Structural Steel Design (6th Edition)
Structural Steel Design (6th Edition)
6th Edition
ISBN: 9780134589657
Author: Jack C. McCormac, Stephen F. Csernak
Publisher: PEARSON
bartleby

Concept explainers

bartleby

Videos

Textbook Question
100%
Book Icon
Chapter 8, Problem 8.1PFS

Find the values of S and Z and the shape factor about the horizontal xx axes, for the sections shown in the accompanying figures.

8-1.
Chapter 8, Problem 8.1PFS, Find the values of S and Z and the shape factor about the horizontal x—x axes, for the sections

Expert Solution & Answer
Check Mark
To determine

The values of S and Z and the shape factor about the horizontal x-x axes for the given section.

Answer to Problem 8.1PFS

  194.587in.3 , 350.93in.3 and 1.80

Explanation of Solution

The cross-section is shown below:

  Structural Steel Design (6th Edition), Chapter 8, Problem 8.1PFS , additional homework tip  1

The depth of neutral axis from bottom is given by

  y¯=A1y1+A2y2A1+A2(1)where,y¯isthedepthofneutralaxisfrombottomA1isareaofsection1A2isareaofsection2y1isdepthofcenterofgravityofsection1y2isdepthofcenterofgravityofsection2

The area of both section 1 and section 2 are

  A1=14×3A1=42in.2A2=17×2A2=34in.2

The depth of centre of gravity both section 1 and section 2 are

  y1=17+32y1=18.5in.y2=172y2=8.5in.

Now, substituting the values in equation (1),

  y¯=A1y1+A2y2A1+A2y¯=42×18.5+34×8.542+34y¯=14.026in.

The distance of centre of gravity from section 1 from the Neutral Axis (N.A.) is

  h1=y1y¯h1=18.514.026h1=4.474in.

The distance of centre of gravity from section 2 from the Neutral Axis (N.A.) is

  h2=y¯y2h2=14.0268.5h2=5.526in.

The moment of inertia is

  Ix=[( B× t f 3 12)+( A 1× h 1 2)]+[( t w × d w 3 12)+( A 2× h 2 2)]Ix=[( 14× 3 3 12)+(42× 4.474 2)]+[( 2× 17 3 12)+(34× 5.526 2)]Ix=872.2+1857.08Ix=2729.28in.4

The elastic section modulus is

  Sx=IxcSx=2729.2814.026Sx=194.587in.3

The location of plastic neutral axis is

  Structural Steel Design (6th Edition), Chapter 8, Problem 8.1PFS , additional homework tip  2

The area of flange is greater than the half of the sectional area. Hence the plastic neutral axis is located within the flange as shown in the above figure.

The depth of plastic neutral axis from top of the section x is

  14(x)=(17×2)+14(3x)14(x)=34+4214x28x=76x=2.71in.

The area of both section 1 and section 2 are

  A1=14×2.71A1=38in.2A2=14×(32.71)A2=4.06in.2A3=2×17A3=34in.2

The depths of centre of gravity both section 1 and section 2 from plastic neutral axis are

  y1=x2y1=2.712y1=1.355in.y2=3x2y2=32.712y2=0.145in.y3=(3x)+172y3=(32.71)+172y3=8.79in.

The plastic section modulus is

  Zx=A1y1+A2y2+A3y3Zx=(38×1.355)+(4.06×0.145)+(34×8.79)Zx=350.93in.3

The shape factor is

  Shapefactor=ZxSxShapefactor=350.93194.587Shapefactor=1.80

Conclusion:

The values of S and Z and the shape factor about the horizontal x-x axes are 194.587in.3 , 350.93in.3 and 1.80 respectively.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!
Students have asked these similar questions
Use the Force Method to analyse the structure. After the analysis, draw Bending Moment and Shear Force diagrams. Redundants need to be put at 'j' and 'k' as moments (EI is constant all across the structure)I am so confused as to how to approach the problem. I would really appreciate an answer with a little explanation, or helpful working out!
I got 5.97 mm please show your work clearly. thank you
A 7K SK-> VE 3 F T A=52 E=29000 ksi diagonal members 6' A=30.25.72 E=1800 ksi for horizontal & vertical member ↓ B Oc AD 8 Primary Structures remove roller @C make D a roller For Primary and Cut BF For redundant Ik ↑ ec Ik = @D Ik @BF
Knowledge Booster
Background pattern image
Civil Engineering
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
SEE MORE QUESTIONS
Recommended textbooks for you
Text book image
Fundamentals Of Construction Estimating
Civil Engineering
ISBN:9781337399395
Author:Pratt, David J.
Publisher:Cengage,
Text book image
Architectural Drafting and Design (MindTap Course...
Civil Engineering
ISBN:9781285165738
Author:Alan Jefferis, David A. Madsen, David P. Madsen
Publisher:Cengage Learning
Text book image
Materials Science And Engineering Properties
Civil Engineering
ISBN:9781111988609
Author:Charles Gilmore
Publisher:Cengage Learning
Text book image
Residential Construction Academy: House Wiring (M...
Civil Engineering
ISBN:9781285852225
Author:Gregory W Fletcher
Publisher:Cengage Learning
Text book image
Steel Design (Activate Learning with these NEW ti...
Civil Engineering
ISBN:9781337094740
Author:Segui, William T.
Publisher:Cengage Learning
Text book image
Engineering Fundamentals: An Introduction to Engi...
Civil Engineering
ISBN:9781305084766
Author:Saeed Moaveni
Publisher:Cengage Learning
Properties & Application Of Different Carbon Steels - Metals, Alloys, Cement & Refractory Materiall; Author: Ekeeda;https://www.youtube.com/watch?v=lwT0Bdd8bPE;License: Standard YouTube License, CC-BY