Page 103 - Handbook of Civil Engineering Calculations, Second Edition

1.86 STRUCTURAL STEEL ENGINEERING AND DESIGN

ECCENTRIC LOAD ON A WELDED CONNECTION

1
The bracket in Fig. 61 is connected to its support with a /4-in. (6.35-mm) fillet weld. De-
termine the maximum stress in the weld.

Calculation Procedure:

1. Locate the centroid of the
weld group
Refer to the previous eccentric-load cal-
culation procedure. This situation is
analogous to that. Determine the stress
by locating the instantaneous center of
rotation. The maximum stress occurs at
A and B (Fig. 61).
Considering the weld as concentrat-
ed along the edge of the supported
member, locate the centroid of the weld
group by taking moments with respect
to line aa. Thus m 2(4)(2)/(12 2
4) 0.8 in. (20.32 mm).
2. Replace the eccentric load
FIGURE 61 with an equivalent concentric
load and moment
Thus P 13,500 lb (60,048.0 N); M
124,200 in·lb (14,032.1 N·m).
3. Compute the polar moment of inertia of the weld group
This moment should be computed with respect to an axis through the centroid of the weld
2
3
3
3
group. Thus I x (1/12)(12) 2(4)(6) 432 in (7080.5 cm ); I y 12(0.8)
2
3
3
3
2
2(1/12)(4) 2(4)(2 0.8) 29.9 in (490.06 cm ). Then J I x I y 461.9 in 3
3
(7570.54 cm ).
4. Locate the instantaneous center of rotation O
This center is associated with this eccentric load by applying the equation h J/(eL),
where e eccentricity of load, in. (mm), and L total length of weld, in. (mm). Thus, e
10 0.8 9.2 in. (233.68 mm); L 12 2(4) 20 in. (508.0 mm); then h
461.9/[9.2(20)] 2.51 in. (63.754 mm).
5. Compute the force on the weld
Use the equation F Mr
/J, lb/lin in (N/m), where r
distance from the instantaneous
center of rotation to the given point, in. (mm). At A and B, r
8.28 in. (210.312 mm);
then F [124,200(8.28)]/461.9 2230 lb/lin in (390,532.8 N/m).
6. Calculate the corresponding stress on the throat
Thus, s P/A 2230/[0.707(0.25)] 12,600 lb/sq.in.86,877.0 kPa), where the value
0.707 is the sine of 45°, the throat angle.