Horizontal cladding panels: in-plane seismic performance in precast concrete buildings

Abstract

The paper investigates the in-plane performance of horizontal precast reinforced concrete cladding panels, typically adopted in one-storey precast industrial and commercial buildings. Starting from in-field observations of cladding panels failures in recent earthquakes, the seismic performance of typical connections is evaluated by means of experimental tests on full-scale panels under quasi-static cyclic loading. The failure mechanisms highlight the vulnerability of such connections to relative displacements and, therefore, the need to accurately evaluate the connections displacement demand and capacity. An analytical model is developed to describe the force–displacement relationship of the considered connections and compared to the experimental results. In order to determine the seismic vulnerability of such connections and provide design recommendations, linear and nonlinear analyses are conducted taking as reference a precast concrete structure resembling an industrial precast building. The results of the analyses show the importance of a correct estimation of the column’s lateral stiffness in the design process and how an improper erection procedure leads to a premature failure of such connections.

Appendices

Appendix 1: Derivation of Eq. 1

According to the yield line theory, adopting the yield line pattern shown in Fig. 8c and α equal to 45°, the work (W _ext ) done by the external load (Fig. 8b) is:

$$W_{ext} = \int\limits_{0}^{t} {p \cdot\Delta (x) \cdot dx} = \int\limits_{0}^{t} {p \cdot \theta \cdot x \cdot dx} = p \cdot \theta \cdot \frac{{t^{2} }}{2} = F \cdot \theta \cdot \frac{t}{2}$$

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where θ is the imposed rotation of the plate around yield line 2 (YL₂).

The internal work (W _int ) is:

$$\begin{aligned} W_{\text{int}} & = 2\int\limits_{{YL_{1} }} {M_{pl} \cdot \theta \cdot dx} + \int\limits_{{YL_{2} }} {M_{pl} \cdot \theta \cdot dx} + 2\int\limits_{{YL_{3} }} {M_{pl} \cdot \sqrt 2 \cdot \theta \cdot dx} \\ & = 2M_{pl} \cdot t \cdot \theta + M_{pl} \cdot (2t + i) \cdot \theta + 4M_{pl} \cdot t \cdot \theta = M_{pl} \cdot (8t + i) \cdot \theta \\ \end{aligned}$$

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Equating the external and internal work leads to:

$$\begin{aligned} W_{\text{int}} & = W_{ext} \to M_{pl} \cdot (8t + i) \cdot \theta = F \cdot \theta \cdot \frac{t}{2} \\ F & = M_{pl} (8t + i)\frac{2}{t} = \frac{{f_{u} \cdot s^{2} }}{4}(8t + i)\frac{2}{t} = f_{u} \cdot s^{2} \left( {4 + \frac{i}{2t}} \right) \\ \end{aligned}$$

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Appendix 2: Derivation of Eq. 3

The lateral deflection Δ of a cantilever beam with uniform cross section and length t under a uniform distributed load p is:

$$\Delta (x) =\Delta _{flexure} (x) +\Delta _{shear} (x) = \frac{{p \cdot x^{2} }}{24EJ}\left( {x^{2} + 6 \cdot t^{2} - 4 \cdot t \cdot x} \right) + \frac{p}{{GA_{s} }}\left( {t \cdot x - \frac{{x^{2} }}{2}} \right)$$

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By evaluating the previous equation for x = t and by considering a rectangular cross section b _eq  × s with a shear area A _s  = 5/6 A, it yields:

$$\Delta \left( t \right) = 3 \cdot t^{2} \frac{{p \cdot t^{2} }}{24EJ} + \frac{p}{{GA_{s} }}\frac{{t^{2} }}{2} = 3 \cdot t^{2} \frac{F \cdot t}{{24E\frac{{b_{eq} s^{3} }}{12}}} + \frac{F}{{G\frac{5}{6}b_{eq} s}}\frac{t}{2} = \frac{3}{10}\frac{F \cdot t}{{b_{eq} \cdot s}}\left( {\frac{{5 \cdot t^{2} }}{{E \cdot s^{2} }} + \frac{2}{G}} \right)$$

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Appendix 3: Derivation of Eq. 4

Considering the vertical side of the channel (Fig. 8) as a cantilever with height equal to h and subjected to a tip moment equal to F · t/2, the tip rotation is:

$$\theta_{tip} = \left( {F \cdot t/2} \right)\frac{h}{4EJ}$$

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This rotation leads to an additional channel lip deflection equal to:

$$\Delta_{rot} = \theta_{tip} \cdot t = F \cdot t^{2} \frac{h}{8EJ} = F \cdot t^{2} \frac{h}{{8E\frac{{b_{eq} s^{3} }}{12}}} = \frac{3}{2}\frac{{F \cdot h \cdot t^{2} }}{{E \cdot b_{eq} \cdot s^{3} }}$$

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Therefore the total displacement is:

$$\Delta _{tot} =\Delta _{eq} +\Delta _{rot} =\Delta _{eq} + \frac{3}{2}\frac{{F \cdot h \cdot t^{2} }}{{E \cdot b_{eq} \cdot s^{3} }}$$

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Appendix 4: Mechanical properties of considered connections

Table 4 contains the data used to define the top connection hysteretic behaviour. The application of the proposed analytical formulation leads to the values summarized in Table 5. The lateral force–displacement relationship of the bottom connections is directly evaluated considering the bolt flexibility for BC1 (ϕ _b 24 mm; L _b  = 50 mm; f _u  = 640 MPa) and the flexural stiffness of the tapered steel plate for BC2, modelled as a triangular element with edges 100 mm × 130 mm and thickness 20 mm, f _u  = 350 MPa.

Table 4 Properties of top connections

Table 5 Application of the analytical formulations—top connections

The top and bottom connections are simulated in the FE models by one or more nonlinear springs acting in parallel: Table 6 summarizes the considered hysteresis models. Table 7 shows the combination of the springs in order to obtain the global behaviour of the considered connections.

Table 6 Basic nonlinear springs adopted in the numerical simulations

Table 7 Hysteresis models used for each connection and definition of the main points

In PCS A and PCS B the top connection fails before sliding of the bottom connection, therefore only a spring is provided in BC1. TC1 failure is associated to anchor channel lip. The failure load (11.77 kN) derived from the analytical procedure is lower than recorder during the tests, therefore on the conservative side. Besides this, the numerical investigation was carried out considering the failure load recorded in the tests.

In PCS C/D the top connection develops two plastic hinges at the bolt ends, causing the bolt rotation until contact between the nut and the panel. At this stage, the connection gains stiffness and the lateral load increases until failure of the weakest component: the bolt in shear (27.6 kN according to Eurocode 3). A more accurate description of the connection and bolt behaviour after the contact to the panel could be obtained from refined tridimensional finite element models.

The friction load associated to sliding of TC1, TC2 and BC2 is taken directly from the test results.

Appendix 5: Equivalent stiffness

In this section, the equivalent stiffness of the case-study column is evaluated.

Based on the data of Table 8 the flexural stiffness at yield is:

$$EI_{y} = \frac{{M_{y} }}{{\phi_{y} }} = 9.96 \times 10^{13}\,{\text{Nmm}}^{2}$$

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The stiffness reduction factor is the ratio between the flexural stiffness at yield and the gross stiffness:

$$\frac{{EI_{y} }}{{EI_{g} }} = \frac{{9.96 \times 10^{13}\, {\text{Nmm}}^{2} }}{{3.564 \times 10^{14}\, {\text{Nmm}}^{2} }} = 0.28$$

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Table 8 Properties of the column