Advances for the on-site determination of the stresses state in timber structures in service

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1 Strutural Studies, Repairs and Maintenane of Heritage Arhiteture XIV 771 Advanes for the on-site determination of the stresses state in timber strutures in servie M. Crespo de Antonio, D. Luengas-Carreño & S. Sánhez-Beitia Higher Tehnial Shool of Arhiteture UPV/EHU, Spain Abstrat The assessment of nondestrutive (NDT) or semi-destrutive tehniques (SDT) for the in situ strutural haraterization in existing onstrutions is one of the most important hallenges for the sientifi ommunity. The hole-drilling method is onsidered as a SDT beause the damage aused to the analyzed element affets neither its integrity nor its load-bearing apaity. The experimental proess is to measure the relaxed strains aused by the removal of a small round of material. These relaxed strains are reorded by previously well adhered strain gages aording to the orresponding ASTM standard. It is possible to dedue the stress status before the material removal using the orret mathematial sheme. This paper shows the advanes of the setting of the hole-drilling method for the dedution of the stress-state on supporting wood members in existing strutures (buildings and ivil onstrutions). The relationship between the relaxed strains after removing the material and the stress that auses them has been identified in the laboratory by means of the dedution of its orresponding ompliane matrix. The laboratory-tested samples of Pinus radiata D. Don had a strutural size, being loaded under a known uniaxial ompression imitating piers. The main goal is to omplete ompliane matrix for this material and for ompression situations. The matrix will be useful in deduing the real stresses in regions of timber strutural members made of this kind of wood. Keywords: on site assessment, hole-drilling tehnique, timber strutures, anient onstrutions, ompliane tensor, ompression loading. 1 Introdution Wood is one of the oldest strutural materials and it has been widely used where there was a forest. Due to the inreasing desire to preserve the historial value of WIT Transations on The Built Environment, Vol 153, 2015 WIT Press ISSN (on-line) doi: /str150641

2 772 Strutural Studies, Repairs and Maintenane of Heritage Arhiteture XIV anient buildings and the fat it is the only truly renewable material, wood has experiened a renaissane in onstrution after being forgotten for a while when other attrative modern materials appeared. For many years wood was the only material able to solve horizontal strutures, so it is quite usual to find up timber strutures in restoration works. There are many methods for the assessment of physial and mehanial properties of timber strutures in servie whih are onstantly being improved and developed. Nevertheless, more researh is required to estimate individual member strengths as well as obtain aurate quantifiation of deterioration [1]. Hole-drilling is not inluded between evaluating and assessing methods in existing timber strutures but it ould provide the neessary information to predit in situ member strength [1]. Although hole-drilling is not a new method, indeed it is based on the ASTM E837 standard [2] it does not onsider its appliation on wood, a natural orthotropi material. This tehnique was limited to being used in isotropi materials in other fields of the knowledge far from heritage. Wood is an orthotropi material beause its three main diretions (axial, radial and tangential) are orthogonal one to another. This means that wood features are different in eah main diretion, being the strongest one along the axial diretion. The aim of this researh is to inlude the hole-drilling between in situ assessment tehniques of strutural timber. There are some tehniques based on stress waves, sounding, ground penetrating radar, radiography, resistane drilling, ore-drilling, hardness test and some others [3 5], but none useful to estimate the stress status of a wooden element in servie. 2 Hole-drilling tehnique Sine its ineption by Mathar in the 1930s [6], the hole-drilling method has grown to be one of the most popular proedures to obtain the stresses [7], more speifially residual stresses, in a wide variety of materials [8]. For instane, Sanhez-Beitia and Shueremans [9], Sanhez-Beitia et al. [10] and Sanhez- Beitia and Roa [11] have researhed the method in masonry strutures, onsidered an isotropi material. The proedure involves registering the strain relaxation that is originated when a round of material is removed by drilling. The strain-values are reorded by three strain gages previously glued over the material surfae around the point where the drill is going to be made. The three gages enable to know the stress state before drilling. This proedure is onsidered to be a minor destrutive test beause the hole made by the drill is so small that it does not damage the wholeness of the analyzed wooden element. Three strain gages are enough to omplete a rosette and determine the state of the stresses in two-dimensional situations. The involved dimensions (strain gages rosette loation, hole-diameter and depth of drilling) are well established on the ASTM E837 Standard. The rosettes must be handmade for eah analyzed point beause no ommerial devie is available for wood. Aording to the standard reommendations but also to the available boring tool (18 mm in drill bit- WIT Transations on The Built Environment, Vol 153, 2015 WIT Press ISSN (on-line)

