Moment Frames

The Northridge earthquake demonstrated that the pre-1994 prescriptive connection shown in Fig. 3.3 was inadequate for anticipated seismic demands. Following that earthquake, a number of steel moment-frame buildings were found to have experienced brittle fractures of beam-to-column connections, shattering the belief that steel moment-frame buildings were essentially invulnerable to earthquake-induced structural damage. It was also thought that should such damage occur, it would be limited to ductile yielding of members and connections.

The Northridge earthquake changed all that. Moreover, it showed that brittle fracture was initiated within connections at very low levels of plastic demand and, in some cases, while the structures remained essentially elastic. Fractures at the complete joint penetration (CJP) weld, between the beam bottom flange and column bottom flange, once initiated, progressed along a number of paths, depending on individual joint conditions.

Based on test results of more than 150 connection assemblies, the Federal Emergency Management Agency (FEMA) published a July 2000 document titled "Recommended Seismic Design Criteria for New Steel Moment-Frame Buildings"—FEMA 350. This publication allows new prequalifications for connection details believed to be capable of providing reliable service when subjected to large earthquake demands. The criteria given in the publication allow the design of steel moment-frame structures to be performed in a straightforward, select-design-detail method, and are believed to provide the reliability incorrectly assumed to exist in pre-Northridge moment-frame connections. For the majority of structures and conditions of use, the designer is now able to select, design, and detail prequalified moment-frame connections using FEMA 350 criteria without the need to perform project-specific prototype qualification testing. For connection details other than those included in FEMA 350, qualification tests must still be performed.

As many as eight types of prequalified connections (including two proprietary types) for use in special moment frames (SMFs) are given in FEMA 350. Of these, only two—the welded flange plate (WFP) and reduced beam section (RBS), shown in Figs. 3.57 and 3.58—are considered here.

Figure 3.57. Prequalified reduced beam section (RBS) connection.

Note: For SMFs, this connection is limited to use with W12 and W14 columns and with W36 and shallower beams, maximum weight of 300 lbs/ft. See FEMA 350 for exceptions.

Figure 3.57. Prequalified reduced beam section (RBS) connection.

Note: For SMFs, this connection is limited to use with W12 and W14 columns and with W36 and shallower beams, maximum weight of 300 lbs/ft. See FEMA 350 for exceptions.

3.11.3.1. Reduced Beam Section (RBS) Connection

This type of connection, shown in Fig. 3.57, utilizes circular radius cuts in both top and bottom flanges of the beam to reduce the flange area over a length of the beam near the ends of the beam span. Welds of beam flanges to column flanges are complete joint penetration (CJP) groove welds. In this connection, no reinforcement other than weld metal is used to joint the flanges of the beam to the column. Web joints may be either CJP groove welds, or bolted or welded shear tabs. When this type of connection is used, the elastic drift calculations should consider the effect of flange reduction. In lieu of specific calculations, a drift increase of 9% may be applied for flange reductions of up to 50% of the beam flange width, with linear interpolation for lesser values of flange reduction.

The flange reduction referred to as the RBS cut is normally made by thermal cutting. The requirements for minimizing the notch effects are described in FEMA 353.

3.11.3.2. Welded Flange Plate (WSP) Connection

Figure 3.58 shows a typical detail for this type of connection. Observe that there is no direct connection between the beam and column flanges. Instead, the flange plates are used to connect the beam flanges to the column flanges. The flange-plate-to-column-flange-joint is

Figure 3.58. Prequalified welded flange plate (WFP) connection.

Note: For SMFs this connection is limited to use with W12 and W14 columns and with W36 and shallower beams. FEMA 350 specifies no weight limit for beams.

Figure 3.58. Prequalified welded flange plate (WFP) connection.

Note: For SMFs this connection is limited to use with W12 and W14 columns and with W36 and shallower beams. FEMA 350 specifies no weight limit for beams.

a CJP groove weld. The flange plates are fillet welded to the top and bottom of beam flanges. This connection, rather than the cover-plated connection, is recommended by FEMA because the welding of a single plate is considered more reliable than the welding of the combination of beam flange and cover-plate.

3.11.3.3. Connections Designed to Induce Plastic Hinges Within Beam Span: Design Principles

The formation of plastic hinges at the beam-column interface during a seismic event results in large inelastic strain demands at the connection leading to brittle failure. To prevent this occurrence, the prequalified connections are designed to produce the plastic hinges within the beam span, as shown in Fig. 3.59. This condition may be achieved by reducing the section of the beam at the desired location of the plastic hinge or by reinforcing the beam at the connection to prevent the formation of a hinge in this region. By this means, the connection at the beam-column interface remains nominally elastic and the inelastic deformation occurs away from the connection. The hinge location distances given are valid for beams in which gravity loading represents only a small portion of the flexural demand.

