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Due Date: Tuesday, March 24, 20091/3 DEPARTMENT OF CIVIL, STRUCTURAL AND ENVIRONMENTAL ENGINEERING CIE 619 STRUCTURAL DYNAMICS AND EARTHQUAKE ENGINEERING II Spring 2009 ASSIGNMENT No. 5 Due Date: Tuesday, March 24, 2009 The six-story steel building structure shown in Fig. 1 has been modeled with the general purpose computer program IDARC2D. A data file, representing a two-dimensional model of the building, has been posted on the class web site (input file name: building.idarc.dat). The building is rectangular in shape and is braced in the North-South direction by two exterior moment-resisting frames. Design gravity loads include the roof dead load (3.8 kPa), the floor dead load (4.5 kPa), the roof live load (1.0 kPa), the floor live load (3.8 kPa), and the weight of the exterior cladding (1.7 kPa). The steel grade is assumed to be A36 (nominal Fy = 290 MPa) for all members. Figure 1 – Six-Story Steel Building Structure. N2/3 Modeling with IDARC2D Geometry Only half of the building is modelled, as the structure is symmetrical. As shown in Fig. 1, the model then includes only one exterior frame, together with one gravity column that represents all interior frame columns. The total gravity loads acting on the interior columns are applied to the gravity column in the model and both the gravity column and the exterior frame are constrained to experience the same lateral deformation at each floor. Material Only the bare steel frame is included in the analyses, i.e., the slab participation as a composite beam is not included. The inelastic response is concentrated in plastic hinges that could form at both ends of the frame members. These plastic hinges are assigned a bi-linear hysteretic behaviour with a curvature strain-hardening ratio of 0.02. An axial load-moment interaction is considered for the columns of the structure. Rigid-end offsets are specified at the end of the frame members to account for the actual size of the members at the joints. The panel zones of the beam-column connections are assumed to be stiff and strong enough to avoid any panel shear deformation and yielding under strong earthquakes. This assumption represents the most critical condition for the inelastic curvature demand on the welded beam-to-column joints, as all the hysteretic energy must be dissipated only through plastic hinging in the beams and the columns. The columns are fixed at the ground level, except the gravity column that is assumed pinned at the base and at each level. Nodal weights Half the weight of the building (dead loads and cladding), along with 20% of each roof and floor live load, are included in the weights assigned at each level of the frame. Axial loads on the columns and concentrated static loads on the nodes Gravity loads acting on the frame during the earthquake are assumed equal to the roof and floor dead loads, and a portion of the floor live load which is 0.7 kPa. P-delta effects are accounted for in the analyses, including P-delta forces generated in the interior frames. REQUIRED: Perform a dynamic analysis using the given dataA. , assuming Rayleigh damping of 5% based on the first two elastic modes of vibration of the structure. All analyses should be performed at a time-step increment of 0.001 s. From the information in the input data file : a) Draw an elevation view of the analyzed frame indicating the positions of all nodes and members. b) Draw a Table indicating for each member the following properties: member’s depth, cross-sectional area, moment of inertia around the bending axis, yields bending moment, and yield axial force. (use AISC manual for additional data) c) Draw for each column member, a graph of the axial load-moment interaction diagram. B. Using information from the output data file: d) Draw a Table showing the first 5 periods of vibration of the building structure.3/3 e) For each of these 5 periods of vibration, draw the corresponding mode shape. Indicate the numerical values corresponding to the lateral displacement of each floor level. C. Modify the input data file to execute a “pushover” analysis f) Using the procedure described in page 81 of the IDARC2D Theory Manual (NCEER Technical Report 96-0010), perform a pushover analysis on the structure. Use and inverse triangular seismic loading distribution for which the lateral inertia force, Fi, at level i is proportional to the weight, Wi, of that level: hWh W= Fjj1=jiii ∑6 where hi is the height of level i over the base. Target ultimate base shear coefficient for the pushover analysis of the structure is 0.21. g) Present the results of the pushover analysis in graphical form, indicating the variation of the base shear with the top floor lateral displacement. Clearly indicate on this graph the following points: - The formation of the first plastic hinge in the beams, identify also its location; - The formation of the first plastic hinge in the columns, identify also its location; NOTE: Data for the assignment should be downloaded separately from the class website. Read the “Note” file, before proceeding with the solution for the


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UB CIE 619 - CIE619 Assignment No 5

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