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Problem 17 pushover analysıs

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Problem 17 pushover analysıs

  1. 1. CE 227 Homework #6 Solutions Adapted from Ady Aviram 1 Problem 17 – Pushover Analysis In this problem we carry out a static pushover analysis of the 3-story building frame. The procedure and results obtained from SAP2000 NL structural analysis package are presented. Since steel elements usually display maximum ductility values of 8-9 (we use 6 as a conservative value in this example) and assuming a rotation hardening of 3%, we can define the nonlinear behavior of beam and column plastic hinge using the Frame Hinge Property- Moment M3 in SAP2000 NL as follows: The yield moment and rotation of the beam and column plastic hinges are automatically calculated in SAP2000 NL, according to the corresponding section properties. The hinges are assigned to both ends of the frame elements. The load pattern for the pushover analysis is proportional to the first mode of the structure, which captures around 83% of the participating translational mass of the frame, and is specified in SAP2000 NL as a separate load case. In problem 14 we determined the target roof displacement of the frame Sd=13.8 in (for a first-mode period of 1.09 sec) for the response spectra corresponding to 2% in 50 yr PE hazard level. According to FEMA 350, the displacement-controlled pushover analysis will be carried out up to a limiting roof displacement of 1.5Uroof=1.5×13.8=20.7 in, in order to capture the nonlinear response of the frame including the degradation of strength or failure point. However, to capture the full behavior of the frame, it makes sense to push the frame further than this (I’m going to 50 in). If the beam and column plastic hinges are defined correctly and approximate well the actual nonlinear behavior of these elements, the displacement and ductility capacity of the frame, as well as its ultimate strength, can be determined from the pushover curve. The pushover analysis case is defined in SAP2000 NL as follows:
  2. 2. CE 227 Homework #6 Solutions Adapted from Ady Aviram 2 a. The resulting pushover curve (roof displacement vs. base shear) is presented below: b. Equivalent SDOF system: In problem 14 we had obtained the effective modal mass of one frame of the building: - Effective modal mass: k-sec2 /in. From the pushover curve for the MDOF systems we obtain the following approximate values: First yield point (uroof,p=8 in, Vp=2150 k) and ultimate point (uroof,u=33 in, Vu=2450 k). We proceed to calculate the remaining properties of the equivalent SDOF systems as follows: - Displacements: →dy=6.2in, du=26in. - Yield strength: k. - Ultimate strength: k.
  3. 3. CE 227 Homework #6 Solutions Adapted from Ady Aviram 3 - Effective stiffness: k/in. - Period (may be different from T1 due to curve fitting of pushover curve): sec. m=1 k-sec2 /in k=55 k/in ζ=5% Q