Concept explainers
For the beam and loading shown, determine (a) the equation of the elastic carve, (b) the slope at end A, (c) the deflection at the midpoint of the span.
Fig. P9.159
(a)
The equation of the elastic curve (y) of the beam.
Answer to Problem 159RP
The equation of the elastic curve (y) of the beam is
Explanation of Solution
Calculation:
Write the load equation (w).
Integrate the Equation (1).
Substitute the boundary condition 0 for x and 0 for M in Equation (2).
Substitute the boundary condition L for x, 0 for
Substitute
Calculate the equation of the elastic curve (y) by integrating the Equation (3).
Substitute 0 for x and 0 for
Substitute the boundary condition L for x, 0 for
Substitute the boundary condition 0 for
Thus, the equation of the elastic curve (y) of the beam is
(b)
The slope
Answer to Problem 159RP
The slope
Explanation of Solution
Calculation:
Calculate the slope
Substitute
Thus, the slope
(c)
The deflection
Answer to Problem 159RP
The deflection
Explanation of Solution
Calculation:
Calculate the deflection
Substitute
Thus, the deflection
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Chapter 9 Solutions
Mechanics of Materials, 7th Edition
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