Steel Design (Activate Learning with these NEW titles from Engineering!)
Steel Design (Activate Learning with these NEW titles from Engineering!)
6th Edition
ISBN: 9781337094740
Author: Segui, William T.
Publisher: Cengage Learning
Question
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Chapter 8, Problem 8.8.3P
To determine

(a)

The design of a four-bolt unstiffened end-plate connection for a W18×40 beam to a W8×40 column for the full moment and shear capacities of the beam by using LRFD.

Expert Solution
Check Mark

Answer to Problem 8.8.3P

PL114×7×2'118''and four 114-in. diameter Group A fully tightened bolts at each flange

9/16-in. fillet weld at each flange.

¼-in. fillet weld on each side of the web in the tension region.

½-in. fillet weld on each side of the web between mid-depth and the compression flange.

Explanation of Solution

Given:

A992 steel for members

A36 steel for the end plate

Group A pretensioned bolts

Formula used:

Pt=FtAb

Pt is bolt strength

Ft is the ultimate tensile stress of the bolt

Ab is the bolt area

Mn=2Pt(h0+h1)

Mn is required moment strength

h0 is distance from center of beam compression flange to center ofouter row of bolts on the tension side.

h1 is distance from center of compression flange to center of inner rowof bolts.

tp=1.11ϕMnϕbFyYp

tp isend plate thickness

Yp is yield line mechanism parameter

ϕb=0.90

Calculation:

From the Zx tables, for a W18×40,

Mu=ϕbMpx=294ftkipsVu=ϕvVn=169kips

From the dimensions and properties tables

d=17.9in.tw=0.315in.bfb=6.02in.tfb=0.525in.

Workable gauge = 3.50 in.

For the bolt pitch, try pfo=pfi=2in.

For the gauge distance, use the workable gauge g = 3.50 in.

Required bolt diameter:

h0=dtfb2+pfo=17.90.5252+2=19.64in.h1=dtfb2tfbpfi=17.90.52520.5252=15.11in.dbRequired=2MuπϕFt(h0+h1)=2(294×12)π(0.75)(90)(19.64+15.11)=0.979in.

Try db=1in.

Moment strength based on bolt strength:

Pt=FtAb=90(π(1)24)=70.69kips/boltMn=2Pt(h0+h1)=2(70.69)(19.64+15.11)=4913in.kipsϕMn=0.75(4913)=3685in.kips=307.1ftkips>ϕbMpx=294ftkips

Therefore, use ϕMn=ϕbMpx=294ftkips=3528in.kips

Determine end-plate width:

Minimum le=114in.

The minimum plate width is g+2le=3.50+2(1.25)=6in. but no less than the beam flange width of 6.02in.

Maximum effective end-plate width = bfb+1=6.02+1=7.02in.

Try bp=7in.

Determine the required plate thickness:

s=12bpg=127(3.5)=2.457in.>pfi

Therefore, use the original value of pfi=2in.

Yp=bp2[h1(1pfi+1s)+h0(1pfo)12]+2g[h1(pfi+s)]=72[15.11(12+12.475)+19.64(12)12]+23.5[15.11(2+2.475)]=119.1

Required tp=1.11ϕMnϕbFyYp=1.11(3528)0.9(36)(119.1)=1.01in.

Try tp=114in.

Beam flange force:

Ffu=Mudtfb=294×1217.90.525=203.1kipsFfu2=203.12=101.6kips

The shear yield strength of the end plate is

ϕ(0.6)Fytpbp=0.90(0.6)(36)(1.25)(7)=170.1kips>101.6kips (OK)

Shear rupture strength of end plate:

An=tp[bp2(db+18)]=1.25[72(1+18)]=5.938in.2

ϕ(0.6)FuAn=0.75(0.6)(58)(5.938)=155kips>101.6kips (Ok)

Check bolt shear:

The compression side bolts must be capable of resisting the entire vertical shear.

Ab=πdb24=π(1)24=0.785in.2ϕRn=ϕFnvAb=0.75(54)(0.7854)=31.81kips/bolt

For 4 bolts,

ϕRn=4×31.81=127.2kips

Vu=169kips>127.2kips (N.G.)

Try 114in.

Ab=πdb24=π(1.25)24=1.227in.2ϕRn=ϕFnvAb=0.75(54)(1.227)=49.69kips/bolt

For 4 bolts, ϕRn=4×49.69=199kips>169kips (OK)

Recompute the plate dimensions:

For 114in. diameter bolts,

Minimum le=158in.

