2006 ASCE/SEI Structures Congress St. Louis, MO May Manual and Inelastic-Analysis Based Design of Partially-Restrained Frames Using the 2005 AISC Specifications By Christopher M. Foley, PhD, PE John Schaad, MS, EIT Marquette UniversityJezerinac, Geers, & Associates Milwaukee, WIDublin, OH 2006 ASCE-SEI Structures Congress St. Louis, MO May 18-20

2006 ASCE/SEI Structures Congress St. Louis, MO May AISC Specifications are becoming more liberalized in the designer's favor and are beginning to allow software capabilities to be exploited. There are new demands on the structural engineer to understand phenomena that software is now able to consider. How do we teach these concepts and specification developments to students? MOTIVATION FOR PRESENTATION Focus can now be on SYSTEM BEHAVIOR rather than members or components and designing for target behavior is possible. Address Wooten's Third Law of Steel Column Design - Corollary Number 2: "The computer renders obsolete the necessity of rationalizing and simplifying problems - or even of understanding them" (Wooten 1971) It would be very beneficial to have a manual methodology to get starting sizes for inelastic analysis-based design.

2006 ASCE/SEI Structures Congress St. Louis, MO May N TYPICAL FRAMING PLAN PR Connections Flexible (pin) Connections A B C D E 30 ft. ft ft. X-Braced Bay Superimposed DL: 63 psf Comp. Slab: 46 psf Ceiling: 2 psf Fireproofing: 3 psf MEP systems:12 psf Superimposed LL: 30 psf Steel Framing: 5 psf 30 ft. Wind, WL:20 psf Steel Material: A992 Superimposed DL: 83 psf Comp. Slab: 46 psf Ceiling: 2 psf Fireproofing: 3 psf MEP systems:12 psf Partitions: 20 psf Superimposed LL: 50 psf Roof Level: Floor Level: Cladding: 25 psf (wall area)

2006 ASCE/SEI Structures Congress St. Louis, MO May A B C D E BASE ANALYTICAL MODEL

2006 ASCE/SEI Structures Congress St. Louis, MO May BILINEAR CONNECTION MODELS FLOOR BEAM ROOF BEAM BASE PLATE

2006 ASCE/SEI Structures Congress St. Louis, MO May AISC APPENDIX 7 - Preliminary Design Member design can be greatly streamlined if the following constraints on member selection are included. Choose a target interstory drift to meet target 2nd order sway amplification: Choose member sizes to avoid stiffness reduction; Choose member sizes to avoid effect; Implies that behavior is "nearly" linear up to first hinge formation.

2006 ASCE/SEI Structures Congress St. Louis, MO May AISC APPENDIX 1 - Preliminary Design Local Buckling: Flanges; Webs in Combined flexure and axial compression; Stability and Nonlinear Geometric Effects Lateral-Torsional Buckling (column members)(beam members)

2006 ASCE/SEI Structures Congress St. Louis, MO May Moment capacity in presence of axial loading Assume column bent in reverse curvature and the inflection point is at 2/3 column height: Therefore, if then; AISC APPENDIX 1 - Preliminary Design

2006 ASCE/SEI Structures Congress St. Louis, MO May LOADING COMBINATIONS ASCE Strength Limit State (with corrections): ASCE Serviceability Limit State 0.2% notional loads

2006 ASCE/SEI Structures Congress St. Louis, MO May DESIGN ASSUMPTIONS The following assumptions are made in the design: Unbraced lengths for columns were taken as the story height. The compression flange for beams in positive flexure is fully braced. The compression flange for girders subjected to negative flexure is braced at column lines and at beam lines. Compression forces in beams is negligible. Columns are pin-pin for minor axis bending. Beams are non-composite with floor system.

