Chapter 8, Problem 8.2.1P

To determine

The maximum bolt shear force in the given bracket connection by using an elastic analysis.

Answer to Problem 8.2.1P

$22.253kips$

Explanation of Solution

Given:

Calculation:

Determine the direct shear components:

$\begin{array}{l}{P}_x=\frac{3}{5}\left(15\right)=9kips\\ P_y=\frac{4}{5}\left(15\right)=12kips\\ P_{cx}=\frac{9}{4}=2.25kips\to \\ P_{cy}=\frac{12}{4}=3kips\downarrow \end{array}$

Eccentricity:

$\begin{array}{l}{e}_x=12in.\\ e_y=9+1.5-4.5=6in.\end{array}$

$M=9\left(6\right)+12\left(12\right)=198in-kips$ (Clockwise)

${\displaystyle \sum \left(x^2+y^2\right)=2\left[{\left(4.5\right)}^2+{\left(1.5\right)}^2\right]}=45in{.}^2$

Top bolt is critical.

$\begin{array}{l}x=0\\ y=\frac{9}{2}=4.5in.\\ p_{mx}=\frac{My}{{\displaystyle \sum \left(x^2+y^2\right)}}=\frac{198\left(4.5\right)}{45}=19.8kips\to \\ {\displaystyle \sum p_x}=2.25+19.8=22.05kips\to \\ {\displaystyle \sum p_y}=3kips\downarrow \\ p=\sqrt{{\left({\displaystyle \sum p_x}\right)}^2+{\left({\displaystyle \sum p_y}\right)}^2}=\sqrt{{\left(22.05\right)}^2+{\left(3\right)}^2}=22.253kips\end{array}$

Conclusion:

The maximum bolt shear force in the given bracket connection is $22.253kips$.