**Problem Statement:**An unsymmetrical flexural member consists of a \( \frac{3}{8} \times 14 \) in. top flange, a \( \frac{3}{8} \times 10 \) in. bottom flange, and a \( \frac{3}{8} \times 20 \) in. web.**Questions:**(a) Determine the distance \( \overline{y} \) from the top of the shape to the horizontal plastic neutral axis (P.N.A.).(b) If A572 Grade 50 steel is used, what is the plastic moment \( M_p \) for the horizontal P.N.A.?(c) Compute \( Z_y \), the plastic section modulus with respect to the minor principal axis.(d) Calculate the ratio of \( Z_y / S_y \). (Note: \( S_y \) is the (elastic) section modulus with respect to the minor principal axis.)**Steps to Solve:**1. **Determine Distance to P.N.A.** - Calculate the area of each section: top flange, bottom flange, and web. - Use the areas and distances to find the centroid of the shape. - The distance \( \overline{y} \) is then measured from the top to the centroid.2. **Calculate Plastic Moment \( M_p \)** - Use the plastic section modulus and material properties. - For A572 Grade 50 steel, the yield strength \( f_y \) is 50 ksi. - The plastic moment \( M_p \) is given by \( M_p = f_y \cdot Z \).3. **Compute Plastic Section Modulus \( Z_y \)** - Integrate the moments of areas about the horizontal plastic neutral axis. - Sum the individual plastic section moduli for all components.4. **Calculate the Ratio \( Z_y / S_y \)** - Obtain the elastic section modulus \( S_y \) from standard shape tables or calculations. - Compute the ratio of the plastic section modulus to the elastic section modulus.This information can be used for detailed structural analysis and design processes, ideal for civil engineering and materials science students.

given:A572 Grade 50 steelLet us assume, Yield strength (Fy) = 345 MPa (50 ksi)Moment of inertia (I)…

An unsymmetrical flexural member consists of a %x14 in. top flange, a ¾×10 in. bottom flange, and a ¾x20 in. web. (a) Determine the distance y from the top of the shape to the horizontal plastic neutral axis (P.N.A.). (b) If A572 Grade 50 steel is used, what is the plastic moment M, for the horizontal P.N.A.? (c) Compute Zy, the plastic section modulus with respect to the minor principal axis. (d) Calculate the ratio of Z/S,. (Note: S, is the (elastic) section modulus with respect to the minor principal axis.

An unsymmetrical flexural member consists of a %x14 in. top flange, a ¾×10 in. bottom flange, and a ¾x20 in. web. (a) Determine the distance y from the top of the shape to the horizontal plastic neutral axis (P.N.A.). (b) If A572 Grade 50 steel is used, what is the plastic moment M, for the horizontal P.N.A.? (c) Compute Zy, the plastic section modulus with respect to the minor principal axis. (d) Calculate the ratio of Z/S,. (Note: S, is the (elastic) section modulus with respect to the minor principal axis.

Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

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