Question 6.15: Review Example Analyses 12 and 14. Suppose that a maximum al......
Review Example Analyses 12 and 14. Suppose that a maximum allowable shear stress τ_{max} for the bracket rivets is 20,000 psi. Determine the corresponding maximum allowable safe weight load W_{max}.
From Example Analysis 14, Eq. (e), the maximum weight load is:
W_{max}=\pi r^{2} τ_{max} (a)
From Example Analysis 12, the rivet radius r is 1/8 in.
By substituting the given data into Eq. (a) we find the maximum weight load as:
W_{max}=\pi \left\lgroup\frac{1}{8} \right\rgroup ^{2}\left(20\right) 10^{3}=981.7 lb (b)
Comment
Observe that this result is less than the 1363 lb result obtained in Example Analysis 25. Observealso, however, that the only dimension occurring in Eq. (a) is the rivet radius r, whereas in Example Analysis 12, where the tensile stress strength is the quantity of interest, we see from Eq. (d) of Example Analysis 12, that the maximum load W_{max} is governed by the dimensions b, d, and e in addition to r. If, for example, the lateral dimension b is doubled to say 24 in, then the maximum load W_{max} is reduced to 681 lb—less than that of the result in Eq. (b). This shows that \underline{both} the tensile and shear strengths need to be considered in bracket designs.