Copy of Splice LRFD-LFD Design

7/27/2019 Copy of Splice LRFD-LFD Design

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1. NOTICE : COPYRIGHT 2001-2008 C. C. FU, Ph.D., P.E.

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COPYRIGHT NOTICE AND DISCLAIMER

SPLICE DESIGN By LRFD/LFD


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Bolted Splice Design Input Data

2

93.00 ft

25.00 ft

Girder plate sizes Top flange Width Thickness

(inch x inch) 14.00 1.250 in.

Bottom flange Width Thickness

(inch x inch) 16.00 1.500 in.

Web Height Thickness

(inch x inch) 48.00 0.625 in.

Stresses (Strength I) Total positive Top flange Bottom flange

(ksi) -11.24 9.48 ksi

Total negative Top flange Bottom flange

(ksi) 12.14 -10.24 ksi

Stresses (Service II) Total positive Top flange Bottom flange

(ksi) -8.45 7.16 ksiTotal negative Top flange Bottom flange

(ksi) 9.49 -7.92 ksi

Resistance factors Flexural specified ff 1.00 (LRFD Art. 6.5.4.2; Default =1.0)

Shear specified fv 1.00 (LRFD Art. 6.5.4.2; Default =1.0)

Axial compression specified fc 0.90 (LRFD Art. 6.5.4.2; Default =0.9)

Fracture of tension members fu 0.80 (LRFD Art. 6.5.4.2; Default =0.8)

Yielding of tension members fy 0.95 (LRFD Art. 6.5.4.2; Default =0.95)

Bolts bearing on material fbb 0.80 (LRFD Art. 6.5.4.2; Default =0.8)

Flange plate general Top flange Bottom flange

Reduction factor for hybrid girders Rh 1.00 1.00 (LRFD Art. 6.10.1,10.1; For ho

Specific minimum yield strength of the flange Fyf 50.00 50.00 (LRFD Table 6.4.1-1, For gradeSpecific ultimate strength of the flange Fu 65.00 65.00 (LRFD Table 6.4.1-1, For grade

Factor for flange splice design a 1.00 1.00 (LRFD Art. 6.13.6.1.4c; Defaul

Splice bolt general Bolt material 1 (AASHTO M164 [ASTM A325] = 1 or AASHTO M

Bolt Shear Design Strength (ksi) 36.50

Bolt size db 0.875 in.

Hole size dh 1.000 in. (LRFD Table 6.13.2.4.2-1, for standard hole =

Hole size factor Kh 1.00 (LRFD Table 6.13.2.8-2)

Number of slip planes per bolt Ns 2 LRFD Art. 6.13.2.8)

Surface condition factor Ks 0.50 (LRFD Table 6.13.2.8-3)

Min. required bolt tension Pt (kips) 39.00 (LRFD Table 6.13.2.8-1)

Bottom splice design Width Thickness Number

Splice outside plate (inch x inch) 16.00 0.63 1 in.

Splice inside plate (inch x inch) 7.25 0.63 2 in.

Filler plate (inch x inch) 16.00 0.25 in.

Number of bolt row 4

minimum yield strength of splice plates (ksi) 50

Reduction Factor, U 1

Total number of bolt used for each side 24 (after design)

Top splice design Width Thickness Number

Splice outside plate (inch x inch) 14.00 0.50 1 in.

Splice inside plate (inch x inch) 6.25 0.50 2 in.

Filler plate (inch x inch) 14.00 0.50 in.

Number of bolt row 4

Total number of bolt used for each side 20 (after design)

Web splice design Height Thickness Number

Web splice plate (inch x inch) 39.00 0.500 2

No of vertical rows of bolts for each side m 3

Current span number

Current span length (in feet)

Distance from left support to splice on the current span (in feet)


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Splice Design - LRFD/LFD

COMPUTATION SHEET Page ........ of .........

Made By : C. C. Fu, Ph.D., P.E.

