Seismic Design of Steel Moment Frames

Seismic Design of Steel Moment Frames
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Structural steel moment frames are used as part of the seismic force-resisting systems in buildings designed to resist earthquakes with substantial inelastic energy dissipation. They are one of a few select systems that building codes permit without restriction in buildings exceeding 50 mtrs in height, even in the most critical occupancies and in areas mapped as having the highest ground motions. Beams, columns, and beam-column connections in steel moment frames are proportioned and detailed to resist flexural, axial, and shearing actions that result as a building sways through multiple inelastic displacement cycles during strong earthquake ground shaking. Special proportioning and detailing requirements are therefore essential in resisting strong earthquake shaking with substantial inelastic behavior. These moment-resisting frames are called Special Moment Frames because of these additional requirements, which improve the inelastic response characteristics of these frames in comparison with less stringently detailed Intermediate and Ordinary Moment Frames.

Steel

 

 

 

 

 

Design requirements for steel moment frames are contained in a series of standards. Minimum Design Loads for Buildings and Other Structures, sets the basic loading criteria for steel moment frames together with associated lateral drift limits. Seismic Provisions for Structural Steel Buildings provides detailed design requirements relating to materials, framing members (beams, columns, and beam-column joints), connections, and construction quality assurance and quality control. In addition, presents requirements for columns that are not designated as part of the seismic force-resisting system. The numerous interrelated requirements for steel moment frames are covered, Prequalified Connections for Special and Intermediate Steel Moment Frames for Seismic Applications, which need to be written to facilitate and standardize the design of steel special moment frame connections to allow their use without the need for project- specific testing.

This paper follows the requirements of of IS : 875 (Part 1) : 1987, IS : 875(Part 2) : 1987, and IS : 875 (Part 3) : 1987, along with the pertinent design load requirements primarily addresses the seismic design of systems in Seismic Design. The Building Code, which is the code generally adopted throughout the India, refers to of IS : 875 (Part 1) : 1987, IS : 875(Part 2) : 1987, and IS : 875 (Part 3) : 1987 for the determination of seismic loads.

Steel Moment Frame Seismic Behavior

Even in regions of very high seismic risk, like California and Alaska, severe earthquakes are rare events, affecting typical building sites at average intervals of hundreds of years. Given this, it is economically impractical to design structures to resist such severe but rare earthquakes without damage. Instead, the building codes have adopted a design philosophy intended to provide safety by avoiding earthquake-induced collapse in severe events, while permitting extensive structural and nonstructural damage.

Inelastic behavior in steel special moment frame structures is intended to be accommodated through the formation of plastic hinges at beam-column joints and column bases. Plastic hinges form through flexural yielding of beams and columns and shear yielding of panel zones.

In addition to the behaviors discussed above, research and common sense suggest that a number of other failure modes should also be considered when designing steel special moment frame structures, some of which have not necessarily been observed in past earthquakes. These modes, associated with frame behavior and not that of other elements such as diaphragms and foundations, include the following criteria:

 

Design a Strong-column / Weak-beam Frame

In order to avoid development of P-delta instability in multi- story structures, it is desirable to achieve a relatively uniform distribution of lateral drift over the structure’s height. To achieve this, it is important to avoid early formation of single-story mechanisms in which inelastic response is dominated by formation of plastic hinges at the tops and bottoms of columns within a single story. When such single story mechanisms form, most of the inelastic portion of a structure’s drift will occur within these stories, resulting in very large P- delta effects at those locations. In order to avoid this, building codes require designs intended to promote formation of multi- story sidesway mechanisms dominated by hinging of beams, as opposed to column hinging, like the idealized sidesway mechanism. These requirements are termed strong-column/weak-beam design.

It adopts a strong-column/weak-beam design approach that requires that the sum of column flexural strengths at each joint exceed the sum of beam flexural strengths. When determining available column flexural strength, it is important to consider the axial loads that will be simultaneously present in the column along with flexural demands. The provisions provide an expression to determine the column-beam strength ratio and acknowledge that the design requirement is not adequate to completely avoid flexural hinging of columns. The provisions require supplemental lateral bracing of beam-column connections, unless it can be shown that the columns will remain elastic.

 

 

 

 

 

 

 

Ductile Behavior

As a highly ductile system, it is expected that steel moment frames will undergo significant inelastic behavior in numerous members when subjected to severe seismic shaking. The primary source of this inelastic behavior is intended to occur in the form of plastic hinging in the beams, adjacent to the beam-column connections. In a properly configured system, this hinging should occur over multiple stories to spread the total displacement demand and limit the local deformations and member strains to a level that the members can withstand. In addition to the hinging of beams, inelastic behavior can be expected to occur in beam-column joint panel zones and at column bases.

