Chapter 9, Problem 32P

In the design of weldments in torsion it is helpful to have a hierarchical perception of the relative efficiency of common patterns. For example, the weld-bead patterns shown in Table 9–1 can be ranked for desirability. Assume the space available is an a × a square. Use a formal figure of merit that is directly proportional to J and inversely proportional to the volume of weld metal laid down:

$\text{from}=\frac{J}{\text{vol}}=\frac{0.707h{J}_u}{\left(h^{\text{2}}\text{/ 2}\right)l}=1.414\frac{J_u}{hl}$

A tactical figure of merit could omit the constant, that is, fom′ = J_u(hl). Rank the six patterns of Table 9–1 from most to least efficient.