Concept explainers
(a)
Plastic section modulus
Answer to Problem 5.2.1P
The plastic section modulus
Explanation of Solution
Given:
A flexural member is fabricated from two flange plates
Concept used:
The section is a symmetrical section which implies that the plastic neutral axis of the given section is same as the neutral of the given section. Therefore, calculating the lever arm and the centroid of the upper half of the given section, we can find the plastic section modulus.
We have the following figure that will define the terms that we have been given as per the question.
Calculation:
The following is the tabular measurement of every component required:
Elements | |||||
Web | |||||
Flange | |||||
Sum |
Calculating the centroid of the top half as :
Substitute the values in the above equation.
Now, calculating the moment arm, we have the following formula :
Where, a is the moment arm of the section.
Now, the plastic section modulus can be calculated as follows:
Where, Z is plastic section modulus and A is area.
Calculating the plastic moment as follows:
Substitute the value of
Conclusion:
Therefore, the plastic section modulus
(b)
Elastic section modulus,
Answer to Problem 5.2.1P
The elastic section modulus,
Explanation of Solution
Given:
A flexural member is fabricated from two flange plates
Concept used:
The section is a symmetrical section which implies that the elastic neutral axis of the given section is coinciding with the neutral of the given section. Therefore, calculating the moment of inertia at the major axis using parallel axis theorem, we can find the elastic section modulus.
We have the following figure that will define the terms that we have been given as per the question.
Calculation:
The following is the tabular measurement of every component required:
Elements | ||||
Web | ||||
Top Flange | ||||
Bottom Flange | ||||
Sum |
Calculate the Elastic section modulus S with the following formula
Where, C is the distance between the extreme fiber of the section and the neutral axis and is equal to
Here,
By substituting the values in the above equation, we have
Substitute the value of c in the following equation,
Now, calculate the yield moment
Substitute the value of
Conclusion:
Therefore, the elastic section modulus,
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Chapter 5 Solutions
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