Chapter 13, Problem 13.1PFS

To determine

The resultant load on the most stressed bolt using eccentricity method.

Answer to Problem 13.1PFS

17.39k

Explanation of Solution

Given:

The given connection is,

  

Calculation:

Calculate factored load for LRFD.

  $\begin{array}{c} P_u=1.2 \left(50\right)+1.6 \left(100\right)\\ =60+160\\ =220\text{k}\end{array}$

Calculate factored load for ASD.

  $\begin{array}{c} P_u=50+100\\ =150\text{k}\end{array}$

The gross yielding area is calculated as,

  $\begin{array}{c}{A}_g=10\times \frac{5}{8}\\ =12.5{\text{in}}^2\end{array}$

The number of bolts required by using LRFD can be calculated as follows.

  $n=\frac{p_u}{R{\text{'}}_n}$

Where, $R{\text{'}}_n$ is the design strength.

We can calculate the $R{\text{'}}_n$ by using the formula $R{\text{'}}_n=\varphi R_n$ . Where, $R_n$ is the bearing strength of the bolt.

So, we can calculate the bearing strength of the bolt using the formula,

  $R_n=1.2l_{t}c{f}_u$

Substitute the all value in the above formula and we get that,

  $R_n=78.7k$

Substitute these values in the design strength formula then we get that,

  $\begin{array}{l}R{\text{'}}_n=0.75\times 78.7k\\ R{\text{'}}_n=59.06k\end{array}$

Now, calculate the number of bolts required for the connection using LRFD by the formula,

  $\begin{array}{l}R=\left(H^2+{\left(v+\frac{p_u}{n}\right)}^2\right)\\ R=17.39k\end{array}$

Conclusion:

Hence, the resultant force of the bolt is 17.39k.