asd vs lrfd comparison
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1
General Comparison between AISC LRFD and ASD
Hamid ZandGT STRUDL Users Group
Las Vegas, NevadaJune 22-25, 2005
2
AISC ASD and LRFD• AISC = American Institute of Steel
Construction
• ASD = Allowable Stress DesignAISC Ninth Edition
• LRFD = Load and Resistance Factor DesignAISC Third Edition
3
AISC Steel Design Manuals
• 1963 AISC ASD 6th Edition• 1969 AISC ASD 7th Edition• 1978 AISC ASD 8th Edition• 1989 AISC ASD 9th Edition
• 1986 AISC LRFD 1st Edition• 1993 AISC LRFD 2nd Edition• 1999 AISC LRFD 3rd Edition
4
ASD and LRFDMajor Differences
• Load Combinations and load factors• ASD results are based on the stresses and
LRFD results are based on the forces and moments capacity
• Static analysis is acceptable for ASD but nonlinear geometric analysis is required for LRFD
• Beams and flexural members• Cb computation
5
ASD Load Combinations
• 1.0D + 1.0L• 0.75D + 0.75L + 0.75W• 0.75D + 0.75L + 0.75E
D = dead loadL = live loadW = wind loadE = earthquake load
6
ASD Load CombinationsOr you can use following load combinations with theparameter ALSTRINC to account for the 1/3 allowableincrease for the wind and seismic load
1. 1.0D + 1.0L2. 1.0D + 1.0L + 1.0W3. 1.0D + 1.0L + 1.0E
• PARAMETER $ ALSTRINC based on the % increase
• ALSTRINC 33.333 LOADINGS 2 3
7
LRFD Load Combinations
• 1.4D• 1.2D + 1.6L• 1.2D + 1.6W + 0.5L• 1.2D ± 1.0E + 0.5L• 0.9D ± (1.6W or 1.0E)
D = dead loadL = live loadW = wind loadE = earthquake load
8
Deflection Load Combinationsfor ASD and LRFD
• 1.0D + 1.0L• 1.0D + 1.0L + 1.0W• 1.0D + 1.0L + 1.0E
D = dead loadL = live loadW = wind loadE = earthquake load
9
Forces and Stresses
• ASD = actual stress values are compared to the AISCallowable stress values
• LRFD = actual forces and momentsare compared to the AISClimiting forces and momentscapacity
10
ASTM Steel Grade• Comparison is between Table 1 of the AISC ASD 9th Edition
on Page 1-7 versus Table 2-1 of the AISC LRFD 3rd Edition on Page 2-24
• A529 Gr. 42 of ASD, not available in LRFD• A529 Gr. 50 and 55 are new in LRFD• A441 not available in LRFD• A572 Gr. 55 is new in LRFD• A618 Gr. I, II, & III are new in LRFD• A913 Gr. 50, 60, 65, & 70 are new in LRFD• A992 (Fy = 50, Fu = 65) is new in LRFD (new standard)• A847 is new in LRFD
11
Slenderness Ratio
• CompressionKL/r ≤ 200
• TensionL/r ≤ 300
12
Tension Members
• Check L/r ratio• Check Tensile Strength based on the cross-
section’s Gross Area• Check Tensile Strength based on the cross-
section’s Net Area
13
Tension Members
ASDft = FX/Ag ≤ Ft Gross Area
ft = FX/Ae ≤ Ft Net Area
LRFD
Pu = FX ≤ ϕt Pn = ϕt Ag Fy ϕt = 0.9 for Gross Area
Pu = FX ≤ ϕt Pn = ϕt Ae Fu ϕt = 0.75 for Net Area
14
Tension Members
ASD (ASD Section D1)
Gross Area Ft = 0.6Fy
Net Area Ft = 0.5Fu
LRFD (LRFD Section D1)
Gross Area ϕt Pn = ϕt Fy Ag ϕt = 0.9
Net Area ϕt Pn = ϕt Fu Ae ϕt = 0.75
15
Compare ASD to LRFD
ASD 1.0D + 1.0LLRFD 1.2D + 1.6L
0.6Fy (ASD) × (1.5) = 0.9Fy (LRFD)
0.5Fu (ASD) × (1.5) = 0.75Fu (LRFD)
ASD × (1.5) = LRFD
16
Tension Members
X
Y
Z
FIXED JOINT
-400.
o
17
Tension Members• Member is 15 feet long• Fixed at the top of the member and free at the bottom• Loadings are:
• Self weight• 400 kips tension force at the free end• Load combinations based on the ASD and
LRFD codes• Steel grade is A992• Design based on the ASD and LRFD codes
18
Tension Members
ASD
W18x46 Actual/Allowable Ratio = 0.989
LRFD
W10x49 Actual/Limiting Ratio = 0.989
19
Tension Members
ASDW18x46 Area = 13.5 in.2
FX = 400.688 kips Ratio = 0.989
LRFDW10x49 Area = 14.4 in.2
FX = 640.881 kips Ratio = 0.989
20
Tension MembersLoad Factor difference between LRFD and ASD
640.881 / 400.688 = 1.599Equation Factor difference between LRFD and ASD
LRFD = (1.5) × ASD
Estimate required cross-sectional area for LRFD
LRFD W10x49 Area = 14.4 in.2
A rea fo r L R F D 13 5 64 0 88 14 00 6 88
1 01 5
0 9 890 9 89
1 4 3 9 5. ..