A number of features are incorporated into steel special moment frame design to achieve the intended ductility level. One primary feature is the level of compactness required of beam and column members. In addition, steel special moment frame members also must be laterally braced for stability. A maximum spacing distance for lateral bracing of steel special moment frame beams and specifies stiffness and strength criteria for this bracing to avoid lateral-torsional buckling. In most applications where the framing supports a concrete floor slab, the lateral bracing is provided for only the bottom beam flange. Lateral bracing of columns at the floor levels is also required. This bracing is especially important for deep column sections that, while efficient for frame stiffness because of their high moment of inertia to weight per mtr ratio, are more susceptible to lateral-torsional buckling than stockier W14 column shapes.

As mentioned in previous sections, implementing a strong- column/weak-beam design philosophy is important to good steel special moment frame performance. While it is desirable to avoid column hinging, under very intense shaking, columns will invariabily form hinges at the frame base. Frame design should explicitly consider this inelastic demand. Generally, the design of steel special moment frame column bases should be strong enough so that inelastic deformation is limited to a region that can exhibit significant ductility, such as the column member just above the base connection. Another approach, if the steel special moment frame extends to the foundation, is to design and detail anchor bolts to yield as a means of limiting demand on other elements of the connection, or through the formation of yielding in supporting foundation elements. In some cases, engineers may wish to design columns assuming the bases are “pinned.” In those cases, it is important to detail the bases to accommodate the large anticipated rotations without failing the anchorage and attachment to foundations.

Seismically Compact Sections

Reliable inelastic deformation requires that width-thickness ratios of compression elements be limited to a range that provides a cross section resistant to local buckling into the inelastic range. The term “compact” for steel cross sections that are expected to be able to achieve the full plastic section capacity. A higher level of compactness (termed “seismically compact”) is required of both steel special moment frame beams and columns. Seismically compact sections are expected to be able to achieve a level of deformation ductility of at least 4. To be seismically compact, requires member flanges to be continuously connected to the web(s) and the width-thickness ratios of the compression elements must be less than or equal to those that are resistant to local buckling when stressed into the inelastic range. Limiting width-thickness ratios for compression elements are provided.

Demand-Critical Welds

Demand-critical welds as those that require increased quality and toughness requirements based upon inelastic strain demand and the consequence of failure. Unless otherwise designated by AISC 358, or as determined in either prequalification or qualification testing, welds designated demand-critical in steel moment frames are identified specifically as complete – joint penetration groove welds of beam flanges, shear plates, and beam webs to columns. Other complete joint penetration groove welds considered demand-critical include those at a column splice, those joining a column and base plate, and those in built-up members joining a web plate to a flange in the plastic hinge region.

 

 

 

 

 

 

 

Procedure

There are three types of analysis procedures to determine member design forces and design drifts. These include: equivalent lateral force, modal response spectrum, and seismic response history analysis. Equivalent lateral force analysis is the simplest procedure. However, it can lead to excessively conservative designs. Table prohibits this analysis procedure for structures having periods greater than 3.5Ts or structures with certain horizontal or vertical building irregularities.

The equivalent lateral force procedure is based on an approximate fundamental period, unless the period of the structure is determined by more exact analysis. In many cases, exact analysis will determine a substantially longer building period than that determined by the approximate methods. As a result, substantial reduction in base shear forces often can be obtained by calculating building periods using the more exact methods.

Modal response spectrum analysis is the preferred procedure, as it more accurately accounts for a building’s dynamic behavior, takes advantage of a calculated rather than approximated period, and accounts for modal participation, which can result in a lower response than that calculated using the equivalent lateral force procedure. It requires scaling the modal base shear and all corresponding element forces to a minimum of 85 % of the base shear determined using the equivalent lateral force procedure. This provision is intended to guard against the use of analytical models that underestimate a structure’s stiffness and produce unrealistically low estimates of design forces.

For structures with periods calculated to exceed limits specified or for irregular structures, either the modal response spectrum or seismic response history analysis procedures are required. However, elastic response history analysis is more difficult than modal response spectrum analysis, does not provide significant design advantage.

Analysis can use either 2-D or 3-D computer models. Three- dimensional models are recommended, and sometimes required, because they are effective in identifying the effects of any inherent torsion in the lateral system, as well as combined effects at corner conditions.

The requirements for the combination of seismic forces along different building axes. The design forces for the beams and columns are calculated independently for response in each orthogonal direction. It is common to combine the resulting seismic forces using the orthogonal combination procedure in which 100 % of the seismic force in one direction is combined with 30 % of the seismic force in the perpendicular direction. Multiple load combinations are required to bound the orthogonal effects in both directions. The design of each beam and column is based on an axial and biaxial flexural interaction for each load combination. However, this orthogonal force combination procedure is not required in all structures. The requirements should be reviewed and the frame designed accordingly.

