Concept explainers
The magnitude
Answer to Problem 144P
The magnitude
Explanation of Solution
Given information:
The elastic modulus (E) is
The section of the beam is
Calculation:
Refer Appendix C, “Properties of Rolled steel shapes”.
The moment of inertia (I) for the given section is
Use moment area method:
Show the free body diagram of the beam as in Figure 1.
Determine the reaction of the support by taking moment at point B.
Determine the reaction of the support by considering the vertical equilibrium condition:
Substitute
Show the moment
Calculate the moment
Substitute
Calculate the ratio of
Substitute
Calculate the area
Here, b is the width of the triangle in area
Substitute
Calculate the moment
Substitute
Calculate the ratio of
Substitute
Calculate the area
Here,
Substitute
Calculate the moment
Calculate the ratio of
Substitute
Calculate the area
Here,
Substitute
Calculate the moment
Calculate the ratio of
Substitute
Calculate the area
Here,
Substitute
Show the moment
Calculate the moment
Calculate the ratio of
Substitute
Calculate the area
Here,
Substitute
Calculate the slope at the end A related to the point B
Substitute
Calculate the slope
Substitute
Calculate the slope
Substitute
Calculate the slope
Substitute
Let point K be location of the largest downward deflection.
Hence, the slope at point E is greater than zero, the point K of zeros slope lies to the left of the point E.
Calculate the moment
Calculate the ratio of
Substitute
Calculate the moment
Calculate the ratio of
Substitute
Show the moment
Calculate the area
Substitute
Calculate the area
Substitute
Calculate the slope
Substitute
Differentiate the Equation (1).
Solve the value
Iteration 1:
Substitute 5 for
Substitute 5 for
Iteration 2:
Calculate the value
Substitute 5 for
Similarly calculate the value
f | ||
5 | -10.634 | 69.5 |
5.153 | -0.037 | 69.962 |
5.0005 | -10.597 | 69.5.02 |
5.1525 | 0.001 |
The value of
Calculate the slope at the end A related to the point K
Substitute
Calculate the magnitude
Substitute
Thus, the magnitude
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Chapter 9 Solutions
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