Analysis of moment connections

Analysis of Analysis of moment moment

connectionsconnections

Basic principles Basic principles of connection of connection

designdesign

• Provide as direct a load path as possible

• Avoid complex stress conditions

• Weld in the shop, bolt on site

Welded Welded connectionsconnections

Moment connection of an IMoment connection of an I--BeamBeam

M

• Bending moment is carried mainly by the flanges

• Therefore connect flanges for moment transfer

Moment connection of an IMoment connection of an I--BeamBeam

M

• Welded connection• Fillet welds• Full penetration

welds• Compression transfer

can also be accomplished through direct bearing

Resultant tension force T = M/d

d

C = T

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


• Fillet welds in shear are commonly used

• Connect entire web and adjust weld size to suit shear load V

Moment connection of a plateMoment connection of a plateStress in weldσ = M (d/2) / I

= M (d/2) / (ad3/12) [kN/m2]q = σ a

= M (d/2) / (d3/12)= M (d/2) / I’ [kN/m]

WhereI’ = I/a

Then choose a weld size a that will carry q

M

q = σ.awhere a = weld size

d

Moment connection of a plateMoment connection of a plateCan 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

M

q = T/lwhere l = weld length

d


C = T

Welded shear plateWelded shear plate

V

Centroid of weld group

e

V

M = V.e

Simplified approachSimplified 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

V.e’/d

V.e’/d

Vd

e’

““Stress” calculationsStress” calculations

V

M = V.e

V

M = V.e

+

““Stress” calculations for vertical force VStress” calculations for vertical force V

VDivide 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

““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

I’p2 = I’x2 + I’y2

where I’ = I/a

qAx = M yA / I’pqAy = M xA / I’p

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

““Stress” calculations for combined V and MStress” calculations for combined V and M

V

M = V.e

qAx

qAy

qAV

qA

A 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

B

Example of a complex connectionExample of a complex connection

Column tree for Times Square 4, NYC

Bolted connectionsBolted connections

Moment Moment splice in a splice in a

columncolumn

Moment splice of an IMoment splice of an I--BeamBeam

M

• Bolted connection• Divide tension and

compression resultant equally between bolts


d

C = T

Shear Shear connection in connection in

bridge bridge diaphragm diaphragm

girdergirder

(Alex Fraser Bridge)(Alex Fraser Bridge)


• Bolted connections to transfer shear are commonly used

• Connect entire web to avoid stress concentrations and shear lag

V

Shear connection via end plateShear connection via end plate

Coped flanges to fit in between column flanges

End plate

Moment connection with and end Moment connection with and end or base plateor base plate

Moment connection with fully Moment connection with fully welded end platewelded end plate

M

hi

hmax

Ti

Tmax

)Ti = Tmax (hi / hmax

M = Σ Ti hi

C = Σ Ti

PrePre--tensioned moment connectiontensioned moment connection

PrePre--tensioned Moment tensioned Moment ConnectionConnection

Apply both tension and compression forces to pre-tensioned bolts. Compression force can be seen as a release of the tension force.

MMTM

Ti

+

=

Bolted shear plateBolted shear plateP

Centroid of bolt group

e

P

M = Pe

Vertical loadVertical load

P

VP

VPDivide the force by n, the number of bolts

VP = P / n

Moment Moment

M

FxM

FyMFMi yi

xi Treat the bolt group as a cross-section subjected to a torsional moment

Ip = Σi A ri2

= Σi A (xi2 + yi

2)

and with I’P = IP/A

FxM = M yi / I’pFyM = M xi / I’p

FMi = (FxM2 + FyM

2)0.5

Then select a bolt size for the maximum force FM

ri

bolt area A

bolt i

Combined vertical force and Combined 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

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Analysis of moment connections