(a) Explanation Given information: The elastic modulus ( E ) is 29 × 10 6 psi . The section of the beam is C6 × 8.2 . Two channel sections are provided. Calculation: Refer Table, “W shape properties”, the moment of inertia ( I ) for the given section C6 × 8.2 is 13.1 in . 4 Use moment area method: Show the free body diagram of beam by considering the point load as in Figure 1. Draw the moment diagram of the above beam as in Figure 2. Calculate the moment ( M 1 ) by taking moment about point A : M 1 = 1.1 × 6 = 6.6 kips ⋅ ft Calculate the ratio of M 1 E I using the relation: Ratio = − M 1 E I Substitute 6.6 kips ⋅ ft for M 1 , 29 × 10 6 psi for E , and 13.1 in . 4 for I . M 1 E I = − 6.6 kips ⋅ ft 29 × 10 3 × ( 2 × 13.1 ) 144 = 1.251 × 10 − 3 ft − 1 Calculate the area ( A 1 ) due to the moment ( M 1 ) using the formula: A 1 = 1 2 b 1 h 1 Here, b 1 is the width of the triangle and h 1 is the height of the triangle. Substitute 6 ft for b 1 and 1.251 × 10 − 3 ft − 1 for h 1 . A 1 = 1 2 × 6 × ( − 1.251 × 10 − 3 ) = − 3.753 × 10 − 3 Show the free body diagram of beam by considering the second concentrated load as in Figure 3. Draw the moment diagram of the above beam as in Figure 4. Calculate the moment ( M 2 ) by taking moment about point A : M 2 = − 1.1 × 4 = − 4.4 kips ⋅ ft Calculate the ratio of M 2 E I using the relation: Ratio = − M 2 E I Substitute − 4.4 kips ⋅ ft for M 3 , 29 × 10 6 psi for E , and 13.1 in . 4 for I . M 2 E I = − 4 .4kips ⋅ ft 29 × 10 3 × ( 2 × 13.1 ) 144 = − 8.34 × 10 − 4 ft -1 Calculate the area ( A 2 ) due to the moment ( M 2 ) using the formula: A 2 = 1 2 b 2 h 2 Here, b 2 is the width of the triangle and h 2 is the height of the triangle. Substitute 4 ft for b 2 and − 8.34 × 10 − 4 ft − 1 for h 2 . A 2 = 1 2 × 4 × ( − 8.34 × 10 − 4 ) = − 1.668 × 10 − 3 Show the free body diagram of beam by considering the third concentrated load as in Figure 5 (b) To determine Find the deflection ( y D ) at point D .

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

Concept explainers

Slope and Deflection

The slope in a deflected beam is described as an angle in radians made by the tangent of the section with the original axis of the beam. The deflection at any point on the axis of the beam is defined as the lateral displacement of the point before and af…

Videos

Question

Chapter 9.5, Problem 103P

(a)

To determine

Find the slope (θD) at point D.

(b)

To determine

Find the deflection (yD) at point D.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 9.5, Problem 102P

Chapter 9.5, Problem 104P

Students have asked these similar questions

Thermodynamics: Mass and Energy Analysis Of Control Volumes A spring-loaded piston-cylinder device contains 1.5 kg of carbon dioxide. This system is heated from 200kPa and 25◦C to 1200 kPa and 300◦C. Determine the total heat transfer to and work produced by this system.

Can you help with a code in MATLAB?

I need help writing a code in MATLAB. Please help me with question b.6

Chapter 9 Solutions

Mechanics of Materials, 7th Edition

Ch. 9.2 - In the following problems assume that the flexural...Ch. 9.2 - In the following problems assume that the flexural...Ch. 9.2 - In the following problems assume that the flexural...Ch. 9.2 - 9.1 through 9.4 For the loading shown, determine...Ch. 9.2 - 9.5 and 9.6 For the cantilever beam and loading...Ch. 9.2 - 9.5 and 9.6 For the cantilever beam and loading...Ch. 9.2 - For the beam and loading shown, determine (a) the...Ch. 9.2 - For the beam and loading shown, determine (a) the...Ch. 9.2 - Knowing that beam .AB is a W10 33 rolled shape...Ch. 9.2 - Knowing that beam AB is an S200 34 roiled shape...

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 slope ( θ D ) at point D .

Solution Summary: The author shows the free body diagram of beam by considering the point load as in Figure 1.