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Displacements measurement in a building model using the speckle photography technique
Engineering Structures 27 (2005) 1859–1864 www.elsevier.com/locate/engstruct
Displacements measurement in a building model using the speckle photography technique Rolando González-Peñaa, Rosa M. Cibrián Ortiz de Andab,∗, Angel J. Pino-Velázquezc, José Soler-de la Cruzc, Carlos Llanes Burónc, Rosario Salvador Palmerb, Mateo Buendía Gómezb a Physics Department, High Polytechnics Institute “José Antonio Echeverría”, CP 19390, Havana, Cuba b Faculty of Medicine and Odontology, Department of Physiology, Biophysics and Medical Physics Unit, University of Valencia, Avda. Blasco Ibáñez 15,
46010, Valencia, Spain
c Civil Engineering Faculty, High Polytechnics Institute “José Antonio Echeverría”, CP 19390, Havana, Cuba
Received 7 October 2004; received in revised form 13 June 2005; accepted 13 June 2005 Available online 10 August 2005
Abstract The use of reduced scale models in civil engineering has made it possible to study large structures such as buildings. Using non-destructive optical techniques such as double-exposure speckle photography, extremely valuable results can be obtained, where mathematical methods are often not very exact. This work studies the model of an eighteen-storey building in which displacements can be measured at each storey of each view. It also presents a comparison of the displacement field, which was obtained with the Finite Element Method. © 2005 Elsevier Ltd. All rights reserved. Keywords: Speckle photography; Building model; Shear walls
1. Introduction The measurement of deformations under loading conditions is usually obtained in mechanical tests by means of strain gauges glued directly to the specimen, or by displacement transducers connected to points of interest. However, these approaches present some drawbacks: both methods provide values averaged over the evaluated area only and it is often unclear whether or not they affect the measurement [1]. For this reason non-destructive testing (NDT) techniques are increasingly used for strain–stress characterisation of structural elements. Double-exposure speckle photography is a well-established whole-field technique for measuring in-plane displacement, vibration and the tilt of diffusely reflecting surfaces. A major advantage of this method is the relative simplicity ∗ Corresponding author. Tel.: +34 96 3864157; fax: +34 96 3864537.
E-mail address: [email protected] (R.M. Cibrián Ortiz de Anda). 0141-0296/$ - see front matter © 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.engstruct.2005.06.009
of the experimental set-up [2–5]. It has been applied successfully to study structural elements [6,7] and to measure deformation in buildings in situ [8,9]. Some optical tests, however, due to experimental limitations, cannot be applied directly to real structures because of the large dimensions sometimes involved; consequently the use of reduced scale models becomes necessary. A reduced scale model, when the analogy with the real building is correct, makes it possible to see the actual behaviour of the model and to determine experimentally the error in the measurements when certain types of loads are applied. Thus, when the results are extrapolated to the real building, the expected uncertainty can be calculated. In mathematical methods, like the finite element method (FEM), the study is also carried out on a model that approximately reproduces the actual behaviour of the structure. The degree of exactitude becomes greater when the following conditions are fulfilled: when the element type selected is the most suited to simulate the real object; the mesh is finer; the elastic characteristics of the
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material are the most exact; and the boundary conditions are precisely reproduced. In this case, the results of the structure deformation with the simulated load do not include a study of errors, but the usual practice is to apply the percentages of certainty to the structure for it to be correct. Therefore an experimental test on a model may give additional information on the behaviour of the structure which makes it possible to evaluate the suitability of the mathematical model used for this type of structure [10]. In this study an optical method, (double-exposure speckle photography) has been used to analyse the stability of the shear walls that form part of the model of a building with static flexural loads, and also to corroborate the rigidity of the levels, a point which has not previously been addressed in literature and which is novel to Civil Engineering. The corresponding conversion equations for reduced scale models make it possible to analyse the behaviour of the real building. 2. Material and method 2.1. Specimen description The model studied (Fig. 1) belongs to project IMS18.3-PVYC (18 storeys) and is of Yugoslavian origin. The dimensions of the real building are (21.70 m × 21.70 m) surface and 51.30 m height. This system is a skeleton structure: columns and beams made up by the joins of the storeys that become rigid due to the shear walls. The theory of reduced scale models [11] gave a magnitude relation of K = 0.0069 for this model, so it was made of acrylic with Young’s modulus and Poisson coefficient 3.19 ± 0.06 GPa and 0.36 ± 0.01, respectively. The shear walls are 11 mm wide, 3 mm thick and the height depends on the level of the storey, distributed as shown in Fig. 2. It covers a surface of 150 × 150 mm, it is 351.3 mm high and it is mounted on a base made of the same material, but thicker, which represents the foundations of the building. The model was tested regarding flexion by applying a load to the mid-point at the top, and the values were 6.6 and 8.8 N. The two exterior shear walls of each view have been analysed as shown in Fig. 2. 2.2. Experimental description The double-exposure speckle photography set-up is shown in Fig. 3. The specimen surface is illuminated by a He–Ne laser divergent beam (Spectra – Physics, 25 mW), and an OLYMPUS photographic objective (aperture F = 5.6, magnification M1 = 0.24 and 50 mm focal length) is used to focus the image of the object onto a 10E75 Agfa Gevaert photographic plate. One exposure is made without deforming the object and a second exposure is made with the object bearing the load. Once the photographic plate (specklegram) has been developed, the displacement vector at each point in the
Fig. 1. Model of IMS-18.3-PVYC building: views A and B. (↓) The tested shear walls.