The minimum plate width is

g+2le=3.50+2(1.625)=6.75in.

Maximum effective end-plate width = bfb+1=6.02+1=7.02in.

Use the currently selected width of bp=7in.

Because the bolt size has increased, check the shear rupture strength of the end plate:

An=tp[bp2(db+18)]=1.25[72(1.25+18)]=5.313in.2

ϕ(0.6)FuAn=0.75(0.6)(58)(5.313)=138.7kips>101.6kips (OK)

Check bearing in the plate at the compression side bolts.

h=d+116=114+116=1.313in.

For the outer bolts,

lc=pfo+tfb+pfih=2+0.525+21.313=3.212in.ϕRn=ϕ(1.2lctFu)=0.75(1.2)(3.212)(1.25)(58)=209.6kips

The upper limit is

ϕ(2.4dtFu)=0.75(2.4)(1.25)(1.25)(58)=163.1kips<209.6kips

Therefore, use ϕRn=163.1kips/bolt

Since the inner bolts are not near an edge or adjacent bolts, the outer bolts control.

The total bearing strength is

4×163.1=652kips>Vu=169kips (Ok)

Check bearing in the column flange:

Use lc=3.212in.

ϕRn=ϕ(1.2lctFu)=0.75(1.2)(3.212)(0.525)(65)=98.65kips

The upper limit is

ϕ(2.4dtFu)=0.75(2.4)(1.25)(0.525)(65)=76.78kips<98.65kips

Therefore, use ϕRn=76.78kips/bolt

The total bearing strength is

4×76.78=307kips>Vu=169kips (OK)

The plate length, using detailing dimensions and the notation of figure given below from the textbook (Steel design), is

d+2pfo+2de=1778+2(2)+2(158)=2518in.

Steel Design (Activate Learning with these NEW titles from Engineering!), Chapter 8, Problem 8.8.3P , additional homework tip  1

Use a PL114×7×2'118'' and four 114 -in. diameter Group A fully-tightened bolts at each flange.

Beam flange to plate weld design:

The flange force is

Ffu=203.1kips

AISC Design Guide 4 recommends that the minimum design flange force should be 60% of the flange yield strength:

Minimum Ffu=0.6Fy(bfbtfb)=0.6(50)(6.02)(.525)=94.8kips<203.1kips

Therefore, use the actual flange force of 203.1 kips.

The flange weld length is

bfb+(bfbtw)=6.02+(6.020.315)=11.73in.

The weld strength is

ϕRn=1.392D×11.73×1.5

where D is the weld size in sixteenths of an inch and the factor of 1.5 accounts for the direction of the load on the weld. If we equate the weld strength to the flange force,

1.392D×11.73×1.5=203.1

D=8.29 sixteenths

From AISC Table J2.4, the minimum weld size is ¼-in. (based on the thickness of the flange, which is the thinner connected part).

Steel Design (Activate Learning with these NEW titles from Engineering!), Chapter 8, Problem 8.8.3P , additional homework tip  2

Use a 9/16-in. fillet weld at each flange.

Beam web to plate weld design:

To develop the yield stress in the web near the tension bolts, let

1.392D×2=0.6Fytw for two welds, one on each side of the web. The required weld size is

D=0.6Fytw1.392(2)=0.6(50)(0.315)1.392(2)=3.39 sixteenths

Use a ¼-in. fillet weld on each side of the web in the tension region.

The applied shear of Vu=169kips must be resisted by welding a length of web equal to the smaller of the following two lengths:

  1. From the mid-depth to the compression flange.

L=d2tfb=17.920.525=8.425in.

From the inner row of tension bolts plus 2db

  1. to the compression flange:

L=d2tfbpfi2db=17.92(0.525)2.02(1.25)=12.35in.>8.425in.

Equating the weld strength to the required shear strengths, we get

1.392D×8.425×2=169

D=7.21 sixteenths ( w=12in. )

From AISC Table J2.4, the minimum weld size is 3/16-in.

Use a ½-in. fillet weld on each side of the web between mid-depth and the compression flange.

The design is summarized in the figure below:

Steel Design (Activate Learning with these NEW titles from Engineering!), Chapter 8, Problem 8.8.3P , additional homework tip  3

Conclusion:

Use a PL114×7×2'118'' and four 114 -in. diameter Group A fully-tightened bolts at each flange, a 9/16-in. fillet weld at each flange, a ¼-in. fillet weld on each side of the web in the tension region and a ½-in. fillet weld on each side of the web between mid-depth and the compression flange.

