Transcript Slide 1

Provisional ballot:
Direct Strength Method for
CFS compression members
with holes
Cris Moen and Ben Schafer
AISI COS Meeting
February 2009
DSM Holes (3+ years ago…)
Pn = f (Py, Pcre, Pcrd, Pcrl)?
Does f stay
the same?
Gross or net, or
some combination?
Explicitly model hole(s)?
Accuracy? Efficiency?
Identification? Just these
modes?
DSM Holes (today)
Pn = f (Py, Pcre, Pcrd, Pcrl)?
Column strength
limited to Pynet
DSM curves applicable
when elastic buckling
controls, changes needed
though in inelastic regime
Suite of approximate
methods now available,
“Local hole” buckling
modes can affect strength
DSM Holes (today)
Consider three DSM options:
Option 1 - Replace Py with Pynet everywhere
Assumes net section exists along full length of column,
conservative approach, easiest to implement
Option 2 - Cap Pnl and Pnd at Pynet
Places net section strength limit on existing DSM curves,
can be unconservative in some cases
Option 3 - Cap and transition Pnl and Pnd
Transition from elastic buckling regime to net section
cap at “knee” of DSM design curves, most accurate
method but also increases work for engineers
DSM Holes (Option 1)
1.2.X.X Flexural, Torsional, or Flexural-Torsional Buckling
The nominal axial strength [resistance], Pne, for flexural, torsional, or
torsional buckling including the influence of hole(s) shall be calculated in acc
with the following:
Replace Py with Pynet everywhere
(a) For  cnet  1.5

2cnet
Pne =  0.658

(b) For cnet > 1.5

Pynet

 0.877 
P
Pne =  2

 ynet
 cnet 
where
cnet = Pynet Pcre
Pynet = AnetFy
Anet = Net area of section at the location of hole(s)
DSM Holes (Option 1)
1.2.X.X Distortional Buckling
The nominal axial strength [resistance], Pnd, for distortional buckling inclu
influence of hole(s) shall be calculated in accordance with the following:
(a) For dnet  0.561
Pnd
=
Py net
Replace Py with Pynet everywhere
(b) For dnet > 0.561
0.6 

 P
  P

crd 

 crd
Pnd =  1  0.25



P

 Pynet
ynet 



where
dnet = Pynet Pcrd




0.6
Pynet
Pynet = A value as given in Eq. 1.2.X-X
Pcrd
=
Critical elastic local column buckling load inclu
influence of hole(s) determined by analysis in accordance wit
1.1.2
DSM Holes (Option 1)
1
Existing DSM curve (no holes)
0.9
0.8
0.7
Pnd/P y
0.6
Replace Py with Pynet everywhere
(Option 1)
0.5
0.4
0.3
0.2
Assumptions for this plot:
Pynet=0.80Py
0.1
0
0
0.5
1
1.5
2
2.5
distortional slenderness, d or dnet
3
DSM Holes (Option 1)
1.4
Existing DSM curve
1.2
Ptest/P y
1
0.8
FE simulated test data, Pynet=0.80Py
0.6
0.4
0.2
0
0
0.5
1
1.5
2
2.5
3
distortional slenderness,  d=(Py /P crd )0.5
3.5
4
DSM Holes (Option 2)
1.2.X.X Local Buckling
The nominal axial strength [resistance], Pnl, for local buckling includ
influence of holes shall be calculated in accordance with the following:
(a) For l  0.776
Pnl = Pne  Pynet
Cap strength at Pynet
(b) For l > 0.776

P
Pnl = 1  0.15 crl
Pne



where
l = Pne Pcrl



0.4 
P
 crl
 Pne




0.4
Pne  Pynet
Pne = A value as defined in Section 1.2.X.X
Pcrl = Critical elastic local column buckling load including the influ
hole(s) determined by analysis in accordance with Section 1.1.2
Pynet = AnetFy
DSM Holes (Option 2)
1.2.1.3 Distortional Buckling
The nominal axial strength [resistance], Pnd, for distortional buckling i
influence of holes shall be calculated in accordance with the following:
(a) For d  0.561
Pnd
=
Py  Pynet
Cap strength at Pynet
(b) For d > 0.561
0.6 
0.6





Pcrd   Pcrd 


Py  Pynet
Pnd =  1  0.25




Py   Py 




where
d = Py Pcrd
Py
= A value as given in Eq. 1.2.1-4
Pcrd = Critical elastic distortional column buckling load including t
of hole(s) determined by analysis in accordance with Section
DSM Holes (Option 2)
1.4
Existing DSM curve
1.2
DSM Holes Option 2, cap at Pynet
1
Ptest/P y
(b)
0.8
FE simulated test data, Pynet=0.80Py
10%
0.6
0.4
For smaller holes ,data
deviates more gradually from design curve
0.2
0
0
0.5
1
1.5
2
2.5
3
distortional slenderness,  d=(Py /P crd )0.5
3.5
4
DSM Holes (Option 2)
1.4
Existing DSM curve
1.2
Ptest /P y
1
DSM Holes Option 2, cap at Pynet
0.8
FE simulated test data, Pynet=0.60Py
0.6
25%
0.4
0.2
0
0
0.5
1
1.5
2
2.5
3
distortional slenderness,  d=(Py /P crd )0.5
3.5
4
DSM Holes (Option 3)
1.2.X.X Local Buckling
The nominal axial strength [resistance], Pnl, for local buckling in
influence of holes shall be calculated in accordance with the following:
(a) For l   l 1
Pnl = Pne  Pynet
Cap strength at Pynet
(b) For l1   l   l 2
 Pynet  Pl 2 
 l   l1 
Pnl = Pynet  

  l 2   l1 
(c) For l > l 2

 Pcrl

Pnl = 1  0.15

 Pne

where




0.4 
P
 crl
 Pne





0.4
Pne
Transition to Pynet
DSM Holes (Option 3)
1.2.1.3 Distortional Buckling
The nominal axial strength [resistance], Pnd, for distortional buc
influence of holes shall be calculated in accordance with the followi
(a) For d   d 1
Pnd = Pynet
Cap strength at Pynet
(b) For d1   d   d 2
 Pynet  Pd2 
d
Pnd = Pynet  

