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<h1>Steel Moment Frame Analysis and Modeling</h1>
<h3 class="h4">A1. Steel Frame Analysis</h3>
<p>
  ASCE 7 permits four types of analysis procedures to determine frame drift and
  frame member design forces. These are (1) equivalent lateral forces method
  (ELF), (2) modal response spectrum method, (3) linear response history
  analysis and (4) nonlinear response history analysis. ASCE 7-16 Table 12.6-1
  outlines the permitted analysis procedures.
</p>
<p>
  Steel frame analysis can be with either 2D or 3D computer models. A 3D
  computer model is recommended for steel design with metal deck and concrete
  fill since for rigid diaphragms the designer is required to consider effects
  with accidental torsion and any inherent torsion in the structure. 2D computer
  models are acceptable provided lateral loads to the frame have included the
  effects of torsion in the structure
</p>
<h3 class="h4">A2. Connection Modeling</h3>
<p>
  ASCE 7 requires steel moment frame systems to account for the contribution of
  panel zone deformation to the overall story drift. Panel zone deformation can
  be accounted for in analysis software by explicit modeling of the panel zone
  (e.g., using the Krawinkler model or the Scissors model). Nevertheless,
  traditional structural analysis using centerline-to-centerline dimensions
  (i.e., beam and columns represented by lines intersecting at a node) is a
  practical way to account for panel zone contribution according to the NEHRP
  Seismic Design Technical Brief No. 2, Seismic Design of Steel Special Moment
  Frames: A Guide for Practicing Engineers.
</p>
<p>
  In addition to connection modeling, if the member has any modifications such
  as in an RBS connection, designers shall account for the additional
  deformation due to the reduction in the member flange width at the reduced
  beam section. For frames with RBS connections, this reduction can increase
  drift by approximately 5%–10%. For the Simpson Strong-Tie Yield-Link moment
  connection, there are two ways to model the Yield-Links easily in structural
  analysis software for elastic code design:
</p>
<div class="row">
  <div class="col-md-6 col-sm-6 col-xs-12 img-panel">
    <p>1. Moment Release with Partial Fixity Rotational Springs</p>
    <img
      src="https://embed.widencdn.net/img/ssttoolbox/gw402imofh/exact/f-l-ylmcdg20-021a.png"
      alt="Moment Release with Partial Fixity Rotational Springs"
    />
  </div>
  
  <div class="col-md-6 col-sm-6 col-xs-12 img-panel">
    <p>2. Equivalent Elastic Link Elements</p>
    <img
      src="https://embed.widencdn.net/img/ssttoolbox/7neyqmurjn/1710x1226px/f-l-ylmcdg20-021b.png"
      alt="Equivalent Elastic Link Elements"
    />
  </div>
  
</div>

<p>
  The method with rotational spring is for structural analysis software that has
  the functionality to assign partially restrained (PR) releases to the ends of
  a beam. The Equivalent Elastic Link Element method breaks up the beam into
  three elements with the two end elements representing the connection stiffness
  by using a reduced moment of inertia. For more information regarding these two
  modeling methods for the Yield-Link, please refer to the
  <a
    href="/products/structural-steel/yield-link-moment-connection/software/modeling-guide"
    >Yield-Link Moment Connection Modeling Guide (F-L-SMFYLCMG)</a
  >.
</p>
<p>
  For performance design requiring modeling of the Yield-Link moment
  connection&rsquo;s nonlinearity, the user can follow the step-by-step
  procedure to calculate the axial link or rotational link parameters for the
  Yield-Link moment connection documented in Chapter 12 of AISC 358. Once the
  parameters are calculated, designers can use any software that has nonlinear
  elements to model the Yield-Link. These elements can be nonlinear axial spring
  elements (shown in the
  <a
    href="/products/structural-steel/yield-link-moment-connection/software/sap-etabs-plugin"
    >SAP2000</a
  >
  input below) or nonlinear rotational spring elements. Contact Simpson-Strong
  Tie if there are any questions regarding modeling the Yield-Link in your
  structural analysis software.
</p>
<div class="row">
  <div class="col-md-6 col-sm-6 col-xs-12 img-panel">
    <img
      src="https://embed.widencdn.net/img/ssttoolbox/jfd0bc5qzl/500px@2x/f-l-ylmcdg20-022a.png"
      alt="Yield-Link Moment Connection Modeling with Axial Link Elements"
    />
    <div class="image__caption">
      Figure A2.2 — Yield-Link Moment Connection Modeling with Axial Link
      Elements
    </div>
  </div>
  
  <div class="col-md-6 col-sm-6 col-xs-12 img-panel">
    <img
      src="https://embed.widencdn.net/img/ssttoolbox/valfcbjeyc/500px@2x/f-l-ylmcdg20-022b.png"
      alt="SAP2000/ETABS Axial Link Element"
    />
    <div class="image__caption">
      Figure A2.1 — SAP2000/ETABS Axial Link Element
    </div>
  </div>
  
</div>

<p>
  Column base fixity has a considerable effect on the performance of moment
  frames. Currently, engineers typically assume either a fixed-base connection
  (Figure A3.1) or a pinned-base connection (Figure A3.4) in the analysis of
  moment frames. In reality, the performance of the connection is in between the
  two limits. Figure A3.2 shows the AISC definition of a fixed, a pinned and a
  partially restrained (PR) connection in a graphical format. Connections are
  considered fixed when the moment versus rotation stiffness is greater than 20
  EI/L of the member, whereas a connection is considered pinned (simple) when
  the stiffness value is less than 2 EI/L.
</p>
<h3 class="h4">A3. Base Fixity</h3>
<div class="row">
  <div class="col-md-6 col-sm-6 col-xs-12 img-panel">
    <img
      src="https://embed.widencdn.net/svg/ssttoolbox/v6u1wsgbug/f-l-ylmcdg20-023a.svg"
      alt="Fixed Base (FR) Connection in AISC Seismic Design Manual"
    />
    <div class="image__caption">
      Figure A3.1 — Fixed Base (FR) Connection in AISC Seismic Design Manual
    </div>
  </div>
  
