Concept explainers
The wood column has a thickness of 4 in. and a width of 6 in. Using the NFPA equations of Sec.13.6 and Eq.13-30, determine the maximum allowable eccentric load P that can be applied. Assume that the column is pinned at both its top and bottom.
R13−1
Answer to Problem 1RP
The maximum allowable eccentric load on the column is
Explanation of Solution
Given information:
The load applied on the wooden column is
The column is pinned at both the ends.
The width of cross-sectional area of the column is
The depth of cross-sectional area of the column is
The length of the column is
Show the expression ofNFPA Equation of Sec 13.6 as follows:
Here,
Show the expression for Equation 13-30 as follows:
Here,
Calculation:
Calculate the cross-sectional area
Substitute
Calculate the moment of inertia using the relation:
Substitute
The ends of the column are pinned. Thus, the value of
Calculate the value of
Substitute
The value of
Show the expression of NFPA Equation of Sec 13.6 as follows:
Here,
Substitute 30 for
Show the expression for Equation 13-30 as follows:
Here,
The eccentricity
Calculate the value of c using the relation:
Substitute
Substitute
Thus, the maximum allowable eccentric load on the column is
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