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: 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)

Typical Plate Girders

AISC Limiting Ratios

AISC Design of Members for Flexure (about Major Axis)

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)

Vertical Buckling (the compression flange) Lateral buckling Torsional buckling Vertical buckling

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

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

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)

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

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

Classical Shear Theory (applied to plate girder web panel)

Intermediate Stiffener Spacing

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

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)

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

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

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

Forces from Tension-Field

Force in Stiffener (resulting from tension-field action)

State of Stress

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

Shear and Moment Strengths (under combined bending and shear)

Intermediate Transverse Stiffeners (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)

Intermediate Transverse Stiffener connection to flange

Bearing Stiffener (effective cross-sections)

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)

Effect of Longitudinal Stiffener on plate girder web stability

Example – Girder loading and support for design

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

Example - Design Sketch