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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
(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 = 12.0 √E/Fy (AISC-F13.3)
 Stiffened girder (for a/h > 1.5)
h/tw ≤ 0.40E/Fy (AISC-F13.4)
(S & J Table 11.3.1)
 Unstiffened girder h/tw ≤ 260
(proportioning limits for I-shaped members)
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)
(F4-11)
(for WLB)
aw = ratio of web area to compression flange area ( ≤10)
hc = 2 x centroid to inside face of the compression flange
  y
p
r
p
b
y
y
b
cr F
L
L
L
L
F
F
C
F 



















 3
.
0
2
2









t
b
b
cr
r
L
E
C
F

y
t
r
F
E
r
L
7
.
0


1
70
.
5
300
1200
1 












y
w
c
w
w
pg
F
E
t
h
a
a
R
6
/
1
(
12 w
fc
t
a
b
r


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 = FySxt (F5-10)
 




















pf
rf
pf
y
y
cr F
F
F




3
.
0
2
2
9
.
0









f
f
c
cr
t
b
k
F
Rpg bending strength reduction factor
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. 11.8.1 & 11.8.2)
Except (1) end panel
(2) a/h > 3 or a/h > [260/(h/tw)]2
























2
1
15
.
1
1
6
.
0
h
a
C
C
F
A
V v
v
yw
w
n
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 tw
2)≤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 = 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

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SteelDesign_PlateGirder_Fu_New.pdf

  • 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
  • 2. 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 = 12.0 √E/Fy (AISC-F13.3)  Stiffened girder (for a/h > 1.5) h/tw ≤ 0.40E/Fy (AISC-F13.4) (S & J Table 11.3.1)  Unstiffened girder h/tw ≤ 260 (proportioning limits for I-shaped members)
  • 3. 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) (F4-11) (for WLB) aw = ratio of web area to compression flange area ( ≤10) hc = 2 x centroid to inside face of the compression flange   y p r p b y y b cr F L L L L F F C F                      3 . 0 2 2          t b b cr r L E C F  y t r F E r L 7 . 0   1 70 . 5 300 1200 1              y w c w w pg F E t h a a R 6 / 1 ( 12 w fc t a b r   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 = FySxt (F5-10)                       pf rf pf y y cr F F F     3 . 0 2 2 9 . 0          f f c cr t b k F Rpg bending strength reduction factor 11 Limit States in Flexure for plate girder with slender web (AISC-F5) 12 Comparison of LTB (AISC-F5 with AISC-F2)
  • 4. 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. 11.8.1 & 11.8.2) Except (1) end panel (2) a/h > 3 or a/h > [260/(h/tw)]2                         2 1 15 . 1 1 6 . 0 h a C C F A V v v yw w n 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)
  • 5. 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
  • 6. 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)
  • 7. 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 tw 2)≤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 = 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)
  • 8. 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