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 )
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 & )
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 > √(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 )

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

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

19. Buckling of Plate Girder Web
Figure 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
(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 Stiffener connection 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 = 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