Page 375 - Marks Calculation for Machine Design

P1: Sanjay
January 4, 2005
15:14
Brown.cls
Brown˙C08
MACHINE ASSEMBLY
P
H P 357
t
L L o
Front view Side view
FIGURE 8.15 Fillet welds in bending.

which is the same expression for the shear stress (τ fillet ) given by Eq. (8.71) developed for
the fillet weld configurations in Figs. 8.8, 8.9, 8.10, 8.11, and 8.13.
Using the dimensions shown in Figs. 8.15 and 8.16, the normal stress (σ bending ) due to
the bending moment (M) is given by Eq. (8.80),
Md o (PL o ) d o
τ bending = = (8.80)
I group I group
where (L o ) is the perpendicular distance from the centroid of the weld group, point O,to
the applied load (P),(d o ) is the vertical distance from the centroid of the weld group to
the centerline of the weld, and (I group ) is the moment of inertia of the weld areas about the
centroid of the weld group.
P

d o
d o O
H
L
FIGURE 8.16 Fillet weld geometry for bending.
Therefore, using the dimensions shown in Fig. 8.16, the moment of inertia (I group ) for
the fillet welds can be determined from the expression
3
LH
I group = 2 + LHd o 2 (8.81)
12
where the factor 2 reflects the fact that there are two welds and the terms in brackets represent
the application of the parallel axis theorem to the rectangular weld shapes.
For the weld joint arrangement in Fig. 8.17, which is a variation of the weld joint arrange-
ment shown in Fig. 8.15, the moment of inertia (I group ) would be given by Eq. (8.82) as
3
HL
I group = 2 (8.82)
12