_analysis of Moment Resisting Connections (1)

7/31/2019 _analysis of Moment Resisting Connections (1)

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analysis ofmoment

resistingconnections


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Weldedconnections


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moment connection of an I-Beam

M

Bending moment iscarried mainly by theflanges

Therefore connectflanges for momenttransfer


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moment connection of an I-Beam

M

Welded connection Fillet welds

Full penetrationwelds

Compression transfercan also be

accomplished throughdirect bearing

Resultant tension force T = M/d

d

C = T


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shear connection of an I-Beam

Shear is carriedmainly by the web

Therefore connect

the web for sheartransfer V


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Fillet welds in shearare commonly used

Connect entire web

and adjust weld sizeto suit shear load V


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moment 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 = .awhere a = weld size

d


9/30

moment connection of a plate

Can also use simplified

approach:

Break moment into aforce couple

Choose a suitable weld

size

Then calculate therequired length of the

weld to carry the tension

force T

M

q = T/lwhere l = weld length

d


C = T


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welded shear plate

V

Centroidof weldgroup

e

V

M = V.e


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simplified approach

Break eccentric loadup into a verticalforce along thevertical weld and a

pair (couple) ofhorizontal forcesalong the horizontalwelds

Then chooselengths of welds tocarry the calculatedforces

V

V.e/d

V.e/d

Vd

e


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Stress calculations

V

M = V.e

V

M = V.e

+


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Stress 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 forceper length [kN/m]

qV


14/30

Stress calculations for Moment M = V.e

Treat the weld group as a cross-section subjected to a torsionalmoment

Ip

2= Ix

2+ Iy

2

where I = I/a

qAx = M yA/ IpqAy = M xA/ Ip

qAM = (qAx2 + qAy

2)0.5

Similarly for point BThen 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 M

V

M = V.e

qAx

qAy

qAV

qA

Combine the weld stress

components from the verticalforce and the torsional moment

qA = [qAx2 + (qAV + qAy)2]0.5

Similarly for point B or any otherpoint that might be critical

Then select weld size for themaximum value of q

A

B


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example of a complex connection

Column tree for Times Square 4, NYC


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bolted connections


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momentsplice in a

column


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moment splice of an I-Beam

M

Bolted connection Divide tension and

compression resultantequally between bolts


d

C = T


20/30

shear

connection inbridge

diaphragmgirder

(Alex Fraser Bridge)


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Bolted connectionsto transfer shear arecommonly used

Connect entire web toavoid stressconcentrations andshear lag

V


22/30

shear connection via end plate

Coped flanges to fit inbetween columnflanges

End plate


23/30

moment connection with and

end or base plate


24/30

moment connection with fully

welded end plate

M

hi

hmax

Ti

Tmax

Ti = Tmax (hi / hmax)

M = Ti hi

C = Ti


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pre-tensioned MomentConnection

Apply both tension andcompression forces to pre-tensioned bolts.Compression force can be

seen as a release of thetension force.

MMTM

Ti

+

=


27/30

bolted shear plate

P

Centroid ofbolt group

e

P

M = Pe


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vertical load

P

VP

VPDivide the force byn, the number ofbolts

VP = P / n

t


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moment

M

FxM

FyMFMi

yi

xi Treat the bolt group as across-section subjected to atorsional 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 the

maximum force FM

ri

bolt area A

bolt i


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combined vertical force and

moment

P

M = Pe

FxM

FyM

VP

Fmax

Fmax = [FxM2 + (FyM + VP)

2]0.5

Then select a bolt size for themaximum force Fmax

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_analysis of Moment Resisting Connections (1)