CE 591 – Advanced Structural Steel Designjliu/courses/CE591/PDF/ce591plate... · CE 591 Advanced...

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

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


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


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


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


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


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


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)


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.


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


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


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


Check Deflection Limits

Estimate service loads

150 k 150 k

5 k/ft


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


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


Low shear demand – Region BC

150 k 150 k

5 k/ft


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)


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



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)



))/(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


Shear Capacity – Regions AB and CD

150 k 150 k

5 k/ft


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


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”


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



150 k 150 k

5 k/ft


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!



150 k 150 k

5 k/ft


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?


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



150 k 150 k

5 k/ft


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


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


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


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


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”


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


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


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


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


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”


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


Bearing Stiffeners

Will design / check for homework

Use pairs of stiffeners (as shown to left)

Use full depth

CE 591 – Advanced Structural Steel Designjliu/courses/CE591/PDF/ce591plate... · CE 591 Advanced...

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