specklegram can be obtained by a pointwise filtering method in which a direct laser beam passes through a selected point on the picture of the building model recorded in the specklegram. The groups of speckle pairs (corresponding to pictures recorded in the specklegram with and without deformation), which the beam subtends, diffract it, thus forming Young’s fringes on an observation screen. Interference fringes are formed on a translucent screen that allows the fringes to be recorded on a CCD video camera (model XC-75CE, resolution: 752 × 582 pixels, cell size: 8.6 × 8.3 µm and chip size: 7.95 × 6.45 mm) and sent to a
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Fig. 4. Automatic system for analysis of double-exposure speckle photography (pointwise filtering method).
Fig. 2. Distribution of the shear walls in the model of the IMS-18.3-PVYC building. (∗ ) The tested shear walls.
Fig. 5. Optical Fourier processing system or spatial filtering set-up. The position ρ of the orifice on the optical axes makes it possible to determine the frequencies that are filtered. As a result an image of the object with dark and bright fringes can be seen; these correspond to the curves of equal displacements for a given direction. Photographic objective 40x; the focal length of the Fourier transform lens: ( f = 10 cm); distances between objective and specklegram and between specklegram and second transform lens: 5 cm. Fig. 3. Speckle photography set-up for recording specklegrams. A double exposure is made over the object before and after deformation.
computer through a video digitizer for automatic analysis (Fig. 4). The algorithm used to process speckle image fringes is shown in Ref. [12]. This algorithm automatically determines the orientation and the spacing of the fringes at each point of the object in question and shows the magnitude of the in-plane displacement, d, experienced by each object point by means of Eq. (1): d=
λL M2 M1 y
(1)
where L = 114 mm is the plate–screen distance, M1 is the cited object–plate photographic amplification factor (0.24), M2 = 1.54 pixel/mm is the screen–CCD amplification factor, λ = 632.8 nm is the He–Ne laser wavelength and y is the fringe spacing. The displacement direction is perpendicular to the fringe direction. The uncertainty of the measurements of in-plane displacements in the building model depends on the uncertainty of the magnitudes involved in (1) and was calculated by the Gaussian error propagation method. The relative uncertainty for L was less than 0.01% and this was the same in all the experiments. The error in M1 and M2 , together with the error in fringe spacing (order of the pixel
size) makes the relative uncertainty for y around 2.5% (a quarter of a fringe for less than 10 fringes and half a fringe for the rest). Consequently, omitting the error of 0.01% as opposed to 2.5%, the relative deviation in the displacement measured was around 2.5%. Using this experimental device, the correlation length (σ ) of each individual speckle is related to the photographic objective aperture (F = 5.6) and the laser wavelength (λ = 632.8 nm), in accordance with Eq. (2) [13]: σ = 1.22(1 + M1 )λF.
