_analysis of Moment Resisting Connections

analysis of moment resisting connections

basic principles of connection designProvide as direct a load path as possibleAvoid complex stress conditionsWeld in the shop, bolt on site

Welded connections

moment connection of an I-BeamBending moment is carried mainly by the flangesTherefore connect flanges for moment transfer

moment connection of an I-BeamWelded connectionFillet weldsFull penetration weldsCompression transfer can also be accomplished through direct bearing

shear connection of an I-BeamShear is carried mainly by the webTherefore connect the web for shear transfer

shear connection of an I-BeamFillet welds in shear are commonly usedConnect entire web and adjust weld size to suit shear load

moment connection of a plateStress 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]WhereI= I/a

Then choose a weld size a that will carry q

q = .a where a = weld sized

moment connection of a plateCan also use simplified approach:

Break moment into a force coupleChoose a suitable weld sizeThen calculate the required length of the weld to carry the tension force T

q = T/l where l = weld lengthdResultant tension force T = M/dC = T

welded shear plate

simplified approachBreak eccentric load up into a vertical force along the vertical weld and a pair (couple) of horizontal forces along the horizontal weldsThen choose lengths of welds to carry the calculated forcesVV.e/dV.e/dVde

Stress calculations+

Stress calculations for vertical force 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 = V.eTreat the weld group as a cross-section subjected to a torsional moment

Ip2 = Ix2 + Iy2where I = I/a

qAx = M yA / IpqAy = M xA / Ip

qAM = (qAx2 + qAy2)0.5

Similarly for point BThen select weld size for max. q

qAx qAy qBx qBy yAxBxAyBA B qAM qBM

Stress calculations for combined V and MVM = V.eqAx qAy qAV qA 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

A B

example of a complex connectionColumn tree for Times Square 4, NYC

bolted connections

moment splice in a column

moment splice of an I-BeamBolted connectionDivide tension and compression resultant equally between bolts

shear connection in bridge diaphragm girder

(Alex Fraser Bridge)

shear connection of an I-BeamBolted connections to transfer shear are commonly usedConnect entire web to avoid stress concentrations and shear lag

shear connection via end plateCoped flanges to fit in between column flangesEnd plate

moment connection with and end or base plate

moment connection with fully welded end plateMhihmaxTiTmaxTi = Tmax (hi / hmax)

M = Ti hiC = Ti

pre-tensioned moment connection

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

bolted shear plate

vertical loadPVPVPDivide the force by n, the number of bolts

VP = P / n

moment M FxMFyMFMiyixiTreat the bolt group as a cross-section subjected to a torsional moment

Ip = i A ri2 = i A (xi2 + yi2)

and with IP = IP/A

FxM = M yi / IpFyM = M xi / Ip

FMi = (FxM2 + FyM2)0.5

Then select a bolt size for the maximum force FM

ribolt area Abolt i

combined vertical force and momentFxMFyMVPFmax

Fmax = [FxM2 + (FyM + VP)2]0.5

Then select a bolt size for the maximum force Fmax