土木工程外文翻译-原文

外文原文

Response of a reinforced concrete infilled-frame structure to removal of two

adjacent columns

Mehrdad Sasani_

Northeastern University, 400 Snell Engineering Center, Boston, MA 02115, United

States

Received 27 June 2007; received in revised form 26 December 2007; accepted 24

January 2008

Available online 19 March 2008

Abstract

The response of Hotel San Diego, a six-story reinforced concrete infilled-frame structure, is evaluated following 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 used to calculate global and local deformations. The analytical results show good agreement with experimental data. The structure resisted progressive collapse 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 discussed. Three-dimensional Vierendeel (frame) action of the transverse 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 sections without tensile reinforcement and reinforcing bar pull out) are described. The response of the

structure due to additional gravity loads and in the absence of infill walls is analytically evaluated.

c 2008 Elsevier Ltd. All rights reserved.

Keywords: Progressive collapse; Load redistribution; Load resistance; Dynamic response; Nonlinear analysis; Brittle failure

1.Introduction

The principal scope of specifications is to provide general principles and comput ational methods in order to verify safety of structures. The “safety factor ”, which according to modern trends is independent of the nature and combination of the mat erials used, can usually be defined as the ratio between the conditions. This ratio is also proportional to the inverse of the probability ( risk ) of failure of the structure.

Failure has to be considered not only as overall collapse of the structure but als o as unserviceability or, according to a more precise. Common definition. As the rea ching of a “limit state ”which causes the construction not to accomplish the task it was designed for. There are two categories of limit state :

(1)Ultimate limit sate, which corresponds to the highest value of the load-bear ing capacity. Examples include local buckling or global instability of the structure; fail ure of some sections and subsequent transformation of the structure into a mechanis m; failure by fatigue; elastic or plastic deformation or creep that cause a substantial change of the geometry of the structure; and sensitivity of the structure to alternating loads, to fire and to explosions.

(2)Service limit states, which are functions of the use and durability of the stru

cture. Examples include excessive deformations and displacements without instability ; early or excessive cracks; large vibrations; and corrosion.

Computational methods used to verify structures with respect to the different saf ety conditions can be separated into:

(1)Deterministic methods, in which the main parameters are considered as no nrandom parameters.

(2)Probabilistic methods, in which the main parameters are considered as ran dom parameters.

Alternatively, with respect to the different use of factors of safety, computational methods can be separated into:

(1)Allowable stress method, in which the stresses computed under maximum l oads are compared with the strength of the material reduced by given safety factors.

(2)Limit states method, in which the structure may be proportioned on the basi s of its maximum strength. This strength, as determined by rational analysis, shall n ot be less than that required to support a factored load equal to the sum of the factor ed live load and dead load ( ultimate state ).

The stresses corresponding to working ( service ) conditions with unfactored li ve and dead loads are compared with prescribed values ( service limit state ) . Fro m the four possible combinations of the first two and second two methods, we can o btain some useful computational methods. Generally, two combinations prevail:

(1)deterministic methods, which make use of allowable stresses. (2)Probabil istic methods, which make use of limit states.

The main advantage of probabilistic approaches is that, at least in theory, it is p ossible to scientifically take into account all random factors of safety, which are then combined to define the safety factor. probabilistic approaches depend upon :

(1) Random distribution of strength of materials with respect to the conditions of fabrication and erection ( scatter of the values of mechanical properties through o ut the structure ); (2) Uncertainty of the geometry of the cross-section sand of the structure ( faults and imperfections due to fabrication and erection of the structure );

(3) Uncertainty of the predicted live loads and dead loads acting on the structu re; (4)Uncertainty related to the approximation of the computational method used ( deviation of the actual stresses from computed stresses ). Furthermore, probabilisti

c theories mean that the allowable risk can be base

d on several factors, such as :

(1) Importance of the construction and gravity of the damage by its failure; (2 )Number of human lives which can be threatened by this failure; (3)Possibility and /or likelihood of repairing the structure; (4) Predicted life of the structure. All these factors are related 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 ;

(4) Adverse impact on society;

(5) Moral and psychological views.

