Structural Analysis
3.1 The case structure
The house used as a case structure for this analysis is based on a design by Jan Søndergaard, to which this report seeks to function as an initial step in the complete structural design of the house. The house is unique, as it is almost purely constructed of GFRP, and has the ambition of illustrating the architectural potential of building with GFRP, as well as act as a prototype for a possible building system of GFRP. Through the use of translucent plastic and embedded glass fibres, the whole house will be ’alive’, changing with the outdoor environment, and leaving a contrast in the depth of the shadow of the material, depending on the local density of the structure. In regards to structural engineering, these ambitions for the building poses some challenge, as a conventional approach of replacing the critical structural members with steel would compromise the vision of the house. Constructing the entire structural system with GFRP, likewise gives the opportunity to illustrate the potential of GFRP as a structural building material, by utilizing GFRP’s promising mechanical properties. The challenge lies in the lacking norms and traditions to guide the utilization of these properties. This report aims at contributing to the development of such traditions.
3.1.1 Building layout
In the following, the layout of the house is presented, to give a understanding of the background and practical utilization of the analysis performed here. The general concept of the house is shown in figure 3.1. It consists of fully closed fa¸cades along the sides, and large window panels at either end, one of which is lifted, inclining above a terrace area. In the centre of the building is an enclosed garden, with a narrow integrated greenhouse to one of the sides. This, together with the general room distribution and the overall dimensions, are shown in a plan view on figure 3.2. Here, the regularity of the dimensions shall be noted, being a part of the logical structure of the house. Also the transversely, 2 meter spaced frames shall be noted, which are also shown on the elevation in figure 3.3. These frames are the focal point of this structural analysis and are presented together with the overall structural system in the following section.
A more detailed description of the frame alone is given in section 3.1.3.
Figure 3.1: Building: Concept model.
Figure 3.2: Building: Plan view.
Figure 3.3: Building: Elevation.
3.1.2 Structural system
In this section the general structural system is presented. The section highlights the existing challenges that need to be faced in the structural design of the house, while only the regular frames are addressed in detail as the scope of this report. The structural system is presented in figure 3.4 to 3.8 through a possible constructions sequence, in order to illustrate the different elements of the structure. The first step is laying out the foundation. This is shown in figure 3.4.
The foundation is a pole foundation, consisting of crosses of GFRP elements. The foundation poles are connected to a continuous horizontal plate element, placed on stabilizing gravel. The detail of the foundation will not be address further in this report, as it is wished to keep focus upon the regular frames and work with these in depth. However, a control of the risk of crushing and buckling of the pole profiles, will be performed, as this is found to be part of the analyses of the frame. This control is performed in section 3.3.4.
Figure 3.4: Foundation layout.
Upon the foundation poles, frames are erected. The frames constitute the main structural elements in the house, and are a conceptually repeating member in the entire house. A total of eleven similar frames are erected, spanning along the transverse direction of the house’s length.
Three of these frames have a shorter span, supporting the bedroom within the enclosed garden area. The end frame, being part of the inclined end of the roof, is slightly higher than the rest, to meet the inclination of the roof. The remaining seven identical frames are the focus point of this structural analysis. These are chosen to be the scope, as they are considered to be the basic structural element, forming the core of the rest of the structure, which are to follow the same concept as these frame. The seven frames are analysed both in regards to the capacity of the beam and column members, as well as a detailed investigation of the connection between the two members, as a bolted and adhesive connection.
Figure 3.5: Regular frames in structural system.
In addition to the regular frames, a structure must be designed for the inclined end of the house, which can support the large glass panel that will be erected here. Likewise, an additional frame spanning along the length of the house must be designed, to support the green house.
These special elements are added in the structural sketch of figure 3.6. The elements added here cause some structural challenges that must be addressed, which will, however, not be done as part of the scope of this report. The challenge of the length spanning frame is partly that it spans thirteen meters, while the regular frames only span 10 meters. Additionally, the frame has no direct supports, meaning it must be supported by connections to the two regular frames
at the ends, setting these under additional load, and causing highly loaded connections. The structure at the inclined part of the house must be able to transfer the forces to the remaining structure, acting as a cantilever. Here it is suggested to add frames spanning in the direction of the length of the house, activating two foundation poles, which can transfer the moment from the cantilever through a force couple to the ground. To distribute the forces effectively to the other frames and the foundation, it could be advantageous to utilize the potential plate effect of the fa¸cade. This could be done for both the case of the structure at the inclined end of the building and the frame spanning the length of the building. The structure shown on figure 3.6 concludes the skeleton of the structure, to which the roof, floors and fa¸cades are added, which will contribute to the structure as transversely stabilizing elements.
