**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

See similar textbooks

Related questions

Q: 2.10 A square yellow it is subjected t the allowable t mum allowable cross section if

Q: Situation 8. The given angle bar L125x75x10 is connected to a 12 mm gusset plate using 20 mm…

A: Given, L125 x 75 x 10 t = 12 mm db = 20 mm Fy = 248 MPa Fu = 400 MPa NOTE : As per guidelines,…

Q: A 2L 3 x 2 x ¼ LLBB tension double angle, A36 steel is subjected to a dead load of 12 kips and a…

A: For the given double angle member,

Q: An unsymmetrical flexural member consists of a ½ × 12 top flange, a ½ × 7 bottom flange, and a ⅜ ×…

A: a.) A1= A2 A1 = 12×12+38(y-12) = 5.8125 + 0.375y A2 = 7×12+38×(16.5-y) = 9.5875-0.375y After solving…

Q: Problem 4: Use A992 steel and select a W shape. The service dead load is 142 kips, and the service…

A: First we summarise the given data : Service dead load = 142 kips Service live load = 356 kips To…

Q: Found solutions, steel structure

Q: Given: A-in-thick. ASTM A36 eyebar member as shown in Figure D.8, carries a dead load of 25 kips and…

Q: An A36 tension member shown in the figure is connected with three 19 mm diameter bolts. Dia. Of bolt…

Q: A W14X120 is used as a tension member in atruss. The flanges of the member are connected to a gusset…

A: The order of the steel cross sections relies upon the heap that the part can convey prior to…

Q: PROBLEM NO. 2: Two plates each with thickness t = 16mm are bolted together with 6-22mm diameter…

A: Data Given:S1 = 40 mmS2 = 80 mmS3 = 100 mmt = 16 mmBolt diameter (db)= 16 mmAsked:Allowable strength…

Q: A steel plate (called a cover plate) having cross-sectional dimensions W2 5.0 in. x 0.4 in. is…

A: The given data is shown below: W2=5 in.×0.4 in.W1=12 in.×87 in.

Q: Use A992 steel and select a W shape using LRFD. D = 350 k L = 1000 k 35' Strong axis T 10' Figure 4…

A: Span, L = 35 ft Dead load, D = 350 k Live load, L = 1000 k A992 steel; fy = 50 ksi fu = 65 ksi

Q: Evercise:- A cylindrical rod 100 mm diameter of 12 mm long with is subjected to a 30000 N. Assuming…

A: Given,Initial length of the rod, say L = 100 mmInitial diameter of the rod, say D = 12 mmTensile…

Question

**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.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1: Given data.

VIEW

Step 2: Distance ȳ from the top of the shape to the horizontal plastic neutral axis (P.N.A.):

VIEW

Step 3: Plastic moment Mp for the horizontal P.N.A.

VIEW

Step 4: Plastic section modulus with respect to the minor principal axis.

VIEW

Solution

VIEW

Step by step

Solved in 5 steps with 12 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, civil-engineering and related others by exploring similar questions and additional content below.

Similar questions

An unsymmetrical flexural built-up shape member consists of a 2 inch x 20 inch top flange and a 2 inch x 15 inch bottom flange and a ½ inch x 40 inch web. a. Determine the distance "y" from the top of the shape to the horizontal plastic neutral axis. b. If the steel is A572, Grade 50, what is the Plastic Moment, Mp, in ft-kips? Answer: ỹ = 2 x 20 Plate Mp Р.N.A. ½ x 40 Plate 2 x 15 Plate
A steel plate (called a cover plate) having cross-sectional dimensions W2 8.0 in. x 0.7 in. is welded along the full length of the bottom flange of a W, 12.0 in. x 14.0 in. wide-flange beam (see the figure, which shows the beam cross section). I W2 cover plate What is the percent increase in the smaller section modulus (as compared to the wide-flange beam alone)? Round your answer to two decimal places. % in smaller section modulus =|
.
Given the truss shown, solve the following. Use A36 steel and assume there are two lines of three 19 mm bolts in each flange. Hole diameter is assumed to be three mm more than the bolt diameter. Neglect the weight of the section. a.What is the capacity of member CG? b. Design member CG using a W section. c. What is the tensile capacity of the section for CG based on gross area? The following W Section were considered for the design: W10x33 W14x38 W8x40 W16x36 W10x39 W8x13 189 KN 1.50 HL B 145 KN 1.50 E + 137 KN 121 KN -3.00 + 12.00 3.00 154 KN + W4x13 W6x9 W10x12 200 KN -1.50 1.50 1 030 T 1.20 +2.40 0.60 L i 0.30
Design the reinforcements of the given T beam below. bf=900mm bw=420mm tf-120mm d=550mm d'=80mm fc'=34MPa fy=415MPa USE NSCP 2015 A.Mu = 1300kN-m, As = mm2 B.Mu = 1800kN-m, As = mm2, As' = mm2
Select all zero-force members in the truss shown below. Check the box for zero- force members 3 m 3 m 12 m, 8 @ 1.5 m DE O LK ЕР O HF O BC BM EF OM CD BN LO O DK FI O co