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«R. SHANKAR NAIR R. Shankar Nair R. Shankar Nair, Ph.D., P.E., S.E. is a principal and senior vice president of Teng & Associates, Inc. in Chicago. In ...»

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Applying the above methodology to blast condition is problematic. First, the design seismic force, F p, is based on an assumed seismic acceleration, a p. Effective blast force on a particular nonstructural system depends on the expected blast pressure that will affect the system. Second, the qualitative seismic detailing for anchoring building envelope components to the building are all base on expected seismic deformation modes. Blast deformation modes can be different from the seismic ones; in many cases they are the opposite. Blast-specific approach to the design and detailing of building envelope components to mitigate blast conditions is needed.

There are several important considerations that are needed in a blast-specific design for

building envelope:

Considerations of dynamic effects: As was discussed above, the short duration of blast events would excite high frequency modes. Since many of the components of building envelope have frequencies that are within the blast pressure range, their dynamic responses should be accounted for in the design.

Rate effects on Strength and ultimate strains: IT is well known that high loading rates increases the strength of materials. However, these same high loading rates decreases the ultimate strains of materials. This phenomenon should be included in the design.

Balanced Design: Since the building envelope is usually constructed from several components that are made of different materials, it is important to ensure that the load path throughout all the components and the jointing between these components is strong and ductile enough for the postulated blast load. Any weak link can render the whole building assembly unsafe.

Glazing: Shattering of glass is a particularly worrisome occurrence during a blast event.

During different terrorist acts, the shattering of glass was the major cause of human fatalities and injuries. The lack of ductile behavior and the large coefficient of variation in design parameter make it essential that glass design be addressed properly.

Anchoring to Structural systems: Good design of building envelope is not complete without appropriate anchoring to the supporting structural systems. If there is any potential of interaction between the building envelope and the supporting structural system, it should be accounted for in the design.

Un-Reinforced masonry (URM) bearing walls: In many building the URM is used extensively in the building envelope. URM is not ductile systems, and is fairly weak in the transverse direction. Some retrofit measures should be employed for existing buildings that have URMs. For new construction, some form of reinforcement should be used in exterior masonry walls.

A safe and secure building envelope will result from following the above rules. For more information about curtainwall design and behavior, refer to the work by Zhou, 2002.

5 INSIDE THE ENVELOPE

Figure 1 shows the two categories of systems inside the building envelope. They are the Architectural Systems (AS), and the Mechanical, Electrical and Plumping (MEP) systems. The architectural systems include, but not limited to interior partitions and walls, ceilings, light fixtures, furniture and elevated floors, if any. MEPs include generators, transformers, elevators, chillers, etc.

The safe design for blast effects include appropriate anchoring, hardened enclosures and simply installing important MEPs always from harm’s way. For example, it is prudent to locate generators, and other essential equipments, deep inside the building, rather than near the outside. Another subtle, but important consideration is the possible harmful effects that seismic considerations might have on blast considerations. For example, whenever a seismic restraint (snubber) or seismic (or noise) isolation system is placed with a heavy machinery (or even a light weight clean room) the effectiveness of any of those measures should be considered during blast event. In particular, the differences in the operational frequency ranges for different hazards must be studies, see figure 3.

6 CONCLUSIONS

The different aspects of safety of buildings during a blast event were discussed above (not including the structural systems). The flow of hazards from the source all the way to the inside the buildings were illustrated. The change of the type of hazard, from blast pressures to flying glass shards to the disabling of important equipments was highlighted.

In addition, different mitigation options for each of the stages were mentioned.

Secure and safe buildings require early planning as well as integral mitigating strategy, as highlighted by equation1. Without such an integral approach, the result will not be cost effective. Worst yet, it may not end up in a safe building.

7 REFERENCES ASCE, The Oklahoma City Bombing: Improving Building Performance Through MultiHazard Mitigation, Reston, VA., 1996.

Malla, R. B., “Dynamic Response and Progressive Failure of Special Structures,” Proceedings, First Joint ASCE-EMD meeting, Charlottesville, VA, June 1993.

Mays, C. C. and Smith, P. D., Blast Effect on Buildings, Thomas Telford, London, UK, 1995.

Research Council on Performance of Structures, “Structural Failures: Modes, Causes, Responsibilities,” Proceedings, American Society of Civil Engineers National Meeting, Cleveland, OH April 1972.





Zhou, Y. S., The Design of Curtainwalls, Aluminum Windows, Glass Walls, Skylights and Canopies, Wilson, Curtainwall Consultant (HK), Hong Kong, 2002.

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SIMPLE NONLINEAR STATIC ANALYSIS

PROCEDURE FOR PROGRESSIVE COLLAPSE

EVALUATION

WENJUN GUO, PHD, PE Structural Engineer, Gilsanz Murray Steficek, LLP

RAMON GILSANZ, PE, SE

Partner, Gilsanz Murray Steficek, LLP Abstract: There is a concern about progressive collapse of buildings. A simple structural design criterion including definitions for key or important members in a structure is proposed and a single-degree-freedom model is created first to illustrate the analysis procedure of progressive collapse. Then, a nonlinear static analysis procedure for existing buildings is presented. Evaluation of a six-story concrete structure is carried out based on this procedure and the result of this simplified approach is compared with the calculation from a nonlinear dynamic procedure.

