Earthquake Ground Motion Records

Frames With Column Uplift

3.4 Responses Under Various Ground Motions

3.4.3 Earthquake Ground Motion Records

z

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~ w 2 --- --- ---:-

Temporal Scaling Foetor Total Shear

10~~~--~~~~~~--~~

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0.0 0.5 1.0 1.5 2.0

Temporal Scaling Factor

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0.0 0.5 1.0 1.5 2.0

Temporal Scaling Factor

FIXED UPLIFT1 UPLIFT2 UPLIFT3

Figure 3.27: Comparison of peak base shear in frames with different X-braced-bay column base conditions under ground motion B-1 with equal-intensity scaling.

5

~ _FIXED

-~ 4 ... UPUFT1

:r: _- _ UPUFT2

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Temporal Scaling Factor 3rd Story

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- .... UPLIFT1 - - UPLIFT2 _ UPLIFT3

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0.0 0.5 1.0 1.5 2.0

Temporal Scaling Factor

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_FIXED .. UPLIFT1 _ _ UPLIFT2 ___ UPLIFT3 ,·---

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1.5 Temporal Scaling Foetor

_FIXED . _. __ UPLIFT1 _ _ UPLIFT2 ___ UPUFT3

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Temporal Scaling Factor

Figure 3.28: Comparison of peak story drift ofVLC bays in frames with differentX-braced-bay column base conditions under ground motion B-1 with equal-intensity scaling.

The response quantities of the three frames are listed in Tables 3.2 to 3.4.

Table 3.2 summarizes the responses of the frames under the Kobe ground motion re- cord. The first 4 rows show the story drifts in the VLC bays. The story drifts in FIXED are much smaller than those in the other two frames, except for the first story where the braces in FIXED buckled. The large story drifts in UPLIFT2 and UPLIFT3 are the price paid in exchange for smaller X-braced-bay member forces, as shown in rows 13 to 16. Because of the smaller member forces, the deformational story drifts (rows 5 to 8) in the X-braced bay of UPLIFT2 and UPLIFT3 are small.

The plastic energy demands on different structural components are listed in rows 9 to 12.

For UPLIFT2 and UPLIFT3 the energy dissipated by the uplift restraint, which dominates the energy dissipation as do the braces in FIXED, is not included in the table. Comparing the

Frames No. Response Quantities

FIXED UPLIFf2 UPLIFf3

1 1st Story 2.72 2.83 2.97

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2 ^..<:: _-~ ^bJl _~ 2nd Story 0.86 2.40 2.25

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^{3rd Story 0.63 2.40 2.24}

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4 ^<J:l 4th Story 0.40 2.36 2.19

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^{~ 1st Story 2.38 0.18 0.29}

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6 ^Q _Q ^~ 2nd Story 0.80 0.13 0.28

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^{3rd Story 0.57 0.16 0.35}

8 :>< ' _{4th Story 0.34 0.11 0.17}

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9 ~ _~ Beams and Columns 349 156 420

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10 ^bJl

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Braces 1403 0 0

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Beam-to-Column Joints 169 418

() 94

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^{Total 250 838}

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~ ^~ Column CompressiveC²l 6517 2682 7176 14 "'

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Column TensileC²l 4658 1182 602

15 ~ Brace CompressiveC²⁾ 4636 2249 3885

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16 ^';;(

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Brace Tensi!eC²l 5018 2171 3634

17 Base Shear (kN) 8866 4449 7454

18 Left Column Uplift (m)C³l 0.00 0.60 0.21

19 Right Column Uplift (m)C³l 0.00 0.46 0.14

Table 3.2: Peak responses of frames with different column-base anchoring conditions under the Kobe ground motion record. Notes: (I) For frames UPLIFT2 and UPLIFT3 these are the deformational story drifts of the uplift bay; (2) These are the peak axial forces in the first story columns of the X-braced bay; (3) Column uplifts for UPLIFT2 are cumulative values, while those for UPLIFT3 are peak values.

Frames No. Response Quantities

FIXED UPLIFT2 UPLIFT3

1 1st Story 1.84 1.74 1.52

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2 ..c

2nd Story 0.70

bfJ 1.37 1.16

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3rd Story 1.08 1.37 1.15 4

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_ti' ^{4th Story 0.41 1.31 1.09}

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^{~ 1st Story 1.51 0.14 0.13}

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8 :X: 4th Story 0.35 0.09 0.08

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9 ... -"' ~ Beams and Columns 195 30 19

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10

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^{Braces 459 0 0}

11 ~

(.) Beam-to-Column Joints 79 25 60

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^{0... Total 733 55 79}

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Column Compressive<²l

13

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Column Tensi!e<²l

14 ^<!.) 5206 1210 354

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15 _";;; ~ Brace Compressive<²l 4626 2110 2090

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Brace Tensile<²J

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4945 1966 1982

17 Base Shear (kN) 8618 4237 4064

18 Left Column Uplift (m)<³l 0.00 0.14 0.05 19 Right Column Uplift (m)<³l 0.00 0.18 0.11

Table 3.3: Peak responses of frames with different column base anchoring conditions to the Sylmar ground motion record. Notes: (I) For frames UPLIFT2 and UPLIFT3 these are the deformational story drifts of the uplift bay; (2) These are the peak axial forces in the first story columns of the X-braced bay; (3) Column uplifts for UPLIFT2 are cumulative values, while those for UPLIFT3 are peak values.

