ANALISA STRUKTUR GEDUNG UNSYMMETRIC-PLAN DENGAN MODAL PUSHOVER ANALYSIS (MPA) PADA STRUKTUR BETON BERTULANG

Bambang Budiono¹ dan M. Albar Daen²

ABSTRAK

Struktur tidak simetris dalam arah tapak, dapat diklasifikasikan menjadi tiga sistem, unsymmetric-plan Torsionally-stiff system; unsymmetric-plan Torsionally-similarly-stiff system; dan unsymmetric-plan Torsionally-flexible system. Nonlinear Response History Analysis (NLRHA) adalah suatu analisis yang dikembangkan untuk mengestimasi seismic demand dan kapasitas struktur secara akurat. Mengingat perhitungan NLRHA yang menggunakan analisis riwayat waktu non-linier sangat kompleks, maka perlu dilakukan metoda pendekatan untuk menganalisis seismic demand dari struktur, yaitu dengan Modal Pushover Analysis (MPA).Respon final MPA didapat dari masing-masing mode yang dikombinasikan dengan metoda Complete Quadratic Combination (CQC) pada percepatan gempa yang sama. Berdasarkan studi pada struktur beton bertulang 10 lantai untuk sistem portal terbuka ,maka dapat disimpulkan bahwa metode MPA dapat digunakan untuk menggantikan metode NLRHA dengan penambahan kontribusi mode yang lebih tinggi. Dari hasil hasil analisis MPA secara keseluruhan konservatif terhadap NLRHA untuk sistem struktur unsymmetric-plan Torsionally stiff system dan unsymmetric-plan Torsionally flexible system. Tetapi pada system struktur unsymmetric-plan Torsionally similarly stiff system analisis MPA tidak konservatif terhadap analisis NLRH. Ini disebabkan mode-mode awal sangat dipengaruhi oleh Translational dan juga rotasional sehingga sulit di uncoupled kan. Fenomena ini terjadi karena respon total terjadi secara simultan antara translasional dan rotasional.

Kata kunci : Unsymmetrical-Plan, Non-Linear Response History Analysis, Modal Pushover Analysis, Seismic Demand, Torsionally-Stiff, Torsionally-Similarly-Stiff, and Torsionally-Flexible Systems, Single Degree of Fredom System.

ABSTRACT

The unsymmetrical plan of a structure is categorized into three systems, namely Torsionally-Stiff, Torsionally-Similarly-Stiff, and Torsionally-Flexible Systems. The Nonlinear Response History Analysis (NLRHA) is an analysis that is able to predict the seismic demand and capacity of structures accurately. Because of the NLRHA complexity, the study is conducted using the Modal Pushover Analysis (MPA) approach in analyzing the seismic demand of structures, which is less complex. The MPA improves the conventional static pushover analysis namely the Capacity Spectrum Method (CSM), where in the MPA method, the contribution of higher modes of the structure is taken into account not only first mode as in CSM. The total response of MPA is obtained from the combination of each mode response using the Complete Quadratic Combination (CQC) method. As a result of the study for the 10 story building of reinforced concrete frames, it was found that the MPA method can be used to replace the NLRHA method. Based on the results of the MPA method, it is concluded that the MPA method is conservative compared to NLRHA method both for the Torsionally-Stiff and Torsionally-Flexible Systems. However, for the Torsionally-Similarly-Stiff system, in the cases of 10 story structure, the MPA method is not in a good agreement with the NLRHA. For the final remarks, the MPA can be used to replace the NLRHA provided the elastic modes are not strongly coupled. This phenomena occurs when the fundamental periods of the Translation and Rotation modes are closely related.

Keywords: Unsymmetrical-Plan, Non-Linear Response History Analysis, Modal Pushover Analysis, Seismic Demand, Torsionally-Stiff, Torsionally-Similarly-Stiff, and Torsionally-Flexible Systems, Single Degree of Fredom System.

