Uluslararası Çelik ve Alüminyum Yapılar Konferansında...

Uluslararası Çelik ve Alüminyum Yapılar Konferansında (ICSAS 07) Temmuz 2007’de İngiltere’nin Oxford kentinde sunulmuştur…

OPTIMUM GEOMETRY SELECTION FOR ECCENTRICALLY BRACED

STEEL FRAMES WITH SHEAR LINKS

byDevrim ÖZHENDEKCİ

Nuri ÖZHENDEKCİZekeriya POLAT

EBFs are composed of columns, beams, and braces in which one end of each brace connects to a beam at a short distance from an adjacent beam-to-brace connection. This short beam segment, called the link, is intended to serve as a structural fuse; yielding under severe earthquakes while the other components of the frame essentially remain elastic.

ECCENTRICALLY BRACED FRAMES (EBFs)

LINK

LINK

Many experimental and analytical studies about EBFs have been carried out since theverification of the EBF concept on test frames (Roeder and Popov, 1978).

Through out the 1980s, the fundamental principles of the EBF design procedure were constructed based on the inelastic performance assessment of the links.

EBF Research –INITIAL STUDIES–

After the introduction of new steel type (A992) specification in 1997 by ASTM, the research concerning this new material have also begun (Richards and Uang, 2005; Okazaki, Arce, Ryu and Engelhardt, 2005).

EBF Research–RECENT STUDIES –

There is not any conducted parametric study on a large scale that may guide the designers especially during geometry selection, althoughthere are very crucial questions arising:how to choose the link and span lengths, to what extend will these choices affect the global inelastic behaviour and frame cost, etc.

–DEFICIENCY IN THE EBF RESEARCH–

To investigate the effects of the frame geometry on:Frame weight, Frame behaviour under earthquake loading

Basic Goal of this study

A computer program is coded for optimum design of chevron EBFs with shear links, thus the assigned sections are minimums those meeting all of the code requirements.

Design Procedure

LRFD Specification (1999)ASCE 7-05AISC Seismic Provisions (2005)Location Los Angeles, Site Class D (~C USGS)Beams: A992, wide flangeColumns: A992, wide flange W14 seriesBraces: A500-Grade B, rectangular hollow sections with equal depth and width values

Design Procedure-DESIGN ASSUMPTIONS-

Number of stories, n Plan Area, A (m2) Span Length, L (cm) Link Length, e (cm)

3 600 800 606 800 900 75

1000 1000 90105120

________________________________________________________________

Total number of frames = 2x3x3x5=90

Properties of the designed frames

Geometries of the designed frames

SIMPLE FRAME

EBF

L

e

L

e

EBF

EBF

EBF

EBF

The elements outside of the links should be designed to resist the forces generated by the fully yielded and strain hardened links.If link web is properly detailed and restrained

with full-depth stiffeners, shear yielding of the link would be the most ductile yielding mode. To assure that shear yielding dominates the inelastic behaviour of the link, link length should satisfy the following condition:

Capacity Based Design

p

p

VM

e6.1

≤

DRAIN-2DX Uang and Richards’ inelastic link element model (Richards, 2004)20 SAC ground motions of Los Angeles with 2% probability of exceedence in 50 yearsRotation capacity of shear link is 0.08 rad.

Inelastic Analyses

Each earthquake record (for each frame) is scaled in the inelastic time history analyses until one of the links of the framereaches the limit rotation angle of 0.08 radian as given in AISC Seismic Provisions.

Method used for assessment of theseismic behaviour of the frames

Scaling of each earthquake record until the frame’s limit state is an iterative and time-consuming procedure, thus a computer program is coded.

For each iteration, the program modifies drain input file by changing the scale factor, and then starts drain.exe; this process is repeated until the limit rotation angle of one of the links is reached.


Number of 20 scale factors are evaluatedfor each frame under SAC ground motions and the mean value of the scale factors (α) is calculated.

In order to compare the inelastic behaviour of the frames basic parameter is chosen as the mean scale factor.


In order to consider the uncertainties of the response of the same frame to different earthquakes the coefficient of the variation (COV) is also calculated.


Results of the parametric studies– NORMALIZED FRAME WEIGHTS (~FRAME COSTS) –

Effect of link length on the 3-storey frame weight (a) L=8 m, (b) L=9 m, (c) L=10 m(vertical axis represents the ratios of frame weights to the weight of the frame with the link length of 60 cm)

(a)

(b)

(c)


Effect of link length on the 6-storey frame weight (a) L=8 m, (b) L=9 m, (c) L=10 m(vertical axis represents the ratios of frame weights to the weight of the frame with the link length of 60 cm)

(a)

(c)

(b)

For both 3-storey and 6-storey EBFs and for e ≤105cm , the normalized weight of the frames tend to increase slightly with the increase of the link length and reach to a maximum ofapproximately 20%. For the value of e>105 cm there is a sharp

increase that reaches to an average value of nearly 35%, 40%, 50 % for the frames with the span lengths of 8 m, 9 m and 10 m, respectively for 3-storey EBFs. This sharp increase region is comparatively smaller and more sensitive to the plan area for 6-storey EBFs.


Results of the parametric studies– NORMALIZED MEAN SCALE FACTORS –

Effect of link length on the mean scale factors of 3-storey EBF (a) L=8 m, (b) L=9 m,(c) L=10 m (vertical axis represents the ratios of mean scale factors to the factor of the frame with the link length of 60 cm)

(a)

(b)

(c)


Effect of link length on the mean scale factors of 6-storey EBF (a) L=8 m, (b) L=9 m,(c) L=10 m (vertical axis represents the ratios of mean scale factors to the factor of the frame with the link length of 60 cm)

(a)

(b)

(c)

For 3-storey EBF and for e ≤105cm , the normalized mean scale factor tends to increase slightly with the increase of the link length and reaches to a maximum of approximately 20% and for the value of e>105 cm there is generally a sharp increase, but span length and plan area have relatively greater effect in this region.The results for 6-storey EBFs have shown that

with the increase of “e” values; there exists nearly a constant increase in the mean scale factor ratiosand the effect of plan area increases in all regions.


Results of the parametric studies– COEFFICIENTS OF VARIATION OF SCALE FACTORS –

Coefficients of variation of scale factors for (a) 3-storey EBF (b) 6-storey EBF

(a)

(b)

Coefficients of variation (COVs) of mean scale factors are between 0.3 and 0.45 for most of the 3-storey EBFs. There are few frames with COVsbigger than 0.45 especially for the link lengths of 60cm and 75cm. 6-storey EBFs have COVs between 0.35 and

0.47 except for two frames with the link length of 60cm; these two frames have COV values below 0.35. The COV values of 6-storey EBFs are relatively closer which indicates closer degrees of uncertainty for the response calculated underdifferent earthquakes.

Results of the parametric studies– COEFFICIENTS OF VARIATION OF SCALE FACTORS –

The results of the parametric studies indicate that; among the code based designed frames with the same loads and load combinations, plan area, span length, and storey height, but with different link lengths, the frame weight increase can reach a maximum value of nearly60% and the mean scale factor increase can reach a maximum value of approximately 85%.

If the designers have approximate information about the results of link length selection at the beginning of the design procedure, this may change their choices; because one can choose economy rather than more safety or vice versa.

CONCLUDING REMARKS

Thank you for your attention…

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