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CE 591
Advanced Structural Steel Design
Fall 2013
Lecture 7: Plate Girders; Design
Rules of Thumb
Flange-to-web weld
Design Aids
Design Example
Proportioning the Section
Goals
Satisfy limit states
Strength
Serviceability
Minimum cost
assume cost proportional to weight of steel
but remember that least-weight may not provide the most cost effective design!
Rules of Thumb
Span-Depth Ratio
Salmon & Johnson, Steel Structures, 4th ed.
Rules of Thumb, MSC 2000
1210 tod
L
d
bf
L
15d
L
Modern Steel Construction, 2000
“Design It Like You Are Going to Build It”
Karl Frank 2013 NASCC Educator Session: Bridge Design for the Classroom media.aisc.org/NASCC2013/ES1.mp4
Recommendations for composite plate girders for bridges
“Design It Like You Are Going to Build It”
Karl Frank 2013 NASCC Educator Session: Bridge Design for the Classroom media.aisc.org/NASCC2013/ES1.mp4
Recommendations for composite plate girders for bridges
AASHTO Cross Sectional Limits
Similar to AISC eq. F13-2 Not stable if outside limit
Rules of Thumb – Flange Width
d
bf
3.02.0 tod
bf
“deep section”
“shallow section”
Optimum Depth (another option)
Based on minimizing weight (i.e. gross cross-sectional area), supposing no depth restriction
f is average stress on flange (i.e. Fcr)
bw is an assumed constant h/t
bw of 320 for ‘optimum’ proportion A36
C1 is a factor to account for reducing flange size at regions of lower moment
C2 is factor to account for reducing web thickness at regions of reduced shear
Optimum Depth, cont’d
Suppose C1= C2= 1 (i.e. no section reduction in regions of lower stress)
3
2
3
f
Mh
wb
3
12
1
)3(
3
CCf
MCh
w
b
Rules of Thumb – Flange Area
6
wf
A
fh
MA
Mu/f
Average stress on
flange
d
bf
h
Af
Aw
C
T Sx / h
Rules of Thumb – Plate dimensions
Plate widths
2” increments
Stiffener spacing
3” multiples
Rules of Thumb – Plate thickness
Increments (inches)
Range (inches)
1/16 t ≤ 9/16
1/8 5/8 ≤ t ≤ 1-1/2
1/4 t > 1-1/2
Rules of Thumb – Flange Plates, p. 1
Based on minimum volume (weight) and Af equation used earlier
Mmax L/2
L
2
11
f
f
A
A
Af1 Af
Groove weld
Unless save 200 – 300 lbs of material, added cost of weld makes flange plate transition uneconomical (Salmon et al., Steel Structures, 5th ed.)
Rules of Thumb – Flange Plates, p.2
Mmax L/3
L
9
51
f
f
A
A
Af1 Af
Groove weld
Other flange plate recommendations
If concerned about LTB, keep bf /2tf at about the lp value in maximum moment regions
Could then reduce flange thickness in low moment regions (reduce thickness instead of width)
No LTB? Reduce width if desired
“slight advantage in fatigue strength”
Transition slope should be less than 1 in 2-1/2 for either width or thickness change
1 in 4 to 1 in 12 recommended for change in width
2013 NASCC Educator Session: Bridge Design for the Classroom media.aisc.org/NASCC2013/ES1.mp4
Weld of flange to web
Must provide for factored horizontal shear flow
X X
x
u
I
QVflowshear
(kips/in)
1st moment of area of flange about neutral axis
Weld of flange to web, p.2
DOTs typically require SAW for these welds
“more thermally efficient”
More uniform weld cross section and strength
no stops/starts and other irregularities that concentrate stress
SMAW uses stick electrodes of limited length and diameter
X X
Rules of Thumb – Web
“Reasonable range” for web stress
< 9 ksi? May be able to use thinner web
Practical minimum web thickness (tw)
5/16”
ksitoA
V
w
n1612
f
Design Aids – Shear, Stiffeners
Tables 3-16a, 3-17a (without TFA)
36 ksi and 50 ksi steel
Starting on AISC Manual p. 3-152
Tables 3-16b, 3-17b (with TFA)
fvVn/Aw graphed as a function of h/tw and a/h
NOTE: here, Aw = d tw (AISC G2)
a/h > 3.0 kv = 5.0
---- means exceeded “practical limit” on stiffener spacing
2
260
wthh
a
Corresponds approximately to limit for vertical flange buckling
Plate Girder Design Example Consider a simply supported plate girder that carries the factored uniform load and two concentrated loads as shown. Design a doubly symmetric, non-hybrid girder with A36 steel. Assume that lateral support is provided at the ends and at the concentrated loads. 1.2D + 1.6L load combination controls. Factored loads shown. L/360 deflection limit (total service load).
