Concept explainers
Each of the five struts shown consists of a solid steel rod. (a) Knowing that the strut of Fig. (1) is of a 20-mm diameter, determine the factor of safety with respect to buckling for the loading shown. (b) Determine the diameter of each of the other struts for which the factor of safety is the same as the factor of safety obtained in part a. Use E = 200 GPa.
Fig. P10.27
(a)
Find the factor of safety with respect to buckling.
Answer to Problem 27P
The factor of safety with respect to buckling is
Explanation of Solution
The dimeter of the strut (1) is
The centric load in the strut (1) is
The modulus of elasticity of the column is
Determine the moment of inertia of the strut (1)
Here, the diameter of the strut 1 is
Substitute 20 mm for
Both the ends are pin connected.
The effective length of the column
Determine the critical load
Here, the modulus of elasticity is E.
Substitute 200 GPa for E,
Determine the factor of safety (FOS) using the relation.
Here, the allowable load in strut 1 is
Substitute 19.14 kN for
Therefore, the factor of safety with respect to buckling is
(b)
Find the diameter of the other struts for the condition that the factor of safety is same.
Answer to Problem 27P
The diameter of the strut (2) is
The diameter of the strut (3) is
The diameter of the strut (4) is
The diameter of the strut (5) is
Explanation of Solution
Determine the factor of safety (FOS) using the relation.
Therefore, the factor of safety is directly proportional to the critical load.
Here, the moment of inertia of ith strut is
Strut (2);
Show the effective length of the strut (2) as in Figure 1.
The effective length of the strut (2) is twice the length of the strut (1).
Substitute 2 for i, 2L for
Therefore, the diameter of the strut (2) is
Strut (3);
Show the effective length of the strut (3) as in Figure 2.
The effective length of the strut (3) is half the length of the strut (1).
Substitute 3 for i,
Therefore, the diameter of the strut (3) is
Strut (4);
Show the effective length of the strut (4) as in Figure 3.
The effective length of the strut (4) is 0.7 times the length of the strut (1).
Substitute 4 for i,
Therefore, the diameter of the strut (4) is
Strut (5);
Show the effective length of the strut (5) as in Figure 4.
The effective length of the strut (5) is equal to the length of the strut (1).
Substitute 5 for i, L for
Therefore, the diameter of the strut (5) is
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Chapter 10 Solutions
Mechanics of Materials, 7th Edition
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