- Open Access

# The Use of Advanced Optical Measurement Methods for the Mechanical Analysis of Shear Deficient Prestressed Concrete Members

- K. De Wilder
^{1}Email author, - G. De Roeck
^{2}and - L. Vandewalle
^{1}

**10**:135

https://doi.org/10.1007/s40069-016-0135-x

© The Author(s) 2016

**Received:**24 November 2015**Accepted:**26 February 2016**Published:**18 March 2016

## Abstract

This paper investigates on the use of advanced optical measurement methods, i.e. 3D coordinate measurement machines (3D CMM) and stereo-vision digital image correlation (3D DIC), for the mechanical analysis of shear deficient prestressed concrete members. Firstly, the experimental program is elaborated. Secondly, the working principle, experimental setup and corresponding accuracy and precision of the considered optical measurement techniques are reported. A novel way to apply synthesised strain sensor patterns for DIC is introduced. Thirdly, the experimental results are reported and an analysis is made of the structural behaviour based on the gathered experimental data. Both techniques yielded useful and complete data in comparison to traditional mechanical measurement techniques and allowed for the assessment of the mechanical behaviour of the reported test specimens. The identified structural behaviour presented in this paper can be used to optimize design procedure for shear-critical structural concrete members.

## Keywords

- experimental mechanics
- prestressed concrete
- coordinate measurement machine
- stereo-vision digital image correlation

## 1 Introduction

Despite the long-established and worldwide research effort, a widely accepted theory for determining the shear capacity of a structural concrete member remains open for discussion (Balázs 2010; Collins 2010). This can be mainly attributed to the complex nature of shear in structural concrete. Indeed, after the occurrence of inclined cracking, various shear transfer mechanisms are activated (Jeong and Kim 2014). The aforementioned mechanisms are interrelated and highly susceptible to various parameters such as the geometry, the amount of prestressing, material properties, the amount and type of shear and longitudinal reinforcement and the loading conditions. As a consequence, numerous analytical modelling approaches can be found in literature. An overview of recent approaches to shear in structural concrete elements can be found in Fédération Internationale du Béton (fib) (2010).

The on-going debate on how to deal with shear in structural concrete members is also reflected by current codes of practice (European Committee for Standardization 2004; Canadian Standards Association 2004; American Concrete Institute 2011) which propose different design provisions resulting in varying design shear capacities and take factors affecting the shear capacity into account in a different way. Due to our incomplete knowledge and the brittle failure modes typically associated with shear, current codes of practice generally propose highly conservative shear provisions, specifically in the case of prestressed concrete elements (Nakamura et al. 2013). For the design of structural concrete members, these design equations lead to excessive material usage and corresponding construction costs. Reversely, using current codes of practice to determine the shear capacity, existing concrete structures are often found to be unable to withstand the applied service loads whereas no structural problems are reported in reality (Valerio et al. 2011; Lantsoght et al. 2013).

Improving analytical modelling approaches for shear in structural concrete members thus remains of utmost importance to optimize the design and analysis of structural concrete elements. A prerequisite for developing suitable models is a clear understanding of the actual mechanical behaviour observed during experimental tests. Traditional measurement techniques, i.e. linear variable differential transformers (LVDTs) or demountable mechanical strain gauges (DEMEC), usually provide limited test data in one or two directions. If the actual mechanical behaviour is to be understood, more elaborate experimental data is required. This paper therefore investigates on the use of advanced optical measurement methods, i.e. 3D coordinate measurement machines (CMMs) and Stereo-vision digital image correlation (3D DIC), for the mechanical analysis of shear-deficient structural concrete elements. The main focus in this paper will be on prestressed concrete beams. Firstly, the experimental program is elaborated. Secondly, the adopted measurement methods are presented and their corresponding setup is described. Thirdly, the experimental results are presented including the results of the precision assessment of the measurements and the full-scale experimental results. Finally, the mechanical behaviour of the reported test beams is investigated based on the acquired measurement data and compared to current modelling approaches found in codes of practice.

## 2 Experimental Research

### 2.1 Geometry and Materials

Concrete material properties for reported specimens.

Specimens | \(f_{cm,cube}\) (MPa) (\(\#\)*, s**) | \(f_{cm}\) (MPa) (\(\#\), s) | \(E_{cm}\) (GPa) (\(\#\), s) | \(f_{ctm,fl}\) (MPa) (\(\#\), s) | Age (days) |
---|---|---|---|---|---|

B101-B103 | 87.1 (8, 6.8) | 77.5 (5, 10.7) | 43.4 (3, 2.3) | 5.8 (6, 0.6) | 28-233-393 |

B104-B106 | 82.8 (9, 10.5) | 88.9 (6, 10.2) | 43.5 (6, 8.0) | 6.5 (6, 1.0) | 412-404-407 |

B107-B109 | 74.6 (9, 9.6) | 89.3 (6, 14.2) | 42.2 (6, 4.6) | 5.7 (6, 1.1) | 428-424-412 |

Reinforcement properties.

