Mathcad - D1

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Client - EPSTEINProject - Alpina Foods LLCJob No - 11128Calc No - Detail-1

Date - 11.17.2011Calc By - PSChk By - SN

BRACE CONNECTION DETAIL-1 (Connection along Grid B and @ Grid 2.5 at Enlarged roof framing level)

LOADS:- Vertical Shear Force Axial Force (Ten / Comp)

Beam W18x55 V1 15kip:= (Factored) Fa1 70kip:= (Factored)Brace 2L 7x4x3/8

(LLBB)Fb1 135kip:= (Factored)

3"

3"

3"

3"

212"

3"

3"

3"

3"11 2

"

11 2

"

1'-9" (MIN)

3"

3"3"3"3"

3"

13

4"

2" 3" 2"

1'-6

"

12"

1" DIA A490 SC-TYPE (CLASS-A) BOLTS

BOLTS IN STD HOLES

2L7x4

x3/8

LLB

B

W

12x65

W18x55

1/2" THK GUSSET PLATE

12"

(3/4"x3/4" CLIP CORNER)

5/8" THK SHEAR TAB

5/16

5/16

2L 7x4x3/8 LLBB

135ki

p

55

110.

58k

ip

77.43 kip

DETAIL-1

SECTION B-B

5/8" THK STIFFENER PLATE






1/4

1/4

1/2

1/2(FLG)

(3/8)

3/8

1/4

(1/4)

(FLG)3/8

3/8

1/4

1/4

(CJP)

W18x55

1/2" THK GUSSET PLATEGUSSET C/L IN LINE WITH THE BEAM C/L

SECTION A-A

B

3"

3"

3"

3"

3"

1

5

8"

B

12"

12"

A

A

SHEAR TAB TO BE SLOTTED TO

SUIT STIFFENER

CUT FLUSH N/S AND F/S BEAM FLANGES

(MAX)

CUT FLUSH N/S AND F/S BEAM FLANGES

(SLOPED)

1"

JOIST THIS SIDE

3"

13

4"

3/4" A325 SC-TYPE (CLASS-A) BOLTS

BOLTS IN STD HOLES

5/165/16 (3 SIDES)

(3 SIDES)5/16

5/16

1"

Notes :-

1. Connection Design confirming to AISC 13th Edition LRFD

2. All Main steel W-Section are Grade A992 Fy50

3. All Connection material are Grade A36 Fy36

4. All welds are electrode class E70xx

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BRACE CONNECTION DETAIL-1 (Connection along Grid B and @ Grid 2.5 at Enlarged roof framing level)

LOADS:- Vertical Shear Force Axial Force (Ten / Comp)

Beam W18x55 V1 15kip:= (Factored) Fa1 70kip:= (Factored)Brace 2L 7x4x3/8

(LLBB)Fb1 135kip:= (Factored)

SECTION PROPERTIES:-

Beam W18x55

db1 18.1in:= bfb1 7.53in:= tfb1 0.630in:= twb1 0.390in:= kb1 1.3125in:= k1b1 0.8125in:= Zxx1 112in3

:=

Column W12x65

dc1 12.1in:= bfc1 12in:= tfc1 0.605in:= twc1 0.390in:= kc1 1.5in:= k1c1 1in:= Zxx2 96.8in3

:=

Brace 2L 7x4x3/8 (LLBB)

dbr 7in:= bbr 4in:= tbr 0.375in:= Abr 7.96in2

:=MATERIAL PROPERTIES:-

Yield strength of ASTM Grade A992

materialfy50 50ksi:= Shear strength of ASTM Grade

A325 boltfnv 48ksi:=

Ultimate strength of ASTM Grade A992

materialfu50 65ksi:= Tensile strength of ASTM Grade

A325 boltfnt 90ksi:=

Yield strength of ASTM Grade A36

materialfy36 36ksi:= Minimum bolt pre-tension for

3/4" A325 boltTub1 28kip:=

Ultimate strength of ASTM Grade A36

materialfu36 58ksi:= Minimum bolt pre-tension for 1"

A490 boltTub2 64kip:=

Strength of weld for E70xx electrode fw 70ksi:=

DESIGN CALCULATION

Check for slip critical capacity of bolts in brace :-

Bolt diameter d1 0.75in:=

Bolt Grade ASTM Grade = A325

Bolted Connection type Connection = Slip Critical Type (Class-A)