150 k 150 k
5 k/ft
24' 24' 24'Lateral Support
330k
210
60
330210
60
Shear
(kip)
Moment
(ft-kip)
6480 64806840
A B C D
Lateral Support
Design Example, p. 2 150 k 150 k
5 k/ft
24' 24' 24'Lateral Support
330k
210
60
330210
60
Shear
(kip)
Moment
(ft-kip)
6480 64806840
A B C D
Design Example, p. 3a
Sizing the Section, try ‘Rule of Thumb’
1210 tod
L in
ftinft72
12
)/12)(72(
Try h = 72”
Try tw = 5/16” 230
"16/5
"72
wt
h
Design Example, p. 3b
Sizing the Section, try formula for h
33
2
)/(3
2
3
crpg
wuw
FR
M
f
Mh
bfb
in
ksi
ftinkipfth
107
)36)(0.1(2
)320)(/12)(9.0/6840(33
Design Example, p. 3c
Try h = 107”
Try tw = 5/16” 342
"16/5
"107
wt
h
a/h > 1.5 limit will be even smaller …
Also, web substantially heavier than for h=72” with practical minimum web thickness
So, try h=72”
34136
290000.12
max
ksi
ksi
t
h
w
AISC F13.2 for a/h ≤ 1.5
Design Example, p. 4
Check shear stress (recommended)
ksitoA
V
w
n1612
f7.14
)"16
5)("72(
330
kips
A
V
w
u
y
r
F
E70.5l 162
36
2900070.5
ksi
ksirl
Table B4.1b (Case 15)
Slender Web?
r
wt
hl 230
Design Example, p. 5
Double check AISC Limitations, h/tw = 230
5.10.12 h
afor
F
E
t
h
yfw
(F13-3)
34136
290000.12
ksi
ksi
5.140.0
h
afor
F
E
t
h
yw
(F13-4)
32236
)29000(40.0
ksi
ksi √ OK, Limitations satisfied
Design Example, p. 6
Estimate Flange Size
66
w
crPGb
uwf
A
hFR
MA
fh
MA
f
Assume RPG = 1.0, Fcr = Fy
24.316
)"16/5("72
)"72)(36)(0.1)(9.0(
)/12(6840in
ksi
ftinkipftAf
Design Example, p. 7
Possible flange dimensions
tf (in) bf (in) Af (in2) bf /2tf
1.375 24 33.0 8.72
1.25 26 32.5 10.4
1.125 28 31.5 12.4
bf
tf
8.1036
2900038.038.0
yf
pF
El
Use FLB compactness limit to help choose size (optional) – Table B4.1b
34.0))"25.1(2"72(
"26
d
b f Flange width rule of thumb > 0.3
Design Example, p. 8a LTB – Flexural Capacity; Lb = 24 ft
inrt 1.7
)16
5)(12()25.1)(26(
)16
5)(12(
12
1)25.1)(26(
12
1 33
bf
tf
hc/6
tw
=26”
=1.25”
=72”/6 =12”
=5/16”
y
tpF
ErL 1.1
(F4-7)
ftinksi
ksiinLp 5.18222
36
29000)1.7(1.1
y
trF
ErL
7.0
(F5-5)
ftinksi
ksiinLr 1.63757
)36(7.0
29000)1.7(
Design Example, p. 8b Lp = 18.5 ft < Lb = 24 ft < Lr = 63.1 ft
y
pr
pbyybcr F
LL
LLFFCF
)])(3.0([ (F5-3)
150 k 150 k
5 k/ft
24' 24' 24'Lateral Support
330k
210
60
330210
60
Shear
(kip)
Moment
(ft-kip)
6480 64806840
A B C D
~5% difference in Mu within Lb – assume constant moment
ksiFcr 36)]5.181.63
5.1824))(36(3.0(36)[0.1(
ksiFcr 5.34
Design Example, p. 9
Calculate Section Modulus, etc. 26”
1.25”
72”
5/16”
3
323
2602
)25.12
72(
)25.1)(26)(12
1(2)
2
25.1
2
72)(25.1)(26(2)72)(
16
5(
12
1
in
Sx
cfc
wc
wtb
tha 69.0
)"25.1)("26(
)"16/5)("72(wa
<10 √ OK (F4-12)
Design Example, p. 10
Calculate Flexural Capacity
0.1)7.5(3001200
1
yw
c
w
w
pgF
E
t
h
a
aR (F5-6)
97.0)36
290007.5
"16/5
"72(
)69.0(3001200
69.01
ksi
ksi
crpgxcbn FRSM ff (F5-2) and AISC F1
ftkipinkipksiin 653178368)5.34)(97.0)(2602(9.0 3
< Mu = 6840 kip-ft N.G.
