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

ENCE 710 Design of Steel

Structures

VI. Plate GirdersC. C. Fu, Ph.D., P.E.

Civil and Environmental Engineering Department

University of Maryland

2

IntroductionFollowing subjects are covered: Moment strength Shear strength Intermediate transverse stiffener Bearing stiffenerReading: 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

(for doubly symmetric I-shaped sections)

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

7

Vertical Buckling (the compression flange)

(a)Lateral buckling

(b)Torsional buckling

(c) 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 yieldingMn = RpgFySxc (F5-1)

Case 2 – Lateral-Torsional BucklingMn = 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

ypr

pbyybcr F

LL

LLFFCF

3.0

2

2

t

b

bcr

r

L

ECF

y

tr F

ErL

7.0

170.53001200

1

yw

c

w

wpg F

E

t

h

a

aR

6/1(12 w

fct ab

r

10

AISC Nominal Moment Strength (cont.)

Case 3 - Compression flange local bucklingMn = 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)

pfrf

pfyycr FFF

3.0

2

2

9.0

f

f

ccr

t

b

kF

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 AwFysame 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

2

115.1

16.0

h

a

CCFAV vvywwn

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 ≥ jatw

3 (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 StiffenerBearing Stiffener ΦRn ≥ Ru

(1) Bearing Criterion (LRFD – J8.1)Φ = 0.75

Rn= 1.8 FyApb

(2) Column Stability CriterionKL/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