Manual and Inelastic-Analysis Based Design of Partially-Restrained Frames Using the 2005 AISC Specifications By Christopher M. Foley, Ph. D, PE Marquette University Milwaukee, WI John Schaad, MS, EIT Jezerinac, Geers, & Associates Dublin, OH 2006 ASCE-SEI Structures Congress St. Louis, MO May 18 -20 2006 ASCE/SEI Structures Congress St. Louis, MO May 18 -20 1
MOTIVATION FOR PRESENTATION 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. Focus can now be on SYSTEM BEHAVIOR rather than members or components and designing for target behavior is possible. How do we teach these concepts and specification developments to students? It would be very beneficial to have a manual methodology to get starting sizes for inelastic analysis-based design. 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) 2006 ASCE/SEI Structures Congress St. Louis, MO May 18 -20 2
TYPICAL FRAMING PLAN Roof Level: B A 3@10 ft. D C 30 ft. Superimposed DL: 63 psf • Comp. Slab: 46 psf • Ceiling: 2 psf • Fireproofing: 3 psf • MEP systems: 12 psf Superimposed LL: 30 psf E 30 ft. 1 Floor Level: 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 30 ft. 2 3 30 ft. Steel Framing: 5 psf Cladding: 25 psf (wall area) Wind, WL: 20 psf 4 Steel Material: A 992 N PR Connections Flexible (pin) Connections 2006 ASCE/SEI Structures Congress St. Louis, MO May 18 -20 X-Braced Bay 3
BASE ANALYTICAL MODEL A B C D 2006 ASCE/SEI Structures Congress St. Louis, MO May 18 -20 E 4
BILINEAR CONNECTION MODELS FLOOR BEAM ROOF BEAM BASE PLATE 2006 ASCE/SEI Structures Congress St. Louis, MO May 18 -20 5
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 2 nd order sway amplification: Implies that behavior is "nearly" linear up to first hinge formation. • Choose member sizes to avoid stiffness reduction; • Choose member sizes to avoid effect; 2006 ASCE/SEI Structures Congress St. Louis, MO May 18 -20 6
AISC APPENDIX 1 - Preliminary Design Local Buckling: • Webs in Combined flexure and axial compression; • Flanges; Stability and Nonlinear Geometric Effects Lateral-Torsional Buckling (column members) (beam members) 2006 ASCE/SEI Structures Congress St. Louis, MO May 18 -20 7
AISC APPENDIX 1 - Preliminary Design 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 2006 ASCE/SEI Structures Congress St. Louis, MO May 18 -20 then; 8
LOADING COMBINATIONS ASCE 7 - 02 Strength Limit State (with corrections): 0. 2% notional loads ASCE 7 - 02 Serviceability Limit State 2006 ASCE/SEI Structures Congress St. Louis, MO May 18 -20 9
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 18 -20 10
MECHANISM 1 - BEAM STRENGTH Plastic Hinges: - 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 18 -20 11
BEAM SERVICEABILITY Moment Diagram - Kotylar (1996) Moment-Area Principle Yields 2006 ASCE/SEI Structures Congress St. Louis, MO May 18 -20 12
BEAM DESIGN Strength: Assume connection strength at 50% of the plastic moment capacity: Assume that the beams are bent in reverse curvature: Compute the ultimate simply-supported beam moment. Compute the required strength of the PR beam. Using the unbraced length establish: Select a beam for strength considerations. Serviceability: Assume that beam connection stiffness results in PR behavior: Check total, DL and LL deflections at mid-span. Check that connections do not exceed yield moment at service level loads. Adjust beam size as required. Beams Selected: W 16 x 40 (roof) W 21 x 55 (floor) 2006 ASCE/SEI Structures Congress St. Louis, MO May 18 -20 13
MECHANISM 2 - Gravity and Notional Loading Gravity and notional loading are assumed to be applied in a proportional manner - therefore, a combined mechanism is targeted. 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. 2006 ASCE/SEI Structures Congress St. Louis, MO May 18 -20 14
MECHANISM 3 - Gravity and Lateral Loading Lateral and gravity loading combinations are applied in a proportional manner therefore, a combined mechanism is targeted. Plastic Hinges: - beam hinge - connection hinge Plastic hinges form in beams indicating SCWB behavior. Previous beam design indicates that plastic hinges will NOT form when gravity loading at the following magnitude is applied: 2006 ASCE/SEI Structures Congress St. Louis, MO May 18 -20 15
