DISPLACEMENTS OF SIDE WALLS WITH WALL-GIRTS IN INDUSTRIAL BUILDINGS UNDER VERTICAL SETTLEMENTS

The localized settlement of columns in large metal industrial buildings induces out-of-plane displacements of side walls of the same order as the settlement, which may affect service conditions in the building. For a structural configuration formed by frames, side-walls and wall-girts, this work reports results from testing a small-scale model together with computational modeling of the full-scale structure. Dimensional analysis was used to scale the geometry and properties from full-scale to small-scale, leading to an overall scale factor of 1:15. Differential settlements having a controlled amplitude were imposed at the central column, and displacements were monitored using mechanical devices. The computational model employed shell elements for side-walls and wall-girts. Good agreement was found between tests and computer modeling. The results at the full-scale level, indicate that, for settlements likely to occur in granular soils, the associated lateral displacements exceed those allowed by current US regulations. Stiffening the structure was investigated by use of stiffer girts, as well as by reducing their spacing. The influence of frame height was also investigated. The overall conclusion is that out-of-plane displacements of side-walls may easily exceed allowable values unless they are specifically considered at a design stage.


INTRODUCTION
The effects due to localized settlements of part of the foundation in metal industrial buildings are not taken into account at a design stage; however, they frequently occur during the service life of a building. Such problems may become important when the building is constructed on compressible soils, in which the load-bearing capacity depends on soil type and moisture contents. Metal industrial buildings designed to process and store agricultural products are often built in zones with natural or artificial irrigation, in which the soil may lose part of its load-carrying capacity. Further, soil moisture may increase due to seasonal rains or due to accidents in an adjacent channel or piping system.
Light-weight industrial structures have low redundancy in their load-transfer mechanisms, so that differential settlements may cause changes in the way equilibrium is provided by the frame and roof system. Of special concern in this paper are settlements between adjacent columns or at the corners of a building.
Damage due to vertical settlements may affect the main resisting structure, secondary elements, and equipment protected by the construction, and their consequences are typically observed as out-of-plane displacements in the side walls. Such lateral displacements arise due to buckling of the side walls under imposed vertical displacements [1]. All this may weaken the overall structural strength and stiffness of the building; and may also affect the service conditions of the building, including the normal functioning of large sliding doors.
Only a small number of references have focused on this problem with reference to sustainability issues [2]. Effects of support settlements have been considered in metal cylindrical shells [3]. Buckling of storage tanks due to support settlements was studied by Godoy and Sosa [4], Zhao et al. [5], Gong et al. [6], Cao and Zhao [7] and Fan et al. [8]. Darmawan [9] reported severe damage induced by column settlement on a metal frame structure. The non-linear behavior of soil in a two-story frame building was studied by Agrawal and Hora [10]. All those results were based on computational modeling. Codes of practice, such as ASCE [11], specify limits to lateral displacements of the side walls in metal buildings in the order of H/400 to H/600, where H is the height of the building. Such limits were established based on wind pressures acting on the building and do not considerer either buckling or settlement of supports.
Previous works by the authors showed that the out-of-plane displacements in side walls due to vertical settlements are larger than allowed values when considering the main resisting structure but neglecting the contributions of secondary elements in side walls [1]. This paper aims to evaluate the influence of wall-girts as a strengthening aid in cases of localized support settlement in metal industrial buildings.

FULL-SCALE PROTOTYPE AND REDUCED-SCALE PHYSICAL MODEL
A physical model was built and tested in this research in order to obtain empirical evidence to validate computer models. A full-scale prototype was first defined and then a small-scale model was built using similitude theory (see, for example, [12]).

