1. analysis of moment resisting connections

2. basic principles of connection design
Provide as direct a load path as possible
Avoid complex stress conditions
Weld in the shop, bolt on site

3. Welded connections

4. moment connection of an I-Beam
Bending moment is carried mainly by the flanges
Therefore connect flanges for moment transfer

5. moment connection of an I-Beam
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

6. shear connection of an I-Beam
Shear is carried mainly by the web
Therefore connect the web for shear transfer V

7. 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

8. 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 M d
q = σ.a
where a = weld size

9. 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 M
C = T d
Resultant tension force T = M/d
q = T/l
where l = weld length

10. welded shear plate V
Centroid of weld group e V
M = V.e

11. 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’

12. “Stress” calculationsV
M = V.e V
M = V.e +

13. “Stress” calculations for vertical force VqV 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]

14. “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
M = V.e
qAy
qAM yA
qBy yB
qBM B
qBx

15. “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

16. example of a complex connection
Column tree for Times Square 4, NYC

17. bolted connections

18. moment splice in a column

19. moment splice of an I-Beam
Bolted connection
Divide tension and compression resultant equally between bolts
Resultant tension force T = M/d d
C = T

20. shear connection in bridge diaphragm girder (Alex Fraser Bridge)

21. 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

22. shear connection via end plate
Coped flanges to fit in between column flanges
shear connection via end plate

23. moment connection with and end or base plate

24. moment connection with fully welded end plate
Tmax
Ti = Tmax (hi / hmax)
M = Σ Ti hi Ti M
hmax hi
C = Σ Ti

25. pre-tensioned moment connection

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

27. bolted shear plate P
Centroid of bolt group e P
M = Pe

28. vertical load Divide the force by n, the number of bolts P VP = P / n

29. 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

30. combined vertical force and momentP
M = Pe
FxM
FyM
Fmax VP
Fmax = [FxM2 + (FyM + VP)2]0.5
Then select a bolt size for the maximum force Fmax