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 18 -20 16
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 18 -20 17
SUB-ASSEMBLAGE DISPLACEMENTS Using modifications to the work of Englekirk (1994), displacement expressions for interior, exterior and column base segments can be generated. Interior Sub-Assembly Exterior Sub-Assembly 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 18 -20 18
"SMALL" 2 nd ORDER EFFECTS AND SERVICEABILITY Exterior and Interior Columns: 2 nd Floor Beam: Assume inflection points at mid-heights: Connection and base plate stiffness: 2006 ASCE/SEI Structures Congress St. Louis, MO May 18 -20 19
"SMALL" 2 nd ORDER EFFECTS - STRENGTH L. S. with notional loading at 1 st story 2006 ASCE/SEI Structures Congress St. Louis, MO May 18 -20 20
"SMALL" 2 nd ORDER EFFECTS - STRENGTH L. S. without notional loading at 1 st story 2006 ASCE/SEI Structures Congress St. Louis, MO May 18 -20 21
SERVICEABILITY LIMIT STATE without notional loading at 1 st story 2006 ASCE/SEI Structures Congress St. Louis, MO May 18 -20 22
FRAME FOR MECHANISM ANALYSIS The framework shown below is the system that resulted from the serviceability and 2 nd 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. 2006 ASCE/SEI Structures Congress St. Louis, MO May 18 -20 23
MECHANISM 2 - Combined Mechanism 2006 ASCE/SEI Structures Congress St. Louis, MO May 18 -20 24
EVALUATION OF DESIGN USING INELASTIC ANALYSIS The frame designed preliminarily using the preceding procedure was checked using MASTAN 2 (Ziemian and Mc. Guire). The following loading combinations were evaluated: The yield surface of MASTAN 2 was manipulated as follows: Default MASTAN 2 yield surface connects end points. 2006 ASCE/SEI Structures Congress St. Louis, MO May 18 -20 25
EVALUATION OF DESIGN USING INELASTIC ANALYSIS Node 15 Elem. 35 2006 ASCE/SEI Structures Congress St. Louis, MO May 18 -20 26
EVALUATION OF DESIGN USING INELASTIC ANALYSIS Elem. 39 Node 15 Elem. 35 2006 ASCE/SEI Structures Congress St. Louis, MO May 18 -20 27
EVALUATION OF DESIGN USING INELASTIC ANALYSIS Elem. 39 Elem. 35 Node 15 Elem. 100 2006 ASCE/SEI Structures Congress St. Louis, MO May 18 -20 28
SERVICEABILITY EVALUATION OF DESIGN No connections hit the yield moment Vertical beam deflections were well below acceptable thresholds No connections hit yield moment at service levels. Typical limit on interstory drift is: 2006 ASCE/SEI Structures Congress St. Louis, MO May 18 -20 29
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 18 -20 30
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. 648 -660. Kotylar, N. (1996) "Formulas for Beams with Semi-Rigid Connections" Engineering Journal, AISC, Fourth Quarter, pp. 142 -146. Wooten, J. (1971) "Wooten's Third Law and Steel Column Design", Engineering Journal, 2 nd Quarter, pp. 1 -3. 2006 ASCE/SEI Structures Congress St. Louis, MO May 18 -20 31
Extra slides showing detailed computations to follow this slide. 2006 ASCE/SEI Structures Congress St. Louis, MO May 18 -20 32
SERVICE LOADING Gravity Loading Roof Floor 2006 ASCE/SEI Structures Congress St. Louis, MO May 18 -20 33
SERVICE LOADING (continued) Wind Loading Roof Floor Leaning Columns Roof Floor 2006 ASCE/SEI Structures Congress St. Louis, MO May 18 -20 34
AISC APPENDIX 7 - DIRECT ANALYSIS Column Nominal Strength computed using Out of plane strength defined in usual manner. Design Analysis Requirements Analysis must incorporate geometric nonlinearity: and construction/erection imperfections. • AISC amplification factors allowed if reduced stiffness is used; Interstory drift, , and axial force demands computed using; 2006 ASCE/SEI Structures Congress St. Louis, MO May 18 -20 35
AISC APPENDIX 7 (continued) Design Analysis Requirements (continued) • effects can be omitted when; • Computer software capable of conducting geometrically nonlinear analysis is allowed. • 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 be applied with gravity load combinations. 2006 ASCE/SEI Structures Congress St. Louis, MO May 18 -20 36
