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ENCE 710 Design of Steel Structures

ENCE 710 Design of Steel Structures. VI. Plate Girders C. C. Fu, Ph.D., P.E. Civil and Environmental Engineering Department University of Maryland. Introduction. Following subjects are covered: Moment strength Shear strength Intermediate transverse stiffener Bearing stiffener Reading:

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ENCE 710 Design of Steel Structures

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  1. ENCE 710 Design of Steel Structures VI. Plate Girders C. C. Fu, Ph.D., P.E. Civil and Environmental Engineering Department University of Maryland

  2. Introduction Following subjects are covered: • Moment strength • Shear strength • Intermediate transverse stiffener • Bearing stiffener Reading: • Chapters 11 of Salmon & Johnson • AISC LRFD Specification Chapters B (Design Requirements) and F (Design of Members for Flexure) and G (Design of Members for Shear)

  3. Typical Plate Girders

  4. AISC Limiting Ratios

  5. AISC Design of Members for Flexure(about Major Axis)

  6. Beam vs Plate Girder Plate Girder: A deep beam “Slender” web problems: 1.Web buckling 2. Buckling of the compression flange due to inadequate stiffness of the web 3. Buckling due to shear (for doubly symmetric I-shaped sections)

  7. Vertical Buckling (the compression flange) • Lateral buckling • Torsional buckling • Vertical buckling

  8. AISC Maximum Web h/tw • Stiffened girder (for a/h ≤ 1.5) h/tw = 11.7 √E/Fy (AISC-F13.3) • Stiffened girder (for a/h > 1.5) h/tw ≤ 0.42E/Fy (AISC-F13.4) (S & J Table 11.3.1) • Unstiffened girder h/tw ≤ 260

  9. AISC Nominal Moment Strength • If h/tw ≤ 5.70√E/Fy – AISC Table B4.1 treated as rolled beams • If h/tw > 5.70√E/Fy • Case 1 – Compression flange yielding Mn = RpgFySxc (F5-1) • Case 2 – Lateral-Torsional Buckling Mn = RpgFcrSxc (F5-2) (a) Lp < Lb ≤ Lr (F5-3) (b) Lb > Lr (F5-4, 5, 6) (for WLB) aw = ratio of web area to compression flange area ( ≤10) hc = 2 x centroid to inside face of the compression flange

  10. AISC Nominal Moment Strength(cont.) • Case 3 - Compression flange local buckling Mn = RpgFcrSxc (F5-7) Fcr a. λ ≤ λp: Fcr = Fy b. λ p < λ ≤ λr : (F5-8) c. λ > λr : (F5-9) kc = 4/√(h/tw) and 0.35 ≤ kc ≤ 0.763 • Case 4 – Tension-flange yielding (Sxt<Sxc) Mn = RptFySxt (F5-10)

  11. Limit States in Flexure for plate girder with slender web (AISC-F5)

  12. Comparison of LTB (AISC-F5 with AISC-F2)

  13. Classical Shear Theory (applied to plate girder web panel)

  14. Intermediate Stiffener Spacing

  15. AISC Nominal Shear Strength • If h/tw ≤ 1.10 √(kvE/Fy) - Vn = 0.6 AwFy same as rolled beam (G3-1) • If h/tw > 1.10 √(kvE/Fy) (G3-2) (S & J Figs. 11.8.1 & 11.8.2) Except (1) end panel (2) a/h > 3 or a/h > [260/(h/tw)]2

  16. AISC Nominal Shear Strength(cont.) • For 1.10 √(kvE/Fy) ≤ h/tw ≤ 1.37 √(kvE/Fy) Cv = 1.10 √(kvE/Fy) / (h/tw) (G2-4) • For h/tw > 1.37 √(kvE/Fy) Cv = 1.51 kvE/[(h/tw)2Fy] (G2-5) kv = 5 + 5/(a/h)2 if a/h ≤ 3 and [260/(h/tw)]2 5 otherwise (S & J Fig. 11.8.3)

  17. Shear Capacity Available Figure 11.8.1 Shear capacity available, considering post-buckling strength.

  18. Tension-Field Action. Figure 11.8.2 Tension-field action.

  19. Buckling of Plate Girder Web Figure 11.7.3 Buckling of plate girder web resulting from shear alone—AISC-G2

  20. Forces from Tension-Field

  21. Force in Stiffener (resulting from tension-field action)

  22. State of Stress

  23. Intermediate Transverse Stiffeners(at nominal shear strength Vn including tension-field action)

  24. Shear and Moment Strengths (under combined bending and shear)

  25. Intermediate Transverse Stiffeners Intermediate Transverse Stiffener (not required if h/tw ≤ 2.45√E/Fy) (1) Stiffness Criterion • Ist ≥ jatw3 (G2-6) where j = 2.5/(a/h)2 – 2 ≥ 0.5 (2) Strength Criterion • Ast > Fy/Fyst (0.15 Dshtw (1 – Cv) Vu/ΦvVn – 18 tw2)≤0 (G3-3)

  26. Intermediate Transverse Stiffenerconnection to flange

  27. Bearing Stiffener (effective cross-sections)

  28. Bearing Stiffener Bearing Stiffener ΦRn ≥ Ru (1) Bearing Criterion (LRFD – J8.1) Φ = 0.75 Rn= 1.8 FyApb (2) Column Stability Criterion KL/r = 0.75 h/r where r of 12 tw or 25tw ΦcFcr = LRFD Table 3-36 Reqd. Ast = Ru/ΦcFcr → Reqd. t (3) Local Buckling Criterion (AISC 13th Edition Table B4.1 Case 3) Min. t = w/(0.56/√E/Fy)

  29. Effect of Longitudinal Stiffener on plate girder web stability

  30. Example – Girder loading and support for design

  31. Example - Factored moment and factored shear envelopes for two-span continuous beam of illustrative example

  32. Example - Design Sketch

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