(2)
This correlation longitude coincides with the minimum displacement this optical technique can measure, which in this case was 5.36 µm, because for lower values the speckle correlation is lost and fringes do not appear in the transform Fourier plane. To corroborate the rigidity of the quarter landings or levels of the model a Fourier spatial filtering [14] of the speckle photographs was carried out (Fig. 5). When the specklegram is illuminated by a parallel laser beam, the spatial frequency spectrum for all the dots in the speckle photograph appears on the Fourier plane (the focus of the lens). An orifice of 1 mm in diameter, situated at distance ρ from the optical axis, filters the different spatial frequencies depending on the distance between the orifice and the optical
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Table 1 Horizontal displacements in one of the exterior shear walls of view A determined by speckle photography (SP) and the Finite Element Method (FEM) for an 8.8 N load Storey 1 2 3 4 5 6 7 8 9
SP Displac. (µm) – – – – 19.7 24.4 34.5 40.2 47.1
FEM Displac. (µm) 0.5 0.7 1.1 1.4 21.3 23.6 30.1 38.2 45.1
Storey 10 11 12 13 14 15 16 17 18
SP Displac. (µm) 49.4 62.1 73.2 82.9 93.2 99.4 106.5 118.1 118.5
FEM Displac. (µm) 53.4 60.1 70.5 79.6 90.1 97.7 103.5 113.1 117.4
Uncertainty around: ±2.5 µm. ‘–’ displacements below the sensitivity of the optical method: 5.36 µm.
Fig. 6. Comparison of the horizontal displacements of an exterior shear wall in view A with regard to the height over the ground, determined by both speckle photography (SP) and the Finite Element Method (FEM).
axis (ρ). As a result, a picture is obtained of the building model, covered with fringes that correspond to the areas of the same displacement. Finally, the FEM is used to calculate the displacements in the structure, taking all the loading and boundary conditions into account to compare the results obtained by the optical method. 3. Results and discussion Table 1 and Fig. 6 show the horizontal displacements measured in the model, in one of the exterior shear walls of view A, when the above-mentioned test was applied using an 8.8 N load using both the optical method and the FEM. The results show a good correlation between the optical experimental method and the mathematical method of finite elements. At the bottom levels, the finite element method gives displacement values of the order of a micron,
but the optical method cannot determine them as they are below the 5.36 µm sensitivity of this method. Therefore, in order to compare the results we have considered that the displacements of these storeys according to the optical method would be below 5.36 µm and they are represented in Table 1 as “–”. Table 2 shows the horizontal displacements for views A and B of the model, using the optical method; view B presents greater displacements than view A. This can be explained by the greater rigidity of the model in the transversal direction, because when the load is applied towards this direction, the shear walls involved are closer to the rotation axis; this means that the associated moment of inertia is lower. The opposite occurs when the other view is analysed. The photos of the optical filtering process show horizontal fringes when the position of the filter is in a horizontal position with regard to the light. This means that the horizontal displacements are the same (within the sensitivity limits of the method) in both shear walls of the view analysed. As an example the filter for view A is shown in Fig. 7. Table 3 shows the maximum displacements at each of the shear walls with the loads studied. Likewise, this table shows that the difference between the horizontal displacements in both exterior shear walls, receiving the same load, is not significant in either case, which highlights the rigidity of the storey in the model. This coincides with the qualitative information obtained from the optic filter where horizontal fringes corresponding to equal deformation at both exterior shear walls can be seen. Likewise, in order to give an idea of the stability of the measurement results using this method, Table 3 shows the quotients of maximum deflection/load of both views with the different loads (Q). The quotient obtained must be independent of the load as it must only be a function of the geometric and elastic parameters of the model. The maximum displacement values for the real building, whose stability was similar to the assay carried out on the model, are obtained by the theory of models, by dividing the
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Table 2 Comparison of horizontal displacements in both views obtained by speckle photography for an 8.8 N load View A Displac. (µm) – – – – 19.7 24.4 34.5 40.2 47.1
Storey 1 2 3 4 5 6 7 8 9
View B Displac. (µm) – – – 5.4 30.7 36.9 45.7 58.7 68.8
Storey 10 11 12 13 14 15 16 17 18
View A Displac. (µm) 49.4 62.1 73.2 82.9 93.2 99.4 106.5 118.1 118.5
View B Displac. (µm) 73.6 75.9 95.8 104.8 116.2 131.1 142.1 152.4 152.8
Uncertainty around: ±2.5 µm. ‘–’ displacements below the sensitivity of the optical method: 5.36 µm.