 

 

 

 

 

 

 

 

 

Panel Zone Stiffness on Drift

The contribution of panel zone deformation in drift calculations. This is also required as a precondition to the use of the panel zone design shear strength equations, which allows for the increased panel zone strength that can be mobilized by including the effect of column flanges.

Elastic panel zone deformation contributions to story drift can be accounted for by either explicit modeling of panel zone shear behavior or by adjusting the lengths of beams and columns in a manner that accounts implicitly for the contributions of panel zone deformations to drift. Many analysis programs permit the insertion of rigid offsets at the ends of beams and columns as a means of accounting for panel zone stiffness. The use of rigid offsets is not recommended unless the dimensions of the offsets are obtained by rational analysis.

A practical way of accounting implicitly for the contribution of panel zone deformations to story drift is through the use of centerline dimensions for beams and columns. In this approach, the contributions of beam and column flexural deformations to drift are overestimated, while the contributions of panel zone shear deformations are ignored. In most practical cases, the resulting story “racking” drift is larger than that obtained from incorporating elastic panel zone shear deformations explicitly. Equations 1 through 3, which provide estimates of the contributions of beam and column flexure and of panel zone shear deformations to drift, can be used to check the validity of this observation. These equations are based on the subassembly freebody shown in Figure, which assumes points of inflection at beam midspans and column midheights. These assumptions should be reasonable except in the bottom story where a larger story height and column base boundary conditions have a large effect on drift.

 

 

 

 

 

 

 

Where:

= story drift due to beam flexure, in

= story drift due to column flexure, in

= story drift due to panel zone shear deformations, in

Vcol = column shear force, kip

h = story height (centerline dimension), in

l1 and l2 = beam spans (centerline dimensions), in

I1 and I2 = beam moment of inertia, in4

Ic = column moment of inertia, in4

db = depth of beam, in

dc = depth of column, in

tp = thickness of joint panel zone, in

The equation for is based on the following simplifying assumptions: panel zone shear force, Vpz = Mb/db – Vcol, where Mb = Vcolh, and angle of shear distortion of the panel zone, = Vpz/(tpdcG).

The total drift obtained from summing all three equations provides a baseline estimate of drift. If centerline dimensions are used and joint panel zone deformations are ignored (two compensating errors), the panel zone parameters db and dc in Equations become zero, which greatly simplifies these equations, and Equation is not needed. In this manner, these equations can be used to assess the accuracy obtained from drift estimates based on centerline dimensions. If centerline dimensions are used, the required bending strength for column design is not obtained directly from a computer analysis, but it can be obtained by interpolation from the column moments at beam centerlines or the ends of offsets to the moments at the beam flange levels.

One desirable option is to incorporate the effects of panel zone shear deformations directly in the analytical model. In a frame analysis program that consists only of line elements, panel zone behavior can be modeled in an approximate manner by means of scissors elements or more accurately by creating interpolation from the column moments at beam centerlines or the ends of offsets to the moments at the beam flange levels compensating errors), the panel zone parameters db and dc in Equations become zero, which greatly simplifies these equations, and Equation is not needed. In this manner, these equations can be used to assess the accuracy obtained from drift estimates based on centerline dimensions. If centerline dimensions are used, the required bending strength for column design is not obtained directly from a computer analysis, but it can be obtained by.a panel zone with rigid elements linked by hinges at three corners and by a rotational spring in the fourth corner, as illustrated in Figure. In the scissors model, the rotation is controlled by a spring that relates the sum of moments in the beams to the spring rotation. The sum of moments can be related to the joint shear force, and the spring rotation is equal to the panel zone shear distortion angle. In this model, the right angles between the panel zone boundaries and the adjacent beams and columns are not maintained, which results in approximations in deflections. The parallelogram model (Figure) avoids this approximation, but requires the addition of eight rigid elements per panel zone. These eight rigid elements create a panel zone that deforms into a parallelogram. The strength and stiffness properties of the panel zone can be modeled by a rotational spring located in one of the four panel zone corners. In this case, the elastic spring stiffness is defined as Ks = (Vpz/)db = tpdcdbG.

Beam Stiffness Reductions

For Reduced Beam Section connections, the beam flange width is reduced near the beam-ends, where curvature effects are at a maximum under lateral frame loading. It is important to account for the resulting reduction in beam stiffness in analytical models. Some software packages used for such analysis have explicit elements that can model the reduced stiffness of beams having Reduced Beam Section cutouts. Alternatively, use of 90 % of the beam section properties is typically a reasonable approximate representation of this effect, when 50 % reductions in flange width are used and is a conservative approximation when smaller reductions in beam section are used.

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