Question 6.20: Consider again the dynamically loaded bracket of Example Ana......
Consider again the dynamically loaded bracket of Example Analyses 18 and 19 and as shown again here in Figure a. As before, let the bracket and wall support by rigid. Let the dimensions of the bracket, the rivets, and the wall thickness be as follows:
a = 6 in
b = 18 in
c = 6 in
d = 12 in
e = 5 in
h = 0.375 in
r = 0.1875 in
t = 0.625 in
Let the elastic modulus E of the rivets be:
E=30\times 10^{6} lb/in^{2} (b)
Finally, let the weight W of the suddenly applied block B be:
W = 500 lb (c)
Determine the maximum stresses in the rivets and the maximum downward displacement of the bracket of the point of application of the block.
From the results of Example Analysis 37 we have these expressions for the dynamic stresses:
\sigma _{A}=2Wb\left(d+e\right)/ \left(\pi r^{2}\right)\left[\left(d+e\right)^{2}+e^{2} \right] (a)
\sigma _{B}=2Wbe/ \left(\pi r^{2}\right)\left[\left(d+e\right)^{2}+e^{2} \right] (b)
Also, from the result of Example Analysis 19, the maximum downward displacement δ, due to the suddenly applied load is:
\delta=2Wb^{2}\ell /E\left(\pi r^{2}\right)\left[\left(d+e\right)^{2}+e^{2} \right] (c)
By direct substitution of the given data we immediately obtain the results:
\sigma_{A}=(2)(500)(18)(12+5)/(\pi)(0.1875)^{2}\left[\left(12+5\right)^{2}+(5)^{2} \right]or
\sigma_{A}=8823 lb/in^{2} (psi) (d)
and
\sigma_{B}=(2)(500)(18)(5)/(\pi)(0.1875)^{2}\left[\left(12+5\right)^{2}+(5)^{2} \right]or
\sigma_{B}=2595 lb/in^{2} (e)
and
\delta=(2)(500)(18)^{2}(1.0)/(30)(10)^{2}(\pi)(0.1875)^{2}\left[\left(12+5\right)^{2}+(5)^{2} \right]or
\delta=3.114 ×10^{−4} in (f)
where in the last computation we have assigned the rivet length P as h + t.