Transcript Analysis of moment connections

Analysis of
moment
connections
Basic principles
of connection
design
• Provide as direct a load
path as possible
• Avoid complex stress
conditions
• Weld in the shop, bolt
on site
Welded
connections
Moment connection of an I-Beam
• Bending moment is
carried mainly by the
flanges
• Therefore connect
flanges for moment
transfer
M
Moment connection of an I-Beam
• Welded connection
C=T
• Fillet welds
• Full penetration
welds
• Compression transfer
d
can also be
accomplished through
direct bearing
Resultant tension force T = M/d
M
Shear connection of an I-Beam
• Shear is carried
mainly by the web
• Therefore connect
the web for shear
transfer
V
Shear connection of an I-Beam
• Fillet welds in shear
are commonly used
• Connect entire web
and adjust weld size
to suit shear load
V
Moment connection of a plate
Stress in weld
σ = M (d/2) / I
= M (d/2) / (ad3/12) [kN/m2]
q =σa
= M (d/2) / (d3/12)
= M (d/2) / I’ [kN/m]
Where
I’ = I/a
M
d
Then choose a weld size a that will
carry q
q = σ.a
where a = weld size
Moment connection of a plate
Can also use simplified
approach:
• Break moment into a
force couple
• Choose a suitable weld
size
• Then calculate the
required length of the
weld to carry the tension
force T
C=T
Resultant tension force T = M/d
M
d
q = T/l
where l = weld length
Welded shear plate
V
V
Centroid
of weld
group
e
M = V.e
Simplified approach
• Break eccentric load
up into a vertical
force along the
vertical weld and a
pair (couple) of
horizontal forces
along the horizontal
welds
• Then choose
lengths of welds to
carry the calculated
forces
V.e’/d
V
d
V
V.e’/d
e’
“Stress” calculations
V
V
+
M = V.e
M = V.e
“Stress” calculations for vertical force V
qV
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]
“Stress” calculations for Moment M = V.e
xB
xA
Treat the weld group as a crosssection subjected to a torsional
moment
A qAx
qAy qAM
yA
qAx = M yA / I’p
qAy = M xA / I’p
M = V.e
qBy
qBM
qBx
yB
B
I’p2 = I’x2 + I’y2
where I’ = I/a
qAM = (qAx2 + qAy2)0.5
Similarly for point B
Then select weld size for max. q
“Stress” calculations for combined V and M
A
qAx
qAy
V
qAV
qA
M = V.e
B
Combine 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 q
Example of a complex connection
Column tree for Times Square 4, NYC
Bolted connections
Moment
splice in a
column
Moment splice of an I-Beam
• Bolted connection
C=T
• Divide tension and
compression resultant
equally between bolts
M
d
Resultant tension force T = M/d
Shear
connection in
bridge
diaphragm
girder
(Alex Fraser Bridge)
Shear connection of an I-Beam
• Bolted connections
to transfer shear are
commonly used
• Connect entire web to
avoid stress
concentrations and
shear lag
V
End plate
Coped flanges to fit in
between column
flanges
Shear connection via end plate
Moment connection with and end
or base plate
Moment connection with fully
welded end plate
Tmax
Ti = Tmax (hi / hmax)
Ti
M = Σ Ti hi
hmax
hi
C = Σ Ti
M
Pre-tensioned moment connection
Pre-tensioned Moment
Connection
Apply both tension and
compression forces to pretensioned bolts.
Compression force can be
seen as a release of the
tension force.
Ti
+
TM
M
=
M
Bolted shear plate
e
P
P
Centroid of
bolt group
M = Pe
Vertical load
VP
P
Divide the force by
n, the number of
bolts
VP = P / n
VP
Moment
Treat the bolt group as a
cross-section subjected to a
torsional moment
xi
bolt i
FxM
ri
FyM
FMi
M
bolt area A
yi
Ip = Σi A ri2
= Σi A (xi2 + yi2)
and with I’P = IP/A
FxM = M yi / I’p
FyM = M xi / I’p
FMi = (FxM2 + FyM2)0.5
Then select a bolt size for the
maximum force FM
Combined vertical force and
moment
FxM
FyM
P
Fmax
VP
M = Pe
Fmax = [FxM2 + (FyM + VP)2]0.5
Then select a bolt size for the
maximum force Fmax