By Amanuel Gebremeskel,
Development Engineer, SAISC
There have been a number of structural failures in South Africa over the past few years in connections that use lapped gusseted joints in compression. These types of connections typically occur in lightly loaded braces and trusses because they help to facilitate easy fabrication, transportation and erection. Therefore they deserve an equally economical and easy method to check their capacity.
The following simple equation is proposed to evaluate the capacity of such connections:
Cr = b (120t – 2.2L) [N]
Where 5 < L/t ≤ 30
Equation 12.30 of the SAISC Green Book presents a more rigorous approach, repeated below right, that also accounts for the eccentricity between the gusset plate that is attached to the support and the spade plate that is attached to the brace member.
As discussed in the Green Book axially loaded members in braces and trusses are commonly attached to columns and beams, or truss chords, using gusset plates. When the attachment is concentric one needs to check the gusset plate for axial yielding or buckling. Moreover if the gusset plate is supported on at least two edges it can typically be assumed to be braced against lateral sway.
Figures 1 (a), (b) and (c) below illustrate that the challenge with lapped joints lies in the eccentric loading that occurs due to the attachment of the spade plate on the side of the gusset plate rather than on its edge. To add to the problem gusset plates in lapped joints are commonly supported only on one edge, causing them to sway sideways.
It is important to remember that the vast majority of real cases will be controlled by the capacity of the lapped joint rather than that of the brace member itself. Both approaches below (Figure 1) make that assumption. This matters because if the brace member is relatively slender and has a lower buckling strength than the lapped joint then the overall buckling is likely to resemble that shown in Figure 1 (d) rather than (c). It is best to avoid such slender brace members in the first place, but in the rare event that they occur the capacity of the lapped joint has to be recalculated assuming free rotation at the brace end of the spade plate. In other words effective length l = 2L in equation 12.30 of the Green Book.
The equations on page 38 also assume that local buckling of the gusset plate – typically checked using the Whitmore section between the dotted line and the support in Figure 1 (b) – does not control the design of the system. Lastly it is common to ignore the bending moment due to eccentricity from the spade plate into the brace member for relatively stout braces. However for slender braces, where this moment is greater than 5% of the flexural capacity of the brace, the effects of flexure must be taken into account when evaluating the capacity of the brace member.
When designing lapped joints the arrangement shown in Figure 1 (c) is idealised to that shown in (e). This is reasonable as long as the conservative thinner and narrower values of t and b of the gusset and spade plates in the joint are used. The buckling length L is identified by locating the likely fold lines – at the ends of the gusset and spade plates in most cases – of the plates as illustrated with the dotted line in (b).
Finally a third approach can be used to evaluate a lower bound capacity of the joint using SANS 10162-1 if one assumes that the lapped plates represent beam-columns with axial load and flexure that are amplified for geometric second order effects (P- Δ). Such an approach is less attractive because it requires iteration to solve Cr and all of the assumptions above would have to hold anyway. In the graph (Graph 1) below all three approaches discussed herein are compared to the capacity that is obtained if lapped joints are designed by mistakenly assuming concentric loading.
As a conclusion to the discussion an example may help to illustrate the simplicity of the proposed methodology. Consider a truss where the connection illustrated in Figure 2 is used. Assume that 6mm plates are used for the gussets and spades while the brace member is an 88.9 x 3 circular hollow section. Also assume that the distance between the work points on either end of the brace is 3.0m and a factored load of 85 kN needs to be supported. All steel is S355JR.
L = 80 mm t = 6 mm b = 90 mm
At 3.0m length the circular hollow section has an ultimate axial capacity of 111 kN from Table 4.14 of the Red Book.
111 kN > 85 kN Good!
5 < L/t ≤ 30 ⇒ L/t = 80/6 = 13.33
so we can use the proposed equation
Cr = b (120t – 2.2L) ⇒ Cr = 90(120*6 – 2.2*80)
= 48 960 N
Cr = 48.9 kN < 85 kN No Good! Use 10mm plate
Cr = 90(120*10 – 2.2*80) = 92160 N
L/t = 80/10 = 8
so we can use the proposed equation
Cr = 92.1 kN > 85 kN but also less than 111 kN.
Thus it is not controlled by brace member buckling and thus safe.
When using equation 12.30 in the Green book Cr = 95.3 kN. It is also greater than 85 kN and less than 111 kN. This further validates the final design using 10mm thick plates.