The definition of all these parameters, for a given safety factor, allows con struction at the optimum cost. However, the difficulty of carrying out a complete prob abilistic analysis has to be taken into account. For such an analysis the laws of the d istribution of the live load and its induced stresses, of the scatter of mechanical prop erties of materials, and of the geometry of the cross-sections and the structure have to be known. Furthermore, it is difficult to interpret the interaction between the law o f distribution of strength and that of stresses because both depend upon the nature o f the material, on the cross-sections and upon the load acting on the structure. Thes e practical difficulties can be overcome in two ways. The first is to apply different saf ety factors to the material and to the loads, without necessarily adopting the probabili stic criterion. The second is an approximate probabilistic method which introduces so me simplifying assumptions ( semi-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 Defense [2] developed regulations to evaluate progressive collapse resistance of structures. ASCE/SEI 7 [3] defines progressive collapse as the spread of an initial local failure from element to element eventually resulting in collapse of an entire structure or a disproportionately large part of it. Following the approaches proposed by Ellinwood and Leyendecker [4], ASCE/SEI 7 [3] defines two general methods for structural design of buildings to mitigate damage due to progressive collapse: indirect and direct design methods. General building codes and standards [3,5] use indirect design by increasing overall integrity of structures. Indirect design

is also used in DOD [2]. Although the indirect design method can reduce the risk of progressive collapse [6,7] estimation of post-failure performance of structures designed based on such a method is not readily possible. One approach based on direct design methods to evaluate progressive collapse 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. These regulations are meant to evaluate general integrity of structures and their capacity of redistributing the loads following severe damage to only one element. While such an approach provides insight as to the extent to which the structures are susceptible to progressive collapse, 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 collapse 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 inserted 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 two separate 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 second

floor of one of the annex buildings. Fig. 3 shows a typical plan of this building, whose response 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. Based 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, based on tension tests of two steel samples having 1/2 in (12.7 mm) square sections, 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 set 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 present.

3. Sensors

Concrete and steel strain gages were used to measure changes in strains of beams and columns. Linear potentiometers were used 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 several hundred kHz sampling rate. The sampling rate used in the experiment was 1000 Hz. Potentiometers were used 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 m/s).

4. Finite element model

Using the finite element method (FEM), a model of the building was developed in the SAP2000 [8] computer program. The beams and columns are modeled with Bernoulli beam elements. Beams have T or L sections with effective flange width on each side of the web equal to four times the slab thickness [5]. Plastic hinges are assigned to all possible locations where steel bar yielding can occur, including the ends of elements as well as the reinforcing bar cut-off and bend locations. The characteristics of the plastic hinges are

obtained using section analyses of the beams and columns and assuming a plastic hinge length equal to half of the section depth. The current version of SAP2000 [8] is not able to track formation of cracks in the elements. In order to find the proper flexural stiffness of sections, an iterative procedure is used as follows. First, the building is analyzed assuming all elements are uncracked. Then, moment demands in the elements are compared with their cracking bending moments, Mcr . The moment of inertia of beam and slab segments are reduced by a coefficient of 0.35 [5], where the demand exceeds the Mcr. The exterior beam cracking bending moments under negative and positive moments, are 516 k in (58.2 kN m) and 336 k in (37.9 kN m), respectively. Note that no cracks were formed in the columns. Then the building is reanalyzed and moment diagrams are re-evaluated. This procedure is repeated until all of the cracked regions are properly identified and modeled.

The beams in the building did not have top reinforcing bars except at the end regions (see Fig. 4). For instance, no top reinforcement was provided beyond the bend in beam A1–A2, 12 inches away from the face of column A1 (see Figs. 4 and 5). To model the potential loss of flexural strength in those sections, localized crack hinges were assigned at the critical locations where no top rebar was present. Flexural strengths of the hinges were set equal to Mcr. Such sections were assumed to lose their flexural strength when the imposed bending moments reached Mcr.

The floor system consisted of joists in the longitudinal direction (North–South). Fig. 6 shows the cross section of a typical floor. In order to account for potential nonlinear response of slabs and joists, floors are molded by beam elements. Joists are modeled with T-sections, having effective flange width on each side of the web equal to four times the slab thickness [5]. Given the large joist spacing between axes 2 and 3, two rectangular beam elements with 20-inch wide sections are used between the joist and the longitudinal beams of axes 2 and 3 to model the slab in the longitudinal direction. To model the behavior of the slab in the transverse direction, equally spaced parallel beams with 20-inch wide rectangular sections are used. There is a difference between the shear flow in the slab and that in the beam elements with rectangular sections modeling the slab. Because of this, the torsional stiffness is set

equal to one-half of that of the gross sections [9].

The building had infill walls on 2nd, 4th, 5th and 6th floors on the spandrel beams with some openings (i.e. windows and doors). As mentioned before and as part of the demolition procedure, the infill walls in the 1st and 3rd floors were removed before the test. The infill walls were made of hollow clay tiles, which were in good condition. The net area of the clay tiles was about 1/2 of the gross area. The in-plane action of the infill walls contributes to the building stiffness and strength and affects the building response. Ignoring the effects of the infill walls and excluding them in the model would result in underestimating the building stiffness and strength.

