Page 538 - Shigley's Mechanical Engineering Design

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512 Mechanical Engineering Design
9–38 Write a computer program to assist with a task such as that of Prob. 9–37 with a rectangular weld-
bead pattern for a torsional shear joint. In doing so solicit the force F, the clearance a, and the
largest allowable shear stress. Then, as part of an iterative loop, solicit the dimensions b and d of
the rectangle. These can be your design variables. Output all the parameters after the leg size has
been determined by computation. In effect this will be your adequacy assessment when you stop
iterating. Include the figure of merit J u /(hl) in the output. The fom and the leg size h with avail-
able width will give you a useful insight into the nature of this class of welds. Use your program
to verify your solutions to Prob. 9–37.
9–39 Fillet welds in joints resisting bending are interesting in that they can be simpler than those resist-
ing torsion. From Prob. 9–33 you learned that your objective is to place weld metal as far away
from the weld-bead centroid as you can, but distributed in an orientation parallel to the x axis.
Furthermore, placement on the top and bottom of the built-in end of a cantilever with rectangu-
lar cross section results in parallel weld beads, each element of which is in the ideal position. The
object of this problem is to study the full weld bead and the interrupted weld-bead pattern.
Consider the case of Fig. 9–17, p. 487, with F = 10 kips, the beam length is 10 in, b = 8 in, and
d = 8 in. For the second case, for the interrupted weld consider a centered gap of b 1 = 2 in exist-
ing in the top and bottom welds. Study the two cases with τ all = 12.8 kpsi. What do you notice
about τ, σ, and τ max? Compare the fom .

9–40 For a rectangular weld-bead track resisting bending, develop the necessary equations to treat
cases of vertical welds, horizontal welds, and weld-all-around patterns with depth d and width b
and allowing central gaps in parallel beads of length b 1 and d 1 . Do this by superposition of par-
allel tracks, vertical tracks subtracting out the gaps. Then put the two together for a rectangular
weld bead with central gaps of length b 1 and d 1 . Show that the results are

A = 1.414(b − b 1 + d − d 1 )h

3
(b − b 1 )d 2 d − d 1 3
I u = +
2 6
I = 0.707hI u
l = 2(b − b 1 ) + 2(d − d 1 )

I u
fom =
hl
9–41 Write a computer program based on the Prob. 9–40 protocol. Solicit the largest allowable shear
stress, the force F, and the clearance a, as well as the dimensions b and d. Begin an iterative loop
by soliciting b 1 and d 1 . Either or both of these can be your design variables. Program to find
the leg size corresponding to a shear-stress level at the maximum allowable at a corner. Output
all your parameters including the figure of merit. Use the program to check any previous problems
to which it is applicable. Play with it in a “what if” mode and learn from the trends in your
parameters.
9–42 When comparing two different weldment patterns it is useful to observe the resistance to bend-
ing or torsion and the volume of weld metal deposited. Measure of effectiveness, defined as sec-
ond moment of area divided by weld-metal volume, is useful. If a 3-in by 6-in section of a can-
tilever carries a static bending moment of 100 kip · in in the weldment plane, with an allowable
shear stress of 12 kpsi realized, compare horizontal weldments with vertical weldments. The
horizontal beads are to be 3 in long and the vertical beads, 6 in long.