Subject :ROUTE 1 OVER CONRAIL Date :

Splice Design Checked By :

S-1 No. 1 Splice Date :

Splice Design for Maximum Positive

25.00 ft

93.00 ft

span 1

Splice at span2

ft

ft

Stresses

ksi

-11.24 9.48 12.14 -10.24

Actual Factored Stresses (ksi) (Strength I)

Total Positive

Bolt Shear Design Strength = 36.50

Actual Factored Stresses (ksi) (Service II)

Total Positive Total Negative

Top Flange

Total Negative

Top Flange Bottom Flange Top Flange Bottom Flange

Bottom Plate 16.00 1.500

Web Plate 48.00 0.625

Width, in Thickness, in

Top Plate 14.00 1.250

Plate Sizes

Distance from left support

Top flange plate

25.00

Span No. 2

Span Length 93.00

14 in x 1.25 in

16 in x 1.5 inBottom flange plate

Web plate 48 in x 0.625 in

Bottom Flange Top Flange Bottom Flange

-8.45 7.16 9.49 -7.92

176768463.xls.ms_office printed on 10/1/2013 @ 6:49 PM 6 of 23


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1. Flange Allowable Stress/ Force

1.A: Top flange Flange: Top

fcf= -11.24 ksi

Rh = Reduction factor for hybrid girders (AASHTO LRFD 6.13.6.1.4C)

Rh = 1.00 (or AASHTO Std 10.53.1.2)

Fyf= Specific minimum yield strength of the flange

Fyf= 50.00 ksi Fu = 65.00 ksi

a = Factor for flange splice design a = 1.00

ff= Resistance factor for flexural specified ff= 1.00 for flexural

Fcf= Design strength for the controlling flange at a point of splice

Fcf= 1/2(|fcf/Rh|+affFyf) (AASHTO LRFD 6.13.6.1.4C-1)

Fcf= 30.62 ksi (or AASHTO Std 10-4b)

OR

Fcf= 0.75affFyf (AASHTO LRFD 6.13.6.1.4C-1)

Fcf= 37.50 ksi (governs) (or AASHTO Std 10-4b)

1.B: Bottom flange Flange: Top

fncf=

fncf= 9.48 ksi

Rcf= Absolute value of the ratio of Fcf to fcf for the controlling flange

Rcf= |Fcf/fcf|

Rcf= 3.34


Fyf= 50.00 ksi Fu = 65.00 ksi



Fncf= Design stress for the non-controlling flange at apoint of spliceFncf= Rcf(|fncf/Rh|) (AASHTO LRFD 6.13.6.1.4C-3)

Fncf= 31.63 ksi (or AASHTO Std 10-4c)

OR

Fncf= 0.75affFyf (AASHTO LRFD 6.13.6.1.4C-3)

Fncf= 37.50 ksi (governs)

Flexural stress due to the factored loads at the mid-thickness of the non-controlling flange at a point

of splice concurrent with fcf

fcf= Maximum elastic flexural stress due to the factored loads at the mid-thickness of the controlling flange at

the point of splice



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2. Design force for the flange at a point of splice

2.A: Top Flange in compression and in control Flange: Top

0.875 in. 4

1.00 in.

Ag = gross area of Top flange = 17.50 in2

An = net area of the flange (AASHTO LRFD 6.8.3 orStd 10.16.4)

An = Ag - # bolt row *dh*t= (


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3. Calculate numbers of bolts on top and bottom flanges

3.A: Top Splice in compression and in control Flange: Top

Outside Plate : 1 PL - 14 in x 0.5 in

Inside Plate : 2 PL - 6.25 in x 0.5 in

Fu = 65.00 ksi Fyf= 50.00 ksi

Fy = Specific minimum yield strength of splice plates Fy = 50.00 ksi

Pcf= 656.25 Kips Ae,req = 13.13 in2

fu = resistance factor for fracture of tension members = 0.80

fy = resistance factor for yielding of tension members = 0.95

fc = resistance factor for axial compression = 0.90

U = Reduction Factor 1.00 AASHTO LRFD 6.13.5.2

Ag = gross ares of top splice plates = 13.25 in2

An = net area of splice plates (AASHTO LRFD 6.8.3 orStd 10.16.4)



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Ag = gross ares of bottom splice plates = 19.06 in2




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Check for slip critical connection:

7.16 ksi

171.84 kips

1.00

Number of slip planes per bolt = Ns = 2.00

Surface conditiion factor = Ks = 0.50

Min. required bolt tension = Pt = 39.00 kips

Flange slip resistance = Rr= 39.00 kips

Case (3) - Min. # of bolts to prevent slip 4.41 bolts

Min. # of bolts to use from all cases= 19.24 boltsUse 20 bolts each side for bottom splice OK

4. Design force on web

4A: Design force due to moment

48 in x 0.625 in

Rh = 1.00 Fcf= 37.50 ksi

Rcf= 3.34 fncf= 9.48 ksi

Muw =

Muw = twD2/12*|RhFcf-Rcffncf| (AASHTO LRFD C6.13.6.1.4b-1)

Muw = 704.63 kips-in. (AASHTO Std 10-4l)

Muw = 58.719 kips-ft

Bolt diameter = db = 0.875 in.

