A cantilever beanie B is loaded by a uniform load q and a concentrated load P, as shown in the figure.
- Select the most economical steel C shape from Table F-3(a) in Appendix F; use q = 20 lb/ft and P = 300 lb (assume allowable normal stress is cra= IS ksi).
Note: For parts (a), (b), and (c), revise your initial beam selection as needed to include the distributed weight of the beam in addition to uniform load q.
(a)
The most economical steel
Answer to Problem 5.6.5P
The most economical steel
Explanation of Solution
Given information:
The uniform distributed load is
The following figure shows the free body diagram:
Figure-(1)
Write the expression for the maximum moment of beam.
Here, the load is
Write the expression for the section modulus.
Here, the maximum stress is
Write the expression for the maximum stress.
Here, the maximum stress is
Calculation:
Substitute
Substitute
Refer to the table
Substitute
Substitute
Here, the maximum stress is greater than the calculated stress, so we neglect this section.
Refer to the table
Substitute
Substitute
Hence, from the table “Appendix F” we will use the value
Conclusion:
The most economical steel
(b)
The most economical steel
Answer to Problem 5.6.5P
The most economical steel
Explanation of Solution
Given Information:
The uniform distributed load is
Write the expression for the maximum moment of beam.
Write the expression for the section modulus.
Write the expression for the maximum stress.
Calculation:
Substitute for
Substitute
Refer to the table
Substitute
Substitute
Here, the maximum stress is greater than the calculated stress, so we neglect this section.
Refer to the table
Substitute
Substitute
Hence, from the table “Appendix F” we will use the value
Conclusion:
The maximum value of load
(c)
The most economical steel
Answer to Problem 5.6.5P
The most economical steel
Explanation of Solution
Given Information:
The uniform distributed load is
Write the expression for the maximum moment of beam.
Write the expression for the section modulus.
Write the expression for the maximum stress.
Calculation:
Substitute
Substitute
Refer to the table
Substitute
Substitute
Hence, from the table “Appendix F” we will use the value
Conclusion:
The maximum value of load
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Chapter 5 Solutions
Mechanics of Materials, SI Edition
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