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

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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

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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