Design Example, p. 11
TRY 28” x 1.5” flange
Recalculate properties:
242 inAf
28”
1.5”
72”
5/16”
inrt 74.7
8.1033.9)"5.1(2
"28
2 p
f
f
t
bl
ftLLftL rbp 7.68241.20
compact wrt FLB
33285inSx 535.0wa
ksiFcr 8.35
Design Example, p. 12
Recalculate Flexural Capacity, cont’d.
973.0)36
290007.5
"16/5
"72(
)535.0(3001200
535.01
ksi
ksiRpg
tfkipinkip
ksiin
FRSM crpgxcbn
8582102985
)8.35)(973.0)(3285(9.0 3
ff
Design Example, p. 13
Check against Mu including self-weight
2106)16
5)(72()5.1)(28(2 inininininArea
ftlbpcf
ft
in
inWeight /361)490(
144
106
2
2
2
ftkip
ftkiplbs
ftlb
ftkipMu 71208
)72(/1000
/361
2.16840
2
un MMf flexural capacity of section is adequate
< 8582 kip-ft
Design Example, p. 14
Check Deflection Limits
Estimate service loads
150 k 150 k
5 k/ft
24' 24' 24'Lateral Support
330k
210
60
330210
60
Shear
(kip)
Moment
(ft-kip)
6480 64806840
A B C D
kipskipsPP
ftkw
ftkftkftkw
uservice
service
u
1005.1/1505.1/
/62.35.1/43.5
/43.5)/361.0(2.1/5
a
Design Example, p. 15
Deflection limits, cont’d.
4323 183,123)"72)("
16
5(
12
1)
2
"5.1
2
"72)("5.1)("28)(2()"5.1)("28)(
12
1(2 inI x
inftftinksi
ftinftkips
inksi
ftinftftkaL
EI
aP
EI
Lw serviceservice
25.164.061.0))24(4)72(3()183,123)(000,29(24
)/1728)(24(100
)183,123)(000,29(384
)/1728)(72)(/62.3(5)43(
24384
5
22
4
33
4
33422
4
inftinftL
40.2360
)/12(72
360max > 1.25 in √ OK
Design Example, p. 16
Low shear demand – Region BC
150 k 150 k
5 k/ft
24' 24' 24'Lateral Support
330k
210
60
330210
60
Shear
(kip)
Moment
(ft-kip)
6480 64806840
A B C D
260230 wt
h
0.8736
)29000(0.537.137.1230
ksi
ksi
F
Ek
t
h
yw
v
w
260 is limit for unstiffened girders (F13.2); stiffeners not required unless needed for capacity
y
w
vv
Ft
h
EkC
2)(
51.1
12.0)36)(230(
)29000)(5(51.12
ksi
ksi
(G2-5)
Design Example, p. 17
Shear Capacity – Region BC
28.1230
260 2
)6.0(9.0 vywn CFAV f
50.9(0.6)(75")( ")(36 )(0.12) 54.6
16ksi kips
(G2-1) and AISC G1
<Vu = 60 kips w/o self-weight N.G. 2
260
wthh
a
"2.92)"72(28.128.1 haa = 90” a/h=1.25
Design Example, p. 18
Shear Capacity – Region BC
2)/(
55
hakv 2.8
)25.1(
55
2vk
23011136
)29000(2.837.137.1
wy
v
t
h
ksi
ksi
F
Ek
yw
w
vv
Ft
h
EkC
2)(
51.1 19.0
)36)(230(
)29000)(2.8(51.12
ksi
ksi
(G2-5)
Design Example, p. 19
Shear Capacity – Region BC
))/(115.1
1)(6.0(9.0
2ha
CCFAV v
vywn
f
2
5 1 0.190.9(0.6)(75")( ")(36 )(0.19 )
16 1.15 1 1.25
86 200 286
ksi
kips
(G3-2)
>>Vu = 60 kips √ OK By inspection, adequate for Vu
including self-weight
panelspanelin
ftinft2.3
/90
)/12(24 0.1
"72
"72;72
4
)/12(24
h
ain
spaces
ftinfta
Small adjustment needed later since ‘a’ is clear distance between stiffeners
Design Example, p. 20