Bolt Area = Ab = pdb2/4 = 0.60 in

2

Bolt strength (double shear) = 0.6Fu*2*Ab = 43.90 kips

Bolt strength (bearing) Rr= fbbRn = fbb*(2.4*Fu*db*tw) (AASHTO LRFD 6.13.2.9)

fbb = bolt bearing on material = 0.80 (AASHTO LRFD 6.5.4.2)

Rr= 68.25 kips

Huw = Horizontal design force resultant in the web at a point of spliceHuw = twD/2*(RhFcf+Rcffncf) (AASHTO LRFD C6.13.6.1.4b-2)

Huw = 1036.92 kips (AASHTO Std 10-4m)

Web Plate =

Design moment at the point of splice representing the portion of the flexural moment assumed to

be resisted by the web

Design Stress= Fs = fs/Rh =

Design Force = Ps = Fs*Ag =

Hole size factor = Kh =



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4B: Design force due to shear

Vu = LRFD Max. Shear Table 1.2.22.16

Vu = 240.51 Kips

Vn = Unstiffened or Stiffened Shear Capacity

Vn = 671.60 Kips

Vr= fvVn = 1.0*Vn = 671.60 kips

Vuw = Design shear in the web at the point of splice

Vuw = 1.5*Vu = 360.77 kips (Vu0.5Vr) (AASHTO Std 10-4i & 10-4j)

e =

e = 4.88 in.

Muv = Design Moment due to the eccentricity of the design shear at the point of splice

Muv = Vuw*e

Muv = 146.56 Kips-ft

Mtotal = Total design moment ( due to web flexure and eccentricity )

Mtotal = Muv+Muw = 205.28 Kips-ft

m = no. of vertical rows of bolts = 3

n = no. of bolts in one vertical row = 13

s = the vertical pitch = 3.00 in.

g = the horizontal pitch = 3.00 in.

Ip = nm/12*[s2(n

2-1)+g

2(m

2-1)] = 5148.00 in

4 (AASHTO LRFD C6.13.6.1.4b-3)

Ps = Vuw/Nb = Vuw/(n*m) = 9.25 Kips

PH = Huw/Nb = Huw/(n*m) = 26.59 Kips

x= 3.0 in.

y= 18.0 in.

PMV = Mtotal*x/Ip = 1.44 Kips

PMH = Mtotal*y/Ip = 8.61 Kips

Pr=

Pr= 36.79 Kips < Pvb = 43.90 kips OK

(Ps + PMV)2

+ (PH + PMH)2

Distance from the centerline of the splice to the centroid of the connection on the side of the joint

under consideration



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5.Check flexural yielding of the web splice plates:

2 PL - 39 in x 0.5 in

253.50 in3

39.00 in2

(Mvu+Muw)/Spl+Huw/Apl < Fy

36.31 ksi < Fy = 50.00 ksi

6. Check the factor resistance shear, (AASHTO LRFD 6.13.5.3)

(AASHTO Std 10.48.8)

Vuw < Rr= fvRn = fv*0.58Apl.Fy (AASHTO LRFD 6.13.5.3-2 or Std 10-115)fv = 1.00 (AASHTO LRFD 6.5.4.2)

Vuw = 456.06 kips

1131.00 kips

Vuw = 456.06 kips < Rr= 1131.00 kips OK

2

# of platest, in.

0.500

Rr = fv*0.58Apl.Fy =

Apl = 2*t*d =

Spl = 2*t*d2/6 =

Web Splice Plate =

(Mvu+Muw)/Spl+Huw/Apl=

Plate d, in.

