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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