94529877 Analysis of Steel Moment Connections

8/13/2019 94529877 Analysis of Steel Moment Connections

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Analysis ofAnalysis ofmomentmoment

connectionsconnections


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Basic principlesBasic principles

of connectionof connectiondesigndesign

Provide as direct a load

path as possible Avoid complex stress

conditions

Weld in the shop, bolton site


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WeldedWeldedconnectionsconnections


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Moment connection of an IMoment connection of an I--BeamBeam

M

Bending moment is

carried mainly by the

flanges

Therefore connectflanges for moment

transfer


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Moment connection of an IMoment connection of an I--BeamBeam

M

Welded connection

Fillet welds

Full penetration

welds Compression transfer

can also be

accomplished throughdirect bearing

Resultant tension force T = M/d

d

C = T


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Shear connection of an IShear connection of an I--BeamBeam

Shear is carried

mainly by the web Therefore connect

the web for shear

transfer V


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Fillet welds in shear

are commonly used Connect entire web

and adjust weld size

to suit shear load V


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Moment connection of a plateMoment connection of a plate

Stress in weld

= M (d/2) / I

= M (d/2) / (ad3/12) [kN/m2]

q = a

= M (d/2) / (d3/12)

= M (d/2) / I [kN/m]

Where

I = I/a

Then choose a weld size a that willcarry q

M

q = .a

where a = weld size

d


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Moment connection of a plateMoment connection of a plate

Can also use simplified

approach:

Break moment into a

force couple

Choose a suitable weld

size

Then calculate therequired length of the

weld to carry the tension

force T

M

q = T/l

where l = weld length

d


C = T


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Welded shear plateWelded shear plate

V

Centroid

of weld

group

e

V

M = V.e


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Simplified approachSimplified approach

Break eccentric loadup into a vertical

force along thevertical weld and apair (couple) of

horizontal forcesalong the horizontalwelds

Then chooselengths of welds tocarry the calculatedforces

V

V.e/d

V.e/d

V

d

e


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Stress calculationsStress calculations

V

M = V.e

V

M = V.e+


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Stress calculations for vertical force VStress calculations for vertical force V

V

Divide shear equally

amongst all the weld lines

q = V / (total length of weld)

Choose a weld size that can

carry the stress q

Note q is actually a force

per length [kN/m]

qV


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Stress calculations for Moment M =Stress calculations for Moment M = V.eV.e

Treat the weld group as a cross-

section subjected to a torsional

moment

Ip2 = Ix

2 + Iy2

where I = I/a

qAx = M yA/ IpqAy = M xA/ Ip

qAM = (qAx2 + qAy

2)0.5

Similarly for point B

Then select weld size for max. q

M = V.e

qAx

qAy

qBx

qBy

yA

xB xA

yB

A

B

qAM

qBM


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Stress calculations for combined V and MStress calculations for combined V and M

V

M = V.e

qAx

qAy

qAV

qA

ACombine the weld stress

components from the vertical

force and the torsional moment

qA = [qAx2 + (qAV + qAy)

2]0.5

Similarly for point B or any other

point that might be critical

Then select weld size for the

maximum value of qB

E l f l tiExample of a complex connection


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Example of a complex connectionExample of a complex connection

Column tree for Times Square 4, NYC


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Bolted connectionsBolted connections


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MomentMoment

splice in asplice in acolumncolumn


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Moment splice of an IMoment splice of an I--BeamBeam

M

Bolted connection

Divide tension and

compression resultant

equally between bolts


d

C = T


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ShearShearconnection inconnection in

bridgebridgediaphragmdiaphragm

girdergirder

(Alex Fraser Bridge)(Alex Fraser Bridge)


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Bolted connections

to transfer shear arecommonly used

Connect entire web to

avoid stressconcentrations and

shear lag

V


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Shear connection via end plateShear connection via end plate

Coped flanges to fit in

between column

flanges

End plate

M t ti ith d d


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Moment connection with and endMoment connection with and end

or base plateor base plate

M t ti ith f llM t ti ith f ll


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Moment connection with fullyMoment connection with fully

welded end platewelded end plate

M

hi

hmax

Ti

Tmax

)Ti = Tmax (hi/ hmax

M = Ti hi

C = Ti

PrePre--tensioned moment connectiontensioned moment connection


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PrePre--tensioned moment connectiontensioned moment connection

P i d M


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PrePre--tensioned Momenttensioned Moment

ConnectionConnectionApply both tension and

compression forces to pre-

tensioned bolts.Compression force can be

seen as a release of the

tension force.

MMTM

Ti

+

=


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Bolted shear plateBolted shear plateP

Centroid of

bolt group

e

P

M = Pe


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Vertical loadVertical load

P

VP

VPDivide the force by

n, the number ofbolts

VP = P / n

MomentMoment


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MomentMoment

M

FxM

FyM FMi yi

xi

Treat the bolt group as a

cross-section subjected to a

torsional moment

Ip = i A ri2

= i A (xi2 + yi

2)

and with IP = IP/A

FxM = M yi/ Ip

FyM = M xi/ Ip

FMi = (FxM2 + FyM

2)0.5

Then select a bolt size for themaximum force FM

ri

bolt area A

bolt i

Combined vertical force andCombined vertical force and


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Combined vertical force andCombined vertical force and

momentmoment

P

M = Pe

FxM

FyM

VP

Fmax

Fmax = [FxM2 + (FyM + VP)

2]0.5

Then select a bolt size for the

maximum force Fmax

94529877 Analysis of Steel Moment Connections

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