Chapter 5, Problem 5.2.1P

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6th Edition

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ISBN: 9781337094740

Textbook Problem

A flexural member is fabricated from two flange plates

**a**. Compute the plastic section modulus *Z* and the plastic moment

**b**. Compute the elastic section modulus *S* and the yield moment

To determine

**(a)**

Plastic section modulus

Answer

The plastic section modulus

Explanation

**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

To determine

**(b)**

Elastic section modulus,

Answer

The elastic section modulus,

Explanation

**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,

Ch-5 P-5.2.1PCh-5 P-5.2.2PCh-5 P-5.2.3PCh-5 P-5.2.4PCh-5 P-5.4.1PCh-5 P-5.4.2PCh-5 P-5.4.3PCh-5 P-5.5.1PCh-5 P-5.5.2PCh-5 P-5.5.3P

Ch-5 P-5.5.4PCh-5 P-5.5.5PCh-5 P-5.5.6PCh-5 P-5.5.7PCh-5 P-5.5.8PCh-5 P-5.5.9PCh-5 P-5.5.10PCh-5 P-5.5.11PCh-5 P-5.5.12PCh-5 P-5.5.13PCh-5 P-5.5.14PCh-5 P-5.5.15PCh-5 P-5.5.16PCh-5 P-5.6.1PCh-5 P-5.6.2PCh-5 P-5.6.3PCh-5 P-5.6.4PCh-5 P-5.8.1PCh-5 P-5.8.2PCh-5 P-5.8.3PCh-5 P-5.8.4PCh-5 P-5.10.1PCh-5 P-5.10.2PCh-5 P-5.10.3PCh-5 P-5.10.4PCh-5 P-5.10.5PCh-5 P-5.10.6PCh-5 P-5.10.7PCh-5 P-5.11.1PCh-5 P-5.11.2PCh-5 P-5.11.3PCh-5 P-5.11.4PCh-5 P-5.11.5PCh-5 P-5.11.6PCh-5 P-5.11.7PCh-5 P-5.11.8PCh-5 P-5.11.9PCh-5 P-5.12.1PCh-5 P-5.12.2PCh-5 P-5.12.3PCh-5 P-5.13.1PCh-5 P-5.13.2PCh-5 P-5.14.1PCh-5 P-5.14.2PCh-5 P-5.14.3PCh-5 P-5.14.4PCh-5 P-5.15.1PCh-5 P-5.15.2PCh-5 P-5.15.3PCh-5 P-5.15.4PCh-5 P-5.15.5PCh-5 P-5.15.6PCh-5 P-5.15.7PCh-5 P-5.15.8P

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