Full-scale prototype
With reference to Figure 1, the geometry of the prototype was characterized by height H, height of columns h, frame width B, and span between frames ℓ. The main resisting structure is formed by a set of steel frames, whereas secondary elements include wall panels which are strengthened by wall-girts and roof purlins. Previous studies [1] showed that settlement of a single column may have severe consequences on the side walls that extend to the next frame in both directions, but do not extend further to other frames. For this reason, the fabricated model was limited to three frames, which includes the side walls with five wall-girts, whereas the computational model could use symmetry conditions and reduce the domain of interest to two frames, as shown in Figure 2.a. The initial casestudy investigated had H = 6m, h = 4m, ℓ = 5m, and B = 15m. Separation between girts, shown in Figure 2.a, was s = 0.90m. Such secondary elements are considered in this work to investigate their influence in reducing side displacements. The roof purlins and wall-girts were assumed as a C-shape cold-formed cross section with dimensions shown in Figure 2.b. The values of dimensions for the assumed prototype are given in the second column in Table 1.  The side-walls in the prototype were initially assumed with a trapezoidal T1010 section. However, for both computational and experimental modeling, the cross section was substituted by another one with uniform thickness, in which the thickness was evaluated to have the same modulus of inertia as the trapezoidal section. This yields an equivalent thickness of side walls equal to twall=9.6mm. The modulus of elasticity of steel was assumed as Ep = 204GPa, with density ρp = 7850Kg/m 3 .

Reduced-scale physical model
The full-scale building was modeled down to reduced-scale dimensions, and the resulting small-scale model was fabricated and tested during this research. Geometric similitude was used to scale the geometry, together with a similitude to represent the constitutive materials. The overall dimensions in Figure 2.a were scaled down to Bm = 1m, so that there is a scale factor in the geometry given by: This scale factor αA was used to identify the geometry of the small-scale physical model, leading to model dimensions Hm = 400mm, hm = 267mm, ℓm = 333mm, and sm = 60mm. However, because of the considerable differences between the overall building dimensions and the side wall panels and wall-girts, different scale factors were used to identify the thicknesses, thus leading to a geometrically distorted model. The adopted material for the main frame in the model is aluminum with a square cross-section having 12mm sides, with elastic properties are E = 70GPa, μ = 0.33. The side walls were made of acetate sheets with commercially available thickness tm = 0.22mm. Mechanical properties for acetate were evaluated following ASTM D882-02 [13] and the values were Em = 2294MPa (Young ´s modulus) and μm = 0.4 (Poisson´s modulus), the density were also measured (ρm = 1320Kg/m 3 ). The material scales for acetate are thus given by: where  is the ratio between the weight of side wall panels (Fp for prototype and Fm for small-scale model). The scale factor for thicknesses is As required, the relation between θ, γ, and α satisfies the condition The third column in Table 1 (small-scale model of prototype) shows the cross section of a wall-girt under a scale factor 15 and 43.6 for thickness. However, such details could not be achieved in the small-scale model, with the consequence that a simplified section with dimensions shown in the fourth column of Table 1, based on an equivalence of the moment of inertia, were used. The settlement was induced in the central column, as shown in Figure 3.b. The settlements of the column and the out-of-plane displacements were measured with 0.01mm precision. The relations between the imposed settlements in prototype and model are shown in Table 2. Limits in prototype settlement are usually given as 25mm in civil engineering structures (see, for example, [14] [15]).

EXPERIMENTAL RESULTS FOR THE SMALL-SCALE PHYSICAL MODEL
Testing was carried out by imposing a vertical displacement at the central column, thus causing a relative displacement δ with respect to the side frames. To facilitate visualization of points on the side walls, a grid formed by 30 × 30 mm squares was drawn in the model. As a consequence of this vertical displacement, there are out-of-plane displacements w on the side walls, forming diagonal shear bands with alternate inwards and outwards displacements. These bands form a Vshape with a vertex at the joint between wall-girts and column, being symmetric with respect to the central column in which δ is imposed. The displacements in the model are scaled up to the prototype dimensions by use of the scale factor αA = 15, so that inwards and outwards displacements in the horizontal direction of the prototype can be plotted in Figure 4. The deflected shape is a function of settlement, with nonlinear changes in shape and amplitude. For example, for δ = 5mm there are outward displacements in Figure 4.b with a maximum of about w = 35mm; this increases to close to w = 50mm at δ = 10mm; but for larger settlements δ = 20mm and δ = 25mm the lateral displacement becomes inwards in the order of w = 25mm. On the other hand, the number of bands increases with increasing δ. A reduction in w is seen to occur near the columns and wall-girts, which induce a restraint to lateral deflections. This effect can also be noticed in Figure 5, in which the vertical variation of displacements along the central column and at two intermediate positions, is shown, together with the location of the wall-girts in elevation. A summary of results is shown in Table 3, in which inward displacements (w) are identified with negative values; and outward displacements are positive values. The largest outward displacement occurs for δ = 10mm, whereas the largest inward displacement occurs for a low value δ = 5mm.

