_analysis of Moment Resisting Connections (1)
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Transcript of _analysis of Moment Resisting Connections (1)
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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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shear connection of an I-Beam
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
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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
Resultant tension force T = M/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
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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
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
Resultant tension force T = M/d
d
C = T
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shear
connection inbridge
diaphragmgirder
(Alex Fraser Bridge)
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shear connection of an I-Beam
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 and
end or base plate
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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
+
=
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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
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