Reinf. type | Type | \(d_{s}\) \(d_{p}\)* (mm) | \(E_{s}\) \(E_{p}\) (GPa) | \(f_{ym}\) \(f_{p0.1m}\) (MPa) | \(f_{tm}\) \(f_{pm}\) (MPa) | \(\epsilon _{su}\) \(\epsilon _{pu}\) (\(\%\)) |
---|---|---|---|---|---|---|

Top prestress. reinf. | 7-wire | 9.3 | 198.0 | 1737 | 1930 | 5.20 |

Bot. prestress. reinf. | 7-wire | 12.5 | 198.0 | 1737 | 1930 | 5.20 |

Shear reinf. | Cold worked | 6.0 | 210.0 | 608 | 636 | 2.73 |

Splitting reinf. | Cold worked | 8.0 | 203.0 | 542 | 603 | 5.97 |

### 2.2 Experimental Setup

*a*, i.e. the distance between the support point and the load point, was equal to 1600 mm (specimens B101, B104 and B107) or 2000 mm (B102–B103, B105–B106, B108–B109). Given the geometry and reinforcement layout, this resulted in shear span-to-effective depth ratios (\(\frac{a}{d}\)-ratio) between 2.91 and 3.91. An overview of the investigated parameters per specimen is given in Table 3.

Overview of the investigated parameters per specimen.

Specimen | Type | d (mm) | \(\sigma _{p0}\) (MPa) |
(mm) | \(\frac{a}{d}\) (−) | \(\rho _{l}^{**}\) (−) | \(\rho _{w}^{***}\) (\(\times 10^{-3}\)) |
---|---|---|---|---|---|---|---|

B101 | I | 511 | 1488 | 1600 | 3.13 | 0.0208 | 2.693 |

B102 | I | 511 | 1488 | 2000 | 3.91 | 0.0208 | 2.693 |

B103 | I | 511 | 1488 | 2000 | 3.91 | 0.0208 | 0 |

B104 | I | 511 | 750 | 1600 | 3.13 | 0.0208 | 2.693 |

B105 | I | 511 | 750 | 2000 | 3.91 | 0.0208 | 2.693 |

B106 | I | 511 | 750 | 2000 | 3.91 | 0.0208 | 0 |

B107 | I | 550 | 1488 | 1600 | 2.91 | 0.0097 | 2.693 |

B108 | I | 550 | 1488 | 2000 | 3.64 | 0.0097 | 2.693 |

B109 | I | 550 | 1488 | 2000 | 3.64 | 0.0097 | 0 |

### 2.3 Adopted Measurement Methods

#### 2.3.1 CCD-LED Coordinate Measurement Machine (CMM)

#### 2.3.2 Stereo-Vision Digital Image Correlation (3D-DIC)

The analysis of the frames taken during the loading was done with specialized software. In this work, the in-house code MatchID (KU Leuven, Campus Ghent) (Lava et al. 2009, 2010, 2011; Wang et al. 2011) was used. To reveal the displacements and deformations of an object during an experiment, typically a square subset of (\(2M+1\)) pixels (px) from the undeformed image is taken and its location in the deformed image is traced. The principle of the stereo-vision DIC algorithm is clearly explained by Lava et al. (2011). Matching of two (2*M*+1) px subsets in the undeformed image \({\mathbf{F}}(x_{i},y_{j})\) and deformed image \({\mathbf{G}}^{\mathrm {t}}(x_{i},y_{j})\) at a certain time *t* (i.e. load step) is performed by adopting an optimization routine for a degree of similarity expressed by a correlation criterion. Here, the Zero Normalized Sum of Squared Differences (ZNSSD) correlation criterion was adopted. This correlation criterion is independent of scale and offset in lighting (Sutton et al. 2009) and is therefore the most suitable correlation criterion to yield accurate results, especially in the zones where the lighting conditions are difficult to control, i.e. transition zones between web and flange of the I-shaped specimens. The mathematical formalism is clearly explained in the reference work by Sutton et al. (2009).

*it has already been shown that the subset size is a critical parameter in the correlation process*(Knauss et al. 2003).