Hole type in brace leg and gusset plate Type = STD Holes

Dia. of bolt hole (in brace) dh1 0.8125in:=

Dia of bolt hole (In gusset plate) dh2 0.8125in:=

End distance end1 1.5in:=

Bolt gage on the leg g1 2.5in:=

Bolt gage on the leg g2 3in:=

Edge distance edg1 7in g1 g2+( ):= edg1 1.50 in=Bolt spacing Sbg 3in:=

Mean slip co-effecient for Class-A surfaces 0.35:=

Ratio of mean installed bolt pretension

to the specified minimum bolt pretension

Du 1.13:=

Hole factor (For STD Holes) hsc 1:=

Number of slip planes Nsb 2:=

Slip resistance offered by one

3/4" A325 SC Type - (Class A) boltRslip1

Du hsc Nsb Tub1

1.0:= Rslip1 22.15 kip=

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No. of 3/4" A325 SC Type - (Class A) bolts

requiredNb

Fb1

Rslip1

:= Nb 6.10=

Provide 4 rows x 2 columns (Total of 8 Nos.) of 3/4" A325 SC Type - (Class A) Bolts @ 3" Spacing

Check for tension capacity of brace member :-

No. of bolt rows in brace member leg Nr 4:=

Length of the connection Lc Nr 1( ) Sbg:= Lc 9.00 in=

Distance of C.G of the brace angle

to the bolt connection C.Gx1 g1 g2+( ) 2.35in:= x1 3.15 in=

Shear lag factor U 1x1

Lc

:= U 0.65=

Gross tension capacity of the brace Ftgb 0.9 Abr fy36:= Ftgb 257.90 kip=

Net tension capacity of the brace Ftnb U Abr 4 dh11

16in+

tbr

0.75 fu36:= Ftnb 187.96 kip=

Minimum capacity of brace member

in tensionFtb min Ftgb Ftnb,( ):= Ftb 187.96 kip=

F.tb (187.97 kip) > F.b1 (135.01 kip): Therefore O.K.

Check for block shear capacity of brace member :-

No. of bolt columns in brace member leg Nc 2:=

Gross shear area Agv1 Nr 1( ) Sbg end1+ tbr:= Agv1 3.94 in2

=

Net shear area Anv1 Nr 1( ) Sbg end1+ Nr 0.5( ) dh1 116 in+

tbr:= Anv1 2.79 in2=

Net tension area Ant1 g2 edg1+ Nc 0.5( ) dh11

16in+

tbr:= Ant1 1.20 in2

=

Ubs 0.5:= (Tension stress concentration is Non-Uniform, Refer J.4.3 AISC 13th Ed)

Block shear capacity Fblock1 2 min 0.45 Agv1 fy36( ) 0.45 Anv1 fu36( ), 0.75 Ubs Ant1 fu36+:=

F.block1 (179.58 kip) > F.b1 (135.01 kip): Therefore O.K.Fblock1 179.57 kip=

Check for block shear capacity of gusset plate :-

Thickness of the gusset plate tg 0.5in:=

Gross shear area Agv2 2 Nr 1( ) Sbg end1+ tg:= Agv2 10.50 in2

=

Net shear area Anv2 2 Nr 1( ) Sbg end1+ Nr 0.5( ) dh21

16in+

tg:= Anv2 7.44 in2

=

Net tension area Ant2 g2 dh21

16in+

tg:= Ant2 1.06 in2

=

Ubs 1:= (Tension stress concentration is Uniform, Refer J.4.3 AISC 13th Ed)

Block shear capacity Fblock2 min 0.45 Agv2 fy36( ) 0.45 Anv2 fu36( ), 0.75 Ubs Ant2 fu36+:=F

block2216.32 kip=

F.block2 (216.33 kip) > F.b1 (135.01 kip): Therefore O.K.

Check for compression capacity of gusset plate :-

Max effective length for out of plane buckling Leff 18in:=

Effective length factor k1 0.75:=

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Minimum radius of gyration rtg

2

12:= r 0.14 in=

Slenderness ratio k1

Leff

r:= 93.53=

Modulus of elasticity E 29000ksi:=

Elastic critical buckling stress fe

2E

2

:= fe 32.72 ksi=

Compressive strength Fcs 0.658

fy36

fe

fy36 fe 0.44 fy36if

0.877 fe( ) fe 0.44 fy36if

:= Fcs 22.71 ksi=

Max available dispersion length Wd tan 30deg( ) Nr 1( ) Sbg 2 g2+:= Wd 13.39 in=Compression capacity of gusset plate Fcg 0.9 Wd tg Fcs:= Fcg 136.89 kip=

Fcg (136.89 kip) > F.b1 (135.01 kip): Therefore O.K.

Check for tension capacity gusset plate :-

Effective width of gusset plate Wd tan 30deg( ) Nr 1( ) Sbg 2 g2+:= Wd 13.39 in=Gross area of the gusset plate in tension Ag2 Wd tg:= Ag2 6.70 in

2=

Net area of the gusset plate in tension An2 tg Wd 2 dh2 116in+

:= An2 5.82 in2=

Tension capacity of gusset plate Ftg min 0.9 Ag2 fy36 0.75 An2 fu36,( ):= Ftg 216.96 kip=

F.tg (216.97 kip) > F.b1 (135.01 kip): Therefore O.K.