Figure 3.59. Inelastic drift of special moment frames with plastic hinges within beam span. A frame in which inelastic excursion occurs through the formation of plastic hinges within the beam span is capable of dissipating large amounts of energy. Such a behavior may be obtained by: 1) locally stiffening and strengthening fully restrained connections; or 2) locally reducing the beam section at desired locations.

Figure 3.59. Inelastic drift of special moment frames with plastic hinges within beam span. A frame in which inelastic excursion occurs through the formation of plastic hinges within the beam span is capable of dissipating large amounts of energy. Such a behavior may be obtained by: 1) locally stiffening and strengthening fully restrained connections; or 2) locally reducing the beam section at desired locations.

The probable beam plastic moment, allowing for overstrength of the steel, the difference in yield strengths of the beam flanges and web materials, and the estimated strain-hardening is given by

Mpr = CprRyZbeFy where

Ry = overstrength coefficient

= ratio of the expected yield stress to the minimum specified yield strength of the material

Fy = minimum specified yield stress of the beam

Zbe = effective plastic section modulus of the beam at the zone of plastic hinging Cpr = peak connection strength coefficient given as

= 1.15... for reduced beam section connections = 1.2... for other connections Fu = minimum specified tensile strength of the beam

The shear force at the plastic hinge is given by

where wu = factored gravity load on the beam L = length between plastic hinges

Neglecting the gravity load on the length x (as shown in Fig. 3.60), the resulting bending moment at the face of the column is

For reduced beam section connections, the bending moment at the face of the column is limited to

Mf < RyZbFy

Figure 3.60. Calculation of shear and moment demands at critical sections of SMF.

Figure 3.60. Calculation of shear and moment demands at critical sections of SMF.

where

Zb = plastic section modulus of the beam at the column face The resulting shear force at the face of the column is

The resulting bending moment at the center of the column (as shown in Fig. 3.60) is given as

For the general case, with beams framing into both sides of the column

3.11.3.4 Strong Column-Weak Beam

A strong column-weak beam concept should be adopted to ensure frame stability, as the formation of plastic hinges in the columns of a story may cause a weak story condition. In addition, large inelastic displacements produced in the columns increase the P-delta effect and may lead to column failure. The strong column-weak beam concept may be achieved in accordance with the requirement

where

'LM*pc = sum of the nominal flexural strengths of the column above and below the joint at the beam centerline with a reduction for the factored axial force in the column as given by = ZZF - PJAg) Puc = required axial compression strength in the column Zc = plastic section modulus of the column Fyc = minimum specified yield stress of the column Ag = gross area of the column ~LMc = sum of the bending moments at the center of the column resulting from the development of the probable beam plastic moments

Provided that a column complies with the width-thickness ratio provisions of Table 3.2, AlSC-Seismic relaxes the strong column-weak beam requirement. In addition, for this relaxation to be allowed, the column is also required to have an axial stress less than 0.3Fy and

1. Be located in a one-story building or in the top story of a multistory building.

2. Be located in a column line in which the design shear strength of all exempted columns is less than 33% of the required shear strength of the column line, and the design shear strength of all exempted columns in the story is less than 20% of the required shear strength of the story.

AlSC-Seismic also provides an exemption for a column located in a story with a design shear strength 50% greater than that of the story above.

3.11.3.5. Beam Buckling

To limit local flange buckling, AISC-Seismic specifies the use of sections with a maximum flange width-to-thickness ratio of bf Htj = 52/(F/-5

This ratio may be determined, in reduced beam section connections, at the ends of the center two-thirds of the reduced section of the beam, unless gravity loading moves the hinge point significantly from the center of the reduced section.

To prevent stress concentrations resulting in a brittle mode of failure, abrupt changes of flange area are not permitted in the hinging area. The hinging area is defined as the distance from the face of the column to one-half the beam depth beyond the theoretical hinge point. Connections, shear studs, or other attachments are not permitted in the hinging area.

To provide adequate web stability, the height-to-thickness ratio of the web shall not exceed hc/tw = 418/(F/-5

Lateral bracing is necessary on the top and bottom flanges of the beam to prevent instability. Bracing is required near all concentrated loads, at changes in cross section, where a hinge may form, and at a maximum spacing of lcr = 2500ry/Fy

When the beam supports a concrete slab along its whole length, lateral bracing is not required.

