Transcript The Direct Strength Method of Cold

Purlin DIY Problem #1
• Find My, Mcrl, Mcrd and Mcre for 72”
centerline dimensions
h = 7.507 in.
b = 1.889 in.
d = 0.795 in.
r = 0.217 in.
t = 0.059 in.
properties
E = 29500 ksi
n = 0.3
G = 11346 ksi
fy = 55 ksi
DSM for Purlin DIY Problem #1
Date:
July 23rd 2006
Name:
BWS
Beam strength calculations using the Direct Strength Method of Appendix 1
Given:
Notes: DIY Beam Purlin Example
My =
107.52
kip-in
Mcrℓ/My =
Mcrℓ =
0.85
91.392 kip-in
Mcrd/My =
Mcrd = 82.7904 kip-in
0.77
Mcre/My =
1.22
Mcre = 131.1744 kip-in
1.2.2.1 Lateral-Torsional Buckling
Lateral-torsional
buckling
nominal
flexural
per DSM
1.2.2.1
The nominal
flexural
strength,
Mne, forstrength
lateral-torsional
buckling
is
for Mcre < 0.56My
Mne = Mcre
for 2.78My > Mcre > 0.56My
(Eq. 1.2.2-1)
10M y

10
M y 1 

9
36M cre

for Mcre > 2.78My
Mne =




(Eq. 1.2.2-2)
Mne = My
(Eq. 1.2.2-3)
where
M1.2.2.2
92.266
kip-in
Local
Buckling
ne =
My = SfFy , where Sf is the gross section modulus referenced to
Local buckling
nominal
flexural
strength
per
DSM
1.2.2.2
The nominal
flexural
Mnl,in
for
local
buckling
is
the strength,
extreme
fiber
first
yield
(Eq. 1.2.2-4)
776
for ll  0.M
cre = Critical elastic lateral-torsional buckling moment determined
Mnl = Mnein accordance with Section 1.1.2
(Eq. 1.2.2-5)
for ll > 0.776

M
Mnl =  1  0.15 crl

 M ne

where ll
= M ne M crl




0.4 
 M crl
 M
 ne




0.4
M ne
Critical elastic local
buckling moment
determined in
lℓ = Mcrl =1.00
(local-global
slenderness)
accordance with Section 1.1.2
Mnℓ =
78.2
kip-inin Section
(local-global
interaction reduction)
M is defined
1.2.2.1.
ne
(Eq. 1.2.2-6)
(Eq. 1.2.2-7)
Date: August 19, 2003 Final Version
1.2.2.3 Distortional Buckling
Distortional
buckling
nominal
flexural
strength
per DSM
1.2.2.3
The
nominal flexural
strength,
Mnd
, for distortional
buckling
is
for ld  0.673
Mnd = My
(Eq. 1.2.2-8)
for ld > 0.673
where
ld =
Mnd =
0.5 
0.5

M

M



 crd  M
Mnd =  1  0.22 crd 

y


M
y 

 M y 



(Eq. 1.2.2-9)
ld
(Eq. 1.2.2-10)
= M y M crd
Mcrd = Critical elastic distortional buckling moment determined in
1.14
accordance with(distortional
Section 1.1.2.slenderness)
My is given in Eq. 1.2.2-4.
76.1 kip-in
(distortional reduction)
Nominal flexural strength of the beam per DSM 1.2.2
Mn =
76.13 kip-in
(distortional controls)
Does this section meet the prequalified limits of DSM Section 1.1.1.2? (Y/N)
f=
W=
0.9
1.67
design strength fMn =
allowable design strength Mn/W =
Y
68.52 kip-in
45.59 kip-in
Remember Distortional Buckling Gotcha!
Test 8.5Z092 - comparison of two series of tests
14
Pcrd
12
Py
10
P
local
distortional
8
6
4
2
0
0
0.5
1
1.5
Test 8C043
Δ
2
2.5
3
3.5
Local buckling test
Distortional buckling test
99% of NAS
83% of NAS
Local buckling test
Distortional buckling test
Pcrd
4
Py
3.5
PcrL
3
2.5
P
2
local
distortional
1.5
1
0.5
0
0
0.5
1
Δ
106% of NAS
1.5
2
2.5
90% of NAS
Review DB in AISI Specification
• Distortional buckling provisions are integral to
the Direct Strength Method of Appendix 1
• The main Specification now has distortional
buckling provisions as well, see Ballot 227B
227B Spec.
227B Comm.
Distortional Buckling Commentary
• “Testing on 8 and 9.5 in. (203 and 241 mm) deep Zsections with a thickness between 0.069 (1.75 mm) and
0.118 in. (3.00 mm), through-fastened 12 in. (205 mm)
o.c., to a 36 in. (914 mm) wide, 1 in. (25.4 mm) and 1.5
in. (38.1 mm) high steel panels, with up to 6 in. (152
mm) of blanket insulation between the panel and the Zsection, results in a kf between 0.15 to 0.44 kipin./rad./in. (0.667 to 1.96 kN-mm/rad./mm) (MRI 1981).”
Purlin DIY Problem #1 with spring
• Find My, Mcrl, Mcrd and Mcre for 72” with kf=0.15 kip-in/rad/in
centerline dimensions
h = 7.507 in.
b = 1.889 in.
d = 0.795 in.
r = 0.217 in.
t = 0.059 in.
properties
E = 29500 ksi
n = 0.3
G = 11346 ksi
fy = 55 ksi
Given:
Notes: DIY Beam Purlin Example with Spring
My =
107.52
kip-in
Mcrℓ/My =
Mcrℓ =
0.85
91.392 kip-in
Mcrd/My =
0.97
Mcre/My =
1.22
1.2.2.3 Distortional Buckling
Mcrd = 104.2944 kip-in
Date: August 19, 2003 Final Version
Mcre = 131.1744 kip-in
Distortional
buckling
nominal
flexural
strength
per DSM
1.2.2.3
The
nominal flexural
strength,
Mnd
, for distortional
buckling
is
for ld  0.673
Mnd = My
(Eq. 1.2.2-8)
for ld > 0.673
where
ld =
Mnd =
0.5 
0.5

M

M



 crd  M
Mnd =  1  0.22 crd 

y


My

 M y 




(Eq. 1.2.2-9)
ld
(Eq. 1.2.2-10)
= M y M crd
Mcrd = Critical elastic distortional buckling moment determined in
1.02
accordance with(distortional
Section 1.1.2.slenderness)
My is given in Eq. 1.2.2-4.
83.0 kip-in
(distortional reduction)
Nominal flexural strength of the beam per DSM 1.2.2
Mn =
78.18 kip-in
(local-global controls)
Does this section meet the prequalified limits of DSM Section 1.1.1.2? (Y/N)
f=
W=
0.9
1.67
design strength fMn =
allowable design strength Mn/W =
Y
70.36 kip-in
46.81 kip-in