3 Strutural Studies, Repairs and Maintenane of Heritage Arhiteture XIV 773 diameter) and ommerial strain gages size (12 mm in length), new dimensions for the experimental situation are 18 mm in hole-diameter, 16 mm in depth of drill, 40 mm in rosette-diameter. Despite this inrease, proportions between holediameter, strain gages size, and the irumferene diameter of the strain gages disposal have been maintained in order to ensure the stresses relaxation after the elimination of material after drilling. The experimental proedure explained here has been developed for Pinus radiata D. Don beause it is a widely used material as a building material for timber strutures in many zones of Europe. Wood is an orthotropi material with two main orthotropi diretions of elastiity named, in this ase, x and y, whih their related elastiity moduli are named Ex (transversal-to-grain diretion) and Ey (fibre diretion). It is generally assumed that radial and tangential diretions an be onsidered similar in terms of physi and mehanial properties but very different in omparison with the axial one. In this ase, transversal diretion is assumed to be both radial and tangential. All the stress-states are dedued in a plane state of stresses where the prinipal diretions oinide with the fibre and tangential diretions shown in figs 1 and 2. In a plane state of stresses the orrelation between the relaxed trains after the elimination of material and the stress supported by the material is shown in eqn. (1) [12, 13] y xy x E x E y (1) In this equation ij are the dimensionless onstants of ompliane. When x and y diretions of the rosette oinide with the prinipal elasti diretions of the orthotropi material, the omplianes 12 and 32 both equal zero [12]. σy, σxy and σx are the stresses in the x-y plane. ε 1, ε 2, and ε 3 are the relaxed strains reorded by three strain gages (figs 1 and 2). Ex and Ey are the prinipal moduli of elastiity. The referene system shown in fig. 1 has been applied in all the tests. Two gages are in mutually perpendiular diretions, with a third along one of the bisetors; y axis, where strain gage 1 is plaed, oinides with the fibre diretion, whereas the x axis, where strain gage 3 is plaed, always oinides with the transversal diretion (fig. 2). From eqn. (1) the following expressions an be obtained. 11 y 13 x ExE y 1 (2) 21 y 22 xy 23 x ExE y 2 (3) 31 y 33 x ExE y 3 (4) WIT Transations on The Built Environment, Vol 153, 2015 WIT Press ISSN (on-line)

4 774 Strutural Studies, Repairs and Maintenane of Heritage Arhiteture XIV Figure 1: Plane referene system where fibre diretion oinides with the y axis. The lines drawn model the fibre diretion. Figure 2: Shemati sight of the tested bloks, hole-position (dark irle) and strain gages loation (dark retangles). Bloks have been tested under uniaxial ompression in axial (left) and tangential diretion (right). 3 Analytial and experimental planning Ten bloks (20 m x 20 m x 20 m) have been loaded at the laboratory. The material has been taken from a forest in the north of Spain and has been ut and tested without any previous treatment. The environmental onditions of the laboratory are 20ºC and 50% of relative humidity. The material onditions WIT Transations on The Built Environment, Vol 153, 2015 WIT Press ISSN (on-line)

5 Strutural Studies, Repairs and Maintenane of Heritage Arhiteture XIV 775 reprodue the real being of timber strutures in existing buildings where this researh is going to be ontinued in the following months. However, the values of the elastiity moduli in the bibliography for bloks with these dimensions and this kind of wood are not available [14]. When the bloks are loaded under a known axial ompression (σyᶜ) in y diretion, the onstants of ompliane 11, 21 and 31 an be obtained from a hole-drilling test by using the following expressions obtained from eqns (2), (3) and (4), being σx = σxy = 0: E E (5) 11 y x y 1 E E (6) 21 y x y 2 E E (7) 31 y x y 3 The same proess has been repeated loading the bloks under a known transversal/tangential ompression (σxᶜ) in the x diretion. The onstants of ompliane 13, 23 and 33 an be obtained from a hole-drilling test using the following expressions obtained from eqns (2), (3) and (4), in this ase σy = σxy = 0: E E (8) 13 x x y 1 E E (9) 23 x x y 2 E E (10) 33 x x y 3 A omplementary test has to be designed to obtain the onstant of ompliane 22. One the bloks have been tested under axial and transversal/tangential loads, ten new samples are obtained from the originals and ut to ahieve the ten new bloks with the fibre diretions tilted (as shown in fig. 3). Their final dimensions are 12 m x 12 m in setion and 14 m in height. These bloks have been tested under a known ompression load (σ ). The following expression shows the orrelation between the σ and the stress state in the x-y system referene: 2 x sen xy sen os 2 os y (11) From eqns (3) and (11) an be obtained the following expression whih allows the dedution of 22 : os 22 ( sen os ) 23 sen ExE y (12) 2 WIT Transations on The Built Environment, Vol 153, 2015 WIT Press ISSN (on-line)

