Concept explainers
(a)
Find the maximum allowable eccentricity e.
(a)
Answer to Problem 128RP
The maximum allowable eccentricity is
Explanation of Solution
Given information:
The effective length of the steel tube is
The magnitude of the vertical load is
The allowable yield strength in the column is
The modulus of elasticity of the material is
Calculation:
The outer dimension
The inner dimension
Find the cross sectional area of the steel tube (A) using the equation.
Substitute 4 in. for
Find the moment of inertia of the square cross section (I) using the equation.
Substitute 4 in. for
Find the minimum radius of gyration (r) using the relation.
Substitute
Find the slenderness ratio
Here, the modulus of elasticity of the material is E and the allowable yield stress is
Substitute
Find the ratio of effective length
Find the effective stress
Substitute
Find the critical stress
Substitute 36 ksi for
Calculate the allowable stress
Substitute 18.398 ksi for
Find the moment acting in the column (M) using the relation.
Here, the vertical load is P and the eccentricity of the load is e.
Substitute 55 kips for P.
The distance between the neutral axis and the outermost fibre is;
Find the allowable stress in the column
Substitute 11.017 ksi for
Therefore, the maximum allowable eccentricity is
(b)
Find the maximum allowable eccentricity e.
(b)
Answer to Problem 128RP
The maximum allowable eccentricity is
Explanation of Solution
Given information:
The effective length of the steel tube is
The magnitude of the vertical load is
The allowable yield strength in the column is
The modulus of elasticity of the material is
Calculation:
The outer dimension
The inner dimension
Find the cross sectional area of the steel tube (A) using the equation.
Substitute 4 in. for
Find the moment of inertia of the square cross section (I) using the equation.
Substitute 4 in. for
Find the minimum radius of gyration (r) using the relation.
Substitute
Find the slenderness ratio
Substitute
Find the ratio of effective length
Find the effective stress
Substitute
Find the critical stress
Substitute 36 ksi for
Calculate the allowable stress
Substitute 18.398 ksi for
Find the moment acting in the column (M) using the relation.
Substitute 35 kips for P.
The distance between the neutral axis and the outermost fibre is;
Find the allowable stress in the column
Substitute 11.017 ksi for
Therefore, the maximum allowable eccentricity is
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Chapter 10 Solutions
EBK MECHANICS OF MATERIALS
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