Concept explainers
A steel tube of 80-mm outer diameter is to carry a 93-kN load P with an eccentricity of 20 mm. The tubes available for use are made with wall thicknesses in increments of 3 mm from 6 mm to 15 mm. Using the allowable-stress method, determine the lightest tube that can be used. Assume E = 200 GPa and σY = 250 MPa.
Fig. P10.105
Find the thickness of the lightest tube.
Answer to Problem 105P
The thickness of the lightest steel tube is
Explanation of Solution
Given information:
The length of the steel tube is
The outer diameter of the steel tube is
The magnitude of the axial load is
The eccentricity of the load in steel tube is
The allowable yield stress of the steel tube is
The modulus of elasticity of the steel tube is
Calculation:
The effective length of the column
Find the inner diameter of the steel tube
Here, the thickness of the steel tube is t.
Substitute 80 mm for
Find the cross sectional area of the steel tube (A) using the equation.
Substitute 80 mm for
Find the moment of inertia of the steel tube (I) using the equation.
Substitute 80 mm for
Find the minimum radius of gyration (r) using the relation.
Substitute
Find the distance between the neutral axis to the extreme fibre (c) using the relation.
Substitute 80 mm for
Find the slenderness ratio
Here, the modulus of elasticity of the material is E and the allowable yield strength is
Substitute 200 GPa for E and 250 MPa for
Find the ratio of the effective length to the minimum radius of gyration.
Consider
Find the effective stress
Substitute 200 GPa for E and
Find the critical stress
Substitute 250 MPa for
Find the allowable stress
Substitute
Find the maximum moment (M) using the relation.
Here, the allowable load is P and the eccentricity of the load is e.
Substitute 93 kN for P and 20 mm for e.
Find the thickness of the lightest tube (t) using the equation.
Substitute
Solve the equation;
The thickness is
The nearest 3 mm increment of the thickness is 12 mm.
Check:
Substitute 12 mm for t in Equation (1).
Therefore, the thickness of the lightest steel tube is
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Chapter 10 Solutions
Mechanics of Materials, 7th Edition
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