*On the one hand it should be chosen small enough to allow for a reasonable linear approximation of the displacement field, within the region of the subset. On the other hand the subset size should not be chosen too small, to avoid correlation problems due to the non-uniqueness of the subset information content. This indicates the importance of an adequate speckle pattern for digital image correlation.*From a solely black or white pattern, no valuable displacement information can be gathered so that the subset size should be larger than the speckle size. Destrycker (2012) states that

*to isolate the effect of the speckle pattern, there should be a way of applying the speckle pattern in a controlled way, e.g. controlling the speckle size, the speckle size distribution, the grey value distribution and the actual colour of the black and white paint.*Therefore, to be able to generate suitable DIC speckle patterns, a numerical technique recently proposed by Bossuyt (2012) was adopted. In his work, Bossuyt (2012) firstly defines two concepts which are used to assess the suitability of a speckle pattern for DIC measurements. Firstly, the autocorrelation peak sharpness radius of a pre-processed image of the considered pattern is proposed to quantitatively evaluate how a particular strain sensor pattern influences the sensitivity of a DIC measurement. Secondly, the autocorrelation margin is proposed to evaluate how that pattern influences the robustness of the DIC measurement. The former is related to the measurement precision whereas the latter is correlated to the measurement accuracy. Ideal patterns for DIC would combine a sharp autocorrelation peak with a well-defined autocorrelation margin. For simple patterns, these characteristics vary in direct proportion to each other. However, Bossuyt (2012) proposes a method based on morphological image processing and Fourier transform to synthesize a DIC pattern with wide autocorrelation margins even though the autocorrelation peaks are sharp. Such patterns are exceptionally well-suited for DIC measurements. A detail of the numerically generated speckle pattern is shown in Fig. 7a. The generated pattern is then applied onto each specimen where the DIC technique was used by adopting a heat-sensitive stencil printing technique which consists of three layers: a vinyl base layer, the inverse of the speckle pattern and a top protective heat-sensitive polypropylene layer. The printed speckles have a precalculated oversampling of at least five pixels in order to avoid aliasing effects in the obtained results due to the expected small magnitude of the displacement and deformation field. Given the camera sensor properties and the dimensions of the field of view, speckles with a diameter of nearly 5 mm were required. Obtaining large speckles is nearly impossible with traditional speckle techniques (i.e. spray painting). However, the adopted numerical technique allows for the generation of a speckle pattern tailored to the needs of the experiment. Figure 7b shows the same detail as presented in Fig. 7a applied onto beam B105. Figure 7c shows the speckle pattern, area of interest and adopted subset size. Since full-field displacement data is readily available, Green-Lagrange strains can be easily derived from the aforementioned displacement data. Therefore, the displacement data is smoothed over a certain zone to damp out the effect of noise and local uncertainties. A bilinear plane can be fitted through the displacement values in the points around the center of the strain window.

*N*pairs of reference images obtained from both DIC systems for specimen B103. Comparable results were found for the remaining specimens where the DIC technique has been adopted.

Measurement settings for the DIC tests.

Unit | B103 | B104 | B105 | B106 | B107 | B108 | B109 | |
---|---|---|---|---|---|---|---|---|

Subset | (px) | 27 | 27 | 27 | 27 | 27 | 27 | 27 |

Step | (px) | 3 | 3 | 3 | 3 | 3 | 3 | 3 |

Measurement points | (−) | 68327 | 67482 | 67819 | 70290 | 68843 | 68868 | 75864 |

Temporal resolution | (fps) | 2 | 2 | 2 | 2 | 2 | 2 | 2 |

Camera distance | (mm) | 2700 | 2700 | 2700 | 2700 | 2700 | 2700 | 2700 |

Interpolation | (−) | b.c.s.\(^{\dag }\) | b.c.s. | b.c.s. | b.c.s. | b.c.s. | b.c.s. | b.c.s. |

Displacement | ||||||||

Spatial resolution | (mm) | 31.2 | 30.9 | 29.9 | 29.5 | 29.9 | 30.8 | 28.4 |

In-plane resolution\(^{\dag }\) | (mm) | 0.018 | 0.019 | 0.034 | 0.027 | 0.020 | 0.021 | 0.023 |

Out-of-plane resolution\(^{\ddag }\) | (mm) | 0.125 | 0.120 | 0.165 | 0.167 | 0.147 | 0.149 | 0.152 |

## 3 Results and Discussion

- 1.
Prior to the onset of cracking, the stiffness in the elastic regime is comparable for all specimens with the same shear span and overall height. Indeed, prior to the occurrence of cracking, the response of the test specimens to the applied load is governed by the bending stiffness

*EI*. Due to the comparable secant modulus of elasticity, refer to Table 1, and the negligible influence of the area of longitudinal reinforcement on the second moment of inertia, it can be concluded that the bending stiffness is similar for the reported test specimens. - 2.
The occurrence of cracks determines the transition between linear and nonlinear behaviour. All specimens exhibited both bending and web cracks. The load at which web cracks occurs, is function of the amount of prestressing and the concrete tensile strength respectively.

