Concept explainers
(a)
The suitable
Answer to Problem 6.8.7P
The best suitable
Explanation of Solution
Given:
The axial load is
The dead load is the
The live load is the
The length of the column is
The moment at top in x-direction is
The moment at top in y-direction is
The moment at bottom in x-direction is
The moment at bottom in y-direction is
Calculation:
Write the equation to obtain the load factor.
Here, load factor is
Calculate the dead load:
Calculate the live load:
Substitute
Write the equation to obtain the factored bending moment at the bottom of the member for braced condition along x-axis.
Here, factored bending moment at bottom along x-axis is
Calculate the bending moment along x-direction at bottom due to dead load.
Calculate the bending moment along x-direction at bottom due to live load.
Substitute
Write the equation to obtain factored bending moment at the top of the member for braced condition along x-axis.
Here, factored bending moment at top along x-axis is
Calculate the bending moment along x-direction at top due to dead load.
Calculate the bending moment along x-direction at top due to live load.
Substitute
Write the equation to obtain factored bending moment at the bottom of the member for braced condition along y-axis.
Here, factored bending moment at bottom along y-axis is
Calculate the bending moment along y-direction at bottom due to dead load.
Calculate the bending moment along y-direction at bottom due to live load.
Substitute
Write the equation to obtain the factored bending moment at the top of the member for braced condition along y-axis.
Here, factored bending moment at top along y-axis is
Calculate the bending moment along y-direction at top due to dead load.
Calculate the bending moment along y-direction at top due to live load.
Substitute
Write the equation to obtain the ultimate moment along x-axis.
Here, factor for braced condition is
Substitute,
Write the equation to obtain the ultimate moment along y-axis.
Here, factor for braced condition is
Substitute,
The unbraced length and effective length of the member are same.
Try
Write the expression to determine which interaction equation to use.
Here, load factor is
Substitute
Therefore,
Write the expression
Here, load factor is
Substitute,
Further solve the above equation.
Hence, it is safe to use
Try
Write the expression to determine the interaction equation to be used.
Here, load factor is
Substitute
Therefore,
Write the expression
Here, load factor is
Substitute,
Further solve the above equation.
Hence, it is safe to use
Try
Write the expression to determine the interaction equation to be used.
Here, load factor is
Substitute
Therefore,
Write the expression
Here, load factor is
Substitute
Further solve the above equation.
Hence, it is safe to use
Further check
Write the expression
Here, load factor is
Substitute
Further solve the above equation.
Hence, it is safe to use
Conclusion:
Thus, use
(b)
The best suitable
Answer to Problem 6.8.7P
The best suitable
Explanation of Solution
Calculation:
Write the equation to obtain the axial service load.
Here, load factor is
Calculate the dead load:
Calculate the live load:
Substitute
Write the equation to obtain factored bending moment at the bottom of the member for braced condition along x-axis.
Here, factored bending moment at bottom along x-axis is
Calculate the bending moment along x-direction at bottom due to dead load.
Calculate the bending moment along x-direction at bottom due to live load.
Substitute
Write the equation to obtain factored bending moment at the top of the member for braced condition along x-axis.
Here, factored bending moment at top along x-axis is
Calculate the bending moment along x-direction at top due to dead load.
Calculate the bending moment along x-direction at top due to live load.
Substitute
Write the equation to obtain factored bending moment at the bottom of the member for braced condition along y-axis.
Here, factored bending moment at bottom along y-axis is
Calculate the bending moment along y-direction at bottom due to dead load.
Calculate the bending moment along y-direction at bottom due to live load.
Substitute
Write the equation to obtain factored bending moment at the top of the member for braced condition along y-axis.
Here, factored bending moment at top along y-axis is
Calculate the bending moment along y-direction at top due to dead load.
Calculate the bending moment along y-direction at top due to live load.
Substitute
Write the equation to obtain the ultimate moment along x-axis.
Here, factor for braced condition is
Substitute
Write the equation to obtain the ultimate moment along y-axis.
Here, factor for braced condition is
Substitute
The unbraced length and effective length of the member are same.
Try
Write the expression to determine which interaction equation to use.
Here, load factor is
Substitute
Therefore,
Write the expression
Here, load factor is
Substitute
Further solve the above equation.
Hence, it is safe to use
Conclusion:
Thus, use
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Chapter 6 Solutions
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