Bond Modelling for the Assessment of Transmission Length in Prestressed-Concrete Members
Abstract
1. Introduction
2. Roles of the Major Parameters Affecting the Transmission Length
3. Analytical Modelling of the Transmission Length
3.1. General Calculation Procedure
3.2. Elastic Analysis Based on the Thick-walled Cylinders Theory
3.3. Anisotropic Analysis for Cracked Concrete
4. Model Calibration and Results
4.1. Global Behaviour: Transmission Length Assessment
4.2. Local Behaviour: Radial Cracking and Bond Stress Development
5. Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
Statement of Data Availability
Nomenclature
Ac | Cross-sectional area of concrete |
Asp | Cross-sectional area of prestressing tendon |
b | Width of the concrete section |
c | Concrete cover thickness |
, | Constants of integration for the solution of u |
Ec | Elastic modulus of concrete |
Eps | Elastic modulus of prestressing steel |
e | Vertical eccentricity of the considered tendon with respect to the centre of gravity of the concrete section |
h | Height of the concrete section |
Jx | Moment of inertia of the concrete section |
Lt | Transmission length of the prestressing tendon |
Lt, experimental | Experimental value of the transmission length |
Lt, theoretical | Theoretical value of the transmission length |
lbp | Basic anchorage length according to fib MC2010 |
P | Initial prestressing-force in the tendon |
r | Radial distance from the tendon centroid |
rjack | Radius of the tendon after release |
rps | Radius of the unstressed tendon |
rtip | Distance from the tendon centroid to the crack tip |
u | Radial displacement |
uc | Radial displacement of the concrete |
ups | Radial displacement of the tendon outer surface |
y | Vertical distance from the centre of gravity of the concrete section |
z | Length of the single finite element in which the prestressing tendon is subdivided |
z | Longitudinal distance from the free-end of the PC member |
αp1 | Coefficient which takes into account the prestress release method, according to fib MC2010 |
αp2 | Coefficient which takes into account the action effect to be verified, according to fib MC2010 |
αp3 | Coefficient which takes into account the influence of bond situation, according to fib MC2010 |
αrel | Coefficient which takes into account the prestress release method, according to the findings proposed by the authors |
Concrete strain (assumed as 0.0003) corresponding to concrete tensile stress equal to 0.15 , according to Han’s softening model | |
Cracking strain of concrete | |
Concrete strain in the radial direction | |
Concrete strain in the circumferential direction | |
Concrete axial strain at the level of the tendon centroid | |
Ultimate concrete strain (assumed as 0.002) corresponding to concrete tensile stress equal to zero, according to Han’s softening model | |
ηp1 | Coefficient which takes into account the type of tendon, according to fib MC2010 |
ηp2 | Coefficient which takes into account the position of the tendon, according to fib MC2010 |
Overall friction coefficient between the tendon and the surrounding concrete, combining actual frictional and mechanical bond | |
Poisson’s ratio of the concrete | |
Poisson’s ratio of the prestressing steel | |
Prestress transfer bond at the interface tendon-concrete | |
Concrete radial stress | |
Concrete circumferential stress | |
Concrete axial stress | |
Tensile strength of concrete | |
Design tensile strength of the prestressing steel | |
Tendon radial stress | |
(rjack) | Radial compressive stress at the interface between steel and concrete, arising from the Hoyer effect |
Increment in tendon stress resulting from the development of bond stress along the finite element | |
Tendon stress at the considered point along the length of the member | |
Jacking stress of the tendon at prestressing-force release | |
φ | Nominal tendon diameter |
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---|---|
Mitchell et al. (1993) [15] | 14 |
Russell and Burns (1996) [24] | 20 |
Russell and Burns (1997) [28] | 12 |
Oh and Kim (2000) [11] | 36 |
Oh et al. (2006) [16] | 24 |
Martì-Vargas et al. (2007) [29] | 12 |
Dang et al. (2017) [30] | 12 |
Friction Coefficient | AVE | COV | RMSE |
---|---|---|---|
= 0.3 | 2.10 | 1.15 | 755.57 |
= 0.4 | 1.62 | 0.67 | 439.31 |
= 0.5 | 1.30 | 0.36 | 232.72 |
= 0.6 | 1.07 | 0.18 | 139.20 |
= 0.7 | 0.92 | 0.16 | 154.16 |
= 0.8 | 0.81 | 0.23 | 207.22 |
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Fabris, N.; Faleschini, F.; Pellegrino, C. Bond Modelling for the Assessment of Transmission Length in Prestressed-Concrete Members. CivilEng 2020, 1, 75-92. https://doi.org/10.3390/civileng1020006
Fabris N, Faleschini F, Pellegrino C. Bond Modelling for the Assessment of Transmission Length in Prestressed-Concrete Members. CivilEng. 2020; 1(2):75-92. https://doi.org/10.3390/civileng1020006
Chicago/Turabian StyleFabris, Nicola, Flora Faleschini, and Carlo Pellegrino. 2020. "Bond Modelling for the Assessment of Transmission Length in Prestressed-Concrete Members" CivilEng 1, no. 2: 75-92. https://doi.org/10.3390/civileng1020006
APA StyleFabris, N., Faleschini, F., & Pellegrino, C. (2020). Bond Modelling for the Assessment of Transmission Length in Prestressed-Concrete Members. CivilEng, 1(2), 75-92. https://doi.org/10.3390/civileng1020006