Paso III Ejecución del diagnóstico.
III.2. Análisis Externo
2.4 Análisis situacional DAFO.
The step-by-step design procedure is a performance-based design approach, which involves the sizing of the main components of the column base, by relating the performance objectives of the column base (Section 3.2) to a specific seismic input level (i.e., ground motion intensity), e.g. DBE, or MCE. The seismic input levels are quantified by specific seismic demands, such as maximum storey drifts, which are derived by the target building performance, outlined in Chapter 5. The rest of the components of the column base (e.g. the anchor stand stiffeners, the base plate, the anchor stand, etc.) are designed to European (BS EN 1993-1-5, 2006; BS EN 1993-1- 1, 2009) and American (AISC, 2010) codes of practice, supplemented by relevant research works (SCI/BCSA Connections Group, 1997, 2013; Lee, 2002; Abidelah, Bouchaïr and Kerdal, 2012) where needed. The design procedure comprises the following steps:
Step 1: Calculation of the initial post-tensioning force, T
Calculate the initial post-tensioning force, T, in each tendon. Select a value for the ratio MIGO/MN,pl,Rd,c and calculate the MIGO. The MN,pl,Rd,c is the plastic moment resistance of the column allowing for interaction with the axial force, determined in Appendix A. The ratio MIGO/MN,pl,Rd,c should be less than one for the SC-MRF to have base shear strength comparable to that of a conventional MRF. Select a value for the ratio MD/MIGO and calculate MD. Tzimas, Dimopoulos and Karavasilis (2015) suggest that MD/MIGO should be greater than 0.5 in order for the column base to approximately achieve self-centering behaviour. Based on experiments, Garlock, Sause and Ricles (2007) proposed a more conservative value of 0.6 for the latter ratio. It applies that the
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higher the value of the MD/MIGO ratio, the higher the self-centering capability of the column base and the earlier – in terms of θ – a column plastic hinge is formed at the lowest part of the column (i.e., in the position where the column is welded on the top of the anchor stand). However, higher values of the MD/MIGO ratio represent lower energy dissipation in the column base. Given the above, T equals:
D N
ERu ERu ERd ERd
M M T n z n z (3.65)
where nERu and nERd are the numbers of the ERus and ERds, respectively.
Step 2: Design the ERs
Select a yield stress for the ERs, fy,ER and assume an initial diameter, DER, for them. To avoid yielding for the target base rotation θt, the minimum required length of the tendons, denoted as LER,min,t, should be taken from the relationship:
,min, , ER ER ERu t ER t y ER ER E A z L f A T (3.66)
where EER is the Young’s modulus (also referred to as modulus of elasticity) of the material of the ERs; and AER is the cross-sectional area of each tendon. From the above equation it is clear that higher values of fy,ER result in shorter tendons. Obtaining a lower LER,min,t for the same θt seems to be of particular importance for the applicability and the practicality of the novel column base for the reasons mentioned below (Section 3.8). This fact, combined with the increasing availability of ultra-high-strength steel grades for post-tensioning applications in the industry (VSL International Ltd, 2013; DYWIDAG-Systems International (DSI), 2017) (which lowers the prices), suggests that a high fy,ER be selected for the tendons. As mentioned above (Section 3.3), θt is
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derived from the building design procedure described in Section 5.3.3.2, and can represent different seismic intensities (e.g. the DBE, the MCE, or 2 times the MCE, etc.), based on the adopted target building performance. Thus, if for example θt corresponds to the MCE, the minimum required yielding avoidance ER length for the MCE is be obtained as follows:
,min, , ER ER ERu MCE ER MCE y ER ER E A z L f A T (3.67)
where θMCE is the base rotation under the MCE seismic hazard level. Similarly to θt,
θMCE can be derived from a preliminary pushover analysis of the building under investigation, following the aforementioned building design procedure. The lever arm of the ERus, zERu, is defined as follows:
ERu ERd CFT
z z h (3.68)
and the lever arm of the ERds, zERd, according to the following relation:
, . 1.20 2 max 2 ER w w c ERd duct bp a L z D t (3.69)
where aER,w is the width of the ER washer plate, derived from the specifications of VSL International Ltd (2013); Lw,c is the leg length of the weld that connects the column on the top of the anchor stand, defined according to Eurocode 3 (BS EN 1993- 1-8, 2010); 1.20 is a clearance coefficient that gives reasonable access for the welding between the anchor stand and the column; and Dduct is the external diameter of the
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steel ducts taken equal to three times the diameter for the ERs, DER, in order to avoid contact between the tendons and the base plate.
Step 3: Design the WHPs
Select the number of the WHPus, denoted as nWHPu, the WHPcs, nWHPc, and the WHPds, nWHPd, and estimate the yield strength of each WHP, denoted as Fy,WHP,i, as follows:
2
, , 2 2 2 0.5 ( ) u IGO CFT ER y WHP i WHPu u WHPc c WHPd d z M N h M F n z n z n z (3.70)where MER(θ2), is the total moment contribution of ERs, at Event 2, equal to:
2 2
2 2
ER ER ERu ERu ERd ERd ERu ERu ERd ERd
M K n z n z
n z n z T
(3.71)
The WHP lever arms zcand zu (refer to Section 3.4) in Equation (3.70) are obtained as follows: 2 CFT c h z (3.72) and u d CFT z z h (3.73)
where the WHP lever arm zd is determined by the length of the web plate, LWP (refer to Figure 3.13). In turn, the value of LWP is obtained from Eurocode 3 (BS EN 1993- 1-1 2009).
