Explanation Given information: The magnitude of the load P is 100 kN . Calculation: Show the cross-section of the beam as shown in Figure 1. Refer to Figure 1. Calculate the total area ( A ) of the cross-section as follows: A = A 1 + A 2 = ( 100 × 20 ) + ( 60 × 20 ) = 2000 mm 2 Show the expression for centroid distance ( Y ¯ ) of the cross-section of the beam as follows: Y ¯ = ∑ A y ¯ ∑ A = ( A 1 y ¯ 1 + A 1 y ¯ 2 A 1 + A 2 ) Consider the distance of centroid of the rectangle 1, 2 from the base is denoted by y ¯ 1 = 10 mm and y ¯ 2 = − 10 mm . Y ¯ = ( A 1 y ¯ 1 + A 1 y ¯ 2 A 1 + A 2 ) Refer Figure 1. Calculate the distance ( Y ¯ ) as follows: Y ¯ = ( 100 × 20 × 10 + 60 × 20 × ( − 10 ) 100 × 20 + 60 × 20 ) = 8 , 000 3 , 200 = 2.5 mm The coordinates of the load point are X p = a and Y p = − 2.5 mm . Show the bending couples M x and M y as follows: M x = P Y p = 100 × ( − 2.5 ) = − 250 kN ⋅ mm M y = − P a = − 100 a Calculate the moment of inertia ( I x ) using the relation: I x = 1 12 b 1 h 1 3 + ( b 1 h 1 ) d 1 2 + 1 12 b 2 h 2 3 + ( b 2 h 2 ) d 2 2 (1) Here, b and h are the width and depth of the section, d is the distance between the neutral axis and centroid of rectangle. Substitute 100 mm for b 1 , 20 mm for h 1 , 7.5 mm for d 1 , 60 mm for b 2 , 20 mm for h 2 , and 12.5 mm for d 2 . I x = [ ( 1 12 × 100 × 20 3 ) + 100 × 20 × ( 7

7th Edition

ISBN: 9780073398235

Author: Ferdinand P. Beer, E. Russell Johnston Jr., John T. DeWolf, David F. Mazurek

Publisher: McGraw-Hill Education

See similar textbooks

Videos

Question

Chapter 4.9, Problem 145P

To determine

Find the largest distance a for which the maximum tensile stress in the beam not exceed 75 MPa.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 4.9, Problem 144P

Chapter 4.9, Problem 146P

Students have asked these similar questions

Sketch h, for Problem 13.64 13 13.65 In Sketch i the tension on the slack side of the left pulley is 20% of that on the tight side. The shaft rotates at 1000 rpm. Select a pair of deep-groove roller bearings to sup- port the shaft for 99% reliability and a life of 20,000 hr. Assume Eq. (13.83) can be used to account for lubricant cleanliness. All length dimensions are in millimeters. b Z 02 0 y 200 500. 187 100 30° B TONE 500 diam 800 N 650 diam 100 N Sketch i, for Problem 13.65 வ

Problem 2: Consider the rectangular wood beam below. Use E=1.0. 1. Determine the slope at A. 2. Determine the largest deflection between A and B. Use the elastic curve equation. Show all work. (20%) 3 kN/m A 2.4 m - 50 mm AT 150 mm 0000 - B C 1.2 m→

Please give a clear solution.

Chapter 4 Solutions

Mechanics of Materials, 7th Edition

Ch. 4.3 - 4.1 and 4.2 Knowing that the couple shown acts in...Ch. 4.3 - 4.1 and 4.2 Knowing that the couple shown acts in...Ch. 4.3 - Using an allowable stress of 155 MPa, determine...Ch. 4.3 - Solve Prob. 4.3, assuming that the wide-flange...Ch. 4.3 - Using an allowable stress of 16 ksi, determine the...Ch. 4.3 - Knowing that the couple shown acts in a vertical...Ch. 4.3 - 4.7 and 4.8 Two W4 13 rolled sections are welded...Ch. 4.3 - 4.7 and 4.8 Two W4 13 rolled sections are welded...Ch. 4.3 - 4.9 through 4.11 Two vertical forces are applied...Ch. 4.3 - 4.9 through 4.11 Two vertical forces are applied...

Knowledge Booster

Learn more about

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

Find the largest distance a for which the maximum tensile stress in the beam not exceed 75 MPa .

Solution Summary: The author calculates the largest distance a for which the maximum tensile stress in the beam not exceed 75mpa.

Videos

Find the largest distance a for which the maximum tensile stress in the beam not exceed 75 MPa.

Want to see the full answer?

Chapter 4 Solutions