Dr. Adeel Zafar, HoD Research,
LOCAL STABILITY
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Dr. Adeel Zafar, HoD Research,
LOCAL STABILITY
Wrinkling at
Isolated Location
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Dr. Adeel Zafar, HoD Research,
LOCAL STABILITY
(λ)
16.1-16)
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Dr. Adeel Zafar, HoD Research,
LOCAL STABILITY
Flange Buckling
Flange is restrained by the web at one edge.
Failure is localized at areas of high stress
(maximum moment) or imperfections.
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Dr. Adeel Zafar, HoD Research,
LOCAL STABILITY
Flange Buckling
Flange is restrained by the web at one edge.
Failure is localized at areas of high stress
(maximum moment) or imperfections.
5
Dr. Adeel Zafar, HoD Research,
LOCAL STABILITY
Flange Buckling
Flange is restrained by the web at one edge.
Failure is localized at areas of high stress
(maximum moment) or imperfections.
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Dr. Adeel Zafar, HoD Research,
LOCAL STABILITY
Flange Buckling
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Dr. Adeel Zafar, HoD Research,
LOCAL STABILITY
Web Buckling
Web is restrained by the flanges.
Failure is localized at
areas of high stress
(maximum moment) or
imperfections.
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Dr. Adeel Zafar, HoD Research,
LOCAL STABILITY
Web Buckling
Web is restrained by the flanges.
Failure is localized at
areas of high stress
(maximum moment) or
imperfections.
9
Dr. Adeel Zafar, HoD Research,
LOCAL STABILITY
Web Buckling
Web is restrained by the flanges.
Failure is localized at
areas of high stress
(maximum moment) or
imperfections.
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Dr. Adeel Zafar, HoD Research,
LOCAL STABILITY
Web Buckling
Web Crippling
Web Deformation
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Dr. Adeel Zafar, HoD Research,
LOCAL STABILITY
Flange Buckling (Unstiffened)
For W-Shapes
Web Buckling (Stiffened)
For W-Shapes
AISC Part 16 (16.1-16 & 17)
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Dr. Adeel Zafar, HoD Research,
LOCAL STABILITY
Local Buckling Criteria
Slenderness of the flange and web, , are used as criteria to determine
whether local buckling might control in the elastic or inelastic range,
otherwise the global buckling criteria controls.
Criteria r are based on plate buckling theory.
For W-Shapes
FLB,  = bf /2tf
E
rf = 0.56 F
y
WLB,  = h/tw
E
rw = 1.49
Fy
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Dr. Adeel Zafar, HoD Research,
LOCAL STABILITY
14
Dr. Adeel Zafar, HoD Research,
LOCAL STABILITY
Un-Stiffened Elements
For un-stiffened elements, which are
supported
along only one edge
parallel to the direction of the
compression force, the width shall be
taken as follows:
• For flanges of I-shaped members
and tees, the width b is half the full
nominal width (bf/2).
• For legs of angles, the width b is the
longer leg dimension.
• For flanges of channels and zees,
the width b is the full nominal
dimension (bf).
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Dr. Adeel Zafar, HoD Research,
LOCAL STABILITY
Stiffened Elements
• For webs of rolled or
formed sections, h is the
clear distance between the
flanges less the fillet or
corner radius at each
flange.
• For built-up sections, h is
the clear distance between
flanges when welds are
used.
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Dr. Adeel Zafar, HoD Research,
LOCAL STABILITY
Reduction Factor (Q)
Part 16.1-40
Q = Net Reduction Factor for local buckling effects. Q = 1 when
section is non-slender. Equations E7-4 to E7-16
Q = QsQa for slender sections.
Qs = Reduction Factor for slender unstiffened element
Qa = Reduction Factor for slender stiffened element
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Dr. Adeel Zafar, HoD Research,
LOCAL STABILITY
Reduction Factor (Q)
QFy


KL
E
F
 4.71
If
, then Fcr  Q 0.658 e  Fy
r
QFy


This defines “inelastic” buckling limit.
If
KL
E
 4.71
, then Fcr = 0.877Fe.
r
QFy
Equation E7-2
Equation E7-3
This defines “elastic” buckling limit similar to non-slender
elements. Q has no impact in this region.
Fe = elastic (Euler) buckling stress
π2E
For a doubly symmetric section, Fe 
2 Equation E3-4
 KL 


