Gunjan ShetyeUMKC

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

ObjectivesLearn 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 IdealizationThe 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: = 5%ᶓ

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) =0.70gScale factor for most intensively scaled ground motion (The ground motion with maximum PGA) =14.0135

Intensively scaled ground motion

0.5 1 1.5 2 2.5 30

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5S

a(T

n),

g

Tn, sec

acceleration design/response spectra pga=1.7212Ground Motion fileNGAno

950

NHO270.AT2

NEHRP-MCE: Ss =2.11, S1 = 1.08

NEHRP-DBE: Ss =1.19, S1 = 0.66Response spectra

DBE Sa(T1=1.08)

Project task 3-

Base shear demand(%)

[bass_dmd1]

Base shear demand(%)

[bass_dmd2]

Ductility demand

[duct_dmd1] (<5)

Ductility demand

[duct_dmd2] (<5)

1 NGA_no_738_NAS180.AT2 4.3309 1.1618 70.0416 55.9780 2.4644 2.2215 7.9852 NGA_no_738_NAS270.AT2 2.1331 0.4467 69.9717 56.3302 2.4620 2.2548 7.9853 NGA_no_1119_TAZ000.AT2 0.9555 0.6626 70.0234 56.6074 2.4638 2.2836 7.9854 NGA_no_1119_TAZ090.AT2 0.8944 0.6204 69.9994 56.5416 2.4629 2.3041 7.9855 NGA_no_1120_TAK000.AT2 0.3767 0.2303 70.0597 56.7669 2.4651 2.3456 7.9856 NGA_no_1120_TAK090.AT2 0.4382 0.2697 70.0945 56.8692 2.4663 2.4058 7.9857 NGA_no_1180_CHY002-N.AT2 4.6584 0.6842 70.0414 57.6076 2.4644 3.1455 7.9858 NGA_no_1180_CHY002-W.AT2 2.5742 0.3018 69.9497 56.2851 2.4612 2.1432 7.9859 NGA_no_1181_CHY004-N.AT2 5.8305 0.5805 69.9912 55.6986 2.4627 2.0987 7.98510 NGA_no_1181_CHY004-W.AT2 9.7076 0.9621 69.9075 57.2941 2.4597 3.0404 7.98511 NGA_no_1182_CHY006-N.AT2 1.8179 0.6275 70.1303 56.5689 2.4675 2.3180 7.98512 NGA_no_1182_CHY006-W.AT2 2.7984 1.0198 69.8808 57.3594 2.4588 3.0089 7.985

Spectral Displacemen

t Demand Sd(T1=1.08)

(inch)

Structural Response Demands

Ground MotionsNo.

Scale factor

ga_scale

PGA for scaled

motion (g)

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.

ConclusionThe 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!