The external thermal insulation composite system, a comprehensive stress-strain analysis

Transcription

1 The external thermal insulation comosite system, a comrehensive stress-strain analysis Amilcare Collina MAPEI S..A. Italy a.collina@maei.it Gian Piero Lignola University of Nales Italy glignola@unina.it Abstract: The External Thermal Insulation Comosite System (ETICS) is the only viable solution for the energetic ugrading of the existing buildings. The effects of the installation of the external thermal insulation comosite system are not limited to the energy saving and comfort. A comrehensive stress strain analysis on the ETICS comonents is resented, which includes detailed evaluations of: (i) the eel stress of the adhesive, generated by the restrained thermal gradient of the insulation anel; (ii) the shear stress of the adhesive generated by the thermal elongation/shrinkage of the insulation anel; (iii) the buckling henomenon in the anel, due to the resence, in summer, of an eccentric comression load restrained by the adhesive; (iv) the role of mechanical fixings alied in order to increase the safety factor of the installation. The analysis clearly demonstrates that the adhesive is the key comonent of the ETICS. Keywords: Adhesive, Shear stress, Peel stress, Buckling, Mechanical fixings. 1. INTRODUCTION The effects of the installation of the External Thermal Insulation Comosite System (ETICS) are not limited to the energy saving and comfort, caused by the difference between the temerature inside the building and the temerature of the external environment, both in winter and in summer season. Such effects are already well known; in fact ETICS is a feasible solution for the energetic ugrading of buildings. However various stresses rise from the interaction of building structure and ETICS, and related stresses are transferred by the fixing system. ETICS usually include an adhesive, a base coat, an insulation anel, an alkali-resistant reinforcement mesh, a rimer and a finishing coat, as well as sealants and ancillary

2 materials for the installation [1]. Mechanical fixing devices have been also adoted instead or along with adhesives, but frequently without any technical evaluation and design of the alication. This may jeoardize the aim of increasing the safety of the adhesive alication. Restrained differential thermal distortion causes different yet crucial stress states, esecially related to summer when thermal elongation induces comressive stresses in the slender insulating anels of the ETICS. For this reason, a comrehensive stress analysis on the ETICS comonents is resented, which includes detailed evaluations of: 1. the eel stress of the adhesive, generated by the restrained differential thermal distortion of the insulation anel; 2. the shear stress of the adhesive generated by the thermal elongation/shrinkage of the insulation anel; 3. the buckling henomenon in the anel, due to the resence, in summer, of an eccentric comression load restrained by the adhesive; 4. the role of mechanical fixings alied in order to increase the safety factor of the installation. A revious work [2] highlighted that the ETICS allows the thermal gradients to be reduced inside the masonry wall leafs, and temerature rofiles in the whole building system were also rovided. Axial actions in the masonry were redominant and stresses were higher in the external wall leafs. The maximum tensile stresses were reached during winter season and the resence of the ETICS is able to reduce them of about 75%, leading to higher safety margins for the structure. Stresses rise in the adhesives used to fix the anels because the ETICS reduces the temerature variation in the masonry, ushing it inside the insulating anel (Figure 1). Plaster Masonry Insulating Panel External Leaf Internal Leaf Plaster Plaster Masonry Insulating Panel External Leaf Internal Leaf Plaster a) Winter season b) Summer season Figure 1: Temerature rofiles (blue line with ETICS, black line without ETICS) 2. PEELING STRESS WITHIN THE ADHESIVE The masonry is assumed rigid if comared to the insulating anel, because the Young modulus is about five hundred times higher, as well as the thickness is higher for masonry. For eeling stress evaluation, the adhesive is modelled as a series of indeendent normal srings smeared over the masonry. Hence a Winkler tye modelling is adoted leading to a fourth order differential equation [2]. Such a model is sensitive to the curvature rather than the axial linear deformations. For this reason it is adoted to evaluate the effect of thermal gradients in the anel, i.e. the difference of temerature (related to the anel thickness) on the external and internal surface, assumed equal to

