Concept explainers
Determine (a) the critical load for the square strut, (b) the radius of the round strut for which both struts have the same critical load. (c) Express the cross-sectional area of the square strut as a percentage of the cross-sectional area of the round strut. Use E = 200 GPa.
Fig. P10.13 and P10.14
(a)
Find the critical load of the square strut.
Answer to Problem 14P
The critical load of the square strut is
Explanation of Solution
The modulus of elasticity of the strut is
Determine the moment of inertia of the square strut
Substitute 25 mm for a.
Determine the critical load
Here, the modulus of elasticity is E and the length of the strut is L.
Substitute 200 GPa for E,
Therefore, the critical load of the square strut is
(b)
Find the radius of the round strut when the critical load is same for square strut and round strut.
Answer to Problem 14P
The radius of the round strut is
Explanation of Solution
The modulus of elasticity of the strut is
Determine the moment of inertia of the square strut
Here, the size of the square strut is a.
Substitute 25 mm for a.
Determine the critical load
Substitute 200 GPa for E,
The critical load of the square strut and the round strut is equal.
Determine the moment of inertia of the round strut
Substitute 64.3 kN for
Determine the radius of the round strut (c) using the relation.
Substitute
Therefore, the radius of the round strut is
(c)
Find the percentage of cross-sectional area of square strut to the cross-sectional area of round strut.
Answer to Problem 14P
The percentage of cross-sectional area of square strut to the cross-sectional area of round strut is
Explanation of Solution
The modulus of elasticity of the strut is
Find the cross sectional area of the square strut
Here, the size of the square strut is a.
Substitute 25 mm for a.
Find the cross sectional area of the round strut
Here, the radius of the round strut is c.
Substitute 14.27 mm for c.
Find the percentage of area of square strut to the area of round strut as follows;
Substitute
Therefore, the percentage of cross-sectional area of square strut to the cross-sectional area of round strut is
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Chapter 10 Solutions
Mechanics of Materials, 7th Edition
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