Chapter 6, Problem 6.2.1P

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6th Edition

Segui + 1 other

ISBN: 9781337094740

Textbook Problem

Determine whether the given member satisfies the appropriate AISC interaction equation. Do not consider moment amplification. The loads are

**a.** Use LRFD.

**b.** Use ASD.

To determine

**(a)**

The satisfaction of AISC interaction equation using LRFD.

Answer

The member satisfies the AISC interaction equation.

Explanation

**Given:**

The load is

The length of member is

The value of

The flexural load is

**Concept Used:**

Write the LRFD interaction equation.

Here, the factored load is

**Calculation:**

Calculate the factored load.

Here, the dead load is

Substitute

Calculate the effective length of the member.

Here, the unsupported length is

Substitute

Calculate the axial compressive design strength.

From the manual table, the axial compressive design strength of a

Calculate the nominal flexural strength about x-axis.

From the design table, calculate the nominal flexural strength about x-axis by using

Calculate the flexural load about x-axis.

Here, the flexural dead load is

Substitute

There is no bending about y-axis, therefore

Write the equation to calculate the controlling interaction formula.

Substitute

The value is greater than

Calculate the LRFD interaction equation.

Substitute

The interaction equation is satisfied.

**Conclusion:**

Therefore, the interaction equation is satisfied with the AISD interaction equation.

To determine

**(b)**

The satisfaction of AISC interaction equation using ASD.

Answer

The member satisfies the AISC interaction equation.

Explanation

**Concept Used:**

Write the ASD interaction equation.

Here, the factored load is

**Calculation:**

Calculate the factored load.

Here, the dead load is

Substitute

Calculate the allowed compressive strength.

From the manual table, the allowed compressive strength of a

Calculate the nominal flexural strength about x-axis.

From the design table, calculate the nominal flexural strength about x-axis by using

Calculate the flexural load about x-axis.

Here, the flexural dead load is

Substitute

There is no bending about y-axis, therefore

Write the equation to calculate the controlling interaction formula.

Substitute

The value is greater than

Calculate the ASD interaction equation.

Substitute

The interaction equation is satisfied.

**Conclusion:**

Therefore, the interaction equation is satisfied with the ASD interaction equation.

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