Determine the value of the shape-efficiency factor \(\phi_{B}^{f}\) for strength-limited design in bending using the dimensions shown on the diagrams

a. For the tube-section shown in Fig. E10.5(A)

b. For the box section shown in Fig. E10.5(B) 

c. For the channel section shown in Fig. E10.5(C).

The expression for \(\phi_{B}^{f}\) for the first two sections can be read from Table 10.3. You will have to derive the expression for the third.

Data From Fig, E10.5 (A) (B) (C)

Data From TABLE 10.3

10t Outer radius r=5t h = 10t (A) h = 8t 10t (B) FIGURE E10.5 10t 1 5t (C)