Concept explainers
(a)
Find the slope
(a)
Answer to Problem 112P
The slope
Explanation of Solution
Calculation:
Use moment area method:
Show the free body diagram of the beam as in Figure 1.
Determine the reaction of the support by taking the vertical equilibrium condition:
Determine the moment over the span AB by taking the moment:
Substitute
Determine the moment over the span BD by taking the moment:
Show the moment
Due to symmetric beam with symmetric loading, consider the left side of the beam.
Calculate the moment
Substitute
Calculate the ratio of
Substitute
Calculate the area
Here,
Substitute a for
Calculate the moment
Calculate the ratio of
Substitute
Calculate the area
Here,
Substitute a for
Calculate the moment
Calculate the ratio of
Substitute
Calculate the area
Here,
Substitute
Show the tangent slope and deflection related to reference tangent as in Figure 3.
Place the reference tangent at C then the slope
Calculate the slope at the end A related to the point C
Substitute
Calculate the slope at the point A
Substitute 0 for
Thus, the slope
(b)
Find the deflection
(b)
Answer to Problem 112P
The deflection
Explanation of Solution
Calculation:
Calculate the deflection at end C related to the left end A
Substitute
Calculate the deflection at the point C
Substitute
Thus, the deflection
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Chapter 9 Solutions
Mechanics of Materials, 7th Edition
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