6 776 Strutural Studies, Repairs and Maintenane of Heritage Arhiteture XIV By loading the new bloks under a known stresses (σ ), a hole-drilling proedure solves the problem as 21 and 23 have been previously determined in eqns (6) and (9). Figure 3: New sample (dark retangle) built from the initial bloks. 4 Experimental results Two previous problems have to be solved. The first problem involves the values of the two Young s elasti moduli for this material and its strutural size. Before this researh, twenty bloks (20 m x 20 m x 20 m) were tested under ompression stresses within the elasti zone, obtaining the average values Ey= 9442 MPa and Ex= 621 MPa. All the bloks were loaded in fibre and transversal -to-fibre diretions. Some samples show a high dispersion, but the average values fall into the expeted ranges. The strains were reorded by the same strain gages to those used after measuring the strains in the hole-drilling proedure and in the point where the hole is going to be made. Consequently, elasti moduli are not obtained aording to the onventional test proedures. The results are only valid for the drilling point, so it is a loalized measure and it should be taken into onsideration for the whole blok. The barrel effet in the samples was eliminated using a layer of standard lithium grease on the ontat surfaes between the samples and the jaws of the ompression mahine. This layer drastially redues the dispersion and the anomalous values of the reorded strains. Lithium grease has been used in all the tests shown here in order to avoid as many errors as possible. It has also to be onfirmed that the dimensions of the drill assure the stress relaxation in its surroundings (where the strain gages are plaed). Previous tests have shown that greater drill depth does not affet the strains reorded in the three strain gages. A 21-mm drill depth was reahed in three bloks. Negleted variations of ε 1, ε 2, and ε 3 in the three bloks were deteted up to a depth of 16 mm. WIT Transations on The Built Environment, Vol 153, 2015 WIT Press ISSN (on-line)

Strutural Studies, Repairs and Maintenane of Heritage Arhiteture XIV 777 Ten bloks have been loaded under axial ompression in the fibre diretion.

These bloks have also been tested under ompression stresses in the transversal/tangential diretion (the x axis) in the opposite side.

The results for the samples ut with tilted-fibre diretion with respet to the vertial diretion are shown in Tables 3 and 4 (fig. 4, right).

7 Strutural Studies, Repairs and Maintenane of Heritage Arhiteture XIV 777 Ten bloks have been loaded under axial ompression in the fibre diretion. The relaxed strains values after drilling a hole in Side 1 (fig. 4, left) are shown in table 1. These bloks have also been tested under ompression stresses in the transversal/tangential diretion (the x axis) in the opposite side. The registered strains in Side 2 (opposite to Side 1) are shown in Table 2 (fig. 4, middle). The results for the samples ut with tilted-fibre diretion with respet to the vertial diretion are shown in Tables 3 and 4 (fig. 4, right). The hole-drilling test has been applied to both sides of the tilted-fibre bloks and therefore two values of 22 per blok have been obtained. The onstants of ompliane for eah test and their average values obtained from results in the tables 1 to 4 and the eqns (5) to (12) are shown in table 5. Results for the blok number 4 suggest stresses under tensile loads and they have been not onsidered in the next analysis. These anomalous results may be due to a defiient proess of lubriation on the ontat surfaes between the sample and the load group of the mahine in laboratory. In table 5, the results for this blok have been eliminated. Figure 4: Table 1: Samples tested in the fibre diretion (left), perpendiular-to-fibre diretion (middle) and tilted to the vertial load diretion (right) Hole-drilling results under axial ompression (fibre diretion) on Side 1. BFi means Blok tested in the Fibre diretion for blok number i. BF1 BF2 BF3 BF4 BF5 BF6 BF7 BF8 BF9 BF10 σy (MPa) ε₁ (μm/m) ε₂ (μm/m) ε₃ (μm/m) WIT Transations on The Built Environment, Vol 153, 2015 WIT Press ISSN (on-line)