3 -28 C and 20 C in summer and winter season, resectively. Relevant geometrical and mechanical characteristics of an illustrative ETICS (Figure 2) are reorted in Table 1. Table 1 Geometrical and mechanical characteristics Panel Adhesive Young Modulus 12 MPa 1200 MPa Shear Modulus n.a. 500 MPa Thickness 80 mm 4 mm Thermal exansion 70 μm/m C -1 n.a. Half Length 625 mm n.a. Adhesive Insulating Panel Masonry Figure 2: Sketch of half of the ETICS (symmetric with resect to its center) Transverse dislacement, bending moment (and related maximum stress) in the anel and the eeling stress in the adhesive can be evaluated according to the roosed model [2] and they are reorted in Table 2. Tensile eeling stresses are selected because they are resonsible of the bond failure. Table 2 Main effects of thermal gradient inside the insulating anel Summer Winter Bending Moment (maximum stress) 12 kpa 8 kpa Transverse dislacement 1 μm 0.7 μm Peeling stresses (in tension) 63 kpa 195 kpa The comarison between summer and winter season brings to the conclusions: in the summer season, the eeling stress in the adhesive is generally lower than in winter season, indicating that the winter season is more critical; the characteristic length of the henomenon in the assumed examle is about 57 mm, and consequently the only solicited ortion of the adhesive is close to the edges of the anel; the other, inner, ortion of the anel is almost unloaded, so that a reduced alication of the adhesive only along the erimeter of the anel aears safe. Some of these conclusions are misleading because in summer season the comression in the anel, due to the linear thermal exansion, is restrained thus leading to comression stability issues. In this case mechanical stress in the anel could reach much higher values than few kiloascals. However the stability is a crucial issue if the adhesive is sot alied only at the free edges of the anel, as it will be discussed in next Section 3.1.

4 3. SHEAR STRESS WITHIN THE ADHESIVE The ETICS resents a temerature gradient inducing not only a curvature inside the insulating anel, thus leading to eel stresses, but also a temerature linear variation with resect to the reference temerature, T r, corresonding to zero stresses in the wall (building time temerature, assumed equal to about 20 C in the resent work). This linear temerature variation induces shear stresses due to the shear lag henomenon at the free edges of the insulating anel. Assuming again a rigid masonry, the adhesive is modelled as a series of indeendent shear srings smeared over the masonry with stiffness G a /t a, where G a and t a are the shear modulus and the thickness of the adhesive, resectively. Each insulating anel can be modelled searately due to the tyical alication mode: E and t are the Young Modulus and the thickness of the anel, resectively. Shear stresses, τ a, are given by γ G a, where γ is the shear strain given by the ratio between relative dislacement of the anel and the rigid masonry, the latter being negligible, and the thickness of the adhesive. The first derivative of shear stress yields to: dτ dx G a a = ε (1) ta where ε is the derivative of anel s dislacement and is given by ε = ν (2) E where linear thermal exansion or contraction, ν = λ (T-T r ), of the anel is due to the difference between the actual average temerature, T, inside the anel and a reference temerature, T r. The thermal exansion coefficient is λ. Equilibrium of shear and axial stresses in the anel shows that variation of axial stress in the anel,, is related to the shear stress in the adhesive, τ a, according to: t d = τ a (3) dx The second order differential equation governing the system (the sketch of half of the insulating anel and adhesive was reorted in Figure 2) is given by equating eq. (1) to the derivative of eq. (3), yielding to: 2 d dx 2 β = βe ν (4) 2 2 where the arameter β is related to the relative stiffness of adhesive (in shear) and anel (axially): The integral of the differential equation is: G a β = (5) Ett a

5 Coshβ x = Eν 1 Coshβ L The integral is based on the following two boundary conditions: 1. On the axis of symmetry (x=0) the shear stress (roortional to d /dx) is zero due to symmetry. 2. At the free edge of the anel (x=l), where L is half length of the anel, the axial stress,, in the anel is zero (condition at the free edge). Axial stress in the anel,, is given by eq. (6); the maximum of the function, corresonding to maximum axial stress is given at x=0, and it is equal to: ( x 0) = = E ν (7) Shear stress in the adhesive, τ a, is given by eq. (3); the maximum of the function, corresonding to maximum shear stress is given at x=l, and it is equal to: Sinhβ x τa = βte ν τa( x= L) βte ν Coshβ L In fact the hyerbolic function (Tanh βl) is almost 1 for tyical insulation systems. In the following lots the values for the shear stresses in the adhesive and the axial stress in the anel (ositive are comressive stresses) are reorted for summer season, which is the most critical for this henomenon. The relevant geometrical and mechanical characteristics of the materials were reorted in Table 1. The thermal linear variation in the anel is assumed equal to +20 C in summer. Figure 3 shows the shear stress variation in the adhesive in summer season as a function of the distance from the center of the anel. The stress concentration is at the free edge and the maximum shear stress is found equal to 728 kpa (increasing to about 891 kpa in the case of thick anels, t =120 mm). (6) (8) Figure 3: Adhesive shear stresses in summer season