To determine

(b)

The design of a four-bolt unstiffened end-plate connection for a W18×40 beam to a W8×40 column for the full moment and shear capacities of the beam by using ASD.

Expert Solution
Check Mark

Answer to Problem 8.8.3P

PL114×7×2'118''and four 114-in. diameter Group A fully tightened bolts at each flange

9/16-in. fillet weld at each flange.

¼-in. fillet weld on each side of the web in the tension region

½-in. fillet weld on each side of the web between mid-depth and the compression flange.

Explanation of Solution

Given:

A992 steel for members

A36 steel for the end plate

Group A pretensioned bolts

Formula used:

Pt=FtAb

Pt is bolt strength

Ft is the ultimate tensile stress of the bolt

Ab is the bolt area

Mn=2Pt(h0+h1)

Mn is required moment strength

h0 is distance from center of beam compression flange to center ofouter row of bolts on the tension side

h1 is distance from center of compression flange to center of inner rowof bolts

tp=1.11(Mn/Ω)FyYp/Ωb

tp is end plate thickness

Yp is yield line mechanism parameter

Ωb=1.67

Calculation:

From the Zx tables, for a W18×40,

Ma=MpxΩb=196ftkipsVa=VnxΩv=113kips

From the dimensions and properties tables

d=17.9in.tw=0.315in.bfb=6.02in.tfb=0.525in.

Workable gauge = 3.50 in.

For the bolt pitch, try pfo=pfi=2in.

For the gauge distance, use the workable gauge g = 3.50 in.

Required bolt diameter:

h0=dtfb2+pfo=17.90.5252+2=19.64in.h1=dtfb2tfbpfi=17.90.52520.5252=15.11in.dbRequired=Ω(2Ma)πFt(h0+h1)=2.0(2×196×12)π(90)(19.64+15.11)=0.9785in.

Try db=1in.

Moment strength based on bolt strength:

Pt=FtAb=90(π(1)24)=70.69kips/boltMn=2Pt(h0+h1)=2(70.69)(19.64+15.11)=4913in.kipsMnΩ=49132.0=2456.5in.kips=204.708ftkips>MpxΩb=196ftkips

Therefore, use MnΩ=MpxΩb=196ftkips=2352in.kips

Determine end-plate width:

Minimum le=114in.

The minimum plate width is g+2le=3.50+2(1.25)=6in. but no less than the beam flange width of 6.02 in.

Maximum effective end-plate width = bfb+1=6.02+1=7.02in.

Try bp=7in.

Determine the required plate thickness:

s=12bpg=127(3.5)=2.457in.>pfi

Therefore, use the original value of pfi=2in.

Yp=bp2[h1(1pfi+1s)+h0(1pfo)12]+2g[h1(pfi+s)]=72[15.11(12+12.475)+19.64(12)12]+23.5[15.11(2+2.475)]=119.1

Required tp=1.11(Mn/Ω)FyYp/Ωb=1.11(2352)36(119.1)/1.67=1.0084in.

Try tp=114in.

Beam flange force:

Ffu=Madtfb=196×1217.90.525=135.4kipsFfu2=135.42=67.68kips

The shear yield strength of the end plate is

(0.6)FytpbpΩ=0.6(36)(1.25)(7)1.67=113.17kips>67.68kips (OK)

Shear rupture strength of end plate:

An=tp[bp2(db+18)]=1.25[72(1+18)]=5.938in.2

0.6FuAnΩ=0.6(58)(5.938)2.0=103.32kips>67.68kips (Ok)

Check bolt shear:

The compression side bolts must be capable of resisting the entire vertical shear.

Ab=πdb24=π(1)24=0.785in.2RnΩ=FnvAbΩ=54(0.7854)2.0=21.2kips/bolt

For 4 bolts,

RnΩ=4×21.2=84.8kips

Va=113kips>84.8kips (N.G.)

Try 114in.

Ab=πdb24=π(1.25)24=1.227in.2RnΩ=FnvAbΩ=54(1.227)2.0=33.129kips/bolt

For 4 bolts, ϕRn=4×33.129=132.516kips>113kips (OK)

Recompute the plate dimensions:

For 114in. diameter bolts,

Minimum le=158in.

The minimum plate width is

g+2le=3.50+2(1.625)=6.75in.