Pn = Fcr Ag
 r 
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Dr. Adeel Zafar, HoD Research,
LOCAL STABILITY
Reduction Factor (Q)
Qa for Stiffened Elements
Qa = Aeff/Ag
Ag = gross cross-sectional area of the member.
Aeff = summation of the effective areas of the cross
section based on the reduced effective width, be.
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Dr. Adeel Zafar, HoD Research,
LOCAL STABILITY
Reduction Factor (Q)
Qa for Stiffened Elements
Base on slenderness b/t.
E
For b/t ≥ 1.49
f
(ratio is h/tw for a W-shape)

E 
0 .34
be  1 .92t
1
b
f 
t

 

E
b
f 

Equation E7-17
2 more cases:
• Flanges of square and rectangular section
• Flanges of circular sections
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Dr. Adeel Zafar, HoD Research,
LOCAL STABILITY
Reduction Factor (Q)
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Dr. Adeel Zafar, HoD Research,
LOCAL STABILITY
Reduction Factor (Q)
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Dr. Adeel Zafar, HoD Research,
LOCAL STABILITY
Example C 13 (Segui 4.4)
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Dr. Adeel Zafar, HoD Research,
LOCAL STABILITY
Example C 13 (Segui 4.4)
Step 1- Eval Flexural Buckling Strength (Global)
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Dr. Adeel Zafar, HoD Research,
LOCAL STABILITY
Example C 13 (Segui 4.4)
Step 2- Eval Local Buckling Strength
Apply “Reduction
Factor Q”
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Dr. Adeel Zafar, HoD Research,
LOCAL STABILITY
Example C 13 (Segui 4.4)
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Dr. Adeel Zafar, HoD Research,
LOCAL STABILITY
Example C 13 (Segui 4.4)
Step 2- Eval Local Buckling Strength
Qs = Reduction Factor for slender unstiffened element
Qa = Reduction Factor for slender stiffened element
Q = QsQa for slender sections.
Qa = Aeff/Ag
Ag = gross cross-sectional area of the member.
Aeff = summation of the effective areas of the cross
section based on the reduced effective width, be.
Find be
AISC E7.2(b)
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Dr. Adeel Zafar, HoD Research,
LOCAL STABILITY
Example C 13 (Segui 4.4)
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Dr. Adeel Zafar, HoD Research,
LOCAL STABILITY
Example C 13 (Segui 4.4)
Reduction Factor (Q)
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Dr. Adeel Zafar, HoD Research,
LOCAL STABILITY
Example C 13 (Segui 4.4)
Reduction Factor (Q)
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Dr. Adeel Zafar, HoD Research,
LOCAL STABILITY
Example C 13 (Segui 4.4)
Step 2- Eval Local Buckling Strength
he =
he =
t = 0.116”
AISC Table 1-82
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Dr. Adeel Zafar, HoD Research,
LOCAL STABILITY
Example C 13 (Segui 4.4)
Step 2- Eval Local Buckling Strength
AISC B4-1b(d), pp 16.1-15
h=
heff h d
2(h-heff)t
Ag = 2.70 in2
AISC Table 1-82
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Dr. Adeel Zafar, HoD Research,
LOCAL STABILITY
Example C 13 (Segui 4.4)
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Dr. Adeel Zafar, HoD Research,
LOCAL STABILITY
Example C 13 (Segui 4.4)
Step 3 – Check Capacity
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Dr. Adeel Zafar, HoD Research,
LOCAL STABILITY
Reduction Factor (Q)
Qs for Unstiffened Elements
For rolled shapes,
Base on slenderness b/t.
For b/t ≤ 0.56
E
Fy
E
E
For 0.56 F < b/t < 1.03 Fy
y
(except for single angles)
(ratio is bf/2tf for a W-shape)
Qs = 1.0
Equation E7-4
 b  Fy
Qs  1.415-0.74 
t E
Equation E7-5
For b/t ≥ 1.03
E
Fy
0.69 E
Qs 
2 Equation E7-6
Fy b
t
 
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Dr. Adeel Zafar, HoD Research,
LOCAL STABILITY
Reduction Factor (Q)
Qs for Unstiffened Elements
For built-up shapes
slenderness b/t.
For b/t ≤ 0.64
Ek c
Fy
(except for single angles) base on
Qs = 1.0
Equation E7-7
 b  Fy
Ekc
Ekc
Qs  1.415-0.65 
For 0.64
< b/t < 1.17
Fy
Fy
 t  Ekc
Equation E7-8
Ekc
For b/t ≥ 1.17
Fy
0.90 Ekc
Qs 
2 Equation E7-9
Fy b
t
 
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Dr. Adeel Zafar, HoD Research,
LOCAL STABILITY
Reduction Factor (Q)
kc 
4
h
tw
kc shall not be taken less than 0.35 nor greater
than 0.76 for calculation purposes.
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