Question 6.12: Review Example Analysis 11. Consider again the bracket of Fi......
Review Example Analysis 11. Consider again the bracket of Figure a and as shown again here in Figure a. Let the dimensions/distances shown have the values:
a=2 in, b=12 in, c=4 in, d=8 in
e=4 in, h=3/16 in, 2r= 1/4 in (a)
Suppose the allowable rivet stress (the tensile stress) is 25,000 psi. Determine the maximum weight (load) W_{max} that the bracket can hold.
Recall from Eqs. (k) and (Ρ) of the solution for Example Analysis 11 that the rivet tensile stresses are:
\sigma _{A}=\frac{Wb\left(d+e\right) }{\left(\pi r^{2} \right)\left[\left(d+e\right) ^{2}+e^{2} \right] } (b)
and
\sigma _{B}=\frac{Wbe }{\left(\pi r^{2} \right)\left[\left(d+e\right) ^{2}+e^{2} \right] } (c)
By solving these expressions for W we have:
W= \frac{\left(\sigma _{A} \right) \left(\pi r^{2} \right)\left[\left(d+e\right) ^{2}+e^{2} \right]}{\left(b\right)\left(d+e\right) } (d)
and
W= \frac{\left(\sigma _{B} \right) \left(\pi r^{2} \right)\left[\left(d+e\right) ^{2}+e^{2} \right]}{\left(be\right) } (e)
Observe in these expressions that the value of W in Eq. (d) is smaller than that in Eq. (e). Therefore, Eq. (d) provides the maximum safe load W_{max}. (Also, by inspection of Figure a we see that rivet A will bear the greater portion of the load.)
By substituting the given data W_{max} then is:
or
W_{max}=1363 lb =1.363 kip (f)
Comment
Observe in Eq. (d) that the distances a and c, and the thickness dimension t, do not influence the value of the maximum allowable load.