.
...
.
21
Tension MembersCode Check based on the ASD9 and using W10x49
FX = 400.734 kips Ratio = 0.928
Load Factor difference between LRFD and ASD640.881 / 400.734 = 1.599
LRFD W10x49 Ratio = 0.989
L R F D R atio co m p uted fro m A S D 0 9 2 8 6 4 0 8 8 14 0 0 7 3 4
1 01 5
0 9 8 9. ..
.
..
22
Tension MembersASD
Example # 1Live Load = 400 kips
W18x46 Actual/Allowable Ratio = 0.989LRFD
Example # 1Live Load = 400 kips
W10x49 Actual/Limiting Ratio = 0.989Example # 2
Dead Load = 200 kipsLive Load = 200 kips
W14x43 Actual/Limiting Ratio = 0.989Code check W14x43 based on the ASD9
W14x43 Actual/Allowable Ratio = 1.06
23
Compression Members
• Check KL/r ratio• Compute Flexural-Torsional Buckling and
Equivalent (KL/r)e
• Find Maximum of KL/r and (KL/r)e
• Compute Qs and Qa based on the b/t and h/tw ratios
• Based on the KL/r ratio, compute allowable stress in ASD or limiting force in LRFD
24
Compression Members
ASD
fa = FX/Ag ≤ Fa
LRFD
Pu = FX ≤ ϕc Pn = ϕc Ag Fcr
Where ϕc = 0.85
25
Limiting Width-Thickness Ratiosfor Compression Elements
ASD
b/t = h/tw =
LRFD
b/t = h/tw =
9 5 / F y
0 5 6. /E F y
2 5 3 / F y
1 4 9. /E F y
26
Limiting Width-Thickness Ratiosfor Compression Elements
Assume E = 29000 ksi
ASD
b/t = h/tw =
LRFD
b/t = h/tw =
9 5 / F y
9 5 3 6. / F y
2 5 3 / F y
2 5 3 7 4. / F y
27
Compression Members
ASD KL/r ≤ C′c (ASD E2-1 or A-B5-11)
LRFD (LRFD A-E3-2)
F
QKL r
CF
KL rC
KL r
C
ac
y
c c
12
53
38 8
2
2
3
3
/
/ /
F Q FcrQ
yc 0 6 5 8
2
.
W here C EQ Fc
y
2 2
W here c
yKLr
FE
c Q 1 5.
28
Compression Members
ASD KL/r > C′c (ASD E2-2)
LRFD (LRFD A-E3-3)
F E
KL ra 12
2 3
2
2
/W here C E
Q Fcy
2 2
c Q 1 5.
F Fcrc
y
0 8 7 72
.
W here c
yKLr
FE
29
Compression Members
LRFDF Fcr
cy
0 8 7 72
. W here
cyKL
rFE
FKLr
FE
Fcr
y
y
0 87 72
.
F E
KL rcr
0 8 77 2
2
.
/
FE
K L rcr 20 17 123
2
2
./
30
Compression Members
ASD LRFD
Fcr / Fa = 1.681
LRFD Fcr = ASD Fa × 1.681
F E
KL ra
1 2
2 3
2
2
/ F
EK L rcr
2 0 1 7 123
2
2
./
31
Compression Members
ASD
(ASD C-E2-2)
LRFD
λc = Maximum of ( λcy , λcz , λe )
KL rK L
rK L
rKLr
y Y
y
z z
z e
/ , ,
W here KLr
EFe e
32
Compression Members
LRFDWhere:
cy
y y
y
yK Lr
FE
cz
z z
z
yK Lr
FE
ey
e
FF
33
Compression Members
Flexural-Torsional Buckling
F
E C
K LG J
I Iew
x x y z
2
2
1 0.
34
Qs Computation
ASD
LRFD
W hen 9 5 1 9 5/ / / / /F k b t F ky c y c
Q b t F ks y c 1 2 9 3 0 0 0 3 0 9. . ( / ) /
W hen 0 5 6 1 0 3. / / . /E F b t E Fy y
Q b t F Es y 1 41 5 0 7 4. . ( / ) /
k
h th t kc c
4 0 5 7 0 1 00 .46
.