6 Figure 4 shows the axial stress variation in winter season in the anel as a function of the distance from its center. The axial stress is almost constant and it is about 17 kpa. The stress increase is almost concentrated at the free edge; even if stress resents a rather low value, an incorrect alication of adhesive at the edges only of the anel causes an eccentric unctual restraint, thus an eccentric loading on the anel. Figure 4: Axial stresses in the anel in summer season 3.1 Euler stability under eccentric loading The Young modulus of the anel is very low and, additionally, the slenderness, (2L 12)/t, of the anel is very high, so that the critical stress, cr, may be rather low. It may be comarable to the axial stress,, induced by the restrained linear thermal exansion. Only exansion (summer season) is crucial, while contraction, inducing tension, is stable. The critical stress is: 2 2 π Et cr = ( L) The safety factor (i.e. the ratio cr / ) for stability in the case of 80 mm thick anel is 1.6 [2], however, in the case of less thick anels, stability failure can be redicted (e.g. safety factor is smaller than 1 for anel thicknesses lower than about 50 mm). However this analysis is related to the so called ideal elements, but the critical stress is also highly related to the lanarity of the anel and is reduced due to alication defects. Furthermore, adhesive sot alications reresent an eccentric restraint for the anel thus leading to eccentric loadings (see Figure 5). A first order analysis of the anel, neglecting the effect of deflection and stability, allows to evaluate the axial stress variations (ositive are comressive stresses) generated by comression and bending induced by eccentrically restrained linear thermal exansion. The first order bending moment is constant along the anel and is couled with a constant axial comression. (9)

7 Figure 5: ETICS under eccentric loading due to sot adhesive alication However a second order analysis, taking into account the effect of lateral deformation, highlights not only a significant increase in the bending moment, but also a significant increase in terms of lateral dislacement of the anel. Both the two henomena may lead to failure of the ETICS either due to failure of the material of the anel, or due to excessive deformation being not comatible with external finishing. Equating the external moment t (y+e) with internal moment (roortional to second order derivative, d 2 y/dx 2 ), the second order differential equation governing the system is given by: Et 12 dx 3 2 d y 2 + ty= te In this system, eccentricity of the axial load is e and can be assumed equal to half thickness of the anel, t /2. The integral of the differential equation is: cos( α ) ( α ) (10) y = A x + Bsin x e (11) Where two constants (A, B) have to be determined and the arameter α is related to the inverse of reviously defined safety factor for stability (i.e. the ratio / cr recalling eq. (9) where the total length of the anel, L is equal to 2L) and it is: 12 t π 3 Et L cr α = = (12) It is worth noting that this analysis has no sense if cr, in fact, in this case a stability failure can be redicted (e.g. for a thermal variation of about +48 C for the system under exam). The boundary conditions are: at the restraints (x=0 and x=l ) the lateral dislacement, y, is zero. Lateral dislacement of the anel, y, is given by eq. (11); the maximum of the function, corresonding to maximum dislacement is given at mid-san, x=l /2, and it is equal to: L cos α x 2 y= e e L cos α 2 (13a)

8 L L π y x= = e sec α 1 = e sec cr (13b) Similarly bending moment, couled with constant axial comression, deends on y and along the anel is given by M= t (y+e); the maximum of the function, corresonding to maximum bending moment is given at x=l /2, and it is equal to: L L π M x= = te sec α = te sec cr Bending moment thus leads to maximum and minimum axial stresses at the two sides of the anel, outer and inner, resectively [3] : 6M 6e L π = ± = ± = ±,max 1 sec 1 3sec 2 α,min t t 2 2 cr Figure 6 shows the maximum deflection (according to a second order analysis) at mid san of the anel in summer season as a function of thermal variation, T-T r. It is the difference between the actual average temerature, T, inside the anel and a reference temerature, T r. (14) (15) Deflection at mid san [mm] t =80mm t =120mm L /100 L / Thermal variation, T-T r [ C] Figure 6: Maximum deflection (according to a second order analysis) at mid san in summer season The maximum deflection corresonding to a thermal variation, T-T r =+20 C, reviously considered, yields to a crucial value of about 35.5 mm being about L /35. This is certainly a deflection not comatible with usual alications and external finishing. Even thick anels having t =120 mm, show a deflection about L /75.