4. Conclusions Speckle photography provides an effective and powerful method to determine in-plane displacement distribution. These experimental results have been verified by FE calculations. The determination of parameters such as displacements and stresses makes it possible to describe the behaviour of a building model with great accuracy in the laboratory. Thus it verifies the reduced scale model theory for analysing large structures. However, a structural model is never perfect, although it provides an estimation of the structural performance when subjected to various loading functions. Acknowledgements This work has been supported by grants IIARCO2004-A62 of the Consellería de Industria, Comercio y Turismo and CTESIN/2005/004 of the Generalitat Valenciana. Fig. 7. Fringes obtained by optical Fourier processing system of view A, where fringes are observed corresponding to equal displacement.
Table 3 Quotients of maximum deflection/load applied (Q), for the different loads, at the exterior shear walls of each view that was analysed View
Load (N )
Shearwall
Displac. (µm)
Q (µm/N)
A
6.6
1 2 1 2
96.8 ± 3.1 87.0 ± 3.1 118.5 ± 3.1 112.9 ± 3.1
13.9
1 2 1 2
122.7 ± 3.1 122.6 ± 3.1 152.8 ± 3.1 155.9 ± 3.1
18.7
8.8 B
6.6 8.8
13.5
17.7
displacements obtained in the model by the corresponding K , 0.0069 in this case.
References [1] Facchini M. Applicability of electronic speckle pattern interferometry to the characterization of building materials. Proc SPIE Opt Insp Micromeas 1996;2782:386–97. [2] Lehmann M. Decorrelation-induced phase errors in plane — shifting speckle interferometry. App Opt 1997;36(16):3657–67. [3] Rastogi PK, Jacquot P. Speckle metrology techniques a parametric examination of the observed fringes. Opt Eng 1982;21:411–26. [4] Benckert L, Jonsson M, Molin NE. Measuring true in-plane displacements of a surface by stereoscopic white light speckle photography. Opt Eng 1987;26:167–9. [5] Huntley JM. Speckle photography fringes analysis: assessment of current algorithms. Appl Opt 1989;28:4316–22. [6] González R, Cibrian R, Pino A, Soler J, González Y. Displacement measurement in structural elements by optical techniques. Opt Laser Eng 2000;34:75–85. [7] González R, Cibrian R, Pino A, González Y, Salvador R. Determination of strain and stress distribution on shearwalls by using the speckle photography technique. Opt Laser Eng 2003;39:609–18. [8] Chen S, Wang R. The application of white light speckle in analysis of engineering structural joints. Proc SPIE Holog Tech Appl 1988;1026: 133–6.
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[9] Gulker G, Hinsch K, Holscher C, Kramer A, Neumaber H. Electronic speckle pattern interferometry for in situ deformation monitoring on building. Opt Eng 1990;29(7):816–20. [10] González-Peña R. Interferometría de speckle aplicada a estructuras y materiales de construcción. Doctoral thesis, Instituto Superior Politécnico “José A. Echeverría”, Ciudad de la Habana; 2001. [11] Lewcki B. Edificios de viviendas prefabricados con elementos de
grandes dimensiones. Madrid: Inst. E. Torrojas; 1968. [12] Buendia M, Cibrián R, Salvador R, Roldán C, Iñesta JM. Automatic analysis of speckle photography fringes. Appl Opt 1997;36:2395–400. [13] Lauterborn W, Kurz T, Wiesenfeldt M. Coherent optics. Fundamentals and applications. Springer-Verlag; 1995. [14] Françon M. In: Masson ETC, editor. Holographie. Paris; 1969. p. 97–9 [chapter 4].