Transition



d
2
d
1


(c) For d1  d  d 2
0.6 
0.6






 P
P
Pnd =  1  0.25 crd   crd  Py
 Py   Py 


 


where
to Pynet
DSM Holes (Option 3)
1
Existing DSM curve (no holes)
0.9
Transition to Pynet
(Option 3)
0.8
0.7
Pd2/Py
Pnd/P y
0.6
0.5
0.4
0.3
d1
0.2
Assumptions for this plot:
Pynet=0.80Py
0.1
0
d2
0
0.5
1
1.5
2
distortional slenderness, d
2.5
3
DSM Holes (Option 3)
1.4
Existing DSM curve
1.2
Ptest /P y
1
DSM Holes Option 3, cap and transition at Pynet
0.8
FE simulated test data, Pynet=0.60Py
0.6
0.4
0.2
0
0
0.5
1
1.5
2
2.5
3
distortional slenderness,  d=(Py /P crd )0.5
3.5
4
Experiments
Method Option, Description
Local-global interaction
Distortional buckling
# of
# of
tests Mean SD
tests
Mean SD
f
f
1 - Pynet everywhere 1.17 0.09 0.89 47 1.22 0.13 0.87 15
DSM
2 - Cap Pnl, Pnd
Holes
3 - Trans. Pnd,Pnl
all data
Main
within code limits
Spec
outside code limits
1.07
0.08
0.90
42
1.06
0.13
0.85
29
1.06
1.12
1.20
1.06
0.08
0.12
0.12
0.06
0.89
0.87
0.88
0.91
47
63
27
36
1.13
1.11
*---*
*---*
0.10
0.05
*---*
*---*
0.89
0.91
*---*
*---*
26
15
*---*
*---*
Ortiz-Colberg (1981), Sivakumaran (1987), Miller and Peköz (1994), AbdelRahman (1997), Pu et al. (1999), Moen and Schafer (2008)
- All lipped C-sections
- 85% stub columns
- hhole/h varies from 0.10 to 0.60
Simulations
Method Option, Description
Local-global interaction
Distortional buckling
# of
# of
tests Mean SD
tests
Mean SD
f
f
1 - Pynet everywhere 1.14 0.13 0.86 93 1.24 0.18 0.83 176
DSM
2 - Cap Pnl, Pnd
Holes
3 - Trans. Pnd,Pnl
all data
Main
within code limits
Spec
outside code limits
1.06 0.15
0.83
93
1.09 0.17
0.82
186
1.08
1.06
1.04
1.07
0.85
0.86
0.88
0.86
89 1.04 0.19
236 0.91* 0.08
24 *---* *---*
212 *---* *---*
0.79
0.88
*---*
*---*
200
149
*---*
*---*
0.14
0.13
0.10
0.13
- All lipped C-sections, variety of short and long columns
- 35 of 99 SSMA cross-sections represented
- hhole/h varies from 0.10 to 0.80
- hole spacing varies from 8 to 24 inches
Conclusions
Option 1 - Replace Py with Pynet everywhere
• Conservative over all slenderness ranges
• Easy to implement
Option 2 - Cap Pnl and Pnd at Pynet
• Can be unconservative at “knee” of design curve
• Easy to implement
Option 3 - Cap and transition Pnl and Pnd
• Most consistent with observed data trends
• Additional effort to implement, use
Also worth mentioning
• Once DSM Holes is approved, Main Spec
distortional buckling design method can be
replaced
• Should we prequalify hole shapes, sizes in DSM
Holes?
• Simplified elastic buckling methods could be used
to improve Main Spec…
Plate buckling with holes – Section B2, B3, B4
Distortional buckling with holes – C3.4.1, C4.2
Euler buckling with holes – C3.1.2, C4.1
• Goal is to incorporate stiffened holes into DSM
Holes next…
DSM Holes (Option 3)
1.4
1.
1.2
1.
Existing DSM curve (no holes)
1
nl
P /P
y
0.8
P /P
nl y
Transition
to Pynet
Pcre=100P
yg
(Option 3)
Pynet=0.8Pyg
Pl2/Py
0.6
0.4
l1
0
Pcre=100Py (stub column)
Pynet=0.8Py
0
0.5
1
1.5
0.
0.
l2
0.2
0.
2
2.5
local slenderness,  =(P /P )0.5
ne cr l
l
3
3.5
0.
4
DSM Holes (Option 3)
1.4
1.2
P /P
nl y
1
0.8
0.6
0.4
mn)
3.5
Option 3 assumes no net section
influence when Pynet≥Pnl (i.e. existing
DSM curve and DSM Holes curve are
the same when Pynet ≥ Pnl)
Pcre=Py (long column)
Pynet=0.8Py
0.2
4
0
0
0.5
1
1.5
2
2.5
local slenderness,  =(P /P )0.5
ne cr l
l
3
3.5
4