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It is initially assumed that MER(θ2) is solely attributed to T, whilst the additional MER due to θ2 is disregarded. That yields:
2
0
1
ER ER ER ERu ERu ERd ERd
M M M n z n z T (3.74)
The result of Equation (3.74) is substituted into (3.70) and a first estimate of Fy,WHP,i is derived. The first estimates of θ2, θ3 and θ4, are obtained by substituting the estimated Fy,WHP,i in Equations (3.8), (3.10), and (3.12). The estimated θ2 is then used in Equation (3.71) to re-evaluate MER(θ2). The improved MER(θ2) is then substituted into Equation (3.70) to yield a new value for Fy,WHP,i and the process is repeated. WHPs, supporting plates, and web plates, can be designed according to Vasdravellis et al. 2014 (Appendix B) for the obtained value of Fy,WHP,i.
Step 4: Self-centering capability
The self-centering capability of the column base is examined separately, on the basis of Case 1 and Case 2. Distinct mathematical expressions are developed to form the self-centering criteria with respect to the θt level. By definition (Section 1.3.2), self- centering behaviour is achieved when the column base returns to zero θ upon removal of the connection’s moment. In Case 1 this entails that M9 [Equation (3.49)] be equal to or greater than zero. This yields the following set of relations:
For θ2≤θt<θ3:
12 23
2 D M S S (3.75) For θ3≤θt<θ4:
12 23
2
23 34
3 D M S S S S (3.76)111 For θ4≤θt<θERu,Y:
12 23
2
23 34
3
34 45
4 DM S S S S S S (3.77)
Given that MD is a function of T [Equation (3.27)], the self-centering capability of the column base can be tuned by modifying T. Thus, the proposed column base achieves the self-centering mechanism mentioned in Section 3.3.
In Case 2, self-centering behaviour is achieved when M11 [Equation (3.64)] is equal to or greater than zero. This condition yields a set of relations with respect to the θt level. For θt levels up to θ4 [Equation (3.12)], Equations (3.75) and Equation (3.76), remain in effect. Equation (3.77) is also valid but for θ4 ≤ θt < θ5 (θ5=θEDd,PTF). For θ5≤ θt <
θERu,Y the self-centering criterion takes the following form:
12 23
2
23 34
3
34 45
4
45 56
5 DM S S S S S S S S (3.78)
Step 5: Plastic hinge avoidance criterion for a target drift level
To avoid plastic hinge formation in the column base for a target drift level (in terms of base rotation), check that the moment in the position where the column is welded on the top of the anchor stand for θt, is smaller than MN,pl,Rd,c. This can be translated into the following plastic hinge avoidance criterion:
, , , 1 t N pl Rd c M M (3.79)where M(θt) is the moment developed in the column base for θt. M(θt) is derived from Equation (3.37) in Case 1 and from Equation (3.50) in Case 2. If Relation (3.79) is not
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satisfied, return to Step 1 and repeat Steps 1 to 5 with a lower MIGO/MN,pl,Rd,c ratio until the plastic hinge avoidance criterion is satisfied.
3.7
Construction process
Figure 3.23 shows the construction process of the proposed column base. It consists of the following five steps:
Step 1 [Figure 3.23(a)]: Placement of the assembly that consists of the supporting plates of the WHPs, the base plate, the steel ducts, the fixation (steel) cubes at the lower ends of the tendons, and the anchoring plate, welded together from the shop at the exact locations determined by the plan view arrangement.
Step 2 [Figure 3.23(b)]: Installation of the shear bumpers and the (conventional) anchor bolts (also known as holding down bolts). The anchor bolts will used to anchor the base plate to the concrete foundation in the next construction step.
Step 3 [Figure 3.23(c)]: Pouring of the concrete foundation.
Step 4 [Figure 3.23(d)]: Settlement and compaction of the soil backfill, followed by the installation of the ground floor slabs. This step allows for the setting of the concrete foundation of the previous step.
