ENCE 710 Advanced Steel Structures

Transcription

1 ENCE 7 Advanced Steel Structures Design of Beam-Columns & Lateral Bracing Design Tetbook & Related AISC Articles Salmon & Johnson Chapter Combined Bending and Aial Load Chapter C Design for Stability () Direct () Alternate Appendi - Inelastic Analysis and Design Appendi 6 Stability Bracing for Columns and Beams C. C. Fu, Ph.D., P.E. Appendi 7 Alternative Methods of Design for Stability (Effective length & First-order analysis methods) Civil and Environmental Engineering Department University of Maryland Appendi 8 Approimate Second-order Analysis Combined Bending and Aial Load Failure modes: Aial tension and bending; failure usually by yielding Aial compression and bending about one ais; failure by instability in the plane of bending without twisting Aial compression and bending about the strong ais; failure by lateral-torsional buckling Aial compression and biaial bending-torsionally stiff section; failure by instability in one of the principal directions Aial compression and biaial bending-thin-wall open section; failure by combined twisting and bending Aial compression, biaial bending, and torsion; failure by combined twisting and bending 3 Single Curvature without End Translation M z, ma M Pyma M B B C m Pu Pu P E /( KL / r) e 4

2 C-A Primary plus secondary bending moment by end moments Comparison of theoretical C m with AISC straight line approimation by end moments only, without joint translation 7 8

3 Beam-column with sidesway Interaction Equation Case, No Instability Eact nominal strength interaction relationship for typical wide-flange sections (including residual stress) compared with interaction equation Case, no instability 9 Interaction Equation Case, Instability in the Plane of Bending Contours on strength interaction surface for short members where instability does not occur Eact nominal strength interaction curves for typical wideflange sections (including residual stress) compared with interaction equation Case, instability in the plane of bending

4 Compression Member End restraints and effective lengths Table C-A- 7. (S&J Figure 6.9.5) Alignment chart (S&J Figure 6.9.4) Sidesway inhibited (braced frame) Figure C-A-7. Sidesway uninhibited (moment frame) Figure C-A-7. Compact/Noncompact/Slender for compression element Table B4. Chapter E Design of Members for Compression Fleural buckling w/o slender elements (E3) Torsional &fleural-torsional buckling w/o slender elements (E4) Members w/slender elements (E7) 3 Combined Bending and Aial Load Doubly and Singly Symmetric Members in Fleure and Compression P P 8 u u M M u uy For.. (H-a) cp 9 cpn n bm n bm ny Pu P u For. M M u uy. (H-b) cpn cpn bm n bm ny Unsymmetric and Other Members in Fleure and Compression f (H-) a fbw fbz. F F F a bw bz 4 Beam-column for Eample.. Methods of Second-order Analysis Amplified First Order Elastic Analysis (Section C-A8 ) 5 6

5 Second-Order Analysis by Amplified First-Order Elastic Analysis nd -order fleural strength M r B M B M (A8-) M r nt nd -order aial strength P r (A8-) where Pr Pnt B Cm B Pr P P e lt B P P e nt lt (A8-3) (A8-6) 7 Second-Order Analysis by Amplified First-Order Elastic Analysis (cont.) B is an amplifier to account for second order effects caused by displacement between brace points (P-) B is an amplifier to account for second order effects caused by displacements of braced points (P-) If B.5, it is conservative that M r =B (M nt +M lt ) 8 Second-Order Analysis by Amplified First-Order Elastic Analysis (cont.) C m is a coefficient assuming no lateral translation of frame (no transverse loading) C.6.4( M m ) (A8-4) M P e is the elastic critical buckling resistance with zero sidesway EI P e K (A8-5) L P e is the elastic critical buckling resistance for the story EI For moment frames P e K L HL For all types (A8-7) C m : coefficient assuming no lateral translation of the frame For beam-columns not subject to transverse loading Equation (A8-4) For beam-columns subject to transverse loading: analysis or conservatively as Pe RM H 9 Refer to AISC Table C-A-8. for ψ and C m

6 C m : coefficient assuming no lateral translation of the frame (cont.) Summation of forces acting on all columns in one story of a multistory building frame Lowest portion of single-bay multistory unbraced frame for Eample.. Forces from first-order elastic analyses under factored loads Eample.. 3 4

7 Stability Analysis Structure Approach () Any method that considers the influence of second-order effects (including P- and P- effects), fleural, shear and aial deformation, geometric imperfections, and member stiffness reduction due to residual stresses on the stability of the structure and its elements Appendi 7 Effective Length Method & First-order Analysis Method ( nd order/ st order drift.5) Appendi 8 Traditional Secondorder Analysis Method 5 Elastic Analysis Design requirement in Section C. Second-order drift/first-order drift.5 Appendi 7, or by the Direct Analysis Method of Chapter C. Second-order drift/first-order drift >.5 - the Direct Analysis Method of Chapter C. Simplified method (see handout) 6 Structure Approach () Inelastic Analysis Appendi Moment redistribution compact beams and girders Local buckling compact section defined in Table B4. or as modified in Appendi Section.4. Stability and second-order effects First-order inelastic analysis or a plastic mechanism analysis Continuous beams, braced frames and moment frame Second-order inelastic analysis App7.3 C. App7. C. 7 8

8 System Stability Design Requirements Braced-Frame and Shear-all Systems Effective length, K= for compression members Moment-Frame Systems K and Fe for columns and beam-columns specified in Section C (also for knee-braced frame) Gravity Framing Systems K= where P- effects due to loads on the gravity columns shall be transferred to the lateral load resisting systems Combined Systems (also for Eccentrically braced frame systems) Stability Bracing for Columns and Beams Two general types of bracing systems Panel brace Point brace Columns Appendi 6, Section 6. Beams Appendi 6, Section Portal Frame w/ Slant Column Multi-Story Frame Leaning Column Design Multi-Story Ratio Comparison.4..8 Ratio Columns Factored Plastic Analysis Alignment Chart Analysis Direct Anlysis Ratio Columns 6 Factored Plastic Analysis Effective Length Method Direct Analysis Method () nd order plastic analysis with unfactored loads (PA). () nd order plastic analysis with factored loads and a reduced stiffness properties.9ei and.9ea (FPA). (3) nd order elastic analysis with factored loads (ELM). (4) nd order elastic analysis with factored loads including 3 () nd order plastic analysis with unfactored loads (PA). () nd order plastic analysis with factored loads and a reduced stiffness properties.9ei and.9ea (FPA). (3) nd order elastic analysis with factored loads (ELM). (4) nd order elastic analysis with factored loads including 3