Concept explainers
For the loading shown, determine (a) the equation of the elastic curve for the cantilever beam AB, (b) the deflection at the free end, (c) the slope at the free end.
Fig. P9.157
(a)
The equation of elastic curve (y) for the cantilever beam AB.
Answer to Problem 157RP
The equation of the elastic curve for the cantilever beam AB is
Explanation of Solution
Calculation:
Show the free body diagram of the beam as in Figure 1.
Calculate the reaction
Calculate the moment
Show the free body diagram of beam section AE as in Figure 2.
Calculate the moment (M) by taking moment about the point E.
Calculate the equation of the elastic curve (y) by integrating the Equation (1).
Substitute 0 for x and 0 for
Integrate equation (2) and Substitute 0 for
Substitute 0 for x and 0 for y in Equation (3).
Integrate Equation (3) and Substitute 0 for
Multiply the Equation by
Thus, the equation of the elastic curve for the cantilever beam AB is
(b)
The deflection
Answer to Problem 157RP
The deflection
Explanation of Solution
Calculation:
Calculate the deflection
Substitute L for x.
Thus, the deflection
(c)
The slope
Answer to Problem 157RP
The slope
Explanation of Solution
Calculation:
Calculate the slope
Substitute L for x and 0 for
Thus, the slope
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Chapter 9 Solutions
Mechanics of Materials, CE3110