Key Words: Progressive Collapse, Criterion, Nonlinear, Static

–  –  –

After the Murrah Building collapse in Oklahoma City, there is an interest in progressive collapse potential evaluation. The General Services Administration issued “Progressive Collapse Analysis and Design Guidelines – for New Federal Office Buildings and Major Modernization Projects” (GSA, 2003) as a guideline for engineers involved in the evaluations. The guidelines and additional information including standards, references, test data, computer programs and reference projects can be found at the GSA website http://www.oca.gsa.gov/. More information can also be found in other codes including the New York City Code Chapter 18 of Rules and Regulations, The British code and the ACI code. One requirement common to various codes is to verify the presence of an alternate load path in case a column is removed and some prescriptive requirements are not met. Another is to strengthen the key or important members defined as those whose failure can create extensive damage to the structure.

The goal of a designer is to produce designs that are reliable and to avoid creating structures that can have major collapses due to damage in small areas or failure of single elements. To realize these designs engineers should have an overall concept for the structural design, should determine what members are important or key to their design, and have the tools to assess the extent of structural damage if a structural member fails.

The designer should be aware that in an optimally designed structure every square foot has the same reliability for every accidental loading case considered. If this is not the case, one part of the structure is stronger than another and the designer should reinforce the area more prone to fail with material from the area less prone to fail. In practice is most probably impossible to obtain the same reliability everywhere hence the goal should be to obtain a minimum allowable reliability for every square foot of structure.

The designer can identify the key or important members in a structure, as the ones that have bigger influence area and/or carry more loads and/or have higher strain energy and/or those whose failure can create extensive collapse.

The bigger the load a member carries or the bigger the influence area the more load the structure has to redistribute or the bigger is the extent of the damage in case the member fails. The strain energy under dead loads is a measure of the work of the member; the more work the member does the more significant is the member. As the strain energy is the combination of the load and the section properties this is a more complex indicator than the total load or the influence area that are only function of one parameter. Other important indicator is the reserve capacity of the member defined as the ratio of the energy the member can absorb until it fails to the strain energy it has under dead loads. Another indicator is the ratio of the strain energy of the member to the volume of the member or strain energy density that gives an idea of what members are more stressed out. In an ideal structure this density is uniform throughout the structure. The strain energy density is a more exact indicator than the stress level because it takes into consideration the whole volume of the member not just a section. Finally the failure of secondary members that brace or stabilize the primary members can produce significant damage to the structure. These members have a small influence area, carry small loads and have small strain energy. These members cannot be easily associated to a numerical parameter. The designer will identify these members also as key or important to the redundancy of the structure.

The rest of this paper explains to the designer some fundamental concepts to compute the structural behavior under a column removal scenario.

This paper is a further exploration of the energy balance method used by Graham H. Powell in “Collapse Analysis Made Easy (More or Less)” (Graham H. Powell, 2003). The method is the technical basis for the RAM PerformCollapse computer program In this paper, a single-degree-freedom nonlinear system, consisting of a nonlinear spring and a concentrate mass, is created first to illustrate the procedure of progressive collapse. Section I is the detailed description. Section II presents a nonlinear static analysis procedure for existing buildings. The basic concept of the procedure is energy balance, i.e., the structure must absorb the potential energy generated due to the removal of one column. Section III is an example to illustrate the above procedure. Evaluation of a six-story concrete structure is carried out and the result is compared with a nonlinear dynamic procedure

–  –  –

The progressive collapse procedure is similar to a single-degree-freedom system as shown in Figure 1. Figure 2 is the property of the nonlinear spring. Point A, B, C, D and E in Figure 1 and Figure 2 denote same state. Table 1 is the list of system variables.

Energy dissipated in the structure due to damping is minimum compared with the energy absorbed due to plastic deformation. Thus, damping is not considered in the following description of the progressive collapse procedure.

–  –  –

• At point A, when the column is removed, the system has the maximum potential energy. Since the force in the spring is zero at this time, the system is falling down due to the weight of the system, W.

• From point A to B, the downward velocity increases and reaches its maximum at point B. After point B, the downward velocity decreases because the force in the spring is greater than the weight of the system, W. If the yield capacity is greater than 2W, the response of the system is linear static as the straight line AB’ shown in Figure 2.

• At point C, the falling system has zero velocity and all the potential energy is absorbed by the spring. Point C can be obtained by above energy balance condition. After point C, the system starts rebound because force in the spring is greater than the weight of the system, W.

–  –  –

• The magnitude of the vibration between point C and point E is generally small compared with the elastic response and generally there is no load reversal. Hence the system will not fail as it oscillates around point D.

–  –  –

2. If the reaction is less than half of the yield strength of the pushover curve, the structure has low potential for progressive collapse.

3. If the reaction is greater than the maximum strength of the pushover curve, the structure has high potential for progressive collapse.

4. If conditions of 2 and 3 are not satisfied, generate the capacity curve and compare it with the load curve.

This step is illustrated in Section III.

The above procedure can be used as a preliminary screen procedure to verify if conditions of step 2 or 3 are satisfied.

Section III is an example to illustrate step 4. The basic concept is energy balance, i.e., the structure must absorb the potential energy generated due to the removal of one column. The capacity curve is generated by dividing the energy absorbed by the structure, area below the pushover curve, by the displacement. The capacity curve is then compared with the load curve, which is a straight line parallel to X axis with the magnitude equal to the weight supported by the removed column.

–  –  –

A six-story concrete building is analyzed to illustrate the proposed nonlinear static analysis procedure.

Only one 2-D elevation is considered in this report for simplicity. Tables 2 and 3 are the properties of beams and

columns and Figure 3 is the structure elevation:

–  –  –



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