// , .if o therw ise
35
Qs Computation
Assume E = 29000 ksi
ASD
LRFD
W hen 9 5 1 9 5/ / / / /F k b t F ky c y c
Q b t F ks y c 1 2 9 3 0 00 3 0 9. . ( / ) /
W hen 9 5 3 6 1 7 5 4. / / . /F b t Fy y
Q b t Fs y 1 4 1 5 0 0 0 4 3 4 5. . ( / )
36
Qs Computation
ASD
LRFD
W hen b t F ky c/ / / 1 9 5
Q k F b ts c y 2 6 20 0 2/ /
W hen b t E F y/ . / 1 0 3
Q E F b ts y 0 6 9 2. / /
37
Qs Computation
Assume E = 29000 ksi
ASD
LRFD
W hen b t F ky c/ / / 1 9 5
Q k F b ts c y 2 6 2 0 0 2/ /
W hen b t F y/ . / 1 7 5 4
Q F b ts y 2 0 0 1 0 2/ /
38
Qa Computation
ASD
LRFD
b tf b t f
be
25 3 1 4 4 3.
( / )
b t Ef b t
Ef
be
1 91 1 0 34. .
( / )
A ssum e ksiE b tf b t f
e
2 9 0 0 0 3 2 5 2 6 1 5 7 9, . .( / )
39
Compression Members
X
Y
Z FIXED JOINT
-100.o
40
Compression Members• Member is 15 feet long• Fixed at the bottom of the column and free at the top• Loadings are:
• Self weight• 100 kips compression force at the free end• Load combinations based on the ASD and
LRFD codes• Steel grade is A992• Design based on the ASD and LRFD codes
41
Compression Members
ASD
W10x49 Actual/Allowable Ratio = 0.941
LRFD
W10x54 Actual/Limiting Ratio = 0.944
42
Compression Members
ASDW10x49 Area = 14.4 in.2
FX = 100.734 kips Ratio = 0.941
LRFDW10x54 Area = 15.8 in.2
FX = 160.967 kips Ratio = 0.944
43
Compression MembersLoad Factor difference between LRFD and ASD
160.967 / 100.734 = 1.598Equation Factor difference between LRFD and ASD
LRFD Fcr = (1.681) × ASD Fa
Estimate required cross-sectional area for LRFD
LRFD W10x54 Area = 15.8 inch
A rea fo r L R F D 14 4 16 0 9 6 710 0 7 3 4
1 01 6 8 1
1 00 8 5
0 94 10 94 4
1 6 0 5. ..
..
..
..
.
44
Compression MembersCode Check based on the ASD9 and use W10x54
FX = 100.806 kips Ratio = 0.845
Load Factor difference between LRFD and ASD160.967 / 100.806 = 1.597
LRFD W10x54 Ratio = 0.944
L R F D R atio co mp uted fro m A S D 0 8 4 5 1 6 0 9 6 710 0 8 0 6
1 01 6 81
1 00 85
0 94 4. ..
..
..
.
45
Compression MembersASD
Example # 1Live Load = 100 kips
W10x49 Actual/Allowable Ratio = 0.941LRFD
Example # 1Live Load = 100 kips
W10x54 Actual/Limiting Ratio = 0.944Example # 2
Dead Load = 50 kipsLive Load = 50 kips
W10x49 Actual/Limiting Ratio = 0.921Code check W10x49 based on the ASD9
W10x49 Actual/Allowable Ratio = 0.941
46
Flexural Members• Based on the b/t and h/tw ratios determine the compactness of
the cross-section• Classify flexural members as Compact, Noncompact, or Slender• When noncompact section in ASD, allowable stress Fb is
computed based on the l/rt ratio. l is the laterally unbraced length of the compression flange. Also, Cb has to be computed
• When noncompact or slender section in LRFD, LTB, FLB, and WLB are checked
• LTB for noncompact or slender sections is computed using Lb and Cb. Lb is the laterally unbraced length of the compression flange
47
Flexural Members
ASD
fb = MZ/SZ ≤ Fb
LRFD
Mu = MZ ≤ ϕb Mn
Where ϕb = 0.9
48
Limiting Width-Thickness Ratiosfor Compression Elements
ASD
LRFD
Assume E = 29000 ksi
d t Fw y/ / 6 4 0
b t E F y/ . / 0 3 8 h t E Fw y/ . / 3 7 6
b t F y/ / 6 5
b t F y/ . / 6 4 7 h t Fw y/ . / 64 0 3
49
Flexural MembersCompact Section