Displacements measurement in a building model using the speckle photography technique Rolando González-Peñaa, Rosa M. Cibrián Ortiz de Andab,∗, Angel J. Pino-Velázquezc, José Soler-de la Cruzc, Carlos Llanes Burónc, Rosario Salvador Palmerb, Mateo Buendía Gómezb a Physics Department, High Polytechnics Institute “José Antonio Echeverría”, CP 19390, Havana, Cuba b Faculty of Medicine and Odontology, Department of Physiology, Biophysics and Medical Physics Unit, University of Valencia, Avda. Blasco Ibáñez 15,
46010, Valencia, Spain
c Civil Engineering Faculty, High Polytechnics Institute “José Antonio Echeverría”, CP 19390, Havana, Cuba
Received 7 October 2004; received in revised form 13 June 2005; accepted 13 June 2005 Available online 10 August 2005
Abstract The use of reduced scale models in civil engineering has made it possible to study large structures such as buildings. Using non-destructive optical techniques such as double-exposure speckle photography, extremely valuable results can be obtained, where mathematical methods are often not very exact. This work studies the model of an eighteen-storey building in which displacements can be measured at each storey of each view. It also presents a comparison of the displacement field, which was obtained with the Finite Element Method. © 2005 Elsevier Ltd. All rights reserved. Keywords: Speckle photography; Building model; Shear walls
1. Introduction The measurement of deformations under loading conditions is usually obtained in mechanical tests by means of strain gauges glued directly to the specimen, or by displacement transducers connected to points of interest. However, these approaches present some drawbacks: both methods provide values averaged over the evaluated area only and it is often unclear whether or not they affect the measurement [1]. For this reason non-destructive testing (NDT) techniques are increasingly used for strain–stress characterisation of structural elements. Double-exposure speckle photography is a well-established whole-field technique for measuring in-plane displacement, vibration and the tilt of diffusely reflecting surfaces. A major advantage of this method is the relative simplicity ∗ Corresponding author. Tel.: +34 96 3864157; fax: +34 96 3864537.
E-mail address: [email protected] (R.M. Cibrián Ortiz de Anda). 0141-0296/$ - see front matter © 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.engstruct.2005.06.009
of the experimental set-up [2–5]. It has been applied successfully to study structural elements [6,7] and to measure deformation in buildings in situ [8,9]. Some optical tests, however, due to experimental limitations, cannot be applied directly to real structures because of the large dimensions sometimes involved; consequently the use of reduced scale models becomes necessary. A reduced scale model, when the analogy with the real building is correct, makes it possible to see the actual behaviour of the model and to determine experimentally the error in the measurements when certain types of loads are applied. Thus, when the results are extrapolated to the real building, the expected uncertainty can be calculated. In mathematical methods, like the finite element method (FEM), the study is also carried out on a model that approximately reproduces the actual behaviour of the structure. The degree of exactitude becomes greater when the following conditions are fulfilled: when the element type selected is the most suited to simulate the real object; the mesh is finer; the elastic characteristics of the
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material are the most exact; and the boundary conditions are precisely reproduced. In this case, the results of the structure deformation with the simulated load do not include a study of errors, but the usual practice is to apply the percentages of certainty to the structure for it to be correct. Therefore an experimental test on a model may give additional information on the behaviour of the structure which makes it possible to evaluate the suitability of the mathematical model used for this type of structure [10]. In this study an optical method, (double-exposure speckle photography) has been used to analyse the stability of the shear walls that form part of the model of a building with static flexural loads, and also to corroborate the rigidity of the levels, a point which has not previously been addressed in literature and which is novel to Civil Engineering. The corresponding conversion equations for reduced scale models make it possible to analyse the behaviour of the real building. 2. Material and method 2.1. Specimen description The model studied (Fig. 1) belongs to project IMS18.3-PVYC (18 storeys) and is of Yugoslavian origin. The dimensions of the real building are (21.70 m × 21.70 m) surface and 51.30 m height. This system is a skeleton structure: columns and beams made up by the joins of the storeys that become rigid due to the shear walls. The theory of reduced scale models [11] gave a magnitude relation of K = 0.0069 for this model, so it was made of acrylic with Young’s modulus and Poisson coefficient 3.19 ± 0.06 GPa and 0.36 ± 0.01, respectively. The shear walls are 11 mm wide, 3 mm thick and the height depends on the level of the storey, distributed as shown in Fig. 2. It covers a surface of 150 × 150 mm, it is 351.3 mm high and it is mounted on a base made of the same material, but thicker, which represents the foundations of the building. The model was tested regarding flexion by applying a load to the mid-point at the top, and the values were 6.6 and 8.8 N. The two exterior shear walls of each view have been analysed as shown in Fig. 2. 2.2. Experimental description The double-exposure speckle photography set-up is shown in Fig. 3. The specimen surface is illuminated by a He–Ne laser divergent beam (Spectra – Physics, 25 mW), and an OLYMPUS photographic objective (aperture F = 5.6, magnification M1 = 0.24 and 50 mm focal length) is used to focus the image of the object onto a 10E75 Agfa Gevaert photographic plate. One exposure is made without deforming the object and a second exposure is made with the object bearing the load. Once the photographic plate (specklegram) has been developed, the displacement vector at each point in the
Fig. 1. Model of IMS-18.3-PVYC building: views A and B. (↓) The tested shear walls.