Maximum effective end-plate width = bfb+1=6.02+1=7.02in.

Use the currently selected width of bp=7in.

Because the bolt size has increased, check the shear rupture strength of the end plate:

An=tp[bp2(db+18)]=1.25[72(1.25+18)]=5.313in.2

0.6FuAnΩ=0.6(58)(5.313)2.0=92.446kips>67.68kips (OK)

Check bearing in the plate at the compression side bolts.

h=d+116=114+116=1.313in.

For the outer bolts,

lc=pfo+tfb+pfih=2+0.525+21.313=3.212in.RnΩ=1.2lctFuΩ=1.2(3.212)(1.25)(58)2.0=139.722kips

The upper limit is

2.4dtFuΩ=2.4(1.25)(1.25)(58)2.0=108.75kips<139.722kips

Therefore, use RnΩ=108.75kips/bolt

Since the inner bolts are not near an edge or adjacent bolts, the outer bolts control.

The total bearing strength is

4×108.75=435kips>Va=113kips (Ok)

Check bearing in the column flange:

Use lc=3.212in.

RnΩ=1.2lctFuΩ=1.2(3.212)(0.525)(65)2.0=65.766kips

The upper limit is

2.4dtFuΩ=2.4(1.25)(0.525)(65)2.0=51.1875kips<65.766kips

Therefore, use RnΩ=51.1875kips/bolt

The total bearing strength is

4×51.1875=204.75kips>Vu=113kips (OK)

The plate length, using detailing dimensions and the notation of figure given below from the textbook, is

d+2pfo+2de=1778+2(2)+2(158)=2518in.

Steel Design (Activate Learning with these NEW titles from Engineering!), Chapter 8, Problem 8.8.3P , additional homework tip  4

Use a PL114×7×2'118'' and four 114 -in. diameter Group A fully-tightened bolts at each flange.

Beam flange to plate weld design:

The flange force is

Ffu=135.4kips

AISC Design Guide 4 recommends that the minimum design flange force should be 60% of the flange yield strength:

Minimum Ffu=0.6Fy(bfbtfb)=0.6(50)(6.02)(.525)=94.8kips<135.4kips

Therefore, use the actual flange force of 135.4 kips.

The flange weld length is

bfb+(bfbtw)=6.02+(6.020.315)=11.73in.

The weld strength is

RnΩ=1.392D×11.73×1.5

where D is the weld size in sixteenths of an inch and the factor of 1.5 accounts for the direction of the load on the weld. If we equate the weld strength to the flange force,

1.392D×11.73×1.5=135.4

D=5.53 sixteenths

From AISC Table J2.4, the minimum weld size is ¼-in. (based on the thickness of the flange, which is the thinner connected part).

Steel Design (Activate Learning with these NEW titles from Engineering!), Chapter 8, Problem 8.8.3P , additional homework tip  5

Use a 9/16-in. fillet weld at each flange.

Beam web to plate weld design:

To develop the yield stress in the web near the tension bolts, let

1.392D×2=0.6Fytw for two welds, one on each side of the web. The required weld size is

D=0.6Fytw1.392(2)=0.6(50)(0.315)1.392(2)=3.39 sixteenths

Use a ¼-in. fillet weld on each side of the web in the tension region.

The applied shear of Va=113kips must be resisted by welding a length of web equal to the smaller of the following two lengths:

  1. From the mid-depth to the compression flange.

L=d2tfb=17.920.525=8.425in.

From the inner row of tension bolts plus 2db

  1. to the compression flange:

L=d2tfbpfi2db=17.92(0.525)2.02(1.25)=12.35in.>8.425in.

Equating the weld strength to the required shear strengths, we get

1.392D×8.425×2=113

D=4.82 sixteenths ( w=12in. )

From AISC Table J2.4, the minimum weld size is 3/16-in.

Use a ½-in. fillet weld on each side of the web between mid-depth and the compression flange.

The design is summarized in the figure below:

Steel Design (Activate Learning with these NEW titles from Engineering!), Chapter 8, Problem 8.8.3P , additional homework tip  6

Conclusion:

Use a PL114×7×2'118'' and four 114 -in. diameter Group A fully-tightened bolts at each flange, a 9/16-in. fillet weld at each flange, a ¼-in. fillet weld on each side of the web in the tension region and a ½-in. fillet weld on each side of the web between mid-depth and the compression flange.

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Chapter 8 Solutions

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