- 3.
Specimens where shear reinforcement was provided and which failed in shear (B101–B102, B104–B105) exhibited a significant post-cracking stiffness and post-cracking bearing capacity resulting in a brittle shear failure mode due to diagonal tension. Specimens B107 and B108 which failed in bending, show a highly ductile behaviour with a limited post-cracking bearing capacity. Finally, beams without shear reinforcement (B103, B106 and B109) failed immediately after the occurrence of the first inclined web crack.

*z*is the internal lever arm equal to 0.9

*d*whereas \(f_{ywd}\) is the design value of the yield strength of the shear reinforcement bars. Factors \(\alpha _{cw}\) and \(\nu _{1}\) take into account the stress distribution of the compressive chord respectively the effect of lateral tensile straining on the ultimate compressive strength. The width of the web is denoted by \(b_{w}\). The inclination angle \(\theta \) can be chosen freely between certain limits as presented in Eq. (4).

*I*is the second moment of area whereas

*S*is the first moment of area. Finally, \(f_{ctd}\) is the design value of the characteristic uni-axial concrete tensile strength. If Eqs. (1)–(7) are used to estimate the actual failure load, partial safety factors should be omitted and average material properties are to be used rather than characteristic or design values. Eqs. (2)–(3) and Eqs. (5)–(7) are then transformed to Eqs. (8)–(12).

Experimentally observed and analytically predicted failure load and failure mode.

Specimen | Experiment | Eurocode 2 (European Committee for Standardization 2004, Bureau for Standardisation NBN 2010) | ||||
---|---|---|---|---|---|---|

\(V_{u,exp}\) (kN) | Failure mode | \(V_{u,pred}\) (kN) | \(V_{u,bend}\) (kN) | Failure mode | \( \frac{{V_{{u,exp}} }}{{V_{{u,pred}} }} \) (−) | |

B101 | 377.7 | S-DT† | 158.1 | 412.2 | S | 2.39 |

B102 | 321.6 | S-DT | 158.1 | 329.6 | S | 2.03 |

B103 | 262.8 | S-DT |
243.3
| 329.6 | S | 1.08 |

B104 | 281.8 | S-DT | 135.2 | 406.6 | S | 2.08 |

B105 | 251.2 | S-DT | 135.2 | 325.3 | S | 1.86 |

B106 | 179.7 | S-DT |
206.9
| 325.3 | S | 0.87 |

B107 | 271.3 | B | 147.9 | 236.5 | S | 1.83 |

B108 | 213.8 | B | 147.9 | 189.2 | S | 1.45 |

B109 | 181.0 | S-DT | 197.0* | 189.2 | B | 0.92 |

\(\overline{\frac{V_{u,exp}}{V_{u,pred}}}\) | 1.61 | |||||

COV | 55.4 \(\%\) |

- 1.
In general, a poor correlation is found between the experimental results and analytical calculations according to EC 2 for all specimens apart for beams B103, B106 and B109 without shear reinforcement. Even if all partial safety factors are omitted and average material strength properties are used rather than characteristic or design values, an average experimental-to-predicted failure load ratio of 1.61 is found with a coefficient of variation (COV) equal to 55.4 \(\%\).

- 2.
The failure mode is correctly predicted for all specimens apart for beams B107–B109. Specimens B107 and B108 failed due to bending despite having a lower shear capacity in comparison to the corresponding bending strength. Indeed, the experimental failure load correlates well with the theoretical load required to obtain the bending capacity for the aforementioned specimens. Moreover, the wrongly predicted failure mode for specimen B109 can be attributed to the small difference in the analytically calculated shear and bending capacity.

- 3.
As expected, increasing the shear reinforcement ratio, increases the shear capacity (B102–B103, B105–B106, B108–B109).

- 4.
Increasing the shear span-to-effective depth ratio while keeping all other investigated parameters constant, consistently decreases the experimentally observed shear failure load (B101–B102, B104–B105).

- 5.
Increasing the prestressing force while keeping the longitudinal reinforcement ratio approximately constant, increases the shear capacity of specimens with (B101–B104, B102–B105) and without shear reinforcement (B103–B106).

