Post on 03-Jun-2018
8/12/2019 Moment Resisting Connections
1/30
analysis ofmoment
resistingconnections
8/12/2019 Moment Resisting Connections
2/30
basic principlesof connection
design
Provide as direct a loadpath as possible Avoid complex stress
conditions
Weld in the shop, bolton site
8/12/2019 Moment Resisting Connections
3/30
Weldedconnections
8/12/2019 Moment Resisting Connections
4/30
moment connection of an I-Beam
M
Bending moment iscarried mainly by theflanges
Therefore connectflanges for momenttransfer
8/12/2019 Moment Resisting Connections
5/30
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
8/12/2019 Moment Resisting Connections
6/30
shear connection of an I-Beam
Shear is carriedmainly by the web
Therefore connect
the web for sheartransfer V
8/12/2019 Moment Resisting Connections
7/30
shear connection of an I-Beam
Fillet welds in shearare commonly used
Connect entire web
and adjust weld sizeto suit shear load V
8/12/2019 Moment Resisting Connections
8/30
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
8/12/2019 Moment Resisting Connections
9/30
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
Resultant tension force T = M/d
C = T
8/12/2019 Moment Resisting Connections
10/30
welded shear plate
V
Centroidof weldgroup
e
V
M = V.e
8/12/2019 Moment Resisting Connections
11/30
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
8/12/2019 Moment Resisting Connections
12/30
Stress calculations
V
M = V.e
V
M = V.e
+
8/12/2019 Moment Resisting Connections
13/30
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
8/12/2019 Moment Resisting Connections
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
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
8/12/2019 Moment Resisting Connections
15/30
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
8/12/2019 Moment Resisting Connections
16/30
example of a complex connection
Column tree for Times Square 4, NYC
8/12/2019 Moment Resisting Connections
17/30
bolted connections
8/12/2019 Moment Resisting Connections
18/30
momentsplice in a
column
8/12/2019 Moment Resisting Connections
19/30
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
8/12/2019 Moment Resisting Connections
20/30
shearconnection in
bridge
diaphragmgirder
(Alex Fraser Bridge)
8/12/2019 Moment Resisting Connections
21/30
shear connection of an I-Beam
Bolted connectionsto transfer shear arecommonly used
Connect entire web toavoid stressconcentrations andshear lag
V
8/12/2019 Moment Resisting Connections
22/30
shear connection via end plate
Coped flanges to fit inbetween columnflanges
End plate
8/12/2019 Moment Resisting Connections
23/30
moment connection with andend or base plate
8/12/2019 Moment Resisting Connections
24/30
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
8/12/2019 Moment Resisting Connections
25/30
pre-tensioned moment connection
8/12/2019 Moment Resisting Connections
26/30
8/12/2019 Moment Resisting Connections
27/30
bolted shear plate
P
Centroid ofbolt group
e
P
M = Pe
8/12/2019 Moment Resisting Connections
28/30
vertical load
P
VP
VPDivide the force byn, the number ofbolts
VP = P / n
8/12/2019 Moment Resisting Connections
29/30
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
8/12/2019 Moment Resisting Connections
30/30
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