Figure 3.6: Special structural elements in structural system.
In figure 3.7, the roof and floor elements are added, which span along the length of the house, over the frames. The possibility of long profiles from pultrusion, mentioned in section 2.1.3, should be utilized here, to have fewer elements and connections, and allow these profiles to span over several frames, reducing deflections. It is noted, that no roof is shown by the frame spanning along the length of the building. This is due to this being a green house area, where a glass structure, with supporting framing, will be build. This is not considered part of the structural
system, and will not be further addressed. The floor in this area spans the opposite way than the roof and floor in the rest of the building, between the foundation line and the length spanning frame. On the other side of the enclosed garden, there are roof elements spanning four meters, while the other parts of the roof only spans two meters. This sets additional requirements for the roof elements, which possibly need strengthening in this area, which is another challenge that should be address, but is not part of the scope of this report. The floor of this area could be supported by the foundation line.
Figure 3.7: Structural system with added roof and floor.
The final element added to the structure is the fa¸cade, which is present along the entire length of the building, as shown in figure 3.8. Here the possibility of long GFRP elements, produced by pultrusion, has great potential for implementation. As the fa¸cade is continuous along the entire length of the building, it can be utilized as a transversely stabilizing element. Within the scope of this report, the dimensioning of the fa¸cade will not be performed, and neither will the detailing of the connection between the fa¸cades and the frames. The holes remaining in figure 3.8, are to be window panels. These window panels alone invoke challenges, as they are to be connected to the frame, and especially the large window panels at the ends of the house, will
create large forces due to the self-weight of the glass, which must be efficiently transferred to the foundations.
Figure 3.8: Structural system with added fa¸cades.
As stated above, there are several challenges involved with the structural design of the house of GFRP, and far from all these challenges will be addressed in this report. Thus the report shall not be seen as the structural assessment of house, but rather as a report that seeks to highlight some aspects of structural design with GFRP elements, using this case as the basis of this investigation. This investigation is based on the regular frame, reappearing through the house, and being the primary structural elements, and the basis of the structural concept. This frame is presented in larger detail in the following subsection.
3.1.3 Frame structure
In this section the frame is described in more detail, being the main subject of the structural analysis. An isometric view of the frame is shown in figure 3.9. It is noticed that the frame is very slender, having an expected thickness of only about 40mm, likely making it dependent on the roof, floor and walls to stabilize against lateral torsional buckling, and general buckling.
The other dimensions of the frame are shown in figure 3.10. The supports are placed away from the edge, partly to obtain a lighter architectural expression of the building, and partly based on a structural consideration of limiting the span and deflection of the bottom horizontal member.
In this report, the horizontal members are addressed as beam members, and the vertical as column members. In both figure 3.9 and 3.10, the frame appears to be as a single continuous element. This is desired, both architecturally and structurally, in the sense, that it is wished to have a completely rigid frame. A rigid frame is clearly preferred in this house to ensure the transverse stability of the house, while the stability along the length is ensured by the large fa¸cades, acting as plates. A rigid frame is also especially advantageous based on the properties of GFRP. Due to the low modulus of elasticity, the dimensioning factor will tend to be the deflection, which for a ten meter span as present here, would doubtless be the case if the frame corner did not transfer rotation.
Figure 3.9: Isometric view of frame.
Based on the dimension given here, the frame is analysed in the following, both in regards to the actual frame members, and the rigid connections in the corners.
Figure 3.10: Frame layout.
3.1.4 Materials and profiles
The house is to be constructed of GFRP, with characteristics as described in section 2.1. The design of this case structure is carried out solely by the use of standard profiles from Fiberline Composites. The profiles used in the analysis are shown on figure 3.11, while the properties of the different profiles are shown in table 3.1. The data sheets of these profiles are found in appendix E. It is seen that the strip profile is available in different thicknesses, of which a 3mm and 6mm is chosen here for the investigation. Studying the data sheets, it is further noticed that a E-modulus of 23 GPa parallel to the direction of pultrusion is assigned to the plank profiles, while an E-modulus of 17 GPa is assigned the strip profile. Dialogue with Fiberline has revealed that the difference of the E-moduli is due to the geometry of the cross-section, rather than differences in the material. The strip profile consists of three layers of glass-fibre. The top and bottom layer being mats, while the middle layer being roving. The roving layer is stronger and stiffer, as described in section 3.1, but as it is in the centre of the cross-section, bending will happen with small stresses building up in the roving. However, when the strip is used in combination with the plank and furthermore turned vertically, the rovings will be fully utilized, making the profile stiffer and a E-modulus of 23 GPa can be used parallel to the direction of pultrusion.