2006 ASCE/SEI Structures Congress St. Louis, MO May Plastic Hinges: MECHANISM 1 - BEAM STRENGTH - beam hinge - connection hinge Plastic hinges form in beams indicating SCWB behavior. Loading Combinations: Simplified Gravity Load Analysis:

2006 ASCE/SEI Structures Congress St. Louis, MO May BEAM SERVICEABILITY Moment Diagram - Kotylar (1996) Moment-Area Principle Yields

2006 ASCE/SEI Structures Congress St. Louis, MO May BEAM DESIGN Assume connection strength at 50% of the plastic moment capacity: Assume that the beams are bent in reverse curvature: Serviceability: Compute the ultimate simply-supported beam moment. Compute the required strength of the PR beam. Using the unbraced length establish: Assume that beam connection stiffness results in PR behavior: Check total, DL and LL deflections at mid-span. Strength: Select a beam for strength considerations. Check that connections do not exceed yield moment at service level loads. Adjust beam size as required. Beams Selected: W16x40 (roof) W21x55 (floor)

2006 ASCE/SEI Structures Congress St. Louis, MO May MECHANISM 2 - Gravity and Notional Loading Plastic Hinges: - beam hinge - connection hinge Plastic hinges form in beams indicating SCWB behavior. Loading combinations applied in a non-proportional manner (e.g. gravity load first and then lateral load to failure) will likely result in a sway mechanism forming. Gravity and notional loading are assumed to be applied in a proportional manner - therefore, a combined mechanism is targeted.

2006 ASCE/SEI Structures Congress St. Louis, MO May MECHANISM 3 - Gravity and Lateral Loading Lateral and gravity loading combinations are applied in a proportional manner - therefore, a combined mechanism is targeted. Previous beam design indicates that plastic hinges will NOT form when gravity loading at the following magnitude is applied: Plastic Hinges: - beam hinge - connection hinge Plastic hinges form in beams indicating SCWB behavior.

2006 ASCE/SEI Structures Congress St. Louis, MO May SIZING FOR TARGET MECHANISMS SCWB criteria can be used to help ensure assumed targeted mechanisms form.

2006 ASCE/SEI Structures Congress St. Louis, MO May FRAME FOR FURTHER EVALUATION The framework shown below is the system that will be used for displacement evaluation. We will now check the columns and/or beams to ensure second-order effects are "small" and the frame is serviceable with respect to interstory drift.

2006 ASCE/SEI Structures Congress St. Louis, MO May Exterior Sub-Assembly Interior Sub-Assembly SUB-ASSEMBLAGE DISPLACEMENTS Using modifications to the work of Englekirk (1994), displacement expressions for interior, exterior and column base segments can be generated. Partially Restrained Column Bases For simplicity, we will assume inflection points at 1/2 first story height and mid-height of the second story columns.

2006 ASCE/SEI Structures Congress St. Louis, MO May Exterior and Interior Columns: 2nd Floor Beam: Assume inflection points at mid-heights: Connection and base plate stiffness: "SMALL" 2nd ORDER EFFECTS AND SERVICEABILITY

2006 ASCE/SEI Structures Congress St. Louis, MO May with notional loading "SMALL" 2nd ORDER EFFECTS - STRENGTH L.S. at 1st story

2006 ASCE/SEI Structures Congress St. Louis, MO May without notional loading "SMALL" 2nd ORDER EFFECTS - STRENGTH L.S. at 1st story

2006 ASCE/SEI Structures Congress St. Louis, MO May SERVICEABILITY LIMIT STATE without notional loading at 1st story

2006 ASCE/SEI Structures Congress St. Louis, MO May The framework shown below is the system that resulted from the serviceability and 2nd order effects evaluation. We will now simply ensure that the member sizes chosen will result in the targeted mechanisms forming at levels higher than the strength limit state combinations. FRAME FOR MECHANISM ANALYSIS

2006 ASCE/SEI Structures Congress St. Louis, MO May MECHANISM 2 - Combined Mechanism

2006 ASCE/SEI Structures Congress St. Louis, MO May EVALUATION OF DESIGN USING INELASTIC ANALYSIS The frame designed preliminarily using the preceding procedure was checked using MASTAN2 (Ziemian and McGuire). The following loading combinations were evaluated: The yield surface of MASTAN2 was manipulated as follows: Default MASTAN2 yield surface connects end points.