ASD (ASD F1-1)
Fb = 0.66Fy
LRFD (LRFD A-F1-1)
ϕb Mn = ϕb Mp = ϕb Fy ZZ ≤ 1.5Fy SZWhere ϕb = 0.9
50
Flexural MembersCompact Section
X
Y
Z
FIXED JOINT
-15.00
-15.00
o
o
FIXED JOINT
Braced at 1/3 Points
51
Flexural MembersCompact Section
• Member is 12 feet long• Fixed at both ends of the member• Loadings are:
• Self weight• 15 kips/ft uniform load• Load combinations based on the ASD and
LRFD codes• Steel grade is A992• Braced at the 1/3 Points• Design based on the ASD and LRFD codes
52
Flexural MembersCompact Section
ASD
W18x40 Actual/Allowable Ratio = 0.959
LRFD
W18x40 Actual/Limiting Ratio = 0.982
53
Flexural MembersCompact Section
ASDW18x40 Sz = 68.4 in.3
MZ = 2165.777 inch-kips Ratio = 0.959
LRFDW18x40 Zz = 78.4 in.3
MZ = 3462.933 inch-kips Ratio = 0.982
54
Flexural MembersCompact Section
Load Factor difference between LRFD and ASD3462.933 / 2165.777 = 1.5989
Equation Factor difference between LRFD and ASDLRFD = (0.66Sz)(1.5989) / (0.9Zz) × ASD
Zz
LRFDW18x40 Zz = 78.4 in.3
fo r L R F D 6 8 4 3 4 6 2 9 3 32 1 6 5 7 77
0 6 60 9
0 9 590 9 82
7 8 3. ..
..
.
..
55
Flexural MembersCompact Section
Code Check based on the ASD9, Profile W18x40
MZ = 2165.777 inch-kips Ratio = 0.959
Load Factor difference between LRFD and ASD3462.933 / 2165.777 = 1.5989
LRFDW18x40 Ratio = 0.982
L R F D R atio co m puted fro m A S D 0 95 9 34 62 93 321 65 7 7 7
0 660 9
68 478 4
0 98 1. ..
..
.
..
56
Flexural MembersCompact Section
ASDExample # 1
Live Load = 15 kips/ftW18x40 Actual/Allowable Ratio = 0.959
LRFDExample # 1
Live Load = 15 kips/ftW18x40 Actual/Limiting Ratio = 0.982
Example # 2Dead Load = 7.5 kips/ftLive Load = 7.5 kips/ft
W18x40 Actual/Limiting Ratio = 0.859Code check W18x40 based on the ASD9
W18x40 Actual/Allowable Ratio = 0.959
57
Flexural MembersNoncompact Section
ASD• Based on b/t, d/tw and h/tw determine if the section is
noncompact• Compute Cb
• Compute Qs
• Based on the l/rt ratio, compute allowable stress Fb
• Laterally unbraced length of the compression flange (l) has a direct effect on the equations of the noncompact section
58
Flexural MembersNoncompact Section
ASD
fb = MZ/SZ ≤ Fb
LRFD
Mu = MZ ≤ ϕb Mn
Where ϕb = 0.9
59
Limiting Width-Thickness Ratiosfor Compression Elements
ASD
LRFD
6 5 9 5F b t Fy y
d t Fw y 6 4 0
0 3 8 0 8 3. / .E F b t E Fy L
3 7 6 5 7. .E F h t E Fy w y
h t Fw b 7 6 0
60
Limiting Width-Thickness Ratiosfor Compression Elements
Assume E = 29000 ksi
ASD
LRFD
6 5 9 5F b t Fy y
d t Fw y 6 4 0
6 4 7 1 4 1 3. / / . /F b t Fy L
6 4 0 3 9 7 0 7. / . /F h t Fy w y
h t Fw b 7 6 0
61
Flexural MembersNoncompact Section
ASD
(ASD F1-3)
(ASD F1-2)
ASD Equations F1-6, F1-7, and F1-8 must to be checked.
F Fbt
Fb yf
fy
0 7 9 0 0 0 22
. .
I f m inim um o rL L
b
F d A Fb cf
y f y
7 6 2 0 0 0 0
62
Flexural MembersNoncompact Section
ASD
When
(ASD F1-6)
1 0 2 1 0 5 1 0 1 03 3
CF
lr
CF
b
y T
b
y
F
F l r
CF F Qb
y T
by y s
23 1 5 3 0 1 0
0 62
3
/.
63
Flexural MembersNoncompact Section
ASD
When
(ASD F1-7)
lr
CFT
b
y
51 0 10 3
F
C
l rF Qb
b
Ty s
1 7 0 1 00 6
3
2/.
64
Flexural MembersNoncompact Section
ASD
For any value of l/rT
(ASD F1-8)FC
ld AF Qb
b
fy s
1 2 1 00 6
3
/.