1) Staf Pengajar, Kelompok Keahlian Rekayasa Struktur, Teknik Sipil FTSL ITB

2) Mahasiswa Program Magister Rekayasa Struktur Program Studi Teknik Sipil FTSL ITB

Impact of Different Earthquake Types on the Statistics of Ductility Demand

H. P. Hong 1 ; A. D. García-Soto 2 ; and R. Gómez, M.ASCE 3

Abstract

Probabilistic assessments of the seismic ductility demand for hysteretic bilinear single-degree-of-freedom systems have been reported in the literature. However, a systematic assessment of possible differences in the estimated ductility demand for different earthquake types using recorded ground motions is not available, although ground motion prediction equations for different earthquake types are developed. The assessment of the differences can be important for estimating structural reliability and expected damage cost under seismic excitations since partial damage and collapse could be related to the ductility demand. Therefore, if the differences are significant one must use consistent sets of ground motion prediction equation and ductility demand relation for each earthquake type affecting a site of interest to evaluate the seismic hazard and risk. To assess the differences of the ductility demand, 413 records for Mexican interplate earthquakes, 275 records for Mexican inslab earthquakes, and 592 records for California earthquakes are employed. The evaluation considers ranges of values of natural vibration periods and ratios of initial to postyield stiffness. The obtained results indicate that the statistics of displacement ductility demand differs for different earthquake types. The results are used to develop empirical
relations for predicting the expected displacement ductility demand.

DOI: 10.1061/ASCEST.1943-541X.0000177

CE Database subject headings: Ductility; Ground motion; Nonlinear analysis; Probability; Seismic effects; Earthquakes; California.

Author keywords: Ductility; Ground motion; Nonlinear analysis; Probability; Seismic effects.

Fibre Reinforced Polymer

Fibr3 reinforced polymer (FRP) composites have emerged from being exotic materials used  only in niche applications following the Second  World  War,  to  common engineering materials used in a diverse  range of applications. Composites are now used in aircraft, helicopters, space-craft, satellites, ships, submarines,  automobiles, chemical processing equipment, sporting goods and civil infrastructure,  and there is the potential for  common use in medical prothesis and microelectronic devices. Composites have emerged as  important materials because of  their  light-weight, high  specific stiffness, high specific strength, excellent fatigue resistance and outstanding corrosion resistance
compared to most common metallic alloys, such as steel and aluminium alloys.  Other advantages  of  composites  include the  ability  to fabricate directional  mechanical properties, low thermal expansion properties and high  dimensional stability.  It is  the combination of  outstanding physical, thermal  and  mechanical properties  that makes composites attractive  to use in place of metals in many applications, particularly when weight-saving  is critical. FRP  composites can be simply described as multi-constituent materials that consist of  reinforcing  fibres embedded  in  a rigid polymer matrix.  The fibres used  in FRP materials can be in the form of small particles, whiskers or continuous filaments. Most composites used  in  engineering applications contain fibres made of  glass, carbon or aramid.  Occasionally composites are reinforced with other fibre types, such as boron, Spectra@  or thermoplastics. A diverse range of polymers can be used as the matrix to FRP  composites, and these are generally classified as thermoset (eg. epoxy, polyester) or thermoplastic  (eg. polyether-ether-ketone, polyamide) resins. In almost all engineering applications requiring high  stiffness, strength and  fatigue resistance, composites are reinforced with continuous fibres rather than small particles or whiskers.  Continuous fibre composites are characterised by a two-dimensional (2D) laminated structure  in which the fibres are aligned along the plane (x- & y-directions) of the material, as  shown  in Figure 1.1.  A distinguishing feature of 2D laminates  is that no fibres are aligned  in  the  through-thickness  (or  z-)  direction.  The  lack  of  through thickness reinforcing fibres can be a disadvantage in terms of cost, ease of processing, mechanical performance and impact damage  resistance. A  serious disadvantage is that the current manufacturing processes for composite components can be  expensive. Conventional processing techniques used  to  fabricate composites, such as wet hand  lay-up, autoclave and resin transfer moulding, require a high  amount of  skilled labour to cut, stack and  consolidate the  laminate plies into a preformed component.  In the production of  some aircraft structures up  to 60 plies of carbon fabric or carbodepoxy prepreg tape must be  individually stacked and aligned by hand.  Similarly, the hulls of some naval ships are made using up to 100 plies of woven glass fabric that must be stacked and consolidated by hand. The  lack of  a z-direction binder means the plies must be individually stacked and  that adds considerably to  the fabrication time. Furthermore,  the lack of  through-thickness fibres means that the plies can  slip during lay-up, and this can misalign  the fibre orientations  in  the composite component. These  problems can  be  alleviated  to some extent  by  semi-automated processes that  reduce the amount of  labour, although the equipment is very  expensive and  is  often only suitable for fabricating certain  types of  structures, such as flat  and slightly curved panels.  A further problem with fabricating composites is that production
rates are often  low because of  the slow curing of  the resin matrix, even at elevated temperature.