8 778 Strutural Studies, Repairs and Maintenane of Heritage Arhiteture XIV Table 2: Hole-drilling results under transversal ompression on Side 2. BTi means Blok tested in the Transversal diretion for blok number i. BT1 BT2 BT3 BT4 BT5 BT6 BT7 BT8 BT9 BT10 σx (MPa) ε₁ (μm/m) ε₂ (μm/m) ε₃ (μm/m) Table 3: Hole-drilling results under vertial ompression for bloks with the fibre diretion tilted. B1.i means Blok i tested on the Side 1. B1.1 B1.2 B1.3 B1.4 B1.5 B1.6 B1.7 B1.8 B1.9 B1.10 σy (Mpa) ε₁ (μm/m) ε₂ (μm/m) ε₃ (μm/m) Table 4: Hole-drilling results under vertial ompression for bloks with the fibre diretion tilted. B2.i means Blok number i tested on the Side 2. B2.1 B2.2 B2.3 B2.4 B2.5 B2.6 B2.7 B2.8 B2.9 B2.10 θ (º) σy (Mpa) ε₁ (μm/m) ε₂ (μm/m) ε₃ (μm/m) WIT Transations on The Built Environment, Vol 153, 2015 WIT Press ISSN (on-line)

9 Strutural Studies, Repairs and Maintenane of Heritage Arhiteture XIV 779 Table 5: Constants of ompliane for Ex=621 MPa and Ey=9442 MPa. Bi means Blok number i. Blok 4 has been eliminated. B1 B2 B3 B5 B6 B7 B8 B9 B10 Average One the onstants of ompliane have been obtained (see average values of table 5), six new bloks are tested only in the transversal/tangential diretion to hek the validity of those values. The hole-drilling proedure was applied in one side after loading the samples at laboratory under uniaxial ompression (the x diretion at right in fig. 2). The relaxed strains and the onstants of ompliane, table 6, have to reprodue the known load of mahine. From eqn. (1), the stresses from the relaxed strains an be obtained using the following expression: y xy x E x E y (13) where ij are the average values of the onstants of ompliane shown in table 5. The results in table 6 ompare the foreseen loads from eqn. (13) and the known mahine loads. Table 6: Summary of the results for the stresses obtained using the holedrilling method in omparison with the applied stresses at laboratory on six new heking bloks. NBi means New Blok number i. NB1 NB2 NB3 NB4 NB5 NB6 θ (º) Applied mahine load (Mpa) Stresses obtained by Hole Drilling method (Mpa) Differenes between applied and obtained stresses (Mpa) Error (%) WIT Transations on The Built Environment, Vol 153, 2015 WIT Press ISSN (on-line)

10 780 Strutural Studies, Repairs and Maintenane of Heritage Arhiteture XIV 5 Disussion The final objetive of the researh is the dedution of the real stresses on timber strutures in servie and preferably in elements of existing buildings and ivil strutures, where not muh tehnial information is available. Therefore, the material onditions are natural (as it was just taken from the forest without speial treatments), and the dimensions of the elements are large. The tested material and the design of samples reprodue the most ommon timber strutures onditions in many areas of Europe [15]. All the values of the parameters involved in this researh have been speifially dedued from the laboratory tests, and no value has been taken from the bibliography. In these onditions, the results shown in table 6 are very aeptable beause the hole-drilling proedure approahes the real and unknown stresses in five of six bloks less than 22% (83% of the samples), whih means that the tests performed for onstants of ompliane determination are orret and good [3]; the onfidene interval for the onstants of ompliane (table 5) to 80% are: 11 = ± 0.2, 21 = ± 0.2, 31 = ±0.1, 13 = 0±0.1, 23 = ±0.1, 33 = ±0.4 and 22 = ±0.3. The values of the relaxed strain s reorded by the strain gages (tables 1 to 4) an be onsidered without error beause these values were aepted when no variations of the strains were deteted during a five minute period. The foreseen error by the standard unit does not exeed the 1% for eah strain reorded. Attention has to be given to the tilted-fibre diretion (fig. 3), whih yields the obtainment of 22. The tests in transversal/tangential diretion are foused on the final objetive of the researh and are easily reproduible beause neither the samples imposed nor the proedures are omplex. Nevertheless, some experimental onditions have to be taken into aount; the adequate lubriation of the ontat surfaes between the samples and the load group at laboratory, the availability of a well-tested strains reorded unit and the avoidane of defets (raks and knots) in the analyzed areas. Only one blok gave anomalous results in the proess to obtain the onstants of ompliane, most likely due to the barrel effet or unexpeted defets near the analyzed zone. The authors onsider the results to be relevant to the development of a method to dedue the real stresses in beams of timber strutures. The appliability of the results to other kind of wood an be immediate. After this experimental ampaign, the authors will perform flexion tests in beams of the same material. The proedure will be similar to that used here. Aknowledgements The authors aknowledge the sientifi support of the professors Alfonso Basterra and Luis Auña at the Valladolid University in Spain and the finanial support of the Projet PES 11/32 of the Basque Country University (UPV/EHU). WIT Transations on The Built Environment, Vol 153, 2015 WIT Press ISSN (on-line)

