Nonlinear shear beam model

Consider a building modeled as a nonlinear shear beam in the following form ... 

O Figures 24.9 and O 24.10 illustrate distributions of the shear and peel stresses for the composite SLJ predicted by the linear adhesive-beam model based on the Euler beam theory and the nonlinear adhesive-beam model based on the Timoshenko beam theory, respectively. 

In O Figs. 24.9 and O 24.10, the same edge moment factor at = 9 calculated using O Eq. 24.33 is used for both models. Figure 24.9 shows that there are slight differences in values of shear stress predicted by the linear adhesive-beam model based on the Euler beam theory and the nonlinear adhesive-beam model based on the Timoshenko beam theory. However, there exist significant differences in the adhesive peel stress for the two models as shown in Fig. 24.10, including peak values and distribution patterns. 

The equivalent strut method is an oversimplification of the actual behavior of an infill wall and fails to capture some key failure mechanisms, such as the one depicted in Fig. 2c. A strut model will not account for the possible shear failure of a column that could be induced by the frame-wall interaction. There is no simple solution to overcome this problem. A study by Stavridis (2009) based on detailed nonlinear finite element models has demonstrated that the compressive stress field in a masonry infill wall may not be accurately represented by a single diagonal strut and that a strut model ignores the shear transfer between the beam and the infill. Hence, replacing a wall by a diagonal strut will not lead to a realistic representation of the load transfer from the frame to the wall. Moreover, as mentioned previously, it is not possible to have a single strut width to capture both the initial stiffness and load capacity of an infilled frame. 

It is important to note that 3D nonlinear elastic-plastic finite element simulations were performed, while stiffness reduction curves were used for calibration of the material model and for determining (minimal) finite element size. It should also be noted that the largest FEM model had over 0.5 million elements and over 1.6 million DOFs. However, most of simulations were performed with smaller model (with 150 K elements) as it represented mechanics of the problem with appropriate level of accuracy. Working FEM model mesh is shown in Figure 2. The model used, features 484,104 DOFs, 151,264 soil and beam-column elements, and is intended to model appropriately seismic waves of up to 10 Hz, for minimal stiffness degradation of. GjGmax = 0.08, maximum shear strain of y = 1% and with the maximal element size... 

For one, realism means incorporating all pertinent sources of material and geometric nonlinearity that are expected to arise. This should include, for example, plastic-hinge formation zones for moment-resisting frames, brace buckling for braced frames, and P-Delta effects. Nonsimulated failure modes, such as the shear failure of members or the brittle failure of beam-column joints, can be incorporated in the analysis a posteriori. Still, they essentially remove the model s ability to track structural behavior beyond their first occurrence. This means that whenever nonsimulated failures are found to have occurred, one cannot trust the model to provide estimates beyond that point. 

The present subchapter presents a simplified (new) modeling approach based on the work of Zhao et al. (2012) for the nonlinear analysis of SCC beams and composite frames with deformable shear connections (based on the distributed plasticity approach) using line elements to simulate the stmctural beam and column members, layered fiber section to simulate the reinforced concrete slabs, and nonlinear spring elements for the simulation of the interface between the stmctural steel beams and the reinforced concrete slab. Vertical interactions between the slab and steel beams are not expected to be significant, therefore are not accounted into the analysis. The geometry of the model, along with a simple set of details, is outlined below. The assembled model is shown in Fig. 1. 

A finite-element analysis is used to perform a nonlinear dynamic transient analysis of the tunnel. Tuimel segments are modeled using beam elements that take into account shear rigidity. The joints are modeled with nonlinear hyperelastic elements. The bored tunnels at the end of both segments are incorporated in the analysis as beams on viscoelastic foundation. Influence of segment length and joint properties was then investigated parametrically. 

The parameter definitions in the above equation can be found in Oplinger (1994) and are not given here due to complexity. In O Eq. 24.31, the overlap geometric nonlinearity and the adhesive shear, but not peel strain, are considered. In O Eqs. 24.30 and O 24.31, the adherends are modeled as Euler beams and thus the transverse shear stiffiiess is not modeled. 

In this model of adhesively bonded joints with asymmetric and unbalanced adherends, the geometric nonlinearity is not included the adherends are described as the Timoshenko beam and a two-parameter elastic medium is used to model the adhesive. Also, the adhesive stresses should be deemed as those in the adhesive s mid-plane. It should be noted that the predicted shear stress may be slightly lower due to ignoring the geometric nonlinearity. 

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