Frames - The Behaviour and Design of Steel Structures to EC3 - page 348

8.2 Triangulated frames

8.2.1 Statically determinate frames

The primary actions in triangulated frames whose members are concentrically
connectedandwhoseloadsactconcentricallythroughthejointsarethoseofaxial
compression or tension in the members, and any bending actions are secondary
only.Thesebendingactionsareusuallyignored,inwhichcasethememberforces
may be determined by a simple analysis for which the member connections are
assumed to be made through frictionless pin-joints.
If the assumed pin-jointed frame is statically determinate, then each member
force can be determined by statics alone, and is independent of the behaviour
of the remaining members. Because of this, the frame may be assumed to
fail when its weakest member fails, as indicated in Figure 8.1a and b. Thus,
each member may be designed independently of the others by using the pro-
cedures discussed in Chapters 2 (for tension members) or 3 (for compression
members).
If all the members of a frame are designed to fail simultaneously (either by
tensionyieldingorbycompressionbuckling),therewillbenosignificantmoment
interactions between the members at failure, even if the connections are not pin-
jointed.Becauseofthis,theeffectivelengthsofthecompressionmembersshould
be taken as equal to the lengths between their ends. If, however, the members
of a rigid-jointed frame are not designed to fail simultaneously, there will be
momentinteractionsbetweenthematfailure.Whileitisacommonandconserva-
tivepracticetoignoretheseinteractionsandtodesigneachmemberasifpin-ended,
some account may be taken of these by using one of the procedures discussed in
Section8.3.5.3toestimatetheeffectivelengthsofthecompressionmembers,and
exemplified in Section 8.5.1.

Frame fails after
tension diagonal
yields or fractures

Frame fails after
compression diagonal
buckles

Frame remains stable
after compression
diagonal buckles

(a) Determinate frame (b) Determinate frame

with compression
diagonal

(c) Indeterminate frame

with double-braced
panel

with tension diagonal

Figure 8.1 Determinate and indeterminate triangulated frames.