65
Flexural MembersNoncompact Section
LRFD
1. LTB, Lateral-Torsional Buckling2. FLB, Flange Local Buckling3. WLB, Web Local Buckling
66
Flexural MembersNoncompact Section
LRFD– LTB
• Compute Cb
• Based on the Lb, compute limiting moment capacity. Lb is the lateral unbraced length of the compression flange,λ = Lb/ry
• Lb has a direct effect on the LTB equations for noncompact and slender sections
– FLB• Compute limiting moment capacity based on the b/t ratio of
the flange, λ = b/t– WLB
• Compute limiting moment capacity based on the h/tw ratio of the web, λ = h/tw
67
Flexural MembersNoncompact Section
LRFD LTB (Table A-F1.1)
For λp < λ ≤ λr
(LRFD A-F1-2)
Where:Mp = Fy Zz ≤ 1.5Fy Sz
Mr = FLSz FL = Smaller of (Fyf − Fr) or Fyw
λ = Lb/ry
λp =
M C M M M Mn b p p rp
r pp
1 76. E F yf
68
Flexural MembersNoncompact Section
LRFD LTB (Table A-F1.1)
Where:
λr =
X1 =
X2 =
XF
X FL
L1
221 1
S
E G JA
z 2
42C
ISG J
w
y
z
69
Flexural MembersNoncompact Section
LRFD FLB (Table A-F1.1)
For λp < λ ≤ λr
(LRFD A-F1-3)Where:Mp = Fy Zz ≤ 1.5Fy Sz
Mr = FLSz FL = Smaller of (Fyf − Fr) or Fyw
λ = b/tλp =
λr =
M M M Mn p p rp
r p
0 3 8. E F y
0 8 3. E F L
70
Flexural MembersNoncompact Section
LRFD WLB (Table A-F1.1)
For λp < λ ≤ λr
(LRFD A-F1-3)Where:
Mp = Fy Zz ≤ 1.5Fy Sz
Mr = Re Fy Sz
Re = 1.0 for non-hybrid girder
M M M Mn p p rp
r p
71
Flexural MembersNoncompact Section
LRFD WLB (Table A-F1.1)
λ = h/tw
λp =
λr =
3 7 6. E F y
5 7. E F y
72
Flexural MembersNoncompact Section
ASD
LRFD
C M M M M
M MM M M C
b
b
1 7 5 1 0 5 0 3 2 3
1 0
1 2 1 22
1 2
1 2
. . . .
, .maxI f b e tw een and
CM
M M M MMMM
bA B C
A
B
C
1 2 52 5 3 4 3
..
max
max
ab so lute va lue o f m o m ent a t q uarter p o intab so lute value o f m o m ent a t cente rlineab so lute value o f m o m ent a t three q uarte r p o int
73
Flexural MembersNoncompact Section
X
Y
Z
Roller
-12.00
-12.00
o
o
Pin
74
Flexural MembersNoncompact Section
• Member is 12 feet long• Pin at the start of the member• Roller at the end of the member• Cross-section is W12x65• Loadings are:
• Self weight• 12 kips/ft uniform load• Load combinations based on the ASD and LRFD codes
• Steel grade is A992• Check code based on the ASD and LRFD codes
75
Flexural MembersNoncompact Section
ASDW12x65 Cb = 1.0
Actual/Allowable Ratio = 0.988LRFD
W12x65 Cb = 1.136Actual/Limiting Ratio = 0.971
Code check is controlled by FLB.Cb = 1.0 Actual/Limiting Ratio = 0.973
76
Flexural MembersNoncompact Section
ASDExample # 1
Live Load = 12 kips/ftW12x65 Actual/Allowable Ratio = 0.988
LRFDExample # 1
Live Load = 12 kips/ftW12x65 Actual/Limiting Ratio = 0.971
Example # 2Dead Load = 6 kips/ftLive Load = 6 kips/ft
W12x65 Actual/Limiting Ratio = 0.85Code check W12x65 based on the ASD9
W12x65 Actual/Allowable Ratio = 0.988
77
Design for Shear
ASD
fv = FY/Aw ≤ Fv = 0.4Fy (ASD F4-1)
LRFD
Vu = FY ≤ ϕvVn = ϕv0.6Fyw Aw (LRFD F2-1)
Where ϕv = 0.9
h t Fw y/ 3 8 0
h t E Fw yw/ . / 2 45
78
Design for ShearAssume E = 29000 ksiASD
fv = FY/Aw ≤ Fv = 0.4Fy (ASD F4-1)
LRFD
Vu = FY ≤ ϕvVn = ϕv0.6Fyw Aw (LRFD F2-1)
Where ϕv = 0.9
h t Fw y/ 3 8 0
h t Fw yw/ . / 4 1 7 2
79
Design for ShearASD
fv = FY/Ay ≤ (ASD F4-2)
LRFD
Vu = FY ≤ ϕvVn = ϕv (LRFD F2-2)
Where ϕv = 0.9
h t Fw y/ 3 8 0
2 4 5 3 0 7. / / . /E F h t E Fyw w yw
FF
C Fvy
v y 2 8 9
0 4.