Check for bearing / tearing capacity of brace member and gusset plate :-

Bearing capacity at the brace member Fbear1 0.75 2.4 d1 2 tbr Nr Nc fu36:= Fbear1 469.80 kip=

Bearing capacity at gusset plate Fbear2 0.75 2.4 d1 tg Nr Nc fu36:= Fbear2 313.20 kip=

Tear out due to extreme bolt at

gusset plateF

tear12 0.75 1.2 e

nd1

dh2

2

t

g f

u36:= F

tear157.09 kip=

Tear out due to intermediate bolts at

gusset plateFtear2 2 0.75 1.2 Sbg dh2( ) Nr 1( ) tg fu36:= Ftear2 342.56 kip=


brace memberFtear4 2 0.75 1.2 end1

dh1

2

2 tbr fu36:= Ftear4 85.64 kip=


brace memberFtear3 2 0.75 1.2 Sbg dh1( ) Nr 1( ) 2 tbr fu36:= Ftear3 513.84 kip=

Bearing Capacity of the

connectionFbc1 min min Ftear1 Ftear2+( ) Ftear3 Ftear4+( ), min Fbear1 Fbear2,( ),:=

F.bc1 (313.22 kip) > F.b1 (135.01 kip): Therefore O.K.Fbc1 313.20 kip=

To determine beam to gusset and column to gusset interface forces due to brace axial force(Uniform Force Distribution Method) :-

Angle of inclination of the brace

with respect to horizontal1 55deg:=

Length of weld B/W gusset and beam flange Lw1 21in:=

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12in:=

eb

db1

2

:= eb 9.05 in=

ec 0in:= ec 0.00 in=

eb tan 90deg 1( ) ec tan 90deg 1( )+:= 14.74 in=

r ec+( )2

eb+( )2

+:= r 25.70 in=

Vertical shear acting on the gusset and

column interfaceVc

rFb1:= Vc 63.04 kip=

Axial force acting on the gusset and

column interfaceHc

ec

rFb1:= Hc 0.00 kip=

Vertical shear acting on the gusset andbeam interface Vb

eb

r Fb1:= Vb 47.54 kip=

Axial force acting on the gusset and

beam interfaceHb

rFb1:= Hb 77.43 kip=

To check the weld B/W the gusset plate and the beam flange :-

Distance of the weld C.G from dd Lw1

2 1in

bfc1 twc1

2+

:= dd 2.6 in=

Moment on the weld (Since the Vb was

transfered to the gusset to column interface)Me1 Vb := Me1 700.8 kip in=

Shear force per mm on the fillet weld fsw1

Hb

2 Lw1:= fsw1 1.8 kipin

=

Tensile force per mm on the fillet weld

due to Vbftw1

Vb

2 Lw1:= ftw1 1.1

kip

in=

Tensile force per mm on the fillet weld

due to Moment Me1ftmw1

6Me1

2 Lw12

:= ftmw1 4.8kip

in=

Peak stress per mm on weld fpeak ftw1 ftmw1+( )2

fsw12

+:= fpeak 6.18kip

in=

Average stress per mm on weld favgftw1 ftmw1+( )

2fsw1

2

+ ftw1 ftmw1( )2

fsw12

++

2:=

favg 5.13kip

in=

2 atanftw1 ftmw1+( )

fsw1

:= 2 72.64 deg=

Resultant shear per mm on weld Rw max fpeak favg 1.25,( ):= Rw 6.41kip

in=

Size of fillet weld required Sw1

Rw

0.45 0.707 fw 1 0.5 sin 2( )1.5

+

:= Sw1 0.20 in=

Provide a minimum fillet weld of 1/4" B/W the gusset plate and the beam flange

Check for bolts B/W beam web and the shear tab :-

Bolt diameter d2 1in:=

Bolt type (SC-Type / N-Type) Type = SC

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Hole type in member web Type = STD Holes

Hole type in shear tab Type = STD Holes

End distance end 1.625in:= (minimum)