specklegram can be obtained by a pointwise filtering method in which a direct laser beam passes through a selected point on the picture of the building model recorded in the specklegram. The groups of speckle pairs (corresponding to pictures recorded in the specklegram with and without deformation), which the beam subtends, diffract it, thus forming Young’s fringes on an observation screen. Interference fringes are formed on a translucent screen that allows the fringes to be recorded on a CCD video camera (model XC-75CE, resolution: 752 × 582 pixels, cell size: 8.6 × 8.3 µm and chip size: 7.95 × 6.45 mm) and sent to a
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Fig. 4. Automatic system for analysis of double-exposure speckle photography (pointwise filtering method).
Fig. 2. Distribution of the shear walls in the model of the IMS-18.3-PVYC building. (∗ ) The tested shear walls.
Fig. 5. Optical Fourier processing system or spatial filtering set-up. The position ρ of the orifice on the optical axes makes it possible to determine the frequencies that are filtered. As a result an image of the object with dark and bright fringes can be seen; these correspond to the curves of equal displacements for a given direction. Photographic objective 40x; the focal length of the Fourier transform lens: ( f = 10 cm); distances between objective and specklegram and between specklegram and second transform lens: 5 cm. Fig. 3. Speckle photography set-up for recording specklegrams. A double exposure is made over the object before and after deformation.
computer through a video digitizer for automatic analysis (Fig. 4). The algorithm used to process speckle image fringes is shown in Ref. [12]. This algorithm automatically determines the orientation and the spacing of the fringes at each point of the object in question and shows the magnitude of the in-plane displacement, d, experienced by each object point by means of Eq. (1): d=
λL M2 M1 y
(1)
where L = 114 mm is the plate–screen distance, M1 is the cited object–plate photographic amplification factor (0.24), M2 = 1.54 pixel/mm is the screen–CCD amplification factor, λ = 632.8 nm is the He–Ne laser wavelength and y is the fringe spacing. The displacement direction is perpendicular to the fringe direction. The uncertainty of the measurements of in-plane displacements in the building model depends on the uncertainty of the magnitudes involved in (1) and was calculated by the Gaussian error propagation method. The relative uncertainty for L was less than 0.01% and this was the same in all the experiments. The error in M1 and M2 , together with the error in fringe spacing (order of the pixel
size) makes the relative uncertainty for y around 2.5% (a quarter of a fringe for less than 10 fringes and half a fringe for the rest). Consequently, omitting the error of 0.01% as opposed to 2.5%, the relative deviation in the displacement measured was around 2.5%. Using this experimental device, the correlation length (σ ) of each individual speckle is related to the photographic objective aperture (F = 5.6) and the laser wavelength (λ = 632.8 nm), in accordance with Eq. (2) [13]: σ = 1.22(1 + M1 )λF.
(2)
This correlation longitude coincides with the minimum displacement this optical technique can measure, which in this case was 5.36 µm, because for lower values the speckle correlation is lost and fringes do not appear in the transform Fourier plane. To corroborate the rigidity of the quarter landings or levels of the model a Fourier spatial filtering [14] of the speckle photographs was carried out (Fig. 5). When the specklegram is illuminated by a parallel laser beam, the spatial frequency spectrum for all the dots in the speckle photograph appears on the Fourier plane (the focus of the lens). An orifice of 1 mm in diameter, situated at distance ρ from the optical axis, filters the different spatial frequencies depending on the distance between the orifice and the optical
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Table 1 Horizontal displacements in one of the exterior shear walls of view A determined by speckle photography (SP) and the Finite Element Method (FEM) for an 8.8 N load Storey 1 2 3 4 5 6 7 8 9
SP Displac. (µm) – – – – 19.7 24.4 34.5 40.2 47.1
FEM Displac. (µm) 0.5 0.7 1.1 1.4 21.3 23.6 30.1 38.2 45.1
Storey 10 11 12 13 14 15 16 17 18
SP Displac. (µm) 49.4 62.1 73.2 82.9 93.2 99.4 106.5 118.1 118.5
FEM Displac. (µm) 53.4 60.1 70.5 79.6 90.1 97.7 103.5 113.1 117.4
Uncertainty around: ±2.5 µm. ‘–’ displacements below the sensitivity of the optical method: 5.36 µm.