Frames No. Response Quantities

FIXED UPLIFf2 UPLIFT3

1 lst Story 0.37 0.45 0.97

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2 ..c

2nd Story 0.27 0.34 0.74

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3 _Q 3rd Story 0.30 0.36 0.75

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4 ^r/). 4th Story 0.18 0.31 0.68

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^{~ ~} lst Story 0.21 0.12 0.16

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^{;;] .... 3rd Story 0.27 0.14 0.19}

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Beams and Columns 0 0 1

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Total 18 0 41

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^~ _~ Column Compressive<²) 3564 2309 3418

14

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⁰⁾ Column Tensile(²) 2289 891 352

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15 ~ Brace Compressive<²) 2612 1569 2152

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Brace TensiJe(²) 2708 1522 2002

17 Base Shear (kN) 4907 2971 4249

18 Left Column Uplift (m)(³) 0.00 0.11 0.06

19 Right Column Uplift (m)(³⁾ 0.00 0.14 0.06

Table 3.4: Responses of frames with different column base anchoring conditions to the Vina del Mar ground motion record. Notes: (1) For frames UPLIFT2 and UPLIFT3 these are the deformational story drifts of the uplift bay; (2) These are the peak axial forces in the first story columns of the X-braced bay; (3) Column uplifts for UPLIFT2 are cumulative values, while those for UPLIFT3 are peak values.

2000~~~~~~~~~~~~~

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_FIXED ... UPLIFT1 __ UPLIFT2 ___ UPLIFT3

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- - - -

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0.0 0,5 1 .0 1.5 2.0

Temporal Scaling Foetor Left Column Tensile

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_FIXED UPLIFT1 __ UPLIFT2 __ UPLIFT3

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Temporal Scaling Foetor

2000~~~~~~~~~~~~~

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_FIXED UPLIFT1 __ UPLIFT2 ___ UPLIFT3

-8000~--~~--~~~--~--~~

0.0 0.5 1.0 1.5 2.0

Temporal Scaling Foetor Riqht Column Tensile

6000~~~~~~~~~~~--~

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~ 4000

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c 2000 E 0

0 u 1000

FIXED UPLIFT1 UPLIFT2 UPLIFT3

- - - : C .

---

Temporal Scaling Foetor

Figure 3.29: Comparison of peak axial forces in the first-story columns for frames with different X-braced bay column base conditions under ground motion B-1 with equal-intensity scaling.

plastic energy demands on beams and columns and on beam-to-column connections shows that frame UPLIFf2 has the smallest energy demands. As expected, there is a high plastic energy demand on the components of frame FIXED as a result of the brace buckling. But the energy demands on the beams and columns and on the beam-to-column connections of frame UPLIFf3 are also very high. A closer look at the plastic energy demand on the individual members in frame UPLIFf3 reveals that plastic deformation occured mainly in beams and beam-to-column connections adjacent to the uplifting bay. This is probably the result of the extra force and moment resulting from the shear dampers.

The uplift restraint in frame UPLIFf2 is able to reduce the total base shear (row 17) and the member forces in X-braced-bay columns and braces (rows 13 to 16). As a result, the braces in frame UPLIFf2 (also true for UPLIFf3) did not yield under the ground motion.

However, the columns experience substantial uplift (row 18 and 19) and this may not be acceptable in practice. Frame FIXED has high axial forces in the X-braced-bay columns and braces. This is consistent with the column and baseplate failures observed in the Northridge and Kobe earthquakes.

Column Axial Force 2000

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Column U lift

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2 3 4

Time (sec)

5 6

Figure 3.30: Axial force and uplift time histories for the first-story uplifting columns in frame UPL!Ff3.

Solid line-left column; dotted line-right column. Impact occurs when the uplifted column comes down.

The impact causes a sudden increase in the axial force of the column.

Frame UPLIFT3 also has high compressive axial forces in the X-braced-bay columns, apparently resulting from the impact that occurs when an uplifted column comes back down.

Figure 3.30 shows part of the time history for the axial force in the first-story X-braced-bay columns along with the uplift displacement time histories. It is seen that the moments when the columns impact with its supporting surface are accompanied by spikes in the column axial force time history, e.g., at

t

= 4.0 and 4.4 seconds. No impacts occur in frame UP- LIFT2, as evidenced by plots in Figure 3.31.

The responses of the frames under the Sylmar ground motion (Table 3.3) are generally not as severe as, but in most aspects similar to, those under the Kobe ground motion. One

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Column Uplift

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2 4 6 8 10

Time (sec)

Figure 3.31: Axial force and uplift time histories for the first-story uplifting columns in frame UPLIFf2. Solid lines-left column; dotted lines-right column. There is no impact.

difference is that the braces in FIXED buckled on the third floor as well as on the first floor for the Sylmar ground motion. Responses under Vina del Mar ground motion, as shown in Table 3.4, are the least severe among the three ground motion histories. None of the braces buckled and the plastic energy demands on all structural components are minimal.

The push-over result in Figure 3.4 on page 63 shows that the virgin strength of FIXED is much higher than that required by the Uniform Building Code. Nevertheless, the frame suffers very severe deformation when subjected to the Sylmar and Kobe ground motions.

This raises question about the propriety of using the initial buckling strength of the braces as a reference strength in seismic design. A more reasonable approach may be to base the design strength on the post buckling capacity of the braces.