9 Two feasible thresholds are remarked in the lot, namely deflection levels equal to 1/100 and 1/250 of the clear san of the anel L, assumed equal to 1250 mm in this examle. Figure 7 shows the maximum and minimum axial stresses (according to a second order analysis) at mid san of the anel in summer season as a function of the same thermal variation, T-T r. The axial stress is raidly increasing at the inner side of the anel and decreasing at the outer side, reaching critical values corresonding to a thermal variation, T-T r =+20 C, reviously considered; namely 112 kpa in comression and -78 kpa in tension. This value is much higher than the maximum axial stress in the anel, =17 kpa, evaluated according to eq. (7) and it could be crucial if comared to average strength of XPS (Extruded olystyrene having density of about 33 kg/m 3 ) or EPS (Exanded olystyrene having density of about 12 kg/m 3 ) which is about 200 kpa and 50 kpa, resectively, even in the case of thick anels having t =120 mm t =80mm,max Axial stress in the anel [kpa] 200 t =120mm t =120mm t =80mm,min Thermal variation, T-T r [ C] Figure 7: Maximum and minimum axial stresses (according to a second order analysis) at mid san in summer season The alication of the adhesive in a continuous layer and the care of lanarity of the anel are the only ways to overcome these drawbacks. In fact the resence of the adhesive in a continuous layer (srings all over the length of the anel) yields to significantly higher values of the critical stresses [4] and avoids the lateral deflection of the anel. 4. MECHANICAL FIXINGS Mechanical fixings have been seen, in some cases, as an additional safety aid to adhesive, for instance in case of adhesive failure, or even as a ossible substitution of the adhesive. However this idea dangerously jeoardizes the alication of insulating anels. In fact, the entire thermal exansion or contraction of the anel is counteracted by oint restraints and each anchor loads the anel at a much higher level than a feasible value for the integrity of the ETICS. A tyical anel, the one considered so far, is usually installed using four anchors at the four corners and a fifth one in the middle (see Figure 8).

10 Φ 1 = 60 mm. w t Φ 2 = 10 mm. L Figure 8: Tyical (incorrect) scheme for mechanical anchors on a anel The average axial stress in the anel distributed over the cross section of the anel (e.g. w =625 mm wide and t =80 mm thick), localizes at each coule of anchors, over the lateral rojected area of the anchor (e.g. Φ 2 =10 mm wide and t =80 mm deth, according to the simle scheme of Figure 8). The stress, f, transferred by the anchor to the anel reaches eak values of about: w f = n Φ (16) According to the assumed system roerties (having a coule of anchors er side, i.e. n=2), the comressive stress, f, along the anchor is about 530 kpa, yet doubled in the other normal direction (substituting w with L ), being a worrying value for the low strength of tyical insulating anels. Even in the case of a friction-tye connection, to avoid stress localization and to distribute the shear load over a wider surface of the anel, tighten fixings should be adoted tensed at a level roortional to the friction coefficient. The roof load or the tensile stress in each anchor to induce the amount of friction in the total area subservient to that anchor is usually difficult to control using tyical commercial fixing devices for ETICS and it can easily overcome the strength of the anel or roducing grooves over the external surface. For the revious reasons, similarly to sot alications, mechanical fixing devices could not avoid stability failure in summer due to restrained thermal exansion, nor counteract inflexion of the anels due to high thermal gradients. Furthermore they cannot substitute the adhesive (even in the case of adhesive failure) because they would yield to anel localized failures if they are laced at the corners of the anel with thermal variations. However a single central anchor could, in some cases, avoid dangerous downfalls of failed anels, but a last check should consider wind effects. 4.1 Wind effects Even assuming a really high ressure dro during a storm equal to 1 atmoshere, the corresonding uniform stress is about 101 kpa, much lower than the stresses induced in the adhesives by the thermal effects. Conversely in the case of mechanical anchors the stress localizes at the round lates, yielding to otential safety concerns. A more realistic ressure on the anel surface can be given by Eurocode 1 art 1-4 [5]. In this work the wind action is reresented by a simlified set of suctions due to backwind in the leeward direction, based on mean wind velocity. However, wind action deends also 2