11 Strutural Studies, Repairs and Maintenane of Heritage Arhiteture XIV 781 Referenes [1] Kasal, B. & Tannert, T., In situ assessment of strutural timber. RILEM state of the art reports, (7), [2] ASTM, E. 837, Standard Test Method for Determining Residual Stresses by the Hole-Drilling Strain-Gage Method, [3] Bo Kasal and Ronal W. Anthony. Advanes in in situ evaluation of timber strutures. Prog. Strut. Engng. Mater., Vol. 6, pp , [4] Tannert, T., Anthony, R. W., Kasal, B., Kloiber, M., Piazza, M., Riggio, M. & Yamaguhi, N., In situ assessment of strutural timber using semidestrutive tehniques. Materials and strutures, 47(5), pp , [5] Riggio, M., Anthony, R. W., Augelli, F., Kasal, B., Lehner, T., Muller, W., & Tannert, T., In situ assessment of strutural timber using nondestrutive tehniques. Materials and Strutures, 47(5), pp , [6] Mathar, J. Determination of initial stresses by measuring the deformation around drilled holes. Trans. ASME, 56(4), pp , [7] Shajer, G. S., Hole-drilling residual stress measurements at 75: origins, advanes, opportunities. Experimental mehanis, 50(2), pp , [8] Mainjot, A. K., Shajer, G. S., Vanheusden, A. J., & Sadoun, M. J., Residual stress measurement in veneering erami by hole-drilling. Dental materials, 27(5), pp , [9] Sanhez-Beitia, S., & Shueremans, L., The hole drilling tehnique for on site dedution of the stresses states in stone masonry by using eight strain gages. J. Constr. Build. Mater., Vol. 23(5), pp , [10] Sanhez-Beitia, S., Shueremans, L. & Van Balen, K., In site stress measurement on the piers of the Saint Jaobs hurh in Leuven (Belgium). Int. J. Arhit. Heritage: Conserv. Anal. Restor., Vol. 3(2), pp , [11] Sanhez-Beitia, S. & Roa P., Hole Drilling Tehnique for In-Site Stress Measurements of Masonry Piers: Analysis of the Santa Maria del Mar Cathedral in Barelona, Spain. J. Arhitetural Eng. (ASCE), Vol. 20(3), pp , [12] Shajer, G.S. & Yang, L., Residual-stress Measurement in Orthotropi Materials Using the Holedrilling Method. Experimental Mehanis, Vol. 34(4), pp , [13] Bert, C.W. & Thompson, G.L., A Method for Measuring Planar Residual Stresses in Retangularly Orthotropi Materials. J. Composite Mat., Vol. 2 (2), pp , [14] Standard UNE-EN 56544:2011 Clasifiaion visual de la madera aserrada para uso estrutural. Madera de oniferas (in Spanish), [15] Basterra, LA. et al., Strength testing of Poplar duo beams, Populus x eurameriana (Dode) Guinierv. I-214, with fibre reinforement. J. Constr. Build. Mater., Vol. 36, pp , WIT Transations on The Built Environment, Vol 153, 2015 WIT Press ISSN (on-line)

Finite Element Modeling of Pre-Stressed Hollow Core Slabs

Current Siene International Volume : 04 Issue : 04 Ot.-De. 2015 Pages :596-603 Finite Element Modeling of Pre-Stressed Hollow Core Slabs 1 Ali N. Deeb, 2 M. Abou Zeid Tarkhan and 3 E. M. El-Tehewy 1 Syrian