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Presented to Dr. ZhiQiang Chen for CIV-ENGR-
5501DS – Dynamics of structures
Spring 2011




                                               Gunjan Shetye
                                               UMKC
Objectives
 Learn to do basic time-series simulation for both elastic
    and inelastic dynamic systems.
   Understand the basic concept of modal idealization and
    modal reduction.
   Be familiar with the basic characteristics of response
    spectra and the construction method.
   Understand the difference between demand parameters
    resulting from elastic and inelastic systems.
   Enhance knowledge of Matlab[1] programming for pre- and
    post-processing of simulation results
Structure Idealization
The properties for the SDOF oscillator are:

 Linear Elastic Oscillator
      Mass of building: m = 800 kips / g * 0.95 = 760 * 103 lb.
      Lateral stiffness: K = 800 kips / ft
      Structure height: h = 0.75 * 36’ = 27’
      Damping ratio: ᶓ 5%=

 Bilinear Inelastic Oscillator
    Reduced lateral stiffness after yielding αK = 0.025 * K
    Structural displacement at yielding: Xy = 6.5 inch (2% of 27’)
    Maximum ductility: µmax = 5 (i.e. the peak deformation of the structure allowed
       to be 5 * 6.5” = 32.5” or 10% of 26’). This means that if a transient ductility
       number is larger than 5, significant damage (leading to partial or full collapse)
       will happen.
Ground Motions
Ground Motion Scaling




Scaling of plots to match DBE, Sa (T1) =0.70g
Scale factor for most intensively scaled ground motion (The ground motion with
maximum PGA) =14.0135
Intensively scaled ground motion
       acceleration design/response spectra pga=1.7212Ground Motion fileNGA no950NHO270.AT2
                     5
                                                 NEHRP-MCE: Ss =2.11, S1 = 1.08
                    4.5                          NEHRP-DBE: Ss =1.19, S1 = 0.66
                                                 Response spectra
                     4
                                                 DBE Sa(T1=1.08)

                    3.5

                     3
        Sa(Tn), g




                    2.5

                     2

                    1.5

                     1

                    0.5

                     0
                          0.5       1          1.5         2          2.5          3
                                             Tn, sec
Project task 3-
                                                              Structural Response Demands                   Spectral
                                                                               Ductility     Ductility   Displacemen
                                  Scale      PGA for Base shear Base shear demand            demand        t Demand
                                  factor      scaled    demand(%) demand(%) [duct_dm        [duct_dm      Sd(T1=1.08)
No.        Ground Motions        ga_scale   motion (g) [bass_dmd1] [bass_dmd2] d1] (<5)      d2] (<5)        (inch)
 1     NGA_no_738_NAS180.AT2      4.3309      1.1618      70.0416     55.9780   2.4644        2.2215          7.985
 2     NGA_no_738_NAS270.AT2      2.1331      0.4467      69.9717     56.3302   2.4620        2.2548          7.985
 3     NGA_no_1119_TAZ000.AT2     0.9555      0.6626      70.0234     56.6074   2.4638        2.2836          7.985
 4     NGA_no_1119_TAZ090.AT2     0.8944      0.6204      69.9994     56.5416   2.4629        2.3041          7.985
 5     NGA_no_1120_TAK000.AT2     0.3767      0.2303      70.0597     56.7669   2.4651        2.3456          7.985
 6     NGA_no_1120_TAK090.AT2     0.4382      0.2697      70.0945     56.8692   2.4663        2.4058          7.985
 7    NGA_no_1180_CHY002-N.AT2    4.6584      0.6842      70.0414     57.6076   2.4644        3.1455          7.985
 8    NGA_no_1180_CHY002-W.AT2    2.5742      0.3018      69.9497     56.2851   2.4612        2.1432          7.985
 9    NGA_no_1181_CHY004-N.AT2    5.8305      0.5805      69.9912     55.6986   2.4627        2.0987          7.985
10    NGA_no_1181_CHY004-W.AT2    9.7076      0.9621      69.9075     57.2941   2.4597        3.0404          7.985
11    NGA_no_1182_CHY006-N.AT2    1.8179      0.6275      70.1303     56.5689   2.4675        2.3180          7.985
12    NGA_no_1182_CHY006-W.AT2    2.7984      1.0198      69.8808     57.3594   2.4588        3.0089          7.985
For inelastic oscillator the trend suggests that as PGA increases Base shear demand
increases but the same is not true in case of elastic oscillator.
For inelastic oscillator the trend suggests that as PGA increases Ductility
demand increases but the same is not true in case of elastic oscillator.
Conclusion
 The trends in base shear and ductility demand with
  respect to PGA is more realistic in case of inelastic
  oscillator where the demand is rising with Peak
  ground acceleration of the motion.
 However the comparison of PGA to spectral
  displacement demand was not carried out as the
  Spectral demand were plotted for the same scaled
  motion Sa(T1=1.08). and thus the spectral demand
  remained constant for all ground motions.
References-
1. Matlab , a technical-computing language software
   product of MathWorks Inc.
2. SAP2000 Computers and structures Inc., Berkeley
3.Text book ‘ Dynamics of structures’, Author Anil
   Chopra.
Questions -




              Thank you!