Tab. 3: Maximum and minimum lateral displacements, in [mm].
Displacement maps are plotted in Figure 6. Wall-girts are also shown in the figures to facilitate visualization of restrains introduced by secondary elements. The general trend is the development of inclined bands, with an angle close to 45° for δ = 10mm, and the inclination reduces to about 32° for δ = 25mm. There is a clear incidence of wall-girts on displacements, not just by affecting their amplitude but also by modification of the shear bands. Previous computational models [1] showed continuous bands because wall-girts were not included in the model.

Configuration investigated
The prototype structure has been investigated using a finite element model [16]. The analysis requires modelling of the frame, wall-girts and side-walls, as shown in Figure 2.a. Structural symmetry was used to reduce the number of unknowns in the model. Rectangular shell elements (identified as S4R5 in ABAQUS) with five DOF per node and four nodes per element were employed. A finite element mesh with 32,000 elements was defined by means of convergence studies and has been used in the computations reported in the following sections. Wall-girts were modelled using shell elements and the assumed dimensions (120mm×50mm×15mm cross-section and 3.2mm thickness) are shown in Figure 2.b. The separation between girts was 0.90m, thus including five wall-girts in elevation.
Some details regarding modeling of joints need to be presented. (a) Girts are connected with columns by means of welds, which are represented in the model by joint elements identified as "Tie" elements. (b) Side panels are connected with girts by means of screws, and these are modeled by "Beam" joint elements, which restrain displacements and rotations. A total of 100 screws were used in the model, of which 20 were applied in each girt at a spacing of 260mm.

Computational results for the full-scale prototype
A geometrically non-linear static analysis was carried out to investigate the full-scale prototype shown in Figure 2.a. The assumed modulus of elasticity was E = 204GPa, with Poisson ratio μ = 0.3. The imposed vertical settlement was taken as δ = 5mm, 10mm, 20mm, and 25mm, to replicate the experiments. The dimensions of girts were considered as in Figure 2.b. To reduce computations, symmetry was used so that only the right-hand side panel is represented in the finite element discretization, as shown in Figure 2.a, and settlement is imposed on the column to the left of this figure.
Results for the case δ = 25mm are shown in Figure 7.a, leading to maximum out-of-plane displacements w = 25.7mm (inwards) and 33.3mm (outwards). The bands are seen to cross the lines of girts in this case, thus forming continuous diagonals. The values are compared with those measured in the tests (see Figure 6.d) and there are only 5% differences in maximum values, with some differences in the diagonal patterns. In the finite element model the displacements w affect the complete side-wall whereas they tend to be localized in the region where the settlement is imposed in the tests. The same number of shear bands occurs in both computational and physical models, with similar inclination.

Fig. 7 -Computational results for δ = 25mm. (a) Map of out-of-plane displacements; (b) Out-ofplane displacements plotted in elevation z/h, at a distance x/l= 0.18 measured from the central column, and comparison with experiments.
A comparison of vertical variation of displacements is shown in Figure 7.b. The computational results seem to capture the main features of the behavior as detected in the physical model, and this provides confidence in pursuing a more thorough understanding of behavior based on computational modeling.

INFLUENCE OF PARAMETERS CONTROLLING THE RESPONSE
To understand the significance of the lateral displacements reported in the previous section, it is important to refer to what is acceptable in practice. ASCE [11] rules establish limits to out-ofplane deflections which range between H/400 and H/600; in the present case this means bounds between 15mm and 10mm. Such bounds are clearly exceeded by the values reported in the present study. Thus, it would be desirable to understand what parameters may affect the response in order to reduce such lateral displacements.

