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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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Shear connection of an IShear connection of an I--BeamBeam
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
Resultant tension force T = M/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
Resultant tension force T = M/d
d
C = T
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ShearShearconnection inconnection in
bridgebridgediaphragmdiaphragm
girdergirder
(Alex Fraser Bridge)(Alex Fraser Bridge)
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Shear connection of an IShear connection of an I--BeamBeam
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