Concept explainers
Determine (a) the critical load for the steel strut, (b) the dimension d for which the aluminum strut will have the same critical load. (c) Express the weight of the aluminum strut as a percent of the weight of the steel strut.
Fig. P10.117
(a)
Find the critical load for the steel strut.
Answer to Problem 117RP
The critical load of the steel strut is
Explanation of Solution
The modulus of elasticity of the steel strut is
The size of the steel strut is
The length of the steel strut is
Determine the moment of inertia of the steel strut
Here, the size of the steel strut is
Substitute
The effective length
Determine the critical load
Here, the modulus of elasticity of the steel strut is
Substitute
Therefore, the critical load of the steel strut is
(b)
Find the dimension d for the condition that the critical load is same for steel strut and aluminum strut.
Answer to Problem 117RP
The dimension d of the aluminum strut for the given condition is
Explanation of Solution
The modulus of elasticity of the aluminium strut is
The length of the aluminium strut is
The critical load of the steel strut and the aluminum strut is equal.
The effective length
Determine the moment of inertia of the aluminium strut
Here, the critical load in the aluminium strut is
Substitute 647 lb for
Determine the dimension of the aluminum strut (d) using the relation.
Substitute
Therefore, the dimension d of the aluminum strut for the given condition is
(c)
Find the percentage weight of aluminum strut to the steel strut.
Answer to Problem 117RP
The percentage weight of aluminum strut to the steel strut is
Explanation of Solution
The weight density of the aluminium strut is
The weight density of the steel strut is
The length of the steel strut is
The length of the aluminium strut is
The dimension of the aluminium strut is
The size of the steel strut is
In general,
The weight density
Here, the weight of the material is W, the volume of the material is V, the cross sectional area of the material is A, and the length of the material is L.
Write the expression as percentage weight of aluminium strut
Substitute
Therefore, the percentage weight of aluminum strut to the steel strut is
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Chapter 10 Solutions
Mechanics of Materials, 7th Edition
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