Influence of strengthening the cross section of wall-girts
Computational modeling is used in this section to illustrate the influence of the stiffness of wall-girts on lateral deflections under a given settlement. In each case the separation between girts remains fixed at 0.90m, and the cross sections are modified as shown in Table 4. The thickness of the wall-girts is taken as t = 3.2mm, and the overall dimensions change from cases P1 to P7. The case already taken as case study in the previous section is P1. Although typical cross sections in practice range from P1 to P5, two stiffer cases, P6 and P7, were also investigated to understand what would it take to improve the behavior.

Tab. 4: Geometry of cross section of wall-girts considered in the analyses.
Variables a1, a2, a3, t, are illustrated in Figure 2.b. Values in [mm].
Results are shown in Figure 8. The order of these figures corresponds to the order of girts in Table 4. In all cases considered in this section, a settlement δ = 25mm is imposed, and separation between girts is 0.90m. As expected, lateral displacements decrease with increasing stiffness of girts. For "weak" girts, the shear bands are continuous and affect the complete panel across girts. For "robust" girts the shear bands are interrupted and extreme values of w occur between girts.
In comparison with girt P1, the sections P2 and P3 cause a reduction of 19%, but more significant changes are found for P4 (30%) and P7 (52%) always measured with respect to P1. The w values for P7 are 22.2mm (outwards) and -21.4mm (inwards), which are about half of those computed for P1. A summary of results is shown in

Influence of separation between wall-girts
To understand the influence of the separation between wall-girts, their values were reduced from 0.90m to 0.70m and 0.60m, as shown in Table 6. Changes are calculated by comparing the displacements for P1, P2, P3, P4, P5, P6, and P7 in this table with displacements for P1 in Table 5. Because there are positive and negative extreme values, the largest value is considered to compute changes. For reasons of brevity, maps of lateral displacements are not shown here, but the number of bands increases for separation 0.60m, with an inclination of approximately 30°. There is an interruption of bands for P7 caused by the stiff girts. The practical case P5 with separation 0.60m shows a 57% reduction with respect to the reference case P1, but values still exceed those allowed by ASCE specifications.

Influence of ridge height
The influence of the ridge height H of the frame on the deflected pattern was next investigated under an imposed settlement δ = 25mm.
First, consider H = 10m. A summary of results is shown in Table 7 for girt separations in the range s = 0.90m to s = 0.50m, and for various cross-sections of girts. Changes in the last column were computed with respect to values for P1 in the first row. Because of the increase H with respect to the previous results reported in this work for H = 6m, the allowable lateral displacements increase to H/400 = 25mm and H/600 = 17mm. For a spacing s = 0.90m, acceptable lateral displacements are reached for girts P4 to P7. Separations of s= 0.50m and s = 0.60m could be acceptable for all alternatives considered, except for P1.

Tab. 7: Out-of-plane displacements for a frame with H = 10m under an imposed settlement δ = 25mm
Second, ridge height H = 8m was consider as an intermediate case, and results are shown in Table 8. The limit value for lateral displacements in this case is H/400 = 20mm; thus, wall-girts identified as P5, P6 and P7 with s = 0.70m yield satisfactory side displacements.

Wall-girt size and separation for buildings of different ridge height
Based on results of the finite element analyses, the range of wall-girt size and separation which lead to acceptable displacements in industrial buildings is shown in Figure 9. For ridge height equal to or larger than 6m, the displacements remain within acceptable values for wall-girts equal to or larger than P5 (200mm), with separations smaller than 0.6 m. For buildings with H ≥ 8m, displacements remain acceptable provided wall-girt size is at least P4 (180 mm) and separation is s ≤ 0.6m. Finally, admissible displacements in buildings with H ≥ 10m are achieved by using P4 or larger, with s ≤ 0.9m, or else P2 (140mm) with s ≤ 0.5m.

