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## analysis of moment resisting connections

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**basic principles of connection design**• Provide as direct a load path as possible • Avoid complex stress conditions • Weld in the shop, bolt on site**M**moment connection of an I-Beam • Bending moment is carried mainly by the flanges • Therefore connect flanges for moment transfer**C = T**M d Resultant tension force T = M/d moment connection of an I-Beam • Welded connection • Fillet welds • Full penetration welds • Compression transfer can also be accomplished through direct bearing**V**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**M**moment connection of a plate Stress in weld σ = 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] Where I’ = I/a Then choose a weld size a that will carry q d q = σ.a where a = weld size**M**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 d Resultant tension force T = M/d q = T/l where l = weld length**V**V M = V.e Centroid of weld group e welded shear plate**simplified approach**V.e’/d • 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 d V V.e’/d e’**V**V M = V.e M = V.e “Stress” calculations +**V**“Stress” calculations for vertical force V qV 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]**M = V.e**“Stress” calculations for Moment M = V.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’p qAy = M xA / I’p qAM = (qAx2 + qAy2)0.5 Similarly for point B Then select weld size for max. q xB xA qAx A qAy qAM yA qBy yB qBM B qBx**“Stress” calculations for combined V and M**qAx 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 qAy qAV V qA M = V.e B**example of a complex connection**Column tree for Times Square 4, NYC**C = T**M d Resultant tension force T = M/d moment splice of an I-Beam • Bolted connection • Divide tension and compression resultant equally between bolts**shear connection in bridge diaphragm girder(Alex Fraser**Bridge)**V**shear connection of an I-Beam • Bolted connections to transfer shear are commonly used • Connect entire web to avoid stress concentrations and shear lag**shear connection via end plate**End plate Coped flanges to fit in between column flanges**moment connection with fully welded end plate**Tmax Ti = Tmax (hi / hmax) M = Σ Ti hi Ti M hmax hi C = Σ Ti**Ti**+ TM M pre-tensioned Moment Connection Apply both tension and compression forces to pre-tensioned bolts. Compression force can be seen as a release of the tension force. M =**P**e P Centroid of bolt group M = Pe bolted shear plate**vertical load**Divide the force by n, the number of bolts VP = P / n VP P VP**moment**Treat the bolt group as a cross-section subjected to a torsional moment 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 xi bolt i FxM ri FMi FyM yi M bolt area A**P**M = Pe combined vertical force and moment FxM FyM Fmax VP Fmax = [FxM2 + (FyM + VP)2]0.5 Then select a bolt size for the maximum force Fmax