Edge distance edg 2in:=

Bolt spacing Sbg 3in:=

Dia. of bolt hole (In member web) dh1 1.0625in:=

Dia. of bolt hole (In shear tab) dh2 1.0625in:=

Shear tab thickness tsp 0.625in:=

No. of bolt rows Nr2 6:=

No. of bolt columns Nc2 2:=

End clearance ec 1in:=

Bolt gage on the shear tab gc 3in:=

Mean slip co-effecient for Class-A surfaces 0.35:=


to the specified minimum bolt pretensionDu 1.13:=




1" A490 SC Type - (Class A) bolt

Rslip2

Du hsc Nsb Tub2

1.0:= Rslip2 25.31 kip=

Eccentricity of the bolt group C.G

measured from the column webecc1

bfc1 tfc1

2ec+ edg+

gc

2+:= ecc1 10.20 in=

Polar bolt group modulus /

unit area of the boltIbg 342in

2:=

Vertical distance of the outermost bolt

from the bolt group C.Gymax 7.5in:=

Horizontal distance of the outermost bolt

from the bolt group C.Gxmax 1.5in:=

Moment on the bolt group due to beam

shear force and eccentricity ecc1

Mbg V1 ecc1:= Mbg 152.96 kip in=

Vertical Shear force per bolt due to

shear force, V1fsv

V1

Nr2 Nc2:= fsv 1.25 kip=

Horizontal Shear force per bolt due to

beam axial force, Fa1fsh

Fa1

Nr2 Nc2:= fsh 5.83 kip=


moment, Mbg

fsvm

Mbg xmax

Ibg

:= fsvm 0.67 kip=


moment, Mbg

fshm

Mbg ymax

Ibg

:= fshm 3.35 kip=

Resultant shear force / bolt Rb fsv fsvm+( )2 fsh fshm+( )2+:= Rb 9.39 kip=

R.slip2 (25.31 kip) > R.b (9.39 kip): Therefore O.K.

Therefore the bolts B/W the beam web and shear tab are adequate

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Check for shear capacity of shear tab @ beam web :-

Gross shear area Agv Nr2 1( ) Sbg 2 end+ tsp:= Agv 11.41 in2

=

Net shear area Anv Nr2 1( ) Sbg 2 end+ Nr2 dh21

16in+

tsp:= Anv 7.19 in2=

Shear capacity Fshe min 0.6 Agv fy36 0.45 Anv fu36,( ):= Fshe 187.59 kip=

Fshe (187.6 kip) > V1 (15 kip): Therefore O.K.

Check for axial capacity of the shear tab @ beam web in tension :-

Gross tension area Atg Nr2 1( ) Sbg 2 end+ tsp:= Atg 11.41 in2

=

Net tension area Atn Nr2 1( ) Sbg 2 end+ Nr2 dh21

16in+

tsp:= Atn 7.19 in2

=

Tension capacity Fax min 0.9 Atg fy36 0.75 Atn fu36,( ):= Fax 312.66 kip=F.ax (312.67 kip) > F.a1 (70 kip): Therefore O.K.

Check for flexural capacity of the shear tab :-

Eccentricity from the column web face

to the first line of shear tab boltsecc2

bfc1 tfc1

2ec+ edg+:= ecc2 8.70 in=

Moment due to the eccentricity Mp V1 ecc2:= Mp 10.87 kip ft=

Length of the shear tab considered Lst Nr2 1( ) Sbg 2 end+:= Lst 18.25 in=

Critical flexural stress in presence of shear Fcr 0.9 fy36( )2 3V

1tsp Lst

2

:= Fcr 32.32 ksi=

Moment capacity of the shear tab

based on flexural yieldingMsy Fcr

tsp Lst2

4:= Msy 140.16 kip ft=

Net section modulus of the shear tab section Znet

tsp

4Lst

2Sbg

2Nr2 Nr2

21 dh2 0.0625in+( )

Lst

:=

Znet 33.84 in3

=


based on flexural rupture

Msr 0.75fu36 Znet:= Msr 122.66 kip ft=

Minimum capacity of the shear tab

in flexureMm min Msy Msr,( ):= Mm 122.66 kip ft=

M.m (122.66 kip ft) > M.p (10.87 kip ft): Therefore O.K.

To check the tension and flexural interaction of the shear tab @ beam web :-

Interaction Ratio RatioFa1

Fax

8

9

Mp

Mm

+

Fa1

Fax

0.2if

Fa1

2Fax

Mp

Mm

+

otherwise

:= Ratio 0.30=

Since the Interaction Ratio is less than '1', the shear tab is safe in tension and flexure interaction

Check for block shear capacity of shear tab @ beam web for vertical shear (V1) :-

Gross shear area Agv3 Nr2 1( ) Sbg end+ tsp:= Agv3 10.39 in2

=

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Net shear area Anv3 Nr2 1( ) Sbg end+ Nr2 0.5( ) dh21

16in+

tsp:= Anv3 6.52 in2

=

Net tension area Ant3 edg gc+( ) Nc2 0.5( ) dh2 116 in+ tsp:= Ant3 2.07 in2=


Block shear capacity Fblock3 min 0.45 Agv3 fy36( ) 0.45 Anv3 fu36( ), 0.75 Ubs Ant3 fu36+:=Fblock3 213.36 kip=

F.block3 (213.37 kip) > V1 (15 kip): Therefore O.K.

