Chapter 14, Problem 14.1PFS

To determine

The LRFD design load and the ASD design loads for the given connection members.

Answer to Problem 14.1PFS

  $97.2k\text{ and }64.7k$

Explanation of Solution

Given:

  

Calculation:

The ultimate load by LRFD is

  $\begin{array}{l}{P}_u=1.6P_L\\ P_u=1.6\left(32\right)\\ P_u=51.2kips\end{array}$

The factored moment is

  $\begin{array}{l}{M}_u=\frac{P_{u}L}{4}\\ M_u=\frac{51.2\left(40\right)}{4}\\ M_u=512kips-ft\end{array}$

The factored shear force is

  $\begin{array}{l}{V}_u=\frac{P_u}{2}\\ V_u=\frac{51.2}{2}\\ V_u=25.6kips\end{array}$

Refer Table 3-2 in the AISC steel construction manual.

Try $W30\times 124$

  $\begin{array}{l}{\varphi }_v{V}_{nx}\ge V_u\\ 530kips\ge 26.5kips\\ {\varphi }_b{M}_{px}\ge M_u\\ 1530kips-ft\ge 512kips-ft\end{array}$

The required moment of inertia is

  $\begin{array}{l}\frac{L}{1000}=\frac{P_L{L}^3}{48EI}\\ \frac{40\times 12}{1000}=\frac{32\times {\left(40\times 12\right)}^3}{48\left(29000\right)I}\\ I=5296.55in{.}^4\end{array}$

Refer Table 3-3 in the AISC steel construction manual.

Try $W30\times 124$

  $I_x=5360in{.}^4>5296.55in{.}^4$

Hence, it’s safe.

The ultimate load by ASD is

  $\begin{array}{l}{P}_a=P_L\\ P_a=32kips\end{array}$

The factored moment is

  $\begin{array}{l}{M}_a=\frac{P_{a}L}{4}\\ M_a=\frac{32\left(40\right)}{4}\\ M_a=320kips-ft\end{array}$

The factored shear force is

  $\begin{array}{l}{V}_a=\frac{P_a}{2}\\ V_a=\frac{32}{2}\\ V_a=16kips\end{array}$

Refer Table 3-2 in the AISC steel construction manual.

Try $W30\times 124$

  $\begin{array}{l}\frac{V_u}{\Omega }\ge V_u\\ 353kips\ge 16kips\\ \frac{M_{px}}{{\Omega }_b}\ge M_u\\ 1020kips-ft\ge 320kips-ft\end{array}$

The required moment of inertia is

  $\begin{array}{l}\frac{L}{1000}=\frac{P_L{L}^3}{48EI}\\ \frac{40\times 12}{1000}=\frac{32\times {\left(40\times 12\right)}^3}{48\left(29000\right)I}\\ I=5296.55in{.}^4\end{array}$

Refer Table 3-3 in the AISC steel construction manual.

Try $W30\times 124$

  $I_x=5360in{.}^4>5296.55in{.}^4$

By taking from the minimum values we obtained we get the allowable and safe loads.

Conclusion:

Therefore, the required loads by LRFD and ASD are $97.2k\text{ and }64.7k$ respectively.