Steel plate girder

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