Using the SAP2000 computer program [8], two types of modeling for the infills are considered in this study: one uses two dimensional shell elements (Model A) and the other uses compressive struts (Model B) as suggested in FEMA356 [10] guidelines.

4.1. Model A (infills modeled by shell elements)

Infill walls are modeled with shell elements. However, the current version of the SAP2000 computer program includes only linear shell elements and cannot account for cracking. The tensile strength of the infill walls is set equal to 26 psi, with a modulus of elasticity of 644 ksi [10]. Because the formation ofcracks has a significant effect on the stiffness of the infill walls, the following iterative procedure is used to account for crack formation:

(1) Assuming the infill walls are linear and uncracked, a nonlinear time history analysis is run. Note that plastic hinges exist in the beam elements and

the segments of the beam elements where moment demand exceeds the cracking moment have a reduced moment of inertia.

(2) The cracking pattern in the infill wall is determined by comparing stresses in the shells developed during the analysis with the tensile strength of infills.

(3) Nodes are separated at the locations where tensile stress exceeds tensile strength. These steps are continued until the crack regions are properly modeled.

4.2. Model B (infills modeled by struts)

Infill walls are replaced with compressive struts as described in FEMA 356 [10] guidelines. Orientations of the struts are determined from the deformed shape of the structure after column removal and the location of openings.

4.3. Column removal

Removal of the columns is simulated with the following procedure.

(1) The structure is analyzed under the permanent loads and the internal forces are determined at the ends of the columns, which will be removed.

(2) The model is modified by removing columns A2 and A3 on the first floor. Again the structure is statically analyzed under permanent loads. In this case, the internal forces at the ends of removed columns found in the first step are applied externally to the structure along with permanent loads. Note that the results of this analysis are identical to those of step 1.

(3) The equal and opposite column end forces that were applied in the second step are dynamically imposed on the ends of the removed column within

one millisecond [11] to simulate the removal of the columns, and dynamic analysis is conducted.

4.4. Comparison of analytical and experimental results

The maximum calculated vertical displacement of the building occurs at joint A3 in the second floor. Fig. 7 shows the experimental and analytical (Model A) vertical displacements of this joint (the AEM results will be discussed in the next section). Experimental data is obtained using the recordings of three potentiometers attached to joint A3 on one of their ends, and to the ground on the other ends. The peak displacements obtained experimentally and analytically (Model A) are 0.242 in (6.1 mm) and 0.252 in (6.4 mm), respectively, which differ only by about 4%. The experimental and analytical times corresponding to peak displacement are 0.069 s and 0.066 s, respectively. The analytical results show a permanent displacement of about 0.208 in (5.3 mm), which is about 14% smaller than the corresponding experimental value of 0.242 in (6.1 mm).

Fig. 8 compares vertical displacement histories of joint A3 in the second floor estimated analytically based on Models A and B. As can be seen, modeling infills with struts (Model B) results in a maximum vertical displacement of joint A3 equal to about 0.45 in (11.4 mm), which is approximately 80% larger than the value obtained from Model A. Note that the results obtained from Model

A are in close agreement with experimental results (see Fig. 7), while Model

B significantly overestimates the deformation of the structure. If the maximum

vertical displacement were larger, the infill walls were more severely cracked and the struts were more completely formed, the difference between the results of the two models (Models A and B) would be smaller.

Fig. 9 compares the experimental and analytical (Model A) displacement of joint A2 in the second floor. Again, while the first peak vertical displacement obtained experimentally and analytically are in good agreement, the analytical permanent displacement under estimates the experimental value.

Analytically estimated deformed shapes of the structure at the maximum vertical displacement based on Model A are shown in Fig. 10 with a magnification factor of 200. The experimentally measured deformed shape over the end regions of beams A1–A2 and A3–B3 in the second floor

are represented in the figure by solid lines. A total of 14 potentiometers were located at the top and bottom of the end regions of the second floor beams A1–A2 and A3–B3, which were the most critical elements in load redistribution. The beam top and corresponding bottom potentiometer recordings were used to calculate rotation between the sections where the potentiometer ends were connected. This was done by first finding the difference between the recorded

deformations at the top and bottom of the beam, and then dividing the value by the distance (along the height of the beam section) between the two potentiometers. The expected deformed shapes between the measured end regions of the second floor beams are shown by dashed lines. As can be seen in the figures, analytically estimated deformed shapes of the beams are in good agreement with experimentally obtained deformed shapes.

Analytical results of Model A show that only two plastic hinges are formed indicating rebar yielding. Also, four sections that did not have negative (top) reinforcement, reached cracking moment capacities and therefore cracked. Fig.

10 shows the locations of all the formed plastic hinges and cracks.