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

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Vertical Buckling (the compression flange)

(a)Lateral buckling

(b)Torsional buckling

(c) Vertical buckling

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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

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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

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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

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Limit States in Flexure

for plate girder with slender web (AISC-F5)

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

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Classical Shear Theory (applied to plate girder web panel)

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Intermediate Stiffener Spacing

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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

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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)

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Shear Capacity Available

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

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Tension-Field Action.

Figure 11.8.2 Tension-field action.

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Buckling of Plate Girder Web

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

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Forces from Tension-Field

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Force in Stiffener (resulting from tension-field action)

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State of Stress

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

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Shear and Moment Strengths (under combined bending and shear)

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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)

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Intermediate Transverse Stiffener connection to flange

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Bearing Stiffener (effective cross-sections)

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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)

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Effect of Longitudinal Stiffener on plate girder web stability

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Example – Girder loading and support for design

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Example -

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

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Example - Design Sketch