Joints - The Behaviour and Design of Steel Structures to EC3 - page 422

Inthespecialcaseofaforcejointwith M x , V y equaltozero,thecentreofrotation
is at y r =−∞ , and the connector forces are given by
V vi = V z A i A i . (9.44)

Equations 9.43 and 9.44 indicate that the connector stresses V vi / A i caused by
forces V y , V z are constant throughout the joint.
It can be shown that the superposition by vector addition of the components of
V vi obtainedfromequations9.3,9.43,and9.44fortheseparateconnectionactions
of V y , V z , and M x leads to the general result given in equation 9.42.

9.9.2 Out-of-plane joints

The out-of-plane joint shown in Figure 9.11b is subjected to a normal force N x
and moments M y , M z acting about the principal axes y , z of the connector group
(which may consist of bolts or welds) defined by (Section 5.9)
A i y i = 0
A i z i = 0
A i y i z i = 0

(9.45)

in which A i is the area of the i th connector and y i , z i are its coordinates.
It is assumed that the plate components of the joint undergo rigid body relative
rotations δθ y , δθ z aboutaxeswhichareparalleltothe y , z principalaxesandwhich
pass through a point whose coordinates are y r , z r and that only the connectors
transfer forces. If the plates are rigid and the connectors elastic, then it may be
assumed that each connector transfers a force N xi which acts perpendicular to
the plane of the joint, and which has components which are proportional to the
distances ( y i − y r ) ,( z i − z r ) from the axes of rotation, so that

N xi = k t A i ( z i − z r ) δθ y − k t A i ( y i − y r ) δθ z (9.46)

in which k t is a constant which depends on the axial stiffness of the connector.
The centroidal force resultant N x of the connector forces is

N xi = k t − z r δθ y + y r δθ z N x = A i , (9.47)

afterusingequations9.45.Themomentresultants M y , M z oftheconnectorforces
about the centroidal axes are

N xi z i = k t δθ y A i z i ,

M y = (9.48)

N xi y i = k t δθ z A i y i , M z =− (9.49)

after using equations 9.46.