Check for block shear capacity of shear tab @ beam web for axial force :-

Gross shear area Agv4 edg gc+( ) tsp:= Agv4 3.13 in2

=

Net shear area Anv4 edg gc+( ) Nc2 0.5( ) dh21

16 in+

tsp:= Anv4 2.07 in

2

=

Net tension area Ant4 Nr2 1( ) Sbg end+ Nr2 0.5( ) dh21

16in+

tsp:= Ant4 6.52 in2

=


Block shear capacity Fblock4 min 0.45 Agv4 fy36( ) 0.45 Anv4 fu36( ), 0.75 Ubs Ant4 fu36+:=

F.block4 (192.52 kip) > F.a1 (70 kip): Therefore O.K.Fblock4 192.51 kip=

Shear and tension interaction for Block shear of shear tab at beam web :-

Interaction ratio for block shear Ratio Fa1Fblock4

2

V1Fblock3

2

+:= Ratio 0.37=

Since the Interaction Ratio is less than '1', the shear tab is safe in tension and shear

interaction for block shear

Check for shear capacity of beam web :-

Gross shear area Agv2 Nr2 1( ) Sbg 2 end+ twb1:= Agv2 7.12 in2

=

Net shear area Anv2 Nr2 1( ) Sbg 2 end+ Nr2 dh21

16in+

twb1:= Anv2 4.48 in2

=

Shear capacity Fshe2 min 0.6 Agv2 fy50 0.45 Anv2 fu50,( ):= Fshe2 131.19 kip=Fshe2 (131.19 kip) > V1 (15 kip): Therefore O.K.

Check for axial capacity of the beam web in tension :-

Gross tension area Atg2 Nr2 1( ) Sbg 2 end+ twb1:= Atg2 7.12 in2

=

Net tension area Atn2 Nr2 1( ) Sbg 2 end+ Nr2 dh21

16in+

twb1:= Atn2 4.48 in2

=

Tension capacity Fax2 min 0.9 Atg2 fy50 0.75 Atn2 fu50,( ):= Fax2 218.64 kip=

F.ax2 (218.65 kip) > F.a1 (70 kip): Therefore O.K.

Check for flexural capacity of the beam with top & bottom flange flushed on both sides of the web :-


to the second line of shear tab boltsecc3

bfc1 tfc1

2ec+ edg+ gc+:= ecc3 11.70 in=

Moment due to the eccentricity Mbw V1 ecc3:= Mbw 14.62 kip ft=

Length of the beam web considered Lbw db1:= Lbw 18.10 in=

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Critical flexural stress on beam web

in presence of shearFcrb 0.9 fy50( )

23

V1

twb1 Lbw

2

:= Fcrb 44.85 ksi=

Moment capacity of the beam web

based on flexural yieldingMsyb Fcrb

twb1 Lbw2

4:= Msyb 119.38 kip ft=

Net section modulus of the beam

web sectionZnetb

twb1

4Lbw

2Sbg

2Nr2 Nr2

21 dh2 0.0625in+( )

Lbw

:=

Znetb 20.49 in3

=

Moment capacity of the beam web

based on flexural ruptureMsrb 0.75fu50 Znetb:= Msrb 83.23 kip ft=

Minimum capacity of the beam web

in flexure Mmb min Msyb Msrb,

( ):=

Mmb 83.23 kip ft=

M.mb (83.24 kip ft) > M.bw (14.62 kip ft): Therefore O.K.

To check the tension and flexural interaction of the beam web :-

Interaction Ratio RatioFa1

Fax2

8

9

Mbw

Mmb

+

Fa1

Fax2

0.2if

Fa1

2Fax2

Mbw

Mmb

+

otherwise

:= Ratio 0.48=

Since the Interaction Ratio is less than '1', the beam web is safe in tension and flexure interactionCheck for block shear capacity of beam web for vertical shear (V1) :-

Gross shear area Agv5 Nr2 1( ) Sbg end+ twb1:= Agv5 6.48 in2

=


16in+


=

Net tension area Ant5 edg gc+( ) Nc2 0.5( ) dh11

16in+

twb1:= Ant5 1.29 in2

=


Block shear capacity Fblock5 min 0.45 Agv5 fy50( ) 0.45 Anv5 fu50( ), 0.75 Ubs Ant5 fu50+:=Fblock5 150.56 kip=

F.block5 (150.56 kip) > V1 (15 kip): Therefore O.K.

