.03 | 7561.91 |
GIII | −1.14 | −184.20 | 16066.90 | −4.80 | −257.88 | 5270.21 |
GIV | −1.18 | −103.62 | 8705.11 | −4.70 | −145.06 | 2298.44 |
4. Conclusions
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- the stress variations over time within the reinforcement bars may lead to the failure of a structural member because the stresses in the rods approach the available strength (see the analysis concerning a beam reinforced with 8-mm steel bars), thus compromising the safety of the entire structure;
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- the long-term displacements of a structural member may produce, in hyperstatic frames, noticeable stress redistributions due to the continuity conditions, thus affecting the stress state in the entire structure;
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- better deferred behavior of a reinforced polymer concrete column can be expected as the Young’s modulus and overall area of the internal rebars increase.
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Berardi, V.P.; Mancusi, G. Time-Dependent Behavior of Reinforced Polymer Concrete Columns under Eccentric Axial Loading. Materials 2012, 5, 2342-2352. https://doi.org/10.3390/ma5112342
Berardi VP, Mancusi G. Time-Dependent Behavior of Reinforced Polymer Concrete Columns under Eccentric Axial Loading. Materials. 2012; 5(11):2342-2352. https://doi.org/10.3390/ma5112342
Chicago/Turabian StyleBerardi, Valentino Paolo, and Geminiano Mancusi. 2012. "Time-Dependent Behavior of Reinforced Polymer Concrete Columns under Eccentric Axial Loading" Materials 5, no. 11: 2342-2352. https://doi.org/10.3390/ma5112342