Fig. 6. Comparison of the horizontal displacements of an exterior shear wall in view A with regard to the height over the ground, determined by both speckle photography (SP) and the Finite Element Method (FEM).
axis (ρ). As a result, a picture is obtained of the building model, covered with fringes that correspond to the areas of the same displacement. Finally, the FEM is used to calculate the displacements in the structure, taking all the loading and boundary conditions into account to compare the results obtained by the optical method. 3. Results and discussion Table 1 and Fig. 6 show the horizontal displacements measured in the model, in one of the exterior shear walls of view A, when the above-mentioned test was applied using an 8.8 N load using both the optical method and the FEM. The results show a good correlation between the optical experimental method and the mathematical method of finite elements. At the bottom levels, the finite element method gives displacement values of the order of a micron,
but the optical method cannot determine them as they are below the 5.36 µm sensitivity of this method. Therefore, in order to compare the results we have considered that the displacements of these storeys according to the optical method would be below 5.36 µm and they are represented in Table 1 as “–”. Table 2 shows the horizontal displacements for views A and B of the model, using the optical method; view B presents greater displacements than view A. This can be explained by the greater rigidity of the model in the transversal direction, because when the load is applied towards this direction, the shear walls involved are closer to the rotation axis; this means that the associated moment of inertia is lower. The opposite occurs when the other view is analysed. The photos of the optical filtering process show horizontal fringes when the position of the filter is in a horizontal position with regard to the light. This means that the horizontal displacements are the same (within the sensitivity limits of the method) in both shear walls of the view analysed. As an example the filter for view A is shown in Fig. 7. Table 3 shows the maximum displacements at each of the shear walls with the loads studied. Likewise, this table shows that the difference between the horizontal displacements in both exterior shear walls, receiving the same load, is not significant in either case, which highlights the rigidity of the storey in the model. This coincides with the qualitative information obtained from the optic filter where horizontal fringes corresponding to equal deformation at both exterior shear walls can be seen. Likewise, in order to give an idea of the stability of the measurement results using this method, Table 3 shows the quotients of maximum deflection/load of both views with the different loads (Q). The quotient obtained must be independent of the load as it must only be a function of the geometric and elastic parameters of the model. The maximum displacement values for the real building, whose stability was similar to the assay carried out on the model, are obtained by the theory of models, by dividing the
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Table 2 Comparison of horizontal displacements in both views obtained by speckle photography for an 8.8 N load View A Displac. (µm) – – – – 19.7 24.4 34.5 40.2 47.1
Storey 1 2 3 4 5 6 7 8 9
View B Displac. (µm) – – – 5.4 30.7 36.9 45.7 58.7 68.8
Storey 10 11 12 13 14 15 16 17 18
View A Displac. (µm) 49.4 62.1 73.2 82.9 93.2 99.4 106.5 118.1 118.5
View B Displac. (µm) 73.6 75.9 95.8 104.8 116.2 131.1 142.1 152.4 152.8
Uncertainty around: ±2.5 µm. ‘–’ displacements below the sensitivity of the optical method: 5.36 µm.
4. Conclusions Speckle photography provides an effective and powerful method to determine in-plane displacement distribution. These experimental results have been verified by FE calculations. The determination of parameters such as displacements and stresses makes it possible to describe the behaviour of a building model with great accuracy in the laboratory. Thus it verifies the reduced scale model theory for analysing large structures. However, a structural model is never perfect, although it provides an estimation of the structural performance when subjected to various loading functions. Acknowledgements This work has been supported by grants IIARCO2004-A62 of the Consellería de Industria, Comercio y Turismo and CTESIN/2005/004 of the Generalitat Valenciana. Fig. 7. Fringes obtained by optical Fourier processing system of view A, where fringes are observed corresponding to equal displacement.
Table 3 Quotients of maximum deflection/load applied (Q), for the different loads, at the exterior shear walls of each view that was analysed View
Load (N )
Shearwall
Displac. (µm)
Q (µm/N)
A
6.6
1 2 1 2
96.8 ± 3.1 87.0 ± 3.1 118.5 ± 3.1 112.9 ± 3.1
13.9
1 2 1 2
122.7 ± 3.1 122.6 ± 3.1 152.8 ± 3.1 155.9 ± 3.1
18.7
8.8 B
6.6 8.8
13.5
17.7
displacements obtained in the model by the corresponding K , 0.0069 in this case.
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