Check for block shear capacity of beam web for axial force (Fa1) :-

Gross shear area Agv6 edg gc+( ) twb1:= Agv6 1.95 in2

=

Net shear area Anv6 edg gc+( ) Nc2 0.5( ) dh11

16in+


=

Net tension area Ant6 Nr2 1( ) Sbg end+ Nr2 0.5( ) dh11

16

in+

twb1:= Ant6 4.07 in2

=



F.block6 (137.02 kip) > F.a1 (70 kip): Therefore O.K.Fblock6 137.01 kip=

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Shear and tension interaction for Block shear of beam web :-

Interaction ratio for block shear Ratio

Fa1

Fblock6

2V1

Fblock5

2

+:= Ratio 0.52=

Since the Interaction Ratio is less than '1', the beam web is safe in tension and shear

interaction for block shear

Check for bearing / tearing capacity of shear tab at beam web for shear force V1 :-

Bearing capacity at the beam web Fbear1 0.75 2.4 d2 twb1 Nr2 Nc2 fu50:= Fbear1 547.56 kip=

Bearing capacity at shear tab Fbear2 0.75 2.4 d2 tsp Nr2 Nc2 fu36:= Fbear2 783.00 kip=


shear tabFtear1 2 0.75 1.2 end

dh2

2

tsp fu36:= Ftear1 71.37 kip=

Tear out due to intermediate bolts atshear tab

Ftear2 2 0.75 1.2 Sbg dh2( ) Nr2 1( ) tsp fu36:= Ftear2 632.11 kip=


beam webFtear4 2 0.75 1.2 end

dh1

2

twb1 fu50:= Ftear4 49.91 kip=


beam webFtear3 2 0.75 1.2 Sbg dh1( ) Nr2 1( ) twb1 fu50:= Ftear3 442.04 kip=



F.bc2 (491.97 kip) > V.1 (15 kip): Therefore O.K. Fbc2 491.95 kip=

Check for bearing / tearing capacity of shear tab at beam web for axial force Fa1 :-

Bearing capacity at the beam web Fbear1 0.75 2.4 d2 twb1 Nr2 Nc2 fu50:= Fbear1 547.56 kip=



shear tabFtear1 0.75 1.2 edg

dh2

2

Nr2 tsp fu36:= Ftear1 287.51 kip=


shear tabFtear2 0.75 1.2 gc dh2( ) Nr2 tsp fu36:= Ftear2 379.27 kip=


beam webFtear4 0.75 1.2 edg

dh2

2

Nr2 twb1 fu50:= Ftear4 201.06 kip=


beam webFtear3 0.75 1.2 gc dh2( ) Nr2 twb1 fu50( ):= Ftear3 265.22 kip=



F.bc3 (466.3 kip) > F.a1 (70 kip): Therefore O.K.Fbc3 466.28 kip=

Check for weld B/W the shear tab on the beam web side and the column web :-

Length of weld available Lw2 15.5in:=

Shear force per inch on the weld fsw1

V1

2 Lw2:= fsw1 0.48

kip

in=

Size of fillet weld required sw1

fsw1

0.707 0.45 fw

:= sw1 0.02 in=

Provide a fillet weld of 5/16" B/W the shear tab and the column web

Check for weld B/W the shear tab on the beam web side and the top and bottom stiffeners :-

Length of weld available Lw3

bfc1 twc1

20.75in:= Lw3 5.05 in=

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Fa1

4 Lw3

Mbg

Lw2( ) 2 Lw3+:= fsw2 4.44

kip

in=


fsw2

0.707 0.45 fw:= sw2 0.20 in=

Provide a fillet weld of 5/16" B/W the shear tab on beam web side and the top and bottom stiffeners

Size of fillet weld B/W the shear tab and

the column web (for 16" of inch)Dw 5in:=

Minimum shear tab thickness required

for fillet weld size

Minimum column web thickness required

for fillet weld size

tsm

6.19 Dw

58:= tsm 0.53 in= tcm

3.09 Dw

65:= tcm 0.24 in=

Shear tab of 5/8" thk is safe for shear rupture strength of shear tab at weld

Check for bolts B/W gusset plate and the shear tab :-

Bolt diameter d2 1in:=

Bolt type (SC-Type / N-Type) Type = SC


Hole type in gusset plate Type = STD Holes

Hole type in shear tab Type = STD Holes

End distance end 1.75in:=

Edge distance edg 2in:=Bolt spacing Sbg 3in:=

Dia. of bolt hole (In gusset plate) dh1 1.0625in:=

Dia. of bolt hole (In shear tab) dh2 1.0625in:=

No. of bolt rows Nr3 7:=

No. of bolt columns Nc3 2:=

End clearance ec 1in:=

Bolt gage on the shear tab gc 3in:=

Mean slip co-effecient for Class-A surfaces 0.35

:=


to the specified minimum bolt pretensionDu 1.13:=




1" A490 SC Type - (Class A) boltRslip2

Du hsc Nsb Tub2

1.0:= Rslip2 25.31 kip=

Eccentricity of the bolt group C.G

measured from the column webecc1

bfc1 tfc1

2ec+ edg+

gc

2+:= ecc1 10.20 in=

Polar bolt group modulus /unit area of the bolt

Ibg 535.5in2:=

Vertical distance of the outermost bolt

from the bolt group C.Gymax 9in:=

Horizontal distance of the outermost bolt

from the bolt group C.Gxmax 1.5in:=

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Total shear force on gusset to