It is noticed, that the moment of inertia of the HD Plank given in table 3.1, is significantly lower than that given in the data sheet in appendix E. The value given in table 3.1 is calculated
Figure 3.11: Profiles used for analysis.
Table 3.1: Properties of profiles.
Profiles name Moment of inertia Mass Price Inertia/mass Inertia/price
Iy m P Iy/m Iy/P
[mm4] [kg/m] [DKK] [mm4/(kg/m)] [mm4/DKK]
MD Plank 88.0·106 6.57 13.4·106
2x MD Plank 177.1·106 13.14 13.5·106
MD Plank + Strip (3mm) 119.4·106 9.27 12.9·106 MD Plank + Strip (6mm) 150.6·106 11.97 12.6·106
HD Plank 110.2·106 8.53 12.9·106
2x HD Plank 221.3·106 17.06 13.0·106
HD Plank + Strip (3mm) 141.4·106 11.23 12.6·106 HD Plank + Strip (6mm) 172.7·106 13.97 12.4·106
based on the geometry of the profile, and the difference is suspected to be due to a mistake in the data sheet. In table 3.1, the mass is also given, as well as the moment of inertia divided by the mass. This is to give an indication of the utilization of the material to obtain stiffness. It is seen that all profiles have similar values for this, but that the MD Plank obtains slightly better values, while adding a strip, slightly decreases the utilization. The magnitude of the differences is however of small significance, and preference between the profiles cannot be based on this alone.
3.2 Loads
The loads, that are the basis for the structural analysis, are determined and combined in corre-spondence with Eurocode 0 ([D1]), Eurocode 1 ([D2]) and the corresponding national annexes ([D3] and [D4]), as well as the specifications of [D6], mentioned in section 2.3.1. The detailed specification of the different loads are presented in appendix F, to which reference is made for the detailed magnitude of the applied loads.
3.2.1 Load cases used in model
The different types of loads applied in the analysis are summarized in table 3.2. In the table, the category is also stated together with the duration in which the load acts. This is due to the mechanical properties of the material being significantly more reduced in case of long term loading, as described in section 2.3.1. The duration of the loading is based on the definition of [D6], stating that long term loading is measured in years. This leaves only the dead loads to be long term loading, as well as a limited part of the live load, reduced by a factor 0.3, as is suggested for long term live loading of timber structure in [A2].
Table 3.2: Summary of loads applied in analysis.
Case Name Category Load duration Characteristic magnitude
A1 Self-weight of structure Dead load Long term
-A2 Superimposed dead load Dead load Long term 0.5 kN/m2
A3 Snow load Snow Short term 0.8 kN/m2
A4 Live load Live Short/long term 1.5 kN/m2
A5 Wind up and horizontal Wind Short term 0.1 to 1.0 kN/m2
To give an impression of the magnitude of the loads, an indicative characteristic value is given in table 3.2. For the wind load, this magnitude is given as the interval, which the loads varies within. The variation depends on whether the wind load is horizontal or vertical, and where on the structure it operates. For more exact description of the loads, reference is made to appendix F.
3.2.2 Load combinations
In table 3.3 the used load combinations are shown, as well as the enveloped loads for SLS and ULS applied during the structural analysis. For the ULS load combinations it is also stated whether the combination is long term or short term, while the impact of this is not taken into account for the SLS loads, according to [D6]. Variations within the same dominant load are added by a index letter to the combination.
Table 3.3: Load combinations used in analysis.
Case Name Variations Description
C3 SLS Wind up + horizontal (Total 2)
C3a A1+A2+A5
C3b A1+A2+A5+0.3A4
C4 ULS Dead load (long term) 1.35A1+1.35A2
C5 ULS Snow (short term) (Total 2)
C5a 1.35A1+1.35A2+1.5A3
C5b 1.35A1+1.35A2+1.35A3+1.35A4
C6 ULS Live (short term) 1.35A1+1.35A2+1.5A4
C7 ULS Live (long term) 1.35A1+1.35A2+0.45A4
C8 ULS Wind up + horizontal (short term) (Total 2)
C7a 1.0A1+1.0A2+1.5A5