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外文原文
Respon of a reinforced concrete infilled-frame structure to removal of two
adjacent columns
元宵节简单灯谜Mehrdad Sasani_
Northeastern University, 400 Snell Engineering Center, Boston, MA 02115, United
States
Received 27 June 2007; received in revid form 26 December 2007; accepted 24
January 2008艰难的国运与雄健的国民
Available online 19 March 2008
Abstract
The respon of Hotel San Diego, a six-story reinforced concrete infilled-frame structure, is evaluated f
野无遗贤ollowing the simultaneous removal of two adjacent exterior columns. Analytical models of the structure using the Finite Element Method as well as the Applied Element Method are ud to calculate global and local deformations. The analytical results show good agreement with experimental data. The structure resisted progressive collap with a measured maximum vertical displacement of only one quarter of an inch (6.4 mm). Deformation propagation over the height of the structure and the dynamic load redistribution following the column removal are experimentally and analytically evaluated and described. The difference between axial and flexural wave propagations is discusd. Three-dimensional Vierendeel (frame) action of the transver and longitudinal frames with the participation of infill walls is identified as the major mechanism for redistribution of loads in the structure. The effects of two potential brittle modes of failure (fracture of beam ctions without tensile reinforcement and reinforcing bar pull out) are described. The respon of the structure due to additional gravity loads and in the abnce of infill walls is analytically evaluated.
c 2008 Elvier Ltd. All rights rerved.
Keywords: Progressive collap; Load redistribution; Load resistance; Dynamic respon; Nonlinear analysis; Brittle failure
1.Introduction
The principal scope of specifications is to provide general principles and computation al methods in order to verify safety of structures. The “ safety factor ”, which accor ding to modern trends is independent of the nature and combination of the materials u d, can usually be defined as the ratio between the conditions. This ratio is also prop ortional to the inver of the probability ( risk ) of failure of the structure.
Failure has to be considered not only as overall collap of the structure but also as un rviceability or, according to a more preci. Common definition. As the reaching of a “ limit state ” which caus the construction not to accomplish the task it was desi gned for. There are two categories of limit state :
(1)Ultimate limit sate, which corresponds to the highest value of the load-bearing cap acity. Examples include local buckling or global instability of the structure; failure of some ctions and subquent transformation of the structure into a mechanism; failur
e by fatigue; elastic or plastic deformation or creep that cau a substantial change o
f t he geometry of the structure; and nsitivity of the structure to alternatin
g loads, to fir
e and to explosions.
(2)Service limit states, which are functions of the u and durability of the structure. E xamples include excessive deformations and displacements without instability; early o r excessive cracks; large vibrations; and corrosion.
Computational methods ud to verify structures with respect to the different safety co nditions can be parated into:
(1)Deterministic methods, in which the main parameters are considered as nonrandom parameters.
(2)Probabilistic methods, in which the main parameters are considered as random para meters.
Alternatively, with respect to the different u of factors of safety, computational meth ods can be parated into:
(1)Allowable stress method, in which the stress computed under maximum loads ar
e compared with the strength o
少年中国说节选f the material reduced by given safety factors.
(2)Limit states method, in which the structure may be proportioned on the basis of its maximum strength. This strength, as determined by rational analysis, shall not be less than that required to support a factored load equal to the sum of the factored live load and dead load ( ultimate state ).
The stress corresponding to working ( rvice ) conditions with unfactored live and dead loads are compared with prescribed values ( rvice limit state ) . From the four possible combinations of the first two and cond two methods, we can obtain some u ful computational methods. Generally, two combinations prevail:
(1)deterministic methods, which make u of allowable stress. (2)Probabilistic meth ods, which make u of limit states.
祝老人生日祝福语The main advantage of probabilistic approaches is that, at least in theory, it is possible to scientifically take into account all random factors of safety, which are then combin ed to define the safety factor. probabilistic approaches depend upon :
(1) Random distribution of strength of materials with respect to the conditions of fabri cation and erec
tion ( scatter of the values of mechanical properties through out the str ucture ); (2) Uncertainty of the geometry of the cross-ction sand of the structure ( fa ults and imperfections due to fabrication and erection of the structure );
(3) Uncertainty of the predicted live loads and dead loads acting on the structure; (4)U ncertainty related to the approximation of the computational method ud ( deviation of the actual stress from computed stress ). Furthermore, probabilistic theories me an that the allowable risk can be bad on veral factors, such as :
(1) Importance of the construction and gravity of the damage by its failure; (2)Numbe r of human lives which can be threatened by this failure; (3)Possibility and/or likeliho od of repairing the structure; (4) Predicted life of the structure. All the factors are rel ated to economic and social considerations such as：
(1) Initial cost of the construction;
(2) Amortization funds for the duration of the construction;
(3) Cost of physical and material damage due to the failure of the construction;environment
(4) Adver impact on society;
初中数学复习(5) Moral and psychological views.