column web interfaceVtot Vb Vc+:= Vtot 110.59 kip=

Moment on the bolt group due to

shear force Vtotand eccentricity ecc1

M

bg2

V

tot

e

cc1

:= Mbg2

93.97 kip ft=


shear force, Vtot

fsv

Vtot

Nr3 Nc3:= fsv 7.90 kip=


brace horiz. componentfsh

Hc

Nr3 Nc3:= fsh 0.00 kip=


moment, Mbg2

fsvm

Mbg2 xmax

Ibg

:= fsvm 3.16 kip=


moment, M

bg2

fshm

Mbg2 ymax

Ibg

:= fshm 18.95 kip=

Resultant shear force / bolt Rb2 fsv fsvm+( )2

fsh fshm+( )2

+:= Rb2 21.94 kip=

R.slip2 (25.31 kip) > R.b2 (21.94 kip): Therefore O.K.

Therefore 7 rows x 2 column of 1" dia A490 SC-type (Class-A) bolts @ 3" spacing and at 3" gage B/W the

shear tab and gusset plate are adequate

Check for shear capacity of shear tab at gusset and column interface :-

Gross shear area Agv3 Nr3 1( ) Sbg 2 end+ tsp:= Agv3 13.44 in2

=


16

in+

tsp:= Anv3 8.52 in2

=

Shear capacity Fshe3 min 0.6 Agv3 fy36 0.45 Anv3 fu36,( ):= Fshe3 222.26 kip=Fshe3 (222.27 kip) > V.tot (110.59 kip): Therefore O.K.

Check for flexural capacity of the shear tab at gusset and column interface :-


to the first line of shear tab boltsecc2

bfc1 tfc1

2ec+ edg+:= ecc2 8.70 in=

Moment due to the eccentricity Mp2 Vtot ecc2:= Mp2 80.15 kip ft=

Total length of the shear tab Lst2 Nr3 1( ) Sbg 2 end+:= Lst2 21.50 in=

Critical flexural stress in presence of shear Fcr2 0.9 fy36( )2

3Vtot

tsp Lst2

2:= Fcr2 29.10 ksi=


based on flexural yieldingMsy2 Fcr2

tsp Lst22

4:= Msy2 175.13 kip ft=

Net section modulus of the shear tab section Znet2

tsp

4Lst2

2Sbg

2Nr3 Nr3

21 dh2 0.0625in+( )

Lst2

:=

Znet2 47.50 in3

=

Moment capacity of the shear tabbased on flexural rupture

Msr2 0.75fu36 Znet2:= Msr2 172.20 kip ft=

Minimum capacity of the shear tab

in flexureMm2 min Msy2 Msr2,( ):= Mm2 172.20 kip ft=

M.m2 (172.21 kip) > M.p2 (80.16 kip): Therefore O.K.

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Check for block shear capacity of shear tab for shear force Vtot :-

Gross shear area Agv7 Nr3 1( ) Sbg end+ tsp:= Agv7 12.34 in2

=


16in+

tsp:= Anv7 7.77 in2

=


16in+

tsp:= Ant7 2.07 in2

=



F.block7 (245.01 kip) > V.tot (110.59 kip): Therefore O.K.Fblock7 245.00 kip=

Check for shear capacity of gusset plate :-

Gross shear area Agv8 Nr3 1( ) Sbg 2 end+ tg:= Agv8 10.75 in2=


16in+

tg:= Anv8 6.81 in2

=

Shear capacity Fshe4 min 0.6 Agv8 fy36 0.45 Anv8 fu36,( ):= Fshe4 177.81 kip=

Fshe4 (177.82 kip) > V.tot (110.59 kip): Therefore O.K.

