Figure 2.40. Column deformation for use in compatibility considerations. Deformation of column = building deflection AB + diaphragm deflection AD. (Adapted from SEAOC Blue Book, 1999 Edition.)

drift is the most common deformation used in practice, other types of deformation need to be considered, such as

1. Vertical racking of structural framing in eccentrically braced frames.

2. Shear distortions of concrete coupling beams.

3. Vertical racking of structural bays in dual systems.

Figure 2.41. Deformation compatibility consideration of foundation flexibility. (Adapted from SEAOC Blue Book, 1999 Edition.)

The maximum expected seismic deformations are computed for a design ground motion representing a 10% probability of being exceeded in 50 years. For most structures, inelastic response of the structure will occur for this level of ground motion. This inelastic response should be recognized in the computation of the expected deformation. Current code provisions stipulate that all elements and their connections shall be investigated for deformation compatibility. The elements included are structural elements such as columns, beams, walls, slabs, trusses, and bracing that were considered in the design as not being part of the lateral systems. Nonstructural elements such as stairs, cladding, finishes, utilities, and equipment should also be investigated. The intent is to ensure that structural stability and/or life safety are not compromised because of failure of these elements.

It is recognized that many nonstructural elements are not designed directly by the engineer of record. In these cases, the deformation compatibility requirements must nonetheless be satisfied. Specific design requirements, including the maximum expected deformation values, must be included in the performance design specification. The engineer is obligated to notify the client of

1. The predicted deformations of the structure.

2. The code requirements for deformation compatibility.

3. The owner's obligation to comply with the governing building code.

The deformation demand is the greater of the maximum inelastic displacement AM, considering PA effects or the deformation induced by a story drift 0.0025 times the story height. This value of AM must be computed using a structure model that neglects the stiffening effects of those elements not part of the lateral-force-resisting system. This method of evaluating AM = 0.7RAS assumes that the inelastic deformation can be estimated in terms of the deformation of the elastic structure model. When an engineering analysis is made to determine the maximum expected seismic deformations, proper modeling of the structure is needed. Because deformation incompatibility can have profound life safety implications, it is essential that the deformations not be underestimated.

A case in point is the deformation of diaphragms. Although it is common practice in an analysis to ignore deformations of the diaphragm, significant demands can result from diaphragm deformations. Including these effects may require supplemental hand calculations. The deformations of foundations should also be included in the deformation compatibility analysis. Although it is common practice to ignore sources of deformation such as rotation of the foundation, significant increase in deformation demands can result due to these effects.

Structural and nonstructural elements that are not part of the lateral system may initially contribute to structural stiffness, but because this stiffness may degrade when subject to cyclic loads, these stiffness properties must be neglected in the demand analysis for deformation compatibility.

For concrete and masonry elements, flexural and shear stiffness properties should, as a maximum, be computed as one-half of the gross section elastic stiffness. While it may be considered conservative to use gross section properties when computing the period of the structure for purposes of determining the minimum base shear, this practice is not conservative when analyzing the structure for deformation compatibility demands. Concrete and masonry elements generally crack before code force levels are reached. Further increase in load results in a reduction in effective stiffness. When computing the deformation of the structure, realistic effective stiffness properties must be used. It is generally accepted that one-half of the gross section properties adequately reflects the effective stiffness of a cracked structural member. Other, more accurate stiffness properties can be used if substantial by a rational analysis. These reduced stiffness properties must be used for all parts of the lateral-force-resisting system, including beam and column frame-type elements and for shear wall-type elements.

Once the maximum expected seismic deformations have been determined, the adequacy of all structural elements for the imposed deformation demands must be verified. As an alternate, conservative ductile detail for reinforced concrete and structural steel can usually be accepted as compliant measures.

Concrete columns pose a high risk if the design does not address deformation compatibility. The forces induced by interstory drift in the building can result in nonductile shear failures and/or compressive strain failures. Either mode of failure, accompanied by cyclic reversals of load, can destroy the column's ability to support vertical gravity load and can result in partial collapse of the structure. Such behavior can usually be avoided if: 1) the shear strength is in excess of the shear corresponding to the development of flexural strength of column, and 2) the column is confined over the potential plastic hinge region with hoops and crossties in lieu of the minimum lateral ties, to minimize compressive strain failures. Current seismic codes contain specific provisions for concrete members not part of the lateral system and require the aforementioned measures for heavily loaded columns.

Engineering judgment must be exercised when assessing nonstructural elements. It is generally accepted that for minor and moderate earthquakes, damage to nonstructural elements should be minimal; this normally requires that nonstructural elements be capable of accommodating code force-level deformations without damage. To accomplish this, particular attention to and specification of appropriate details is sufficient. Engineering analysis and computations (other than normal drift calculations) are not required.

However, some nonstructural elements of a building that provide a life safety function, or that if damaged become a life safety threat (including blocking emergency exits from the building), require special analysis, design, and detailing for deformation compatibility. Examples include: stair stringers rigidly connected at each end to the building, and cladding systems enveloping a building as a rigid skin.

When the structure deforms laterally, the stringer will act as a brace until the stringer and/or its connections fail. In the case of cladding, failure to accommodate deformations of the structure can result in loss of cladding supports, which, in case of heavy cladding systems such as stone, masonry, and concrete finishes, result in falling hazards with serious life safety threats.

Common elements considered in deformation compatibility checks are

• Concrete columns.

• Miscellaneous bracings.

As mentioned previously, the expected deformations are determined as the greater of the maximum inelastic response displacement AM, considering PA effects, or the deformation induced by a story drift of 0.0025 times the story height. The maximum inelastic response displacement that occurs when the structure is subject to the design basis ground motion (10% probability of exceedence in 50 years) is given by

The quantity AS is the design-level response displacement, which is the elastic displacement that occurs when the structure is subjected to the design seismic forces.

The displacements AS can be obtained from either a static or dynamic analysis. For concrete and masonry elements that are part of the lateral-force-resisting system, the assumed flexural and shear stiffness properties must not exceed one-half of the gross section properties unless a rational cracked section analysis is performed.

The 1997 UBC estimate of the maximum inelastic response displacement, AM, is the equivalent of 3/8 Rw A of the 1994 UBC. The deflection A of 1994 UBC used to be computed under service-level design earthquake forces, whereas AS of 1997 UBC must be computed under strength-level design earthquake forces. Therefore, an approximate comparison between the 1994 and 1997 UBC estimates of AM is given by

Thus, gravity framing is now required to sustain design gravity loads under twice as much imposed lateral displacement as prescribed in 1994 UBC. Also, the lower-bound value of 0.25% of story drift was not included in 1994 UBC. Finally, 1994 UBC did not specifically require that the flexural and shear stiffness properties of concrete and masonry elements that are part of the lateral-force-resisting system be taken no more than one-half of the gross section properties. The stringent requirements come from the experience of the 1994 Northridge earthquake that caused the collapse or partial collapse of at least two parking structures that could be attributed primarily to the failure of interior columns designed to carry gravity loads only. Following the experience, the detailing requirements for frame members not proportioned to resist forces induced by earthquake motions have been extensively rewritten in 1997 UBC.

As noted earlier, the imposed displacement under which gravity frame members must sustain their design loads has gone up by a factor of 1.87 as compared with the 1994 UBC. In addition, it was not a violation of 1994 UBC provisions to compute lateral deflections of the lateral-force-resisting systems using gross section properties. However, under 1997 UBC, cracked-section properties must be used in such computations. This may account for another twofold increase in the imposed displacement under which full design loads must be sustained by the gravity frame see Ref. 98, 99, and 100 for further discussion.

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