COMPARISON WITH OUT-OF-PLANE DISPLACEMENTS UNDER WIND LOADS
Wind loaded industrial buildings are investigated in this section in order to compare outof-plane displacements with those derived from foundation settlements. For low rise buildings, i.e. H≤20m, ASCE [11] specifies the following expression for the pressure qz on the windward walls: where V is the wind speed in [m/s], and qz is evaluated in [N/m 2 ] at elevation z. Kzt is the topographic factor (with unit value for flat terrain); Kd refers to the direction of wind and a value Kd= 0.85 was adopted in this case; and Kz is the exposure factor, and Kh=0.9 was adopted in this case. Wind speed V=48m/s was assumed as a reference value for the design of the industrial building. For a partially enclosed building and for the internal spans between columns, the internal pressure coefficient is (GCpi) =±0.55 whereas the external pressure coefficient is (GCpe) = 0.45.
The maximum displacements computed for the side walls for different locations in elevation are listed in Table 9, together with the limit displacements Ulimit evaluated as H/400 according to ASCE provisions [11]. To perform calculations, the assumed stiffening was the weakest configuration investigated, i.e. P1 with separation s=0.90m. The resulting out of plane displacements for wind speed V=48m/s are lower than those specified by the design provisions, and are one order of magnitude lower than those obtained for a support settlement equal to δ = 25mm.
To identify the level of settlements that induce out-of-plane displacements of similar value to those due to wind, results for several values of δ are listed in Table 9. The out-of-plane displacements due to wind are similar to those computed for rather small settlements: δ = 7mm for H=6m, δ = 3mm for H=8m, δ = 5mm for H=10m.
Values of Ulimit are also shown in Table 9, with the consequence that settlements up to δ = 10mm are acceptable in terms of design provisions. Notice that equivalent values under wind would require wind speed much higher than that adopted for the design of the building.
The first conclusion of this comparison is that the out-of-plane dispacements under a support settlement is dominant with respect to wind effects. A second conclusion is that whenever settlements of supports can occur, then some measures should be adopted to control their effects (i.e., following Item 1.3.3 Self-Straining Forces in Ref. [11]) because wind design does not cover this aspect of behavior of lateral walls in desing buildings. Possible remedial actions depend on their economic evaluation in each case, but may include strengthening the side walls by wall-girts, as described in this work; limiting the settlements by strengthening the soil or the foundation; and/or reducing the presence of water around the building.

CONCLUSIONS
Lateral displacements of side walls induced by a vertical settlement of a column were investigated in this work for metal industrial buildings. Two approaches were used in the research, one based on a physical small-scale model and another one based on a geometrically non-linear finite element model of the structure. The computational modeling was validated by comparison with the small-scale model tested. Finite element results included maps of lateral displacements for various wall-girt configurations for a given settlement at a column.
Based on the results, some conclusions may be drawn: • The computational model discussed in this work adequately represents displacement levels obtained in the physical model. The maximum displacements tend to be located at the center between wall-girts. • Because side-walls made with acetate are very flexible in the physical model, the deflected patterns tend to be interrupted at wall-girts, and there are some differences with patterns obtained in the finite element model, which tend to be continuous bands. • Lateral displacements obtained in this work are considerably reduced (by approximately 50%) with respect to previous studies, in which the influence of wall-girts was not considered [1]. • Decreasing the separation between wall-girts and increasing their cross-section cause significant reductions in lateral displacements, and also change the deflected pattern by an interruption in shear bands as they cross the wall-girts. • To satisfy limits to displacements established by current ASCE regulations, the wall-girt configurations are more stringent in shorter than in taller frames, as given by ridge height. Such limits in ASCE were established based on wind effects and do not take into account effects due to settlement or buckling. • The out of plane displacements in side walls computed for small settlements (in the order of 5mm) are similar to those due to wind speed as used at the design stage. • Special attention should be given to vertical support settlements larger than 10mm and they should be monitored during the service life of the structure. Remedial actions may include stiffening the lateral walls by means of wall-girts or improving the soil/foundation capacity.