  <div class="col-md-6 col-sm-6 col-xs-12 img-panel">
    <img
      src="https://embed.widencdn.net/svg/ssttoolbox/zx9yctifd3/f-l-ylmcdg20-023b.svg"
      alt="Connection Classification per AISC 360"
    />
    <div class="image__caption">
      Figure A3.2 — Connection Classification per AISC 360
    </div>
  </div>
  
</div>

<div class="row">
  <div class="col-md-6 col-sm-6 col-xs-12 img-panel">
    <img
      src="https://embed.widencdn.net/svg/ssttoolbox/uex1opqteq/f-l-ylmcdg20-023c.svg"
      alt="PR Base Detail Connection per AISC"
    />
    <div class="image__caption">
      Figure A3.3 - PR Base Detail Connection per AISC
    </div>
  </div>
  
  <div class="col-md-6 col-sm-6 col-xs-12 img-panel">
    <img
      src="https://embed.widencdn.net/svg/ssttoolbox/o8eedkmtbk/f-l-ylmcdg20-023d.svg"
      alt="Pinned Base (Simple) Connection in AISC Design Guide #1"
    />
    <div class="image__caption">
      Figure A3.4 — Pinned Base (Simple) Connection in AISC Design Guide #1
    </div>
  </div>
  
</div>

<p>
  Table 1 below shows the effects of base fixity on the different performance
  parameters. Pinned column bases will have a higher drift. However, they will
  have lower floor accelerations than columns with a fixed-base connection. A
  partially restrained base will behave somewhere in between pinned and fixed
  bases. Compared to a frame with pinned base connections, a frame with PR bases
  will have less drift, higher base shear and higher floor accelerations. Base
  plate and anchorage design is per designer in accordance with typical codes
  and guidelines and not specific to Yield-Link moment connection or part of the
  design tools.
</p>
<h5>Table 1 — Performance Effects from Different Base Fixities</h5>
<p>
  <img
    src="https://embed.widencdn.net/img/ssttoolbox/e3awwea5sz/800px@2x/f-l-ylmcdg20-024a.png"
    alt="Table — Performance Effects from Different Base Fixities"
  />
</p>
<h3 class="h4">A4. Analysis Methods</h3>
<p>
  AISC 360-16 Chapter C requires that structural stability be considered in
  design. Typically, designers are familiar with the use of the effective length
  method (AISC 360-16 Appendix 7) for stability design. However, since the
  Yield-Link moment connection is considered a PR connection, the alignment
  chart used for calculating the K-factors requires some modification due to
  rigid joint assumption in their development. For columns connected to beams at
  both ends with PR connections with a rotational stiffness Krot, the modified
  stiffness distribution factor per Chen and Lui (Stability Design of Steel
  Frames, 1991) is given as:
</p>
<div class="row">
  <div class="col-md-6 col-sm-6 col-xs-12 img-panel">
    <img
      src="https://embed.widencdn.net/svg/ssttoolbox/2dxefzfjn9/f-l-ylmcdg20-024b.svg"
      alt="Modified Stiffness Distribution Factor"
    />
  </div>
  
</div>

<div class="row">
  <div class="col-md-6 col-sm-6 col-xs-12">
    <p>
      However, with the introduction of the Direct Analysis Method, designers no
      longer have to calculate K-factors. In addition, the Direct Analysis
      Method also applies to frames with PR connections. When using the Direct
      Analysis Method, designers should be aware that it comes in several
      variations as illustrated in the table.
    </p>
  </div>
  
  <div class="col-md-6 col-sm-6 col-xs-12 img-panel">
    <img
      src="https://embed.widencdn.net/img/ssttoolbox/g3xhvkuu9r/500px@2x/f-l-ylmcdg20-024c.png"
      alt="Table – Direct Analysis Method"
    />
  </div>
</div>

<p>
  When using the Amplified First Order Elastic Analysis, force amplification
  factors B1 and B2 (AISC 360-16 Appendix 8) are required to modify the moment
  and axial demand loads from First Order Elastic structural analysis, where B1
  is used to account for P-d affect and B2 is used to account for P-D affect.
  Please note, some analysis programs will only calculate the B1 factor and the
  designer will need to provide the B2 factor.
</p>
<p>
  For the General Second Order Elastic Analysis, stiffness reduction factors for
  EI and EA are required; typically a factor of 0.8 is applied to all the
  stiffness that is considered to contribute to the stability of the structure.
</p>
<p>
  Whether to use variable τb or a fixed τb is up to the designer. Typically, to
  use a fixed τb (τb=1), a notional load coefficient of 0.003 is used where as a
  notional load coefficient of 0.002 is used for the variable τb case. Notional
  loads are used to account for geometric imperfections in structural systems
  when using Direct Analysis Method.
</p>
<p>
  For more information regarding which Direct Analysis Method to use, the
  designer should review AISC 360-16 Chapter C, Appendix 7, Appendix 8 and the
  technical manual for their structural analysis and design software.
</p>

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