Figure 1.1 Schematic  of the fibre structure  to a 2D laminate

Fabricating composites into components with a complex shape increases the cost even further because some fabrics and many prepreg tapes have poor drape. These materials are  not  easily  moulded  into  complex  shapes,  and  as a  result some composite components need to be assembled from a  large number of  separate parts that must be joined by co-curing, adhesive bonding or mechanical fastening. This is a major problem for the aircraft industry, where composite structures  such as wing sections must be made from  a  large  number  of  smaller  laminated parts such  as  skin panels, stiffeners and stringers. These fabrication problems have impeded  the wider use  of  composites in some aircraft structures because it is significantly more expensive than using aircraft grade aluminium alloys. As  well  as  high  cost, another major  disadvantage of  2D  laminates is their  low through-thickness mechanical properties because of  the lack of  z-direction fibres. The two-dimensional arrangement of fibres provides very  little stiffness and strength in the through-thickness direction because these properties are determined  by  the  low mechanical properties of  the resin and fibre-to-resin interface. …..

Nightmare-Avenged Sevenfold

Nightmare!
(Now your nightmare comes to life!)
Drag you down below
Down to the devil's show
To be his guest forever
(Peace of mind is less than never!)
Hate to twist your mind
But God ain't on your side
An old acquaintance severed
(Burn the world your last endevor!)
Flesh is burning
You can smell it in the air
Сause men like you
Have such an easy soul to steal (steal)
So stand in line
While they ink numbers in your head
You're now a slave until the end of time here
Nothing stops the madness turning, haunting, yearning, pull the trigger!
You should have known
The price of evil
And it hurts to know
That you belong here, yeah
Ooooohh it's your fuckin' nightmare!
(While your nightmare comes to life!)
Can't wake up in sweat
Сause it ain't over yet
Still dancing with your demons
(Victim of your own creation)
Beyond the will to fight
Where all that's wrong is right
Where hate don't need a reason
(Love is self-assassination)
You've been lied to just
To rid you of your sight
And now they have the nerve
To tell you how to feel
So sedated as they medicate your brain
And while you slowly go insane
They tell you:
"Given with the best intentions
Help you with your complications!"
You should have known
The price of evil
And it hurts to now
That you belong here, yeah
No one to call
Everybody to fear
Your tragic fate is looking so clear, yeah.
Ooooohh, it's your fuckin' nightmare!
Fight (fight)
Not to fail (fail)
Not to fall (fall)
Or you'll end up like the others
Die (die)
Die again (die)
Drenched in sin (sin)
With no respect for another
Down (down)
Feel the fire (fire)
Feel the hate (hate)
Your pain is what we desire
Lost (lost)
Hit the wall (wall)
Watch you crawl (crawl)
Such a replaceable liar
And I know you hear their voices
(Coming from above)
And I know they may seem real
(These signals of love)
But our life's made up from choices
(Some without appeal)
They took for granted your soul
And it's ours now to steal
(As your nightmare comes to life!)
You should have known
The price of evil
And it hurts to now
That you belong here, yeah
No one to call
Everybody to fear
Your tragic fate is looking so clear, yeah.
Ooooohh, it's your fuckin' nightmare! 

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