.
0 62 45
.. /
/F A
E F
h tyw wyw
w
80
Design for Shear
LRFD
Vu = FY ≤ ϕvVn = ϕv (LRFD F2-3)
Where ϕv = 0.9
3 0 7 26 0. / /E F h tyw w
A E
h tw
w
4 5 22
.
/
81
Design for Shear
X
Y
Z
FIXED JOINT
-15.00
-15.00
o
o
FIXED JOINT
Braced at 1/3 Points
82
Design for Shear• Same as example # 3 which is used for design of flexural
member with compact section• Member is 12 feet long• Fixed at both ends of the member• Loadings are:
• Self weight• 15 kips/ft uniform load• Load combinations based on the ASD and LRFD codes
• Steel grade is A992• Braced at the 1/3 Points• Design based on the ASD and LRFD codes
83
Design for Shear
ASD (Check shear at the end of the member, equation “F4-1 Y”)
W18x40 Actual/Allowable Ratio = 0.8
LRFD (Check shear at the end of the member, equation “A-F2-1 Y”)
W18x40 Actual/Limiting Ratio = 0.948
84
Design for Shear
ASDW18x40 Ay = 5.638 in.2
FY = 90.241 kips Ratio = 0.8
LRFDW18x40 Ay = 5.638 in.2
FY = 144.289 kips Ratio = 0.948
85
Design for ShearCode Check based on the ASD9, Profile W18x40
FY = 90.241 kips Ratio = 0.8Load Factor difference between LRFD and ASD
144.289 / 90.241 = 1.5989Equation Factor difference between LRFD and ASD
LRFD = (0.4)(1.5989) /(0.6)(0.9) × ASD
LRFDW18x40 Ratio = 0.948
L R F D R atio co m puted fro m A S D 0 8 1 4 4 2 8990 2 4 1
0 40 6
1 00 9
0 94 8. ..
.
...
.
86
Design for ShearASD
Example # 1Live Load = 15 kips/ft
W18x40 Actual/Allowable Ratio = 0.8LRFD
Example # 1Live Load = 15 kips/ft
W18x40 Actual/Limiting Ratio = 0.948Example # 2
Dead Load = 7.5 kips/ftLive Load = 7.5 kips/ft
W18x40 Actual/Limiting Ratio = 0.83Code check W18x40 based on the ASD9
W18x40 Actual/Allowable Ratio = 0.8
87
Combined Forces
ASD fa /Fa > 0.15
(ASD H1-1)
(ASD H1-2)
LRFD Pu /ϕPn ≥ 0.2(LRFD H1-
1a)
fF
C f
fF
F
C f
fF
a
a
m y by
a
eyby
m z bz
a
ez
1 1
1 0.
fF
fF
fF
a
y
by
by
bz
bz0 61 0
..
PP
MM
MM
u
n
uy
b ny
u z
b nz
89
1 0.
88
Combined Forces
ASD fa /Fa ≤ 0.15
(ASD H1-1)
LRFD Pu /ϕPn < 0.2
(LRFD H1-1a)
fF
fF
fF
a
a
by
by
bz
bz
1 0.
PP
MM
MM
u
n
u y
b ny
uz
b nz21 0
.
