purlin diy problem #1 find m y, m cr, m crd and m cre for 72” centerline dimensions h = 7.507 in....
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Purlin DIY Problem #1
• Find My, Mcr, Mcrd and Mcre for 72”
centerline dimensionsh = 7.507 in.b = 1.889 in.d = 0.795 in.r = 0.217 in.t = 0.059 in.propertiesE = 29500 ksi = 0.3G = 11346 ksify = 55 ksi
DSM for Purlin DIY Problem #1Date: July 23rd 2006 Name: BWS
Beam strength calculations using the Direct Strength Method of Appendix 1
Given: Notes: DIY Beam Purlin ExampleMy = 107.52 kip-in
Mcrℓ/My = 0.85 Mcrℓ = 91.392 kip-in
Mcrd/My = 0.77 Mcrd = 82.7904 kip-in
Mcre/My = 1.22 Mcre = 131.1744 kip-in
Lateral-torsional buckling nominal flexural strength per DSM 1.2.2.1
Mne = 92.266 kip-inLocal buckling nominal flexural strength per DSM 1.2.2.2
lℓ = 1.00 (local-global slenderness)
Mnℓ = 78.2 kip-in (local-global interaction reduction)
1.2.2.1 Lateral-Torsional Buckling
The nominal flexural strength, Mne, for lateral-torsional buckling is
for Mcre < 0.56My
Mne = Mcre (Eq. 1.2.2-1)
for 2.78My > Mcre > 0.56My
Mne =
cre
yy M36
M101M
910
(Eq. 1.2.2-2)
for Mcre > 2.78My
Mne = My (Eq. 1.2.2-3)
where My = SfFy , where Sf is the gross section modulus referenced to (Eq. 1.2.2-4)
the extreme fiber in first yield Mcre = Critical elastic lateral-torsional buckling moment determined
in accordance with Section 1.1.2
1.2.2.2 Local Buckling
The nominal flexural strength, Mn, for local buckling is
for l 776.0 Mn = Mne (Eq. 1.2.2-5)
for l > 0.776
Mn = ne
4.0
ne
cr4.0
ne
cr MM
M
M
M15.01
(Eq. 1.2.2-6)
where l = crne MM (Eq. 1.2.2-7)
Mcr = Critical elastic local buckling moment determined in
accordance with Section 1.1.2 Mne is defined in Section 1.2.2.1.
Distortional buckling nominal flexural strength per DSM 1.2.2.3
ld = 1.14 (distortional slenderness)
Mnd = 76.1 kip-in (distortional reduction)
Date: August 19, 2003 Final Version 1.2.2.3 Distortional Buckling
The nominal flexural strength, Mnd, for distortional buckling is
for ld 673.0
Mnd = My (Eq. 1.2.2-8)
for ld > 0.673
Mnd = y
5.0
y
crd5.0
y
crd MM
M
M
M22.01
(Eq. 1.2.2-9)
where ld = crdy MM (Eq. 1.2.2-10)
Mcrd = Critical elastic distortional buckling moment determined in
accordance with Section 1.1.2. My is given in Eq. 1.2.2-4.
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) Y
f = 0.9 design strength fMn = 68.52 kip-inW = 1.67 allowable design strength Mn/W = 45.59 kip-in
Test 8.5Z092
Local buckling test Distortional buckling test
Test 8C043
Local buckling test Distortional buckling test
99% of NAS 83% of NAS
106% of NAS 90% of NAS
0 0.5 1 1.5 2 2.5 3 3.50
2
4
6
8
10
12
14
Pcrd
Py
localdistortional
0 0.5 1 1.5 2 2.5 3 3.50
2
4
6
8
10
12
14
Pcrd
Py
localdistortional
Δ
P
0 0.5 1 1.5 2 2.50
0.5
1
1.5
2
2.5
3
3.5
4
Py
PcrL
localdistortional
Pcrd
0 0.5 1 1.5 2 2.50
0.5
1
1.5
2
2.5
3
3.5
4
Py
PcrL
localdistortional
Pcrd
Δ
P
Remember Distortional Buckling Gotcha!- comparison of two series of tests
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 Z-
sections 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 Z-section, results in a kf between 0.15 to 0.44 kip-in./rad./in. (0.667 to 1.96 kN-mm/rad./mm) (MRI 1981).”
Purlin DIY Problem #1 with spring
• Find My, Mcr, Mcrd and Mcre for 72” with kf=0.15 kip-in/rad/in
centerline dimensionsh = 7.507 in.b = 1.889 in.d = 0.795 in.r = 0.217 in.t = 0.059 in.propertiesE = 29500 ksi = 0.3G = 11346 ksify = 55 ksi
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) Y
f = 0.9 design strength fMn = 70.36 kip-inW = 1.67 allowable design strength Mn/W = 46.81 kip-in
Distortional buckling nominal flexural strength per DSM 1.2.2.3
ld = 1.02 (distortional slenderness)
Mnd = 83.0 kip-in (distortional reduction)
Date: August 19, 2003 Final Version 1.2.2.3 Distortional Buckling
The nominal flexural strength, Mnd, for distortional buckling is
for ld 673.0
Mnd = My (Eq. 1.2.2-8)
for ld > 0.673
Mnd = y
5.0
y
crd5.0
y
crd MM
M
M
M22.01
(Eq. 1.2.2-9)
where ld = crdy MM (Eq. 1.2.2-10)
Mcrd = Critical elastic distortional buckling moment determined in
accordance with Section 1.1.2. My is given in Eq. 1.2.2-4.
Given: Notes: DIY Beam Purlin Example with SpringMy = 107.52 kip-in
Mcrℓ/My = 0.85 Mcrℓ = 91.392 kip-in
Mcrd/My = 0.97 Mcrd = 104.2944 kip-in
Mcre/My = 1.22 Mcre = 131.1744 kip-in