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Design of Beams - Limit States

Design of Beams - Limit States. Flexure Elastic Plastic Stability (buckling) Shear Deflection. Nominal Flexural Strength – Compact Shapes. Nominal Flexural Strength – NON-Compact Shapes. FLB. Large concentrated loads placed near beam supports

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Design of Beams - Limit States

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  1. Design of Beams - Limit States • Flexure • Elastic • Plastic • Stability (buckling) • Shear • Deflection

  2. Nominal Flexural Strength – Compact Shapes

  3. Nominal Flexural Strength – NON-Compact Shapes FLB

  4. Large concentrated loads placed near beam supports Rigid connection of beams and columns with webs on the same plane Notched or coped beams Heavily loaded short beams Thin webs in girders Design for Shear

  5. Design for Shear V: Vertical shear at the section under consideration Q: First moment about of neutral axis of area of the cross section between point of interest and top or bottom of section (depends on y) I: Moment of inertia of section b: width of section at point of interest

  6. Design for Shear Small width b d/b=2 Error ~3% d/b=1 Error ~12% d/b=1/4 Error 100% Web fails before flanges Average Shear Stress Nominal Strength if no buckling:

  7. Design for Shear h/tw Failure of Web due to Shear: • Yielding • Inelastic Buckling • Elastic Buckling h/tw>260 Stiffeners are required Appendix F2

  8. Design for ShearAISC Specs G pp 16.1-64 Shear Strength must be sufficient to satisfy LRFD resistance factor for shear=0.9 maximum shear based on the controlling combination for factored loads nominal shear strength depends on failure mode ASD maximum shear based on the controlling combination for service loads Safety factor

  9. AISC Spec requirements for Shear Cv depends on whether the limit state is web yielding, web inelastic buckling or web elastic buckling

  10. AISC Spec requirements for Shear Special Case for Hot Rolled I shapes with Most W shapes with

  11. AISC Spec requirements for Shear Chapter G All other doubly and singly symmetric shapes except round HSS

  12. DEFLECTIONSAISC Specs Chapter L Serviceability Limit State Limiting Value Deflections due to Service Loads < Governing Building Code, IBC etc Use deflection formulas in AISC Part 3 Or standard analytical or numerical methods Calculate due to UNFACTORED (service) loads

  13. Design Shear is rarely a problem in rolled steel beams usual practice Design for Flexure and Check for Shear and Deflections Or Design for Deflections and Check for Flexure and Shear

  14. Design • Compute Required Moment Strength Mu or Ma • Weight of Beam can be assumed and verified or ignored and checked after member is selected • Select shape that satisfies strength requirements • Assume shape, compute strength, compare with required, revise if necessary or • Use beam design aids in Part 3 of the Manual • Check Shear and deflections

  15. HOMEWORK • 5.2-3 • 5.4-1 • 5.5-3 • 5.5-5 • 5.6-2 • 5.8-2

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