89
Combined Forces
X
Y
Z
90
Combined Forces• 3D Simple Frame
• 3 Bays in X direction 3 @ 15 ft• 2 Bays in Z direction 2 @ 30 ft• 2 Floors in Y direction 2 @ 15 ft
• Loadings• Self weight of the Steel• Self weight of the Slab 62.5 psf• Other dead loads 15.0 psf• Live load on second floor 50.0 psf• Live load on roof 20.0 psf• Wind load in the X direction 20.0 psf• Wind load in the Z direction 20.0 psf
91
Combined ForcesASD
<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>< Active Units Weight Unit = KIP Length Unit = INCH >< >< Steel Take Off Itemize Based on the PROFILE >< Total Length, Volume, Weight, and Number of Members >< >< Profile Names Total Length Total Volume Total Weight # of Members >< W10x33 2.1600E+03 2.0974E+04 5.9418E+00 12 >< W12x58 1.4400E+03 2.4480E+04 6.9352E+00 4 >< W12x65 1.4400E+03 2.7504E+04 7.7919E+00 4 >< W12x72 2.1600E+03 4.5576E+04 1.2912E+01 12 >< W6x9 3.2400E+03 8.6832E+03 2.4600E+00 18 >< W8x40 1.4400E+03 1.6848E+04 4.7730E+00 4 >< W8x48 1.4400E+03 2.0304E+04 5.7521E+00 4 ><<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>< ACTIVE UNITS WEIGHT KIP LENGTH INCH >< >< TOTAL LENGTH, WEIGHT AND VOLUME FOR SPECIFIED MEMBERS >< >< LENGTH = 1.3320E+04 WEIGHT = 4.6566E+01 VOLUME = 1.6437E+05 ><<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
92
Combined ForcesLRFD
<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>< Active Units Weight Unit = KIP Length Unit = INCH >< >< Steel Take Off Itemize Based on the PROFILE >< Total Length, Volume, Weight, and Number of Members >< >< Profile Names Total Length Total Volume Total Weight # of Members >< W10x33 3.6000E+03 3.4956E+04 9.9030E+00 16 >< W10x39 1.4400E+03 1.6560E+04 4.6914E+00 4 >< W10x49 7.2000E+02 1.0368E+04 2.9373E+00 4 >< W12x45 1.4400E+03 1.9008E+04 5.3850E+00 4 >< W6x9 3.2400E+03 8.6832E+03 2.4600E+00 18 >< W8x31 1.4400E+03 1.3147E+04 3.7246E+00 4 >< W8x40 1.4400E+03 1.6848E+04 4.7730E+00 8 >< ><<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>< ACTIVE UNITS WEIGHT KIP LENGTH INCH >< >< TOTAL LENGTH, WEIGHT AND VOLUME FOR SPECIFIED MEMBERS >< >< LENGTH = 1.3320E+04 WEIGHT = 3.3874E+01 VOLUME = 1.1957E+05 ><<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
93
Combined Forces
ASD
WEIGHT = 46.566 kips
LRFD
WEIGHT = 33.874 kips
94
Deflection DesignASD
<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>< Active Units Weight Unit = KIP Length Unit = INCH >< >< Steel Take Off Itemize Based on the PROFILE >< Total Length, Volume, Weight, and Number of Members >< >< Profile Names Total Length Total Volume Total Weight # of Members >< W10x33 2.1600E+03 2.0974E+04 5.9418E+00 12 >< W12x58 1.4400E+03 2.4480E+04 6.9352E+00 4 >< W12x65 1.4400E+03 2.7504E+04 7.7919E+00 4 >< W12x72 2.1600E+03 4.5576E+04 1.2912E+01 12 >< W14x43 1.4400E+03 1.8144E+04 5.1402E+00 4 >< W14x48 1.4400E+03 2.0304E+04 5.7521E+00 4 >< W6x9 3.2400E+03 8.6832E+03 2.4600E+00 18 ><<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>< ACTIVE UNITS WEIGHT KIP LENGTH INCH >< >< TOTAL LENGTH, WEIGHT AND VOLUME FOR SPECIFIED MEMBERS >< >< LENGTH = 1.3320E+04 WEIGHT = 4.6933E+01 VOLUME = 1.6566E+05 ><<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
95
Deflection DesignLRFD
<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>< Active Units Weight Unit = KIP Length Unit = INCH >< >< Steel Take Off Itemize Based on the PROFILE >< Total Length, Volume, Weight, and Number of Members >< >< Profile Names Total Length Total Volume Total Weight # of Members >< W10x33 2.1600E+03 2.0974E+04 5.9418E+00 12 >< W10x49 1.4400E+03 2.0736E+04 5.8745E+00 8 >< W10x54 7.2000E+02 1.1376E+04 3.2228E+00 4 >< W12x40 1.4400E+03 1.6992E+04 4.8138E+00 4 >< W14x43 2.8800E+03 3.6288E+04 1.0280E+01 8 >< W14x48 1.4400E+03 2.0304E+04 5.7521E+00 4 >< W6x9 3.2400E+03 8.6832E+03 2.4600E+00 18 ><<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>< ACTIVE UNITS WEIGHT KIP LENGTH INCH >< >< TOTAL LENGTH, WEIGHT AND VOLUME FOR SPECIFIED MEMBERS >< >< LENGTH = 1.3320E+04 WEIGHT = 3.8345E+01 VOLUME = 1.3535E+05 ><<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
96
Deflection Design
ASD
WEIGHT = 46.933 kips
LRFD
WEIGHT = 38.345 kips
97
Compare Design without and with Deflection Design
ASDWithout Deflection Design WEIGHT = 46.566 kipsWith Deflection Design WEIGHT = 46.933 kips
LRFDWithout Deflection Design WEIGHT = 33.874 kipsWith Deflection Design WEIGHT = 38.345 kips
98
Design same example based onCb = 1.0
Code and deflection design with Cb = 1.0
ASDCompute Cb WEIGHT = 46.933 kipsSpecify Cb = 1.0 WEIGHT = 51.752 kips
LRFDCompute Cb WEIGHT = 38.345 kipsSpecify Cb = 1.0 WEIGHT = 48.421 kips
99
Design Similar example based onCb = 1.0 and LL×5
• Code and deflection design with Cb = 1.0 and increase the live load by a factor of 5.