39.00



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Splice Design for Maximum Negative

25.00 ft

93.00 ft

span 1

Splice at span2

ft

ft

Stresses

ksi

16 in x 1.5 inBottom flange plate

Web plate 48 in x 0.625 in

Plate Sizes

Bottom Plate 16.00 1.500

Width, in

14 in x 1.25 in

25.00

Thickness, in

Distance from left support

Top flange plate

Span No. 2

Span Length 93.00

Top Plate 14.00 1.250

Web Plate 48.00 0.625

Actual Factored Stresses (ksi) (Strength I)



-11.24 9.48 12.14 -10.24


Bolt Shear Design Strength = 36.50

Actual Factored Stresses (ksi) (Service II)


-7.92-8.45 7.16 9.49



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1. Flange Allowable Stress/ Force

1.A: Top flange Flange: Top

fcf=

fcf= 12.14 ksi

Rh = Reduction factor for hybrid girders (AASHTO LRFD 6.13.6.1.4C)

Rh = 1.00 (or AASHTO Std 10.53.1.2)


Fyf= 50.00 ksi Fu = 65.00 ksi


ff= Resistance factor for flexural specified ff= 1.00 for flexuralFcf= Design strength for the controlling flange at a point of splice

Fcf= 1/2(|fcf/Rh|+affFyf) (AASHTO LRFD 6.13.6.1.4C-1)

Fcf= 31.07 ksi (or AASHTO Std 10-4b)

OR

Fcf= 0.75affFyf (AASHTO LRFD 6.13.6.1.4C-1)

Fcf= 37.50 ksi (governs) (or AASHTO Std 10-4b)

1.B: Bottom flange

fncf=

fncf= -10.24 ksi

Rcf= Absolute value of the ratio of Fcf to fcf for the controlling flange

Rcf= |Fcf/fcf|

Rcf= 3.09


Fyf= 50.00 ksi Fu = 65.00 ksi



Fncf= Design stress for the non-controlling flange at apoint of splice

Fncf= Rcf(|fncf/Rh|) (AASHTO LRFD 6.13.6.1.4C-3)

Fncf= 31.63 ksi (or AASHTO Std 10-4c)

OR

Fncf= 0.75affFyf (AASHTO LRFD 6.13.6.1.4C-3)

Fncf= 37.50 ksi (governs)

Flexural stress due to the factored loads at the mid-thickness of the non-controlling flange at a

point of splice concurrent with fcf

Maximum elastic flexural stress due to the factored loads at the mid-thickness of the controlling

flange at the point of splice



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2. Design force for the flange at a point of splice

2.A: Top Flange in tension and in control Flange: Top

0.875 in. 4

1.00 in.

Ag = gross area of Top flange 17.50 in2

An = net area of the flange (AASHTO LRFD 6.8.3 orStd 10.16.4)

An = Ag - # bolt row *dh*t = (


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3. Calculate numbers of bolts on top and bottom flanges

3.A: Top Splice in tension and in control Flange: Top

Outside Plate : 1 PL - 14 in x 0.5 in


Fu = 65.00 ksi Fyf= 50.00 ksi


Pcf= 513.16 Kips Ae,req = 10.26 in2





Ag = gross ares of top splice plates = 13.25 in2




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Check if bolts carry loads pass through fillers 0.25 inches or more in thickness:

Option (1): Reduction Factor Approach14.00 in. 0.50 in.

Af= gross area of filler = 7.00 in2

Ap= smaller of either the girder flange of the splice plate areas= 17.50 in2

g= 0.40 R= 0.78

Reduced Bolt Strength 34.14 kips

Case (2) - # Bolts required = Pcf/Reduc 15.03 bolts

Option (2): Extended Filler Plate


Design Stress= Fs = fs/Rh = 9.49 ksi

Design Force = Ps = Fs*Ag = 166.08 kips

Hole size factor = Kh = 1.00






Min. # of bolts to use from all cases= 15.03 boltsUse 16 OK

3.B: Bottom Splice in compression and in noncontrol Flange: Bottom

Outside Plate : 1 PL - 16 in x 0.625 in Use the same width


Fu = 65.00 ksi Fyf= 50.00 ksi


Pncf= 900.00 kips Ag,req = 18.00 in2





bolts each side of top splice

Filler thickness =

Reduce by the web and clearence for the weld

Plate Width, in Thickness, in # of plates

Filler width =

16.00 0.625 1

Inside Plate : 7.25 0.625 2

Outside Plate :