11 on height determined from the terrain, roughness and orograhy. The velocity ressure, q b, is related to wind velocity, v b, deending on air density ρ=1.25 kg/m 3, according to: 1 2 qb= ρ vb (17) 2 Then velocity ressure is reduced according to an external ressure coefficient which, in the case of a vertical downwind wall of a simle building can be assumed equal to -0.4, so that the suction on the anel is a force roortional to the surface of the anel. Assuming a wind velocity, common in Euroe, equal to about 30 m/s, in the illustrative system, the effective external suction is 225 Pa and the force is about 176 N. This force is restrained by the round late of the central anchor having a circular area of 2827 mm 2, assuming Φ 1 =60 mm. In such case the localized ressure on the anel is about 62 kpa, being accetable for XPS systems, but not for EPS systems. This check could bring designer to increase the diameter, Φ 1, of the late of the single central fixing, e.g. u to large lates having Φ 1 =140 mm, thus yielding to localized ressures of about 11 kpa. 5. CONCLUSIONS a) The effects of installation of ETICS are not limited to energy saving and comfort, caused by the difference between the internal and external temerature, both in winter and in summer season. Such effects are already well known; but a variety of stresses rise from the interaction of building structure and ETICS, and related stresses are transferred by the fixing system. b) The main temerature gradient lies inside the insulating anel. This restrained thermal variation is the main reason for the stresses in the adhesives used to fix the anels to the structure. c) The inflexion of the anel due to thermal gradients within the anel thickness leads to eeling stresses in the adhesive. The model roosed to evaluate these stresses shows that the most solicited ortions of the adhesive are close to the anel edges and maximum tensile stresses are relatively high. d) The elongation of the anel due to linear thermal variation within the anel leads to shear stresses in the adhesive. The model roosed to evaluate these stresses shows that the most solicited ortions of the adhesive are again close to the anel edges and shear stresses are considerably high. e) Stresses are generally high so that a high quality adhesive secifically develoed for this alication must be used in order to guarantee the erformance of the system. However stress localization close to the anel edges could suggest, incorrectly, that a reduced alication of the adhesive, along the erimeter of the anel only, seems safe. f) The eccentrically restrained exansion of the anel in summer season yields not only a significant increase in the axial comression and bending moment, but also a significant increase in terms of inflexion of the slender anels, thus stability issues. Both the two henomena may lead to failure of ETICS either due to failure of the insulating material or due to excessive deformation, not comatible with external finishing.

12 g) The stability is more and more crucial for lower thicknesses of the anel. The alication of the adhesive in a continuous layer and the care of lanarity of the anel are the only ways to overcome these stability issues. h) The idea to add safety or substitute the adhesive with mechanical fixings dangerously jeoardizes the alication of insulating anels. Such oint restraints cannot substitute the adhesive (even in the case of its failure) because they would yield to anel localized failures if they are laced at the corners of the anel. Similarly to sot adhesive alications, mechanical fixings could not avoid stability failure in summer due to restrained thermal exansion, nor counteract inflexion due to high thermal gradients within the anel thickness. i) In some cases, a single central fixing could avoid dangerous downfalls of failed anels, but a further check should consider wind effects. Care should be devoted also to masonry substrate rearation, comlying with Euroean ETAG 004 guideline [6]. ETICS are surely attractive from economic and financial oints of view. However, the design and installation of the external thermal insulation comosite system should not be limited to the energy saving and comfort. The critical issues emerged during the comrehensive stress analysis on the ETICS comonents suggest that the adhesive is the key comonent of a successful ETICS. Refined and scientifically sound mechanical analyses are the basis for a correct design and installation involving adhesives, as it was already demonstrated for tile-substrate interaction in the case of shrinkage effects [7]. 6. REFERENCES [1] Collina, A. Comfort and energy saving: the External Thermal Insulation Comosite System (ETICS). 2 nd Portuguese Congress on Construction Mortars (APFAC), Lisboa, Portugal, [2] Collina, A., Lignola, G.P. The External Thermal Insulation Comosite System (ETICS): more than comfort and energy saving. 3 rd Portuguese Congress on Construction Mortars (APFAC), Lisboa, Portugal, [3] Gambarotta, L.; Nunziante, L.; Tralli, A. Scienza delle costruzioni. McGraw-Hill Co. Milano, Italy In Italian [4] Augenti, N. Lezioni di stabilita' delle strutture. Ilardo. Naoli, Italy In Italian [5] Eurocode 1: Actions on structures : EN : Part 1-4: General actions Wind Actions, CEN, [6] ETAG 004: Guideline for Euroean Technical Aroval for EXTERNAL THERMAL INSULATION COMPOSITE SYSTEM WITH RENDERING. EOTA Brussels, Belgium. Edition [7] Lignola, G.P.; Collina, A.; Prota, A.; Manfredi, G. Analysis of tile-substrate behavior subjected to shrinkage. In CD-Proceedings, XIX Convegno AIMETA Associazione Italiana di Meccanica Teorica e Alicata. Ancona, Italia, 2009.