2006 ASCE/SEI Structures Congress St. Louis, MO May EVALUATION OF DESIGN USING INELASTIC ANALYSIS Node 15 Elem. 35

2006 ASCE/SEI Structures Congress St. Louis, MO May EVALUATION OF DESIGN USING INELASTIC ANALYSIS Node 15 Elem. 39 Elem. 35

2006 ASCE/SEI Structures Congress St. Louis, MO May EVALUATION OF DESIGN USING INELASTIC ANALYSIS Node 15 Elem. 39 Elem. 35 Elem. 100

2006 ASCE/SEI Structures Congress St. Louis, MO May SERVICEABILITY EVALUATION OF DESIGN No connections hit yield moment at service levels. Typical limit on interstory drift is: No connections hit the yield moment Vertical beam deflections were well below acceptable thresholds

2006 ASCE/SEI Structures Congress St. Louis, MO May CONCLUDING REMARKS An approximate methodology for sizing members within the context of AISC Appendices 1 and 7 has been outlined. The method has been shown to be relatively accurate given its overall simplicity. The advantage of the approach is that it focuses on "system" behavior while maintaining flexibility to consider beam-columns, beams, and connections. The formulas for displacement have been show to be accurate for preliminary design purposes and they provide the engineer with significant problem feel. Small multiple-story multiple-bay frames can be sized using the procedure to control second-order effects and the resulting designs have significant reserve strength. The best use of the methodology would be to demonstrate the important provisions in the new AISC (2005) specifications in a simplified manner so that algorithms for computer implementation can be developed.

2006 ASCE/SEI Structures Congress St. Louis, MO May REFERENCES Englekirk, R. (1994) Steel Structures - Controlling Behavior Through Design, John Wiley & Sons, Inc., New York, NY. Foley, C.M. and Schinler, D. (2003) "Automated Design of Steel Frames Using Advanced Analysis and Object-Oriented Evolutionary Computation", Journal of Structural Engineering, 129 (5), pp Kotylar, N. (1996) "Formulas for Beams with Semi-Rigid Connections" Engineering Journal, AISC, Fourth Quarter, pp Wooten, J. (1971) "Wooten's Third Law and Steel Column Design", Engineering Journal, 2nd Quarter, pp. 1-3.

2006 ASCE/SEI Structures Congress St. Louis, MO May Extra slides showing detailed computations to follow this slide.

2006 ASCE/SEI Structures Congress St. Louis, MO May SERVICE LOADING Gravity Loading Roof Floor

2006 ASCE/SEI Structures Congress St. Louis, MO May SERVICE LOADING (continued) Wind Loading Leaning Columns Roof Floor Roof Floor

2006 ASCE/SEI Structures Congress St. Louis, MO May AISC APPENDIX 7 - DIRECT ANALYSIS Design Analysis Requirements computed using Out of plane strength defined in usual manner. Column Nominal Strength Analysis must incorporate geometric nonlinearity: and AISC amplification factors allowed if reduced stiffness is used; Interstory drift,, and axial force demands computed using; and construction/erection imperfections.

2006 ASCE/SEI Structures Congress St. Louis, MO May AISC APPENDIX 7 (continued) Design Analysis Requirements (continued) effects can be omitted when; Story out-of-plumb imperfections must be included through notional loading; Out-of-plumbness can be directly inserted into the analytical model (1/500). If second-order amplification is less than 50% notional loads need only need only be applied with gravity load combinations. Computer software capable of conducting geometrically nonlinear analysis is allowed.