- 6.
Decreasing the longitudinal reinforcement ratio while keeping the prestressing force constant does not significantly influence the failure load (B104–B07, B105–B108 and B106–B109). However, the failure mode shifts from a brittle shear induced failure mode towards a more ductile bending induced failure mode for specimens with shear reinforcement.

*x*-axis and the applied load. The measured value for \(|\theta _{\epsilon _{2}}|\) is compared to the adopted value for \(\theta \) used for the presented strength calculations, refer to Table 5. Similar results were obtained for the remaining test specimens.

*x*-axis of the specimen contrary to the assumption made by the VATM approach. Instead, a parabolic course of the angle \(|\theta _{\epsilon _{2}}|\) is observed which does not tend to change significantly if the loading is furthermore increased. This observation if clarified by Figs. 12a and 12b which presents the full-field magnitude and direction of the principal compressive strain field \({{{\varvec{\epsilon} }_{2}}}\) for specimen B104 as a function of the surface coordinates and the applied load. Similar results were observed for the remaining specimens where the DIC technique has been adopted.

- 1.
The possibility of carrying the applied shear force by means of direct strut action significantly increases the shear carrying capacity in comparison to the shear capacity obtained using the variable angle truss model as proposed by Eurocode 2. This provides a possible explanation why the current sectional shear design provisions found in EC2 performed poorly in predicting the shear capacity of the presented prestressed concrete beams.

- 2.
Figure 14 shows the typically observed profile of the horizontal strain \(\epsilon _{x}\) at the top flange of the presented test beams. Figure 14 clearly shows that the horizontal strain at the top of the presented beams rapidly decreases to relatively low strains, and thus relatively low stresses, away from the loading point. Due to the inclined strut action, it is indeed expected that low strain values occur at the top of the specimen near the support point.

## 4 Conclusions

This paper aims to investigate on the use of advanced optical(-numerical) measurement methods for the mechanical analysis of shear-critical prestressed concrete beams. Therefore, an experimental program consisting of nine full-scale prestressed I-shaped beams was drafted. The main investigated parameters were the amount of prestressing, the amount of longitudinal reinforcement and shear reinforcement and the shear span-to-effective depth ratio respectively. All specimens were subjected to a load-controlled four-point bending test until failure. During the experimental research, the use of two advanced optical(-numerical) measurement methods, i.e. *3D coordinate measurement machines* (CMM) and *stereo-vision digital image correlation* (3D-DIC), was explored. Firstly, the experimental setup was elaborated in detail. Specifically in the case of the DIC technique, a novel technique to apply numerically synthesised strain sensor patterns, i.e. speckle patterns, in a controlled way was presented. The presented technique allows for the application of tailor-made strain sensor patterns to virtually any given object’s surface. A reference measurement was performed in unloaded state to asses the measurement precision. Both techniques were found to be comparable in terms of displacement and strain resolution. The maximum standard deviation of the in-plane displacements was equal to approximately 20 \(\times\,10^{-3}\) mm for the CMMs whereas a value of approximately 30 \(\times\,10^{-3}\) mm was found for the DIC technique. Moreover, the expected value of the strains occurring during the experiments well exceeded the observed noise levels on the in-plane horizontal and vertical strains. It can thus be concluded that both techniques are well suited for assessing the structural behaviour of the reported test specimens. However, due to the brittle and highly energy releasing failure modes observed during the tests on specimens failing in shear, the DIC technique is preferred over the CMM technique since the latter technique requires relatively expensive IR LED sensors to be glued onto the concrete side surface which can sustain damage at the moment of failure.

All specimens were designed to fail in shear. However, seven specimens failed in a brittle manner due to shear (diagonal tension failure mode) whereas two specimens failed due to bending in a ductile manner. The experimental results were compared to analytical calculations according to the current design procedures found in Eurocode 2 (EC 2). Based on the work presented in this paper, it can be concluded that EC 2, adopting the variable angle truss model, in general significantly underestimates the experimentally determined failure load. Omitting all partial safety factors and using average material strength properties rather than characteristic values resulted in an average experimental-to-predicted failure load ratio equal to 1.61 (coefficient of variation equal to 55.4 \(\%\)). Based on the extensive amount of experimental displacement and deformation data, it was found that the applied load was primarily carried by means of a direct compression strut in combination with fan regions contrary to the model adopted by EC 2 which assumes that a compression field with constant inclination along the member’s axis is developed. The identified structural behaviour for the reported test specimens can be used to optimize current shear design provisions as proposed by codes of practice.

## Declarations

**Open Access**This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

## Authors’ Affiliations

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