3.11.3.6. Column Design

When the ratio of column moments to beam moments is im;c /ZMC < 2.0

columns shall comply with the slenderness requirements of Table 3.2. Otherwise, columns shall comply with the slenderness requirements of LRFD Table B5.1. When the ratio of column moments to beam moments is

lateral bracing of column flanges at beam column connections shall be provided.

3.11.3.7. Continuity Plates

Continuity plates, as shown in Fig. 3.61, are required when the column flange thickness is less than the value given by either of the following two expressions:

Cfi ffFycRyc or tcf = bf/6 (AISC-Seismic C 9.4)

where tcf = minimum required thickness of column flange when no continuity plates are provided bf = beam flange width tf = beam flange thickness Fyb = minimum specified yield stress of the beam flange Fyc = minimum specified yield stress of the column flange Ryb = ratio of the expected yield strength of the beam material to the minimum specified yield strength Ryc = ratio of the expected yield strength of the column material to the minimum specified yield strength

The minimum continuity plate thickness is tst = tf (for two-sided (interior) connections)

and tst = tf /2 (for one-sided (exterior) connections)

The minimum width of a continuity plate is required to match the beam flange. The maximum width-thickness ratio is defined as bjtst = 1.79/(Fyst/E)05

(b) Elevation

Figure 3.61. Typical continuity plates and doubler plates.

(b) Elevation

Figure 3.61. Typical continuity plates and doubler plates.

When continuity plates are required, they are to be designed as axially loaded columns to support the beam flange force. The effective length is taken as le = 0.75h where h = clear distance between flanges, less the corner radii = dc - 2k k = distance from outer face of column flange to web toe of fillet dc = depth of column

The cross section of the column may be considered to consist of the stiffener and a strip of column web having a width of 25tw.

Continuity plates are welded to the column flange using complete joint penetration groove welds, as shown in Fig. 3.61. Continuity plates are clipped to avoid the column k-area and are welded to the column web to develop the shear capacity of the net length of the continuity plate, which is

Pw = 0'6tstLnetFy where

Lnett = net length of continuity plate = dc - 2(k + 1.5) k = distance from outer face of column flange to web toe of fillet

3.11.3.8. Panel Zone

The thickness of the panel zone to ensure simultaneous yielding of the beam and panel zone is given as t = CyMc(h - db)/[0.9 x 0.6FycRycdc(db - tfb)h]

= Sb/CprZbe

= elastic section modulus of the beam at the zone of plastic hinging = effective plastic section modulus of the beam at the zone of plastic hinging = peak connection strength coefficient defined

= 1.15 (for reduced beam section connections) = 1.2 (for other connections) = moment at center of column

= probable beam plastic moment

= CprRybZbeFyb

= overstrength coefficient

= ratio of the expected yield stress to the minimum specified yield strength of the beam

= minimum specified yield stress of the beam = 2MpJL' + WuL'/2 = factored gravity load on the beam = length between plastic hinges = hinge location distance = overstrength coefficient

= ratio of the expected yield stress to the minimum specified yield strength of the column

= minimum specified yield stress of the column = depth of beam = depth of column = thickness of the beam flange

= average story height of the stories above and below the panel zone

The thickness of the column web must at least equal t, otherwise doubler plates are requred.

The thickness of a doubler plate may be included in t, provided it is connected to the column web with plug welds, as shown in Fig. 3.61, adequate to prevent local buckling of the plate. When the doubler plate is placed against the column web, it shall be welded at top and bottom to develop the proportion of the total force that is transmitted to the doubler plate. The doubler plate shall be either butt- or fillet-welded to the column flanges to develop its shear strength. Doubler plates may be placed between continuity plates or may extend above and below the continuity plates. When the doubler plates are placed away from the column web, they shall be placed symmetrically in pairs and welded to continuity plates, to develop their share of the total force transmitted to the doubler plate.

where

Renewable Energy 101

Renewable Energy 101

Renewable energy is energy that is generated from sunlight, rain, tides, geothermal heat and wind. These sources are naturally and constantly replenished, which is why they are deemed as renewable. The usage of renewable energy sources is very important when considering the sustainability of the existing energy usage of the world. While there is currently an abundance of non-renewable energy sources, such as nuclear fuels, these energy sources are depleting. In addition to being a non-renewable supply, the non-renewable energy sources release emissions into the air, which has an adverse effect on the environment.

Get My Free Ebook


Post a comment