Civil Engineering Reference
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d
c
b
l 1
30°
a
a
l 2
w e
s r
P
a
a
l 3
b
d
l w = ( l 1 + l 2 + l 3 )/3
c
l c
FIGURE 9.17 Whitmore stress block in a gusset plate at an axial member connection.
The limit state of yielding on the gross section, w e t p , immediately below the last
line of bolts is represented by Equation 9.51a and that of tensile failure on the net
section, w ne t p , through the last line of bolts by Equation 9.51b. Compressive design
(considering stability) is based on
P
w e t p
σ ac =
F call ,
(9.52)
where w ne is the net effective length,
σ at is the axial tension stress on effective area,
w e t p or w ne t p ,
σ ac is the axial compression stress on effective area, w e t p , F call is the
allowable axial compression stress based on the effective slenderness ratio, Kl w /r w
(many engineers restrict Kl w /r w
100-120), Kl w is the effective buckling length of
thegussetplate, l w istheaveragedistance, (l 1 +
l 3 )/ 3,fromlastlineofbolts(line
d-d in Figure 9.17) to the edge of the gusset plate. l w may extend to the first row of
bolts at an interface member such as a bottom chord element (line f-f in Figure 9.18).
l 2 +
t p / 12
r w =
t p is the thickness of the gusset plate, K is the effective length factor typically taken as
between 0.50 and 0.65 for properly braced gusset plates (Thornton and Kane, 1999).
The use of block shear rupture and theWhitmore section analysis may be sufficient
for the design of ordinary gusset plates. However, for heavily loaded railway truss
members it is often appropriate to also check beam theory shear forces, bending
moments, and axial forces at critical sections (e.g., lines f-f, g-g, h-h and i-i in
Figure 9.18). The critical sections such a g-g and h-h in Figure 9.18 should be
Equation 9.51a is slightly conservative as the Whitmore section is taken through the center of the last
line of bolts.
If gusset plates are not braced against lateral movement, k may be greater than 1 (see Chapter 6, Figures
6.4 and 6.5, Table 6.4).
An alternative to slender beam theory, the uniform force method, which is strongly dependent on
connection geometry, has been used for building design (Thornton and Kane, 1999).
 
 
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