• Area loads are distributed using two way option instead of one way
• Also change the 2 bays in the Z direction from 30 ft to 15 ft.
ASD WEIGHT = 25.677 kips
LRFD WEIGHT = 22.636 kips
Difference = 3.041 kips
100
Design Similar example based onCb = 1.0 and LL×10
• Code and deflection design with Cb = 1.0 and increase the live load by a factor of 10.
• Area loads are distributed using two way option instead of one way
• Also change the 2 bays in the Z direction from 30 ft to 15 ft.
ASD WEIGHT = 31.022 kips
LRFD WEIGHT = 29.051 kips
Difference = 1.971 kips
101
Stiffness Analysisversus
Nonlinear Analysis• Stiffness Analysis – Load Combinations or Form
Loads can be used.• Nonlinear Analysis – Form Loads must be used.
Load Combinations are not valid.• Nonlinear Analysis – Specify type of Nonlinearity.• Nonlinear Analysis – Specify Maximum Number of
Cycles.• Nonlinear Analysis – Specify Convergence
Tolerance.
102
Nonlinear AnalysisCommands
• NONLINEAR EFFECT• TENSION ONLY• COMPRESSION ONLY• GEOMETRY AXIAL
• MAXIMUM NUMBER OF CYCLES• CONVERGENCE TOLERANCE
• NONLINEAR ANALYSIS
103
Design using Nonlinear AnalysisInput File # 1
1. Geometry, Material Type, Properties, 2. Loading ‘SW’, ‘LL’, and ‘WL’3. FORM LOAD ‘A’ FROM ‘SW’ 1.44. FORM LOAD ‘B’ FROM ‘SW’ 1.2 ‘LL’ 1.65. FORM LOAD ‘C’ FROM ‘SW’ 1.2 ‘WL’ 1.6 ‘LL’ 0.56. FORM LOAD ‘D’ FROM ‘SW’ 0.9 ‘WL’ 1.67. DEFINE PHYSICAL MEMBERS8. PARAMETERS9. MEMBER CONSTRAINTS10. LOAD LIST ‘A’ ‘B’ ‘C’ ‘D’ $ Activate only the FORM loads11. STIFFNESS ANALYSIS12. SAVE
104
Design using Nonlinear AnalysisInput File # 2
1. RESTORE2. LOAD LIST ‘A’ ‘B’ ‘C’ ‘D’3. SELECT MEMBERS4. SMOOTH PHYSICAL MEMBERS5. DELETE LOADINGS ‘A’ ‘B’ ‘C’ ‘D’6. SELF WEIGHT LOADING RECOMPUTE7. FORM LOAD ‘A’ FROM ‘SW’ 1.48. FORM LOAD ‘B’ FROM ‘SW’ 1.2 ‘LL’ 1.69. FORM LOAD ‘C’ FROM ‘SW’ 1.2 ‘WL’ 1.6 ‘LL’ 0.510. FORM LOAD ‘D’ FROM ‘SW’ 0.9 ‘WL’ 1.611. LOAD LIST ‘A’ ‘B’ ‘C’ ‘D’12. STIFFNESS ANALYSIS13. CHECK MEMBERS14. STEEL TAKE OFF15. SAVE
105
Design using Nonlinear AnalysisInput File # 3
1. RESTORE2. LOAD LIST ‘A’ ‘B’ ‘C’ ‘D’3. SELECT MEMBERS4. SMOOTH PHYSICAL MEMBERS5. DELETE LOADINGS ‘A’ ‘B’ ‘C’ ‘D’6. SELF WEIGHT LOADING RECOMPUTE7. FORM LOAD ‘A’ FROM ‘SW’ 1.48. FORM LOAD ‘B’ FROM ‘SW’ 1.2 ‘LL’ 1.69. FORM LOAD ‘C’ FROM ‘SW’ 1.2 ‘WL’ 1.6 ‘LL’ 0.510. FORM LOAD ‘D’ FROM ‘SW’ 0.9 ‘WL’ 1.6
106
Design using Nonlinear AnalysisInput File # 3 (continue)
1. NONLINEAR EFFECT2. GEOMETRY ALL MEMBERS3. MAXIMUM NUMBER OF CYCLES4. CONVERGENCE TOLERANCE DISPLACEMENT5. LOAD LIST ‘A’ ‘B’ ‘C’ ‘D’6. NONLINEAR ANALYSIS7. CHECK MEMBERS8. STEEL TAKE OFF9. SAVE
107
General Comparison between AISC LRFD and ASD
Questions
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