The definition of all the parameters, for a given safety factor, allows constructio n at the optimum cost. However, the difficulty of carrying out a complete probabilistic analysis has to be taken into account. For such an analysis the laws of the distribution of the live load and its induced stress, of the scatter of mechanical properties of mat erials, and of the geometry of the cross-ctions and the structure have to be known. F urthermore, it is difficult to interpret the interaction between the law of distribution of strength and that of stress becau both depend upon the nature of the material, on t he cross-ctions and upon the load acting on the structure. The practical difficulties can be overcome in two ways. The first is to apply different safety factors to the mate rial and to the loads, without necessarily adopting the probabilistic criterion. The co nd is an approximate probabilistic method which introduces some simplifying assump tions ( mi-probabilistic methods ) . As part of mitigation programs to reduce the likelihood of mass casualties following local damage in structures, the General Services Administration [1] and the Department of Defen [2] developed regulations to evaluate progressive collap resistance of structures. ASCE/SEI 7 [3] defines progressive collap as the spread of an initial local failure from element to element eventually resulting in collap of an
entire structure or a disproportionately large part of it. Following the approaches propod by Ellinwood and Leyendecker [4], ASCE/SEI 7 [3] defines two general methods for structural design of buildings to mitigate damage due to progressive collap: indirect and direct design methods. General building codes and standards [3,5] u indirect design by increasing overall integrity of structures. Indirect design is also ud in DOD [2]. Although the indirect design method can reduce the risk of progressive collap [6,7] estimation of post-failure performance of structures designed bad on such a method is not readily possible. One approach bad on direct design methods to evaluate progressive collap of structures is to study the effects of instantaneous removal of load-bearing elements, such as columns. GSA [1] and DOD [2] regulations require removal of one load bearing element. The regulations are meant to evaluate general integrity of structures and their capacity of redistributing the loads following vere damage to only one element. While such an approach provides insight as to the extent to which the structures are susceptible to progressive collap, in reality, the initial damage can affect more than just one column. In this study, using analytical results that are verified against experimental data, the progressive collap resistance of the Hotel San Diego is evaluated, following the simultaneous explosion (sudden removal) of two adjacent columns, one of which was a corner column. In order to explode the columns, explosives were inrted into predrilled holes in the columns. The columns were then well wrapped with a few layers of protective materials. Therefore, neither air blast nor flying fragments affected the structure.
2. Building characteristics
Hotel San Diego was constructed in 1914 with a south annex added in 1924. The annex included tw
o parate buildings. Fig. 1 shows a south view of the hotel. Note that in the picture, the first and third stories of the hotel are covered with black fabric. The six story hotel had a non-ductile reinforced concrete (RC) frame structure with hollow clay tile exterior infill walls. The infills in the annex consisted of two withes (layers) of clay tiles with a total thickness of about 8 in (203 mm). The height of the first floor was about 190–800 (6.00 m). The height of other floors and that of the top floor were 100–600 (3.20 m) and 160–1000 (5.13 m), respectively. Fig. 2 shows the cond floor of one of the annex buildings. Fig. 3 shows a typical plan of this building, who respon following the simultaneous removal (explosion) of columns A2 and A3 in the first (ground) floor is evaluated in this paper. The floor system consisted of one-way joists running in the longitudinal direction (North–South), as shown in Fig. 3. Bad on compression tests of two concrete samples, the average concrete compressive strength was estimated at about 4500 psi (31 MPa) for a standard concrete cylinder. The modulus of elasticity of concrete was estimated at 3820 ksi (26 300 MPa) [5]. Also, bad on tension tests of two steel samples having 1/2 in (12.7 mm) square ctions, the yield and ultimate tensile strengths were found to be 62 ksi (427 MPa) and 87 ksi (600 MPa), respectively. The steel ultimate tensile strain was measured at 0.17. The modulus of elasticity of steel was t equal to 29 000 ksi (200
000 MPa). The building was scheduled to be demolished by implosion. As part of the demolition process, the infill walls were removed from the first and third floors. There was no live load in the building. All nonstructural elements including partitions, plumbing, and furniture were removed prior to implosion. Only beams, columns, joist floor and infill walls on the peripheral
beams were prent.
3. Sensors
Concrete and steel strain gages were ud to measure changes in strains of beams and columns. Linear potentiometers were ud to measure global and local deformations. The concrete strain gages were 3.5 in (90 mm) long having a maximum strain limit of ±0.02. The steel strain gages could measure up to a strain of ±0.20. The strain gages could operate up to a veral hundred kHz sampling rate. The sampling rate ud in the experiment was 1000 Hz. Potentiometers were ud to capture rotation (integral of curvature over a length) of the beam end regions and global displacement in the building, as described later. The potentiometers had a resolution of about 0.0004 in (0.01 mm) and a maximum operational speed of about 40 in/s (1.0 m/s), while the maximum recorded speed in the experiment was about 14 in/s (0.35