Check for block shear capacity of gusset plate for shear force Vtot :-

Gross shear area Agv9 Nr3 1( ) Sbg end+ tg:= Agv9 9.87 in2

=


16 in+

tg:= Anv9 6.22 in2

=


16in+

tg:= Ant9 1.66 in2

=



F.block9 (196.01 kip) > V.tot (110.59 kip): Therefore O.K.Fblock9 196.00 kip=

Check for bearing / tearing capacity of shear tab & gusset plate for shear force Vtot :-

Bearing capacity at the gusset plate Fbear1 0.75 2.4 d2 tg Nr3 Nc3 fu36:= Fbear1 730.80 kip=



shear tabFtear1 2 0.75 1.2 end

dh2

2

tsp fu36:= Ftear1 79.52 kip=


shear tabFtear2 2 0.75 1.2 Sbg dh2( ) Nr3 1( ) tsp fu36:= Ftear2 758.53 kip=


beam webFtear4 2 0.75 1.2 end

dh1

2

tg fu36:= Ftear4 63.62 kip=


beam webFtear3 2 0.75 1.2 Sbg dh1( ) Nr3 1( ) tg fu36:= Ftear3 606.82 kip=


connectionF

bc4min min F

tear1F

tear2+

( )F

tear3F

tear4+

( ), min F

bear1F

bear2,

( ),:=

F.bc4 (670.48 kip) > V.tot (110.59 kip): Therefore O.K. Fbc4 670.44 kip=

Check for weld B/W the shear tab on the gusset plate side and the column web :-

Length of weld available Lw4 Lst2 2 0.75 in:= Lw4 20.00 in=

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Vtot

2 Lw4:= fsw3 2.76

kip

in=


fsw3

0.707 0.45 fw:= sw3 0.12 in=

Provide a fillet weld of 5/16" B/W the shear tab and the column web


the column web (for 16" of inch)Dw 5in:=

Minimum shear tab thickness

required for fillet weld sizetsm

6.19 Dw

58:= tsm 0.53 in=


Shear capacity of the gusset plate at the beam to gusset plate weld :-

Length of weld B/W the gusset andthe beam flange

Lg Lw1:= Lg 21.00 in=

Gross shear capacity of the gusset plate Fsg 0.6 tg Lg fy36:= Fsg 226.80 kip=

F.sg (226.81 kip) > H.b (77.44 kip): Therefore O.K.

Moment capacity of the gusset plate at the beam to gusset weld :-

Critical flexural stress in presence of shear Fcr3 0.9 fy36( )2

3Hb

tg Lg

2

:= Fcr3 29.78 ksi=

Moment capacity of the gusset platebased on flexural yielding

Msy3 Fcr3

tg Lg2

4:= Msy3 136.78 kip ft=

M.sy3 (136.79 kip) > M.e1 (58.4 kip): Therefore O.K.

Check for weld B/W shear tab @ gusset side and middle / bottom most stiffener supporting the gusset :-

Moment on the weld group Me2 Vtot ecc1:= Me2 93.97 kip ft=

Length of weld available for shear tab

weld to stiffenerLw5

bfc1 twc1

20.75in:= Lw5 5.05 in=


Me2

Lw4( ) 2 Lw5:= fsw4 5.58

kip

in=


fsw4

0.707 0.45 fw:= sw4 0.25 in=

Provide a fillet weld of 5/16" B/W the shear tab on gusset plate side and the top and bottom stiffeners


the stiffener plate (for 16" of inch)Dw 5in:=

Minimum shear tab thickness

required for fillet weld sizetsm

6.19 Dw

58:= tsm 0.53 in=


Check for weld B/W the bottom most stiffener supporting the gusset plate with the column flange :-


bfc1 twc1

20.75in:= Lw6 5.05 in=


Me2

Lw4( ) 4 Lw6:= fsw5 2.79

kip

in=

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fsw5

0.707 0.45 fw:= sw5 0.13 in=

Thickness of bottom most stiffener tst1 0.625in:=Shear capacity of the stiffener Ftst1 0.6 Lw6 tst1 fy36:= Ftst1 68.24 kip=

Shear force on the stiffener Fsf1

Me2

Lw4

:= Fsf1 56.38 kip=

Ft.st1 (68.25 kip) > F.sf1 (56.39 kip): Therefore O.K.

Provide a fillet weld of 5/16" B/W the stiffener and the column flange

Check for weld B/W the top most stiffener supporting the shear tab on the beam web side

with the column flange :-


bfc1 twc1

2 0.75in:= Lw7 5.05 in=


Mbg

Lw2 4 Lw7:= fsw6 0.49

kip

in=


fsw6

0.707 0.45 fw:= sw6 0.02 in=

Thickness of top most stiffener tst2 0.625in:=

Shear capacity of the stiffener Ftst2 0.6 Lw7 tst2 fy36:= Ftst2 68.24 kip=

Shear force on the stiffener Fsf2

Mbg

Lw2

:= Fsf2

9.87 kip=

Ft.st2 (68.25 kip) > F.sf2 (9.87 kip): Therefore O.K.

Provide a fillet weld of 5/16" B/W the bottom side of the stiffener and the column flange and 5/16" PPW

B/W the top of the stiffener and the column flange

Date post:	06-Apr-2018
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Upload:	sivanantham-ramachandiran
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