Concept explainers
Fig. P2.41
2.41 Two cylindrical rods, one of steel and the other of brass, are joined at C and restrained by rigid supports at A and E. For the loading shown and knowing that Es = 200 GPa and Eb = 105 GPa, determine (a) the reactions at A and E, (b) the deflection of point C.
(a)
Find the reaction at point A and E.
Answer to Problem 41P
The reaction at point A is
The reaction at point E is
Explanation of Solution
Given information:
The length
The length
The length
The length
The young’s modulus for steel
The young’s modulus for steel
Calculation:
Find the area
Here,
Substitute
Find the value of EA for AC section as follows:
Substitute
Find the area
Here,
Substitute
Find the value of EA for CE section as follows:
Substitute
Sketch the free body diagram of cylindrical rod as shown in Figure 1.
Refer to Figure 1.
Take section A to B.
Find the change in length AB using the relation:
Here, P is the load, L is the length of rod, E is the young’s modulus, and A is the area of the section AB.
Substitute
Take section B to C.
Find the change in length BC using the relation:
Here, A is the area of the section BC.
Substitute
Take section C to D.
Find the change in length CD using the relation:
Here, A is the area of the section CD.
Substitute
Take section D to E.
Find the change in length DE using the relation:
Here, A is the area of the section CD.
Substitute
Take section A to E.
Here,
Substitute
Since the point E cannot move relative to A.
Find the reaction at point A as follows:
Thus, the reaction at point A is
Find the reaction at point E as follows:
Substitute
Thus, the reaction at point E is
(b)
Find the deflection of point C.
Answer to Problem 41P
The deflection of point C is
Explanation of Solution
Calculation:
Determine the deflection of point C using the relation:
Substitute
Substitute
Thus, the deflection of point C is
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Chapter 2 Solutions
Mechanics of Materials, 7th Edition
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