Design of Connections for Steel Members - Design of Modern Steel Railway Bridges - page 390

stress (thickness times net length along lines a-a in Figure 9.16) , A gt is the gross area
subject to tension stress (thickness times gross length along lines b-b in Figure 9.16),
and A nt is the net area subject to tension stress (thickness times net length along line
b-b in Figure 9.16).
AREMA (2008) recommends determination of allowable block shear strength
using Equations 9.48 and either Equation 9.49a or 9.49b, depending on whether the
net fracture strength in tension is greater or less than the net fracture strength in shear.
Connection shear lag effects that require consideration for axial tension member
design are considered in Chapter 6. Shear lag is taken into account for design by
determination of a reduced cross-sectional area or effective net area, A e , which is
based on the connection efficiency.

9.3.4.2.2 Gusset Plates
Ingeneral,gussetplatesshouldbedesignedtobeascompactaspossible.Thisnotonly
reduces material consumption but reduces slenderness ratios and free edge distances
for greater buckling strength. Gusset plates have been traditionally designed using
beam theory to determine axial, bending, and shear stresses at various critical sections
of a gusset plate. However, the slender beam model is not an accurate model, ∗ and
consideration of the limit states of block shear (tear-out) and axial stress, based on an
appropriate area, is used for the design of ordinary gusset plates.
Block shear in a gusset plate is analogous to the situation shown in Figure 9.16
but with the tear-out section extending from the edge of the gusset plate (line c-c in
Figure 9.16) to the furthest line of bolts (line d-d in Figure 9.16). Equations 9.48 and
either Equation 9.49a or 9.49b are also used to determine the allowable block shear
strength of the gusset plate at each member end connection.
The axial stress in the gusset plate is required for comparison to allowable tensile
and compressive axial stresses. Testing has shown that an effective length, w e , per-
pendicular to the last bolt line (line d-d in Figure 9.17) , on which axial stresses act,
may be based on lines 30 ◦ to the bolt row lines (lines a-a in Figure 9.17) from the first
perpendicular bolt line (line b-b in Figure 9.17) (Whitmore, 1952). The Whitmore
effective length, w e ,is

2 l c tan ( 30 ◦ ) w e = + s r = 1.15 l c + s r . (9.50)

The effective length, w e , must often be reduced if it intersects other members or
contains elements with different strengths (e.g., w e in Figure 9.18) . The axial tensile ¯

design of the gusset plate is then based on

P
w e t p ≤

σ at = 0.55 F y (9.51a)

or

P
w ne t p ≤

σ at = 0.47 F U . (9.51b)

∗ For example, tests show shear stresses are closer to V/A than 1.5 V/A as predicted by beam theory.