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3.1 ≤ λ f ≤ 7.14; 6.9 ≤ ≤ 17.7; 42.2 ≤ λ L ≤ 47.9 (2) Experimental tests of twenty-five deeper columns (W24) that are more representative of those commonly used for the construction of moment frames were tested recently (Uang et al., 2015). The web and member slenderness parameters of these columns were much larger than those tested by Newell and Uang |
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f" ≤ 7.14; 6.9 ≤ ≤ 17.7; 42.2 ≤ λ"L |
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4.81 ≤ λ f ≤ 6.94; 28.7 ≤ ≤ 54.6; 71.1 ≤ λ L ≤ 161.2 (3) One column (W24 × 55) that had the highest λ L (=161.2) experienced LTB in the elastic range of response. All the other specimens developed plastic hinges at both ends of the column; however, the failure modes varied significantly between the columns. The formation of plastic hinges affected the global response of the column (or ‘backbone’ curve) and the residual compressive strength of the column. The buckling modes were governed either by local buckling, global member buckling, or a combination of the two. Additionally, most of the W24 columns mentioned above experienced significant column shortening, as seen in Figure 2(b), while the W14 columns did not, which further demonstrates the effect of the buckling mode on the column response |
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f" ≤ 6.94; 28.7 ≤ ≤ 54.6; 71.1 ≤ λ"L" ≤ 161.2 (3)One column (W24×55) that had the highest λ"L |
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2.2 Anti-symmetric Local Buckling (ALB) Mode As the values λ f and λ w increase, the tested W-shapes would experience both FLB and WLB.However, AISC 360 and 341 simplify design by neglecting such interaction, treating each independently. The only exception is that the limiting λ r value in AISC 360 to distinguish between a non-compact and a slender sections in compression from flexure considers the degree of rotational restraint provided by the web:λ = 0.95 . , where = / (4)When this combined local buckling mode develops, FLB and WLB occur simultaneously as the web does not have sufficient rotational stiffness to provide a fix-ended boundary condition for the flange. Instead, the web would buckle while trying to remain perpendicular to the flange at the web-flange junction. The flanges would buckle in an anti-symmetric mode, meaning that two half flanges on each side of the web would buckle in the opposite directions (see Figure 4).Since WLB also participated, the post-buckling strength would degrade significantly.East End Overall West End |
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f" and λ"w" increase, the tested W-shapes would experience both FLB and WLB. However, AISC 360 and 341 simplify design by neglecting such interaction, treating each independently. The only exception is that the limiting λ"r |
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2.62 ≤ λ f ≤ 10.2; 5.66 ≤ ≤ 54.6; 41.1 ≤ λ L ≤ 88.89 (10) The distribution of the buckling modes predicted from the numerical simulation are presented in Figure 11. The proposed curves (4.25 and 8) provide a reasonable boundary to categorize the buckling mode of the columns |
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Tiêu đề: |
f" ≤ 10.2; 5.66 ≤ ≤ 54.6; 41.1 ≤ λ"L |
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2.4. Boundary and loading conditions Since only half of the composite joint was simulated, all nodes along the middle of the column web, the column stiffeners, concrete slab and longitudinal bars (surface 1) were restrained from moving in the X direction and from rotating in the Y and Z directions due to symmetry. In addition, following the experimental set-up described subsequently, all nodes at the bottom surface of the column (surface 2) were restrained from moving and rotating in X, Y and Z directions (Fig. 2).The connections were loaded in two stages in the numerical study. Firstly, the pretension was applied to the bolts located in the connection zone and, subsequently, the external loads were applied on the connection under a displacement-control regime. The general Newton–Raphson method and modified Riks method were used as the solution algorithms in the first and second stages of the loading, respectively.Fig. 2 Boundary conditions |
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Since only half of the composite joint was simulated, all nodes along the middle of the column web, the column stiffeners, concrete slab and longitudinal bars (surface 1) were restrained from moving in the "X" direction and from rotating in the "Y" and "Z" directions due to symmetry. In addition, following the experimental set-up described subsequently, all nodes at the bottom surface of the column (surface 2) were restrained from moving and rotating in "X, Y "and "Z |
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5. Parametric study 5.1. GeneralThe FE model validated by the experimental results was used for conducting a comprehensive parametric study to investigate the effect of different variables on the behaviour of deconstructable HSS semi rigid composite beam-to-column joints with PFBSCs and I-section columns (Table 1). The ranges adopted for different parameters are deemed to be applicable for real beam-to-column joints.The main mechanical properties of the beam-to-column joints including the initial stiffness, moment capacity and rotation capacity were obtained from the FE analysis of deconstructable HSS composite joints with PFBSCs.0 100 200 300 400 500 6000 10 20 30 40 50 60 70Moment (KNm)Rotation (mrad) CJ1 FEM0 100 200 300 400 500 6000 20 40 60Moment (KNm)Rotation (mrad) CJ2 FEM0 100 200 300 400 500 6000 20 40 60Moment (kNm)Rotation (mrad) CJ3 FEM0 100 200 300 400 500 6000 20 40 60Moment (KNm)Rotation (mrad) CJ4 FEMDownloaded from ascelibrary.org by RMIT UNIVERSITY LIBRARY on 01/05/19. Copyright ASCE. For personal use only; all rights reserved |
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(10) the max function refers to the maximum absolute value in time for each component of the vector f d (t), and the result is a vector.Modern seismic codes require to test one damper prototype for each size-group so to verify its force-velocity behavior. As a results, we consider an additional cost component, J p . This component is formulated so that the number of different size-groups of dampers used for retrofitting should be minimized:J p =C p H x 1 T x 2 +H(x 1 T (1-x 2 )) (11)Downloaded from ascelibrary.org by RMIT UNIVERSITY LIBRARY on 01/05/19. Copyright ASCE. For personal use only; all rights reserved |
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[1/kN 0.5 ] C p[#]β [#]Value 0.035 2000 1.1278 0.35 100 1 50 100Downloaded from ascelibrary.org by RMIT UNIVERSITY LIBRARY on 01/05/19. Copyright ASCE. For personal use only; all rights reserved |
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0.5] C"p[#] β [#]Value |
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(9) is independent of the member buckling parameter, λ . Figure 8 presents the test data of four different W14 columns from Newell and Uang (2008) and five different W24 sections from Ozkula et al. (2016) as a function of and ⁄ . Two curves representing equal to 4.25 and 8 are also shown in the figure. It shows that these two constant curves appear to provide good boundaries to separate the three identified buckling modes |
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2.1. Material constitutive laws ConcreteA precast reinforced concrete slab is one of the core components of deconstructable composite beam-to-column joints. In the FE models, the concrete in compression and tension was represented using a damaged-plasticity model that takes advantage of an isotropic damage model in conjunction with an isotropic plasticity-based model that can capture the concrete cracking and crushing under tensile and compressive stress states.Downloaded from ascelibrary.org by RMIT UNIVERSITY LIBRARY on 01/05/19. Copyright ASCE. For personal use only; all rights reserved |
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4. Verification of FEM The bending moment versus rotation curves predicted by the FE models are compared with the experimental results of the composite beam-to-column joints in Fig. 3. It can be seen that the FE results correlate well with the experimental data and the numerical model developed is able to accurately predict the local and global responses as well as failure (associated with a significant drop in the load) of the deconstructable composite joint with a HSS flush end plate and PFBSCs.(a) (b)(c) (d)Fig. 3 Comparison of the FE predictions with the experimental results (a) CJ1, (b) CJ2, (c) CJ3, (d) CJ4 |
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