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Dynamics Project

  • 1. Presented to Dr. ZhiQiang Chen for CIV-ENGR- 5501DS – Dynamics of structures Spring 2011 Gunjan Shetye UMKC
  • 2. Objectives  Learn to do basic time-series simulation for both elastic and inelastic dynamic systems.  Understand the basic concept of modal idealization and modal reduction.  Be familiar with the basic characteristics of response spectra and the construction method.  Understand the difference between demand parameters resulting from elastic and inelastic systems.  Enhance knowledge of Matlab[1] programming for pre- and post-processing of simulation results
  • 3.
  • 4. Structure Idealization The properties for the SDOF oscillator are:  Linear Elastic Oscillator  Mass of building: m = 800 kips / g * 0.95 = 760 * 103 lb.  Lateral stiffness: K = 800 kips / ft  Structure height: h = 0.75 * 36’ = 27’  Damping ratio: ᶓ 5%=  Bilinear Inelastic Oscillator  Reduced lateral stiffness after yielding αK = 0.025 * K  Structural displacement at yielding: Xy = 6.5 inch (2% of 27’)  Maximum ductility: µmax = 5 (i.e. the peak deformation of the structure allowed to be 5 * 6.5” = 32.5” or 10% of 26’). This means that if a transient ductility number is larger than 5, significant damage (leading to partial or full collapse) will happen.
  • 6.
  • 7. Ground Motion Scaling Scaling of plots to match DBE, Sa (T1) =0.70g Scale factor for most intensively scaled ground motion (The ground motion with maximum PGA) =14.0135
  • 8. Intensively scaled ground motion acceleration design/response spectra pga=1.7212Ground Motion fileNGA no950NHO270.AT2 5 NEHRP-MCE: Ss =2.11, S1 = 1.08 4.5 NEHRP-DBE: Ss =1.19, S1 = 0.66 Response spectra 4 DBE Sa(T1=1.08) 3.5 3 Sa(Tn), g 2.5 2 1.5 1 0.5 0 0.5 1 1.5 2 2.5 3 Tn, sec
  • 9.
  • 10.
  • 11. Project task 3- Structural Response Demands Spectral Ductility Ductility Displacemen Scale PGA for Base shear Base shear demand demand t Demand factor scaled demand(%) demand(%) [duct_dm [duct_dm Sd(T1=1.08) No. Ground Motions ga_scale motion (g) [bass_dmd1] [bass_dmd2] d1] (<5) d2] (<5) (inch) 1 NGA_no_738_NAS180.AT2 4.3309 1.1618 70.0416 55.9780 2.4644 2.2215 7.985 2 NGA_no_738_NAS270.AT2 2.1331 0.4467 69.9717 56.3302 2.4620 2.2548 7.985 3 NGA_no_1119_TAZ000.AT2 0.9555 0.6626 70.0234 56.6074 2.4638 2.2836 7.985 4 NGA_no_1119_TAZ090.AT2 0.8944 0.6204 69.9994 56.5416 2.4629 2.3041 7.985 5 NGA_no_1120_TAK000.AT2 0.3767 0.2303 70.0597 56.7669 2.4651 2.3456 7.985 6 NGA_no_1120_TAK090.AT2 0.4382 0.2697 70.0945 56.8692 2.4663 2.4058 7.985 7 NGA_no_1180_CHY002-N.AT2 4.6584 0.6842 70.0414 57.6076 2.4644 3.1455 7.985 8 NGA_no_1180_CHY002-W.AT2 2.5742 0.3018 69.9497 56.2851 2.4612 2.1432 7.985 9 NGA_no_1181_CHY004-N.AT2 5.8305 0.5805 69.9912 55.6986 2.4627 2.0987 7.985 10 NGA_no_1181_CHY004-W.AT2 9.7076 0.9621 69.9075 57.2941 2.4597 3.0404 7.985 11 NGA_no_1182_CHY006-N.AT2 1.8179 0.6275 70.1303 56.5689 2.4675 2.3180 7.985 12 NGA_no_1182_CHY006-W.AT2 2.7984 1.0198 69.8808 57.3594 2.4588 3.0089 7.985
  • 12. For inelastic oscillator the trend suggests that as PGA increases Base shear demand increases but the same is not true in case of elastic oscillator.
  • 13. For inelastic oscillator the trend suggests that as PGA increases Ductility demand increases but the same is not true in case of elastic oscillator.
  • 14. Conclusion  The trends in base shear and ductility demand with respect to PGA is more realistic in case of inelastic oscillator where the demand is rising with Peak ground acceleration of the motion.  However the comparison of PGA to spectral displacement demand was not carried out as the Spectral demand were plotted for the same scaled motion Sa(T1=1.08). and thus the spectral demand remained constant for all ground motions.
  • 15. References- 1. Matlab , a technical-computing language software product of MathWorks Inc. 2. SAP2000 Computers and structures Inc., Berkeley 3.Text book ‘ Dynamics of structures’, Author Anil Chopra.
  • 16. Questions - Thank you!