Shear Capacity – Regions AB and CD
150 k 150 k
5 k/ft
24' 24' 24'Lateral Support
330k
210
60
330210
60
Shear
(kip)
Moment
(ft-kip)
6480 64806840
A B C D
Design End Panels first NO TFA Permitted
kips
ftkiplbs
ftlb
kipsVu 3462
)72(/1000
/361
2.1330
34614.8
(75")(5 /16")
kipsksi
Required Stress
Design Example, p. 21
Shear Capacity, End Panels
Use Table 3-16a (No TFA) for estimate
Will need a/h < 0.5
kipsVV un 346f
Requires: Cv >0.791 kv > 34.4 a/h < 0.41 a < 29.5”
Design Example, p. 22
Shear Capacity, End Panel Try a = 27”; a/h = 0.375
6.40)375.0(
55
)/(
55
22
hakv
23024736
)29000(6.4037.137.1
wy
v
t
h
ksi
ksi
F
Ek
86.0230
)36()29000)(6.40(10.110.1
ksiksi
th
FEkC
w
yv
v
50.9(0.6 ) 0.9(0.6)(75")( ")(36 )(0.86) 392
16n w y vV A F C ksi kips
√ OK
23019936
)29000(6.4010.110.1
wy
v
t
h
ksi
ksi
F
Ek
Design Example, p. 23
Shear Capacity – Regions AB and CD
150 k 150 k
5 k/ft
24' 24' 24'Lateral Support
330k
210
60
330210
60
Shear
(kip)
Moment
(ft-kip)
6480 64806840
A B C D
After End Panels TFA Permitted?
~27”
Check AISC G3.1 (a) and (b) satisfied; (c) and (d) ??
54.0)"5.1)("28(2
)"165)("72(2
)(
2
ftfc
w
AA
A< 2.5 TFA OK!
6.2"28
"72
ftfc b
h
b
h< 6.0 TFA OK!
Design Example, p. 24
Shear Capacity – Regions AB and CD
150 k 150 k
5 k/ft
24' 24' 24'Lateral Support
330k
210
60
330210
60
Shear
(kip)
Moment
(ft-kip)
6480 64806840
A B C D
After End Panels TFA Permitted
~27”
kipsVu 334 Including self-weight
33414.2
(75")(5 /16")
kipsksi
Required Stress
Design
Example, p. 25
Shear Capacity, after End Panels
Use Table 3-16b (with TFA) for estimate
Based on required stress, try a/h = 0.80?
Design Example, p. 26
Shear Capacity, after End Panel, with TFA
Try a = 56”; a/h = 0.78
2.13)78.0(
55
)/(
55
22
hakv
23014136
)29000(2.1337.137.1
wy
v
t
h
ksi
ksi
F
Ek
304.0)36)(230(
)29000)(2.13(51.1
)(
51.12
2
ksi
ksi
Ft
h
EkC
y
w
vv
>334 kips √ OK
2
2
10.9(0.6 )( )
1.15 1 ( / )
5 1 0.3040.9(0.6)(75)( )(36)(0.304 ) 356
16 1.15 1 0.78
vn w y v
CV A F C
a h
kips
Design Example, p. 27
Shear Capacity – Regions AB and CD
150 k 150 k
5 k/ft
24' 24' 24'Lateral Support
330k
210
60
330210
60
Shear
(kip)
Moment
(ft-kip)
6480 64806840
A B C D
After first 2 panels; TFA permitted
27”
kipsVu 309 Including self-weight
30913.2
(75")(5 /16")
kipsksi
Required Stress
56”
Based on Table 3-16b, repeat a/h= 0.78
Design Example, p. 28
Note: ‘a’ dimension used for stiffener spacing; therefore, actual ‘a’ (clear distance) will be smaller (May also modify to get multiples of 3” for spacing)
Repeat process for next panel(s); determine stiffener layout (another layout might be more efficient)
56” 4 @ 72”
27”
56” 73” 76”
C L sym.
