Moment Resisting Connections

8/12/2019 Moment Resisting Connections

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analysis ofmoment

resistingconnections


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basic principlesof connection

design

Provide as direct a loadpath as possible Avoid complex stress

conditions

Weld in the shop, bolton site


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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 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 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 plateStress in weld = M (d/2) / I

= M (d/2) / (ad 3/12) [kN/m 2]q = a

= M (d/2) / (d 3/12)= M (d/2) / I [kN/m]

WhereI = 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 plate

Can also use simplifiedapproach:

Break moment into aforce couple Choose a suitable weld

size

Then calculate therequired length of theweld to carry the tensionforce T

M

q = T/l where 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 load

up 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

V d

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 cancarry the stress q

Note q is actually a forceper length [kN/m]

q V


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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

q Ax = M y A / Ipq Ay = M x A / Ip

q AM = (q Ax2 + q Ay2)0.5

Similarly for point BThen select weld size for max. q

M = V.e

q Ax

q Ay

q Bx

q By

yA

xB xA

yB

A

B

q AM

q BM


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Stress calculations for combined V and M

V

M = V.e

q Ax

q Ayq AV

q A

Combine the weld stresscomponents from the verticalforce and the torsional moment

q A = [q Ax 2 + (q AV + q Ay )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


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shearconnection in

bridge

diaphragmgirder

(Alex Fraser Bridge)


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Bolted connectionsto transfer shear arecommonly used

Connect entire web toavoid stressconcentrations andshear lag

V


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shear connection via end plate

Coped flanges to fit inbetween columnflanges

End plate


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moment connection with andend or base plate


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moment connection with fullywelded end plate

M

h i

h max

Ti

Tmax

Ti = T max (h i / h max )

M = T i h i

C = T i


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pre-tensioned moment connection


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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


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moment

M

FxM

FyM FMi y i

x i Treat the bolt group as across-section subjected to atorsional moment

Ip = i A r i2

= i A (x i2 + y i2)

and with I P = IP /A

FxM = M y i / Ip

FyM = M x i / Ip

FMi = (F xM2 + F yM2)0.5

Then select a bolt size for the

maximum force F M

r i

bolt area A

bolt i


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combined vertical force andmoment

P

M = Pe

FxM

FyM

VP

Fmax

Fmax = [F xM2 + (F yM + V P )2]0.5

Then select a bolt size for themaximum force F max

Moment Resisting Connections

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