Step 5 [Figure 3.23(e)]: Installation of the column subassemblage along with the WHPs and the ERs. The column subassemblage can be either of the following: (a) an assembly composed of the whole ground floor column along with the novel column base and all its components [the lower part of which it can be seen in Figure 3.23(f)]; or (b) an independent connection part which consists of the novel column base and
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just a part of the ground floor column, in case that a column splice is employed to enable a fully demountable column base. The WHPs are also placed through the supporting plates. The ERs are installed and post-tensioned. The installation is facilitated by the special anchoring detailing at the lower ends of the tendons, shown in Figure 3.6. Each tendon is inserted into an extendable steel duct and its lower anchoring part (i.e., the assembly tendon-coupler-threaded bar) is then anchored at the end of that duct. For this anchorage, appropriately shaped steel wings, welded on the couplers are inserted in likewise-shaped notches, cut at the end of the extendable ducts, allowing thus for the removal of the ducts after the completion of the process (i.e., the telescopic installation of the tendons). The post-tensioning is realised with the special detailing of the upper ends of the tendons, as seen in Figure 3.9, determined according to the specifications of VSL International Ltd (2013). In the latter figure it can be seen that a thick washer plate is used under the post-tensioning nuts in order to avoid mild yielding and thus loss of the initial post-tensioning. A clearance is also foreseen between the tendons and the circumferential surface of the anchor stand holes to minimise the contact between the two components. However, as an additional measure, the lower circumferential edge of the anchor stand holes is chamfered to minimise the likelihood of inelastic deformations (damage), in case of contact. The step closes with the filling of the CFT tube with concrete. A hole is foreseen in the anchor stand for that reason (Figure 3.7).
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(a) (b)
(c) (d)
(e) (f)
Figure 3.23 The construction process of the novel column base [(a) Step 1; (b) Step 2; (c) Step 3; (d) Step 4; and (e) Step 5] and the lower part of the column subassemblage (f)
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3.8
Implementation scenarios
The implementation of the proposed column base in a real steel building can be realized under different scenarios. The intent of any possible implementation scenario is to accommodate the final design of the column base, enabling its unobstructed performance under the seismic loads. The critical design parameter that defines the manner under which the column bases will be implemented in the building so that the above intent is satisfied, is the LER,min,t [Equation (3.66)]. The reason for that is that the tendons are the longest component in the column base, something which, coupled with the fact that their biggest part runs unbonded through the building foundation may result in long steel ducts (Figure 3.6) and in turn in a demand for a tall foundation.
(a) (b)
Figure 3.24 Proposed implementation scenarios of the novel column base (a) in a building with basement; and (b) in a building with conventional foundation (grade beams) using
small-height piles
The demand for a tall foundation, which will house the aforementioned steel ducts and tendons, seems not to be a problem when there is a basement in the building. In fact, this is the case in the majority of the mid- to high-rise steel buildings, especially in the earthquake-prone regions, where a basement is often used to enhance the stability of the structure and avoid toppling types of failure (BS EN 1998-1, 2013). Figure 3.24(a)
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shows a proposed implementation scenario in this case, where conventional concrete grade beams are employed. On the other hand, in cases where the demand for a tall foundation cannot be served by the presence of a basement, small-height piles can be constructed under the conventional foundation in the position of the columns, as seen in Figure 3.24(b).
The above two proposed implementation scenarios pertain to a rather small percentage of the cases. That is because in the vast majority of the low- to mid-rise buildings, utilizing high-strength steel tendons and compact wide flange common-sized section columns [e.g. HE 400 A (DIN 1025-2, 1995)], the LER,min,t will be between 2.00 and 3.50 m. Hence, considering that the anchor stand is suggested to be placed between 0.50 and 1.00 m above the ground [in order to allow for the accommodation of the novel column base (and its components) and also to minimally affect the base shear strength of the novel base connection-column subassembly, compared to that of its equivalent conventional subassembly (refer to Section 3.6)], the required height of the foundation should be of the order of 1.50 to 2.50 m. A foundation of that height is representative of the construction practice in low- to mid-rise buildings in seismic regions. High-rise buildings use much taller foundation systems and thus incorporating the proposed column bases comes with no additional foundation elements and thus no extra cost.
In any case, apart from the role of the fy,ER in the determination of the LER,min,t (as described in Step 2 of Section 3.6), the length of the tendons can be compromised by selecting a compact, wide-flange column section, rather than a narrow-flange I-beam (DIN 1025-1, 2009). That is because LER,min,t depends on the zERu, as can be seen from Equation (3.66). In turn, according to Equation (3.68), zERu depends on hCFT. Hence,
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by selecting a wide-flange column instead of a larger (in terms of cross-sectional depth) I-beam to resist the same design loads, a smaller LER,min,t can be achieved and a shorter foundation may be needed.
3.9
Summary
This chapter presented a novel self-centering damage free column base for application in steel buildings with seismic demands. The chapter started by outlining the performance objectives of the proposed column base and continued with a detailed description and a suggested construction process. Analytical expressions that describe the behaviour of the main components of the column base were developed to predict its structural behaviour. These expressions were then used to formulate a detailed analytical model that predicts the hysteretic, the damage-free, and the self-centering behaviour of the column base. A design procedure to Eurocodes was then developed, built on the latter model. The procedure identified the limit states of the column base and sized its main structural components. The chapter closed with proposing the construction method and possible implementation scenarios so as to enable the column base to be effectively incorporated in code-compliant steel buildings.
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Chapter 4
4
NUMERICAL MODELLING
4.1
General
This chapter presents detailed nonlinear FEM models for the proposed column base. The models represent designs derived from the implementation of the design procedure of Section 3.6. Nonlinear static pushover analyses are performed to assess the damage-free behaviour and the self-centering capability of the proposed column base. Based on the results of the analyses, the accuracy of the design procedure is evaluated. All possible limit states are identified.