Design Example, p.29
Size flange-to-web weld
31544)2
"5.1
2
"72)("5.1("28 in
X X
)22
(f
f
thAQ
x
u
I
QVshearflow
inkipsin
inkips/34.4
183,123
)1544(3464
3
Design Example, p. 30
Flange-to-web welds, cont’d
AISC Table J2.4 minimum size
3/16” fillet for 5/16” plate (thinner part joined)
Assume Submerged Arc Weld (SAW)
Try w=1/4”
Use matching weld electrode, 70ksi
X X
Design Example, p. 31
Flange-to-web weld, cont’d.
inkipsksiAFR wEXXn /1.11)"25.0(2
2)70)(6.0)(2(75.0)6.0( ff
inkipsksiAFR gyn /75.6)"3125.0)(36)(6.0(0.1)6.0( ff
inkipsksiAFR nvun /2.8)"3125.0)(58)(6.0(75.0)6.0( ff
Weld Metal (AISC J2)
Base Metal – Shear Yield (AISC J4.2)
Base Metal – Shear Rupture (AISC J4.2) CONTROLS
>4.34 kips/in √ OK
Design Example, p. 32
Intermediate Transverse Stiffeners
Assume single-plate A36 stiffeners
Design stiffener between end panel and first panel with TFA
End panel a/h = 0.375; adjacent panel (TFA) a/h = 0.78
Design Example, p.33 28”
1.5”
72”
5/16”
bst
"8.132
"165"28
stb
Try bst = 8”
(G3-3)
"503.0
9.15"8
9.1536
2900056.056.0
st
st
yst
st
t
t
F
Etb
Try tst = 9/16”
Design Example, p. 34
Intermediate Transverse Stiffeners, cont’d. (adequate stiffness for web buckling; AISC G2.2)
5.02)/(
5.22
ha
j 7.152375.0
5.22
jbtI wst
3
43 9.12)7.15()"16
5)("27( in
Check 8” x 9/16”
43
963
)"8("5625.0inIst
√ OK
End panel a/h = 0.375; adjacent panel (TFA) a/h = 0.78
for adjacent panel a/h = 0.78, Ist = 3.61 in4
4 4
346 13812.9 (29.4 12.9)
356 138
96.0 28.6
stI
in in
Design Example, p. 35
Intermediate Transverse Stiffeners, cont’d.
Adequate stiffness for TFA
12
1121 )(
cc
custststst
VV
VVIIII
√ OK
(G3-4)
45.13.145.13.14
2 4.2929000
36
40
0.172
40in
EFh
Iywst
st
(G3-5)
Check other stiffeners
Design Example, p. 36
Size welds for stiffeners
inkipsksi
ksi
E
Fhf
yw
nv /1.429000
36)"72(045.0045.0
33
Try minimum weld size for 5/16” plate (thinner plate) AISC Table J2.4
w=3/16”
Assume SMAW
Use matching electrode, 70 ksi
Design Example, p. 37
Stiffener welds, cont’d.
inkipsksiAFR wEXXn /35.8)"1875.0)(707.0)(70)(6.0)(2(75.0)6.0( ff
inkipsksiAFR gyn /2.12)"5625.0)(36)(6.0(0.1)6.0( ff
inkipsksiAFR nvun /7.14)"5625.0)(58)(6.0(75.0)6.0( ff
Weld Metal (AISC J2)
Base Metal – Shear Yield (AISC J4.2)
Base Metal – Shear Rupture (AISC J4.2)
CONTROLS
>4.1 kips/in √ OK
inkipsAFR nvun /79.9)"1875.0)(2)(58)(6.0(75.0)6.0( ffor
Design Example, p. 38
Stiffener welds, cont’d.
3/16”
3/16” Use nominal weld size (Table J2.4) to connect to compression flange (to prevent uplift of flange – single stiffener)
"88.1)"16
5(66
"25.1)"16
5(44
w
w
t
t
USE 1.5”
Design Example, p. 39
Bearing Stiffeners
Check LWY, LWC, etc. (given bearing length of support) Design bearing stiffener as needed
Typically make full depth; check capacity of intermediate transverse stiffeners for BEARING
Design Example, p. 40
Bearing Stiffeners
Will design / check for homework
Use pairs of stiffeners (as shown to left)
Use full depth