2006 ASCE/SEI Structures Congress St. Louis, MO May AISC APPENDIX 1 - INELASTIC ANALYSIS AND DESIGN Material Limitations: The yield strength of members shall not exceed 65 ksi. Local Buckling: Flanges; Webs in Combined flexure and axial compression;

2006 ASCE/SEI Structures Congress St. Louis, MO May AISC APPENDIX 1 (continued) Stability and Nonlinear Geometric Effects First order (mechanism) analysis can be used provided second-order effects are considered. Second order inelastic analysis is permitted. Sufficient rotational ductility in columns preserved through limiting axial load levels; Lateral-Torsional Buckling (targeted for column members) (targeted for beam and beam- column members)

2006 ASCE/SEI Structures Congress St. Louis, MO May AISC APPENDIX 1 (continued) Axial Capacity, Moment Capacity and Combined Forces

2006 ASCE/SEI Structures Congress St. Louis, MO May BEAM DESIGN - STRENGTH Roof Beams Floor Beams (negative bending) Assume connection strength at 50% of the plastic moment capacity: At the strength limit state, beams are bent in reverse curvature and ratio of end moments is Try W14x30 Try W16x36

2006 ASCE/SEI Structures Congress St. Louis, MO May BEAM DESIGN - SERVICEABILITY (continued) Roof Beams Floor Beams Assume that beam connection stiffness results in PR behavior: W14x30 W16x36 Check total, DL and LL deflections at mid-span.

2006 ASCE/SEI Structures Congress St. Louis, MO May BEAM DESIGN - SERVICEABILITY (continued) Roof Beams Floor Beams W14x30 W16x36 Ensure end moments are less than connection yield moment at service loads. connection yield moments may be exceeded at service Revise to W16x40Revise to W21x55

2006 ASCE/SEI Structures Congress St. Louis, MO May SIZING FOR TARGET MECHANISMS (continued) Interior 2nd Story Column Exterior 2nd Story Column Interior 1st Story Column Exterior 1st Story Column Gravity loading combinations will be used (axial load in columns greatest). W8x40 W12x58 W8x40

2006 ASCE/SEI Structures Congress St. Louis, MO May COLUMN DESIGN - Out-of-Plane Buckling Interior Column: Exterior Column: W12x58W8x40 Only first-story columns and gravity load combinations will be checked at this point. W12x58 W8x40

2006 ASCE/SEI Structures Congress St. Louis, MO May COLUMN DESIGN - Cross-Section Stability Checks Interior Column: Exterior Column: W12x58 W8x40 W12x58 W8x40

2006 ASCE/SEI Structures Congress St. Louis, MO May FLOOR-LEVEL SUBASSEMBLAGES

2006 ASCE/SEI Structures Congress St. Louis, MO May COLUMN DESIGN - Out-of-Plane Buckling Interior Column: Exterior Column: W10x45W8x35 Only first-story columns and gravity load combinations will be checked at this point. W10x45 W8x35

2006 ASCE/SEI Structures Congress St. Louis, MO May COLUMN DESIGN - Cross-Section Stability and LTB Checks Interior Column: Exterior Column: W10x45 W8x35 W10x45 W8x35

2006 ASCE/SEI Structures Congress St. Louis, MO May LOADING COMBINATIONS Leaning Columns Floor Beam LoadsRoof Beam Loads Notional Loading (applied laterally)

2006 ASCE/SEI Structures Congress St. Louis, MO May LOADING COMBINATIONS (continued) Leaning Columns Floor Beam LoadsRoof Beam Loads Notional Loading (applied laterally)

2006 ASCE/SEI Structures Congress St. Louis, MO May LOADING COMBINATIONS (continued) Leaning Columns Floor Beam LoadsRoof Beam Loads Notional Loading (applied laterally)

2006 ASCE/SEI Structures Congress St. Louis, MO May LOADING COMBINATIONS (continued) Factored Wind Loading Leaning Columns Floor Beam LoadsRoof Beam Loads Notional Loading (applied laterally) Second-order effects will be "small" and thus, no notional loading.

2006 ASCE/SEI Structures Congress St. Louis, MO May FLOOR-LEVEL - EXTERIOR

2006 ASCE/SEI Structures Congress St. Louis, MO May FLOOR-LEVEL - INTERIOR

2006 ASCE/SEI Structures Congress St. Louis, MO May Exterior Sub-Assembly Interior Sub-Assembly STORY STIFFNESS Concrete floor diaphragm provides displacement compatibility. This leads to relationship between interior and exterior shear; Portal frame assumptions regarding shear distribution met when;