ENCE 710
Design of Steel Structures
VI. Plate Girders
C. C. Fu, Ph.D., P.E.
Civil and Environmental Engineering Department
University of Maryland
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)
2
Typical Plate Girders
3
AISC
Limiting
Ratios
4
AISC Design of Members for Flexure
(about Major Axis)
5
Beam vs
Plate Girder
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
(for doubly symmetric I-shaped sections)
6
Vertical Buckling
(the compression flange)
(a) Lateral buckling
(b) Torsional buckling
(c) Vertical buckling
7
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
8
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

Case 2 – Lateral-Torsional Buckling
Mn = RpgFcrSxc
(a)
Lp < Lb ≤ Lr
(b)
L b > Lr
(F5-1)
(F5-2)

 Lb  L p 
  Fy (F5-3)
Fcr  Cb  Fy  0.3Fy  
 L  L 
p 

 r

Fcr 
Cb 2 E
 Lb 
 
 rt 
2
E
Lr  rt
0 .7 F y
rt 
b fc
(F5-4, 5, 6)
12(1  a w / 6
(for WLB)
 hc

E
  5.70
 1
R pg
 tw
Fy 

aw = ratio of web area to compression flange area ( ≤10)
hc = 2 x centroid to inside face of the compression flange 9
aw
 1
1200 300a w
AISC Nominal Moment Strength
(cont.)

Case 3 - Compression flange local buckling
Mn =
RpgFcrSxc
Fcr
a. λ ≤ λp:
Fcr = Fy
b. λ p < λ ≤ λr :
(F5-7)

    pf
Fcr   Fy  0.3Fy 
 

pf
 rf
c. λ > λr :
kc = 4/√(h/tw)

Fcr 
0 .9 k c
 bf

 2t
 f
and
Case 4 – Tension-flange yielding (Sxt<Sxc)
Mn = RptFySxt




(F5-8)
(F5-9)
2




0.35 ≤ kc ≤ 0.763
(F5-10)
10
Limit States
in Flexure
for plate girder
with slender web
(AISC-F5)
11
Comparison of LTB
(AISC-F5 with AISC-F2)
12
Classical Shear Theory
(applied to plate girder web panel)
13
Intermediate Stiffener Spacing
14
AISC Nominal Shear Strength

If h/tw ≤ 1.10 √(kvE/Fy) -
Vn = 0.6 AwFy same as rolled beam

If h/tw
Except


> 1.10 √(kvE/Fy)

1  Cv
Vn  0.6 Aw Fyw  Cv 
2

a
1.15 1   

h

(1)
(2)
(G3-1)







(G3-2)
(S & J Figs. 11.8.1 & 11.8.2)
end panel
a/h > 3
or
a/h > [260/(h/tw)]2
15
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]
kv = 5 + 5/(a/h)2
5
(G2-5)
if a/h ≤ 3 and [260/(h/tw)]2
otherwise
(S & J Fig. 11.8.3)
16
Shear Capacity Available
Figure 11.8.1
Shear capacity available, considering post-buckling strength.
17
Tension-Field Action.
Figure 11.8.2
Tension-field action.
18
Buckling of Plate Girder Web
Figure 11.7.3 Buckling
of plate girder web
resulting from shear
alone—AISC-G2
19
Forces from Tension-Field
20
Force in Stiffener
(resulting from tension-field action)
21
State of Stress
22
Intermediate Transverse Stiffeners
(at nominal shear strength Vn including tension-field action)
23
Shear and Moment Strengths
(under combined bending and shear)
24
Intermediate Transverse Stiffeners
Intermediate Transverse Stiffener
(not required if h/tw ≤ 2.45√E/Fy)
(1) Stiffness Criterion
Ist ≥ jatw3
(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)
25
Intermediate Transverse Stiffener
connection to flange
26
Bearing Stiffener
(effective cross-sections)
27
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)
28
Effect of Longitudinal Stiffener
on plate girder web stability
29
Example –
Girder loading and support for design
30
Example Factored moment and
factored shear
envelopes for two-span
continuous beam of
illustrative example
31
Example - Design Sketch
32