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Ag = gross ares of bottom splice plates = 19.06 in




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Design Stress= Fs = fs/Rh = -7.92 ksi

Design Force = Ps = Fs*Ag = -190.08 kips

Hole size factor = Kh = 1.00






Min. # of bolts to use from all cases= 23.43 bolts

Use 24 bolts each side for bottom splice OK

4. Design force on web

4A: Design force due to moment

48 in x 0.625 in

Rh = 1.00 Fcf= 37.50 ksi

Rcf= 3.09 fncf= -10.24 ksi

Muw =

Muw = twD2/12*|RhFcf-Rcffncf| (AASHTO LRFD C6.13.6.1.4b-1)

Muw = 8295.72 kips-in. (AASHTO Std 10-4l)

Muw = 691.310 kips-ft

Bolt diameter = db = 0.875 in.

Bolt Area = Ab = pdb2/4 = 0.60 in

2

Bolt strength (double shear) = 0.6Fu*2*Ab = 43.90 kips

Bolt strength (bearing) Rr= fbbRn = fbb*(2.4*Fu*db*tw) (AASHTO LRFD 6.13.2.9)

fbb = bolt bearing on material = 0.80 (AASHTO LRFD 6.5.4.2)

Rr= 68.25 kips

Huw = Horizontal design force resultant in the web at a point of splice

Huw = twD/2*(RhFcf+Rcffncf) (AASHTO LRFD C6.13.6.1.4b-2)

= 88.04 kips (AASHTO Std 10-4m)

Design moment at the point of splice representing the portion of the flexural moment assumed to

be resisted by the web

Web Plate =



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4B: Design force due to shear

Vu = LRFD Max. Shear Table 1.2.22.16

Vu = 240.51 Kips

Vn = Unstiffened or Stiffened Shear Capacity

Vn = 671.60 Kips

Vr= fvVn = 1.0*Vn = 671.60 kips

Vuw = Design shear in the web at the point of splice

Vuw = 1.5*Vu = 360.77 kips (Vu0.5Vr) (AASHTO Std 10-4i & 10-4j)

e =

e = 4.88 in.

Muv = Design Moment due to the eccentricity of the design shear at the point of splice

Muv = Vuw*e

Muv = 146.56 Kips-ft

Mtotal = Total design moment ( due to web flexure and eccentricity )

Mtotal = Muv+Muw = 837.87 Kips-ft

m = no. of vertical rows of bolts = 3

n = no. of bolts in one vertical row = 13

s = the vertical pitch = 3.00 in.

g = the horizontal pitch = 3.00 in.

Ip = nm/12*[s2(n

2-1)+g

2(m

2-1)] = 5148.00 in

4 (AASHTO LRFD C6.13.6.1.4b-3)

Ps = Vuw/Nb = Vuw/(n*m) = 9.25 Kips

PH = Huw/Nb = Huw/(n*m) = 2.26 Kips

x= 3.00 in.

y= 18.00 in.

PMV = Mtotal*x/Ip = 5.86 Kips

PMH = Mtotal*y/Ip = 35.16 Kips

Pr=

Pr= 40.35 Kips < Pvb = 43.90 kips OK

Distance from the centerline of the splice to the centroid of the connection on the side of the joint

under consideration

(Ps + PMV)2

+ (PH + PMH)2



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5.Check flexural yielding of the web splice plates:

2 PL - 39 in x 0.5 in

253.50 in3

39.00 in2

(Mvu+Muw)/Spl+Huw/Apl < Fy

(Mvu+Muw)/Spl+Huw/Apl= 41.92 ksi < Fy = 50.00 ksi

6. Check the factor resistance shear, (AASHTO LRFD 6.13.5.3)

(AASHTO Std 10.48.8)

Vuw < Rr= fvRn = fv*0.58Apl.Fy (AASHTO LRFD 6.13.5.3-2 or Std 10-115)fv = 1.00 (AASHTO LRFD 6.5.4.2)

Vuw = 456.06 kips

1131.00 kips

Vuw = 456.06 kips < Rr= 1131.00 kips OK

Plate # of platesd, in. t, in.

2

Rr= fv*0.58Apl.Fy =

Apl = 2*t*d =

Spl = 2*t*d2/6 =

39.00

Web Splice Plate =

0.500

Documents

Copy of Splice LRFD-LFD Design