AISC APPENDIX 1 - INELASTIC ANALYSIS AND DESIGN Material Limitations: The yield strength of members shall not exceed 65 ksi. Local Buckling: • Webs in Combined flexure and axial compression; • Flanges; 2006 ASCE/SEI Structures Congress St. Louis, MO May 18 -20 37
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 beamcolumn members) 2006 ASCE/SEI Structures Congress St. Louis, MO May 18 -20 38
AISC APPENDIX 1 (continued) Axial Capacity, Moment Capacity and Combined Forces 2006 ASCE/SEI Structures Congress St. Louis, MO May 18 -20 39
BEAM DESIGN - STRENGTH 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 0. 50. Floor Beams Roof Beams (negative bending) Try W 14 x 30 Try W 16 x 36 2006 ASCE/SEI Structures Congress St. Louis, MO May 18 -20 40
BEAM DESIGN - SERVICEABILITY (continued) Assume that beam connection stiffness results in PR behavior: Check total, DL and LL deflections at mid-span. Roof Beams W 14 x 30 Floor Beams 2006 ASCE/SEI Structures Congress St. Louis, MO May 18 -20 W 16 x 36 41
BEAM DESIGN - SERVICEABILITY (continued) Ensure end moments are less than connection yield moment at service loads. Roof Beams W 14 x 30 Floor Beams W 16 x 36 connection yield moments may be exceeded at service Revise to W 16 x 40 Revise to W 21 x 55 2006 ASCE/SEI Structures Congress St. Louis, MO May 18 -20 42
SIZING FOR TARGET MECHANISMS (continued) Gravity loading combinations will be used (axial load in columns greatest). Interior 2 nd Story Column W 12 x 58 Interior 1 st Story Column W 12 x 58 Exterior 2 nd Story Column W 8 x 40 Exterior 1 st Story Column W 8 x 40 2006 ASCE/SEI Structures Congress St. Louis, MO May 18 -20 43
COLUMN DESIGN - Out-of-Plane Buckling Only first-story columns and gravity load combinations will be checked at this point. Interior Column: W 12 x 58 Exterior Column: W 8 x 40 W 12 x 58 W 8 x 40 2006 ASCE/SEI Structures Congress St. Louis, MO May 18 -20 44
COLUMN DESIGN - Cross-Section Stability Checks Interior Column: W 12 x 58 Exterior Column: W 8 x 40 2006 ASCE/SEI Structures Congress St. Louis, MO May 18 -20 45
FLOOR-LEVEL SUBASSEMBLAGES 2006 ASCE/SEI Structures Congress St. Louis, MO May 18 -20 46
COLUMN DESIGN - Out-of-Plane Buckling Only first-story columns and gravity load combinations will be checked at this point. Interior Column: W 10 x 45 Exterior Column: W 8 x 35 W 10 x 45 W 8 x 35 2006 ASCE/SEI Structures Congress St. Louis, MO May 18 -20 47
COLUMN DESIGN - Cross-Section Stability and LTB Checks Interior Column: W 10 x 45 Exterior Column: W 8 x 35 W 10 x 45 W 8 x 35 2006 ASCE/SEI Structures Congress St. Louis, MO May 18 -20 48
LOADING COMBINATIONS Roof Beam Loads Floor Beam Loads Leaning Columns Notional Loading (applied laterally) 2006 ASCE/SEI Structures Congress St. Louis, MO May 18 -20 49
LOADING COMBINATIONS (continued) Roof Beam Loads Floor Beam Loads Leaning Columns Notional Loading (applied laterally) 2006 ASCE/SEI Structures Congress St. Louis, MO May 18 -20 50
LOADING COMBINATIONS (continued) Roof Beam Loads Floor Beam Loads Leaning Columns Notional Loading (applied laterally) 2006 ASCE/SEI Structures Congress St. Louis, MO May 18 -20 51
LOADING COMBINATIONS (continued) Roof Beam Loads Floor Beam Loads Leaning Columns Notional Loading (applied laterally) Second-order effects will be "small" and thus, no notional loading. Factored Wind Loading 2006 ASCE/SEI Structures Congress St. Louis, MO May 18 -20 52
FLOOR-LEVEL - EXTERIOR 2006 ASCE/SEI Structures Congress St. Louis, MO May 18 -20 53
FLOOR-LEVEL - INTERIOR 2006 ASCE/SEI Structures Congress St. Louis, MO May 18 -20 54
STORY STIFFNESS Interior Sub-Assembly Exterior Sub-Assembly Concrete floor diaphragm provides displacement compatibility. This leads to relationship between interior and exterior shear; Portal frame assumptions regarding shear distribution met when; 2006 ASCE/SEI Structures Congress St. Louis, MO May 18 -20 55
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