Date: July 19th 2006 Name: BWS

Beam strength calculations using the Direct Strength Method of Appendix 1

Given: Notes: XXXXZXXX Example DSM Beam Calculation (job1.mat)

My = 100 kip-in
Mcrℓ/My = 0.5 Mcrℓ = 50 kip-in
Mcrd/My = 0.5 Mcrd = 50 kip-in
Mcre/My = 1.3 Mcre = 130 kip-in
1.2.2.1 La tera l-Torsiona l Buckling
Lateral-torsional buckling
The nominal nominal
flexural strength,flexural strength per DSM
M , for lateral-torsional 1.2.2.1
buckling is
ne
for Mcre < 0.56My
Mne = Mcre (Eq. 1.2.2-1)
for 2.78My > Mcre > 0.56My
10  10M y 
Mne = My 1   (Eq. 1.2.2-2)
9  36M cre 

for Mcre > 2.78My
Mne = My (Eq. 1.2.2-3)
where
M1.2.2.2
ne = 87.369
Loca kip-in
l Buckling
My = SfFy , where Sf is the gross section modulus referenced to (Eq. 1.2.2-4)
Local buckling nominal flexural
The nominal flexural strength per DSM 1.2.2.2
the strength, Mn,in
extreme fiber for local
first buckling
yield is
for   0.M cre = Critical elastic lateral-torsional buckling moment determined
776
Mn= Mnein accordance with Section 1.1.2 (Eq. 1.2.2-5)
for  > 0.776
 0.4 0.4
M   M cr 
Mn=  1  0.15 cr  
  M ne (Eq. 1.2.2-6)

  M ne   M ne 
where  = M ne M cr (Eq. 1.2.2-7)
lℓ = Mcr 1.32
= Critical elastic local buckling moment
(local-global determined in
slenderness) Date: August 19, 2003 Final Version
accordance with Section 1.1.2
Mnℓ = Distortiona
1.2.2.3 Mne61.5 l kip-in
Buckling
is defined (local-global
in Section 1.2.2.1. interaction reduction)
Distortional
Thebuckling nominal
nominal flexural flexural
strength, M strength per DSM
, for distortional 1.2.2.3
buckling is
nd
for d  0.673
Mnd = My (Eq. 1.2.2-8)
for d > 0.673
 0.5  0.5
 M   M crd 
Mnd =  1  0.22 crd 

 My (Eq. 1.2.2-9)
  My   M y 
    
where d = M y M crd (Eq. 1.2.2-10)
Mcrd = Critical elastic distortional buckling moment determined in
ld = 1.41accordance with(distortional
Section 1.1.2.slenderness)
Mnd = My is given in
59.7 kip-inEq. 1.2.2-4.
(distortional reduction)
Nominal flexural strength of the beam per DSM 1.2.2

Mn = 59.71 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 = 53.74 kip-in

W= 1.67 allowable design strength Mn/W = 35.75 kip-in
Date: July 19th 2006 Name: BWS

Column strength calculations using the Direct Strength Method of Appendix 1

Given: Notes: XXXXZXXX Example DSM Column Calculation (job1.mat)

Py = 100 kip
Pcrℓ/Py = 0.5 Pcrℓ = 50 kip
Pcrd/Py = 0.5 Pcrd = 50 kip
Pcre/Py = 1.3 Pcre = 130 kip
The nominal axial strength, Pne, for flexural, torsional, or torsional-
Flexural, Torsional, or Torsional-flexural Buckling nominal axial strength per DSM 1.2.1.1
flexural buckling is
for  c  1.5
 2 
Pne =  0.658 c Py (Eq. 1.2.1-1)
 
for c > 1.5
 0.877 
Pne   P (Eq. 1.2.1-2)
 2  y
 c 
where c = Py Pcre (Eq. 1.2.1-3)

lc = 0.877
Pne = 72.473 kip
Local buckling nominal axial strength per DSM 1.2.1.2
for   0.776
Pn= Pne (Eq. 1.2.1-5)
for  > 0.776
 0.4 0.4
P   P 
Pn = 1  0.15 cr   cr  Pne (Eq. 1.2.1-6)
  Pne   Pne 

where  = Pne Pcr (Eq. 1.2.1-7)

lℓ = 1.20 (local-global slenderness)

Pnℓ = 54.4 kip (local-global interaction reduction)
Distortional buckling nominal axial strength per DSM 1.2.1.3
for d  0.561
Pnd = Py (Eq. 1.2.1-8)
for d > 0.561
 0.6  0.6
 P   Pcrd 
Pnd =  1  0.25 crd 

 Py (Eq. 1.2.1-9)
  Py   Py 
    
where d = Py Pcrd (Eq. 1.2.1-10)
ld = 1.41 (distortional slenderness)
Pnd = 55.1 kip (distortional reduction)
Nominal axial strength of the column per DSM 1.2.1

Pn = 54.40 kip (local-global controls)

Does this section meet the prequalified limits of DSM Section 1.1.1.1? (Y/N) Y

f= 0.85 design strength fPn = 46.24 kip

W= 1.8 allowable design strength Pn/W = 30.22 kip
Date: July 19th 2006 Name: BWS

Beam-column calculation using DSM results for beam and columns (ASD Format)

Notes:

Required allowable strength (ASD demands)

P= 5 kip
M= 3 kip-in

Compression nominal strength and safety factor

Pn = 54.39502 kip
Wc = 1.8
for the interaction equation the fully braced compressive capacity, P no, is needed
this is found by setting Pne=Py and re-calcualting the "column" worksheet.
lℓ = 1.41
Pnℓo = 67.17 kip
Pndo = 55.09 kip
Pno = 55.09 kip

Bending nominal strength and safety factor

Mn = 59.71 kip-in
Wb = 1.67

Factors to account for approximate 2nd order analysis

Cm = 1 see C5.2.1, 1.0 is conservative

PE = 130 kip This is the flexural buckling load about the axis of
bending, it may be found using the Spec. formula of
p2EI/(KL)2 or read directly from a CUFSM analysis
a= 0.931 per Eq. C5.2.1-4 or -5
note, the 2nd order estimate of required allowable strength is 3.22 kip-in

Interaction equations

0.17 0.09 sums to = 0.26 OK <1

0.16 0.08 sums to = 0.25 OK <1