Explanation Given information: The x ′ and y ′ axes are the principal centroidal axes of the cross section. Calculation: Refer to Figure P6.81 in the text book. I x ′ = 1.428 t a 3 I y ′ = 0.1557 t a 3 β = 15.8 ° Sketch the cross section of the angle section as shown in Figure 1. Refer to Figure 1. Area of the member A ( y ) = ( 2 a − y ) t . Centroid of the member. y ¯ = 1 2 ( 2 a + y ) x ¯ = 0 Calculate the shear along the centroidal axes as shown below. Along x ′ axis: V x ′ = P cos β Substitute 15.8 ° for β . V x ′ = P cos 15.8 ° = 0.9622 P Along y ′ axis: V y ′ = − P sin β Substitute 15.8 ° for β . V y ′ = − P sin 15.8 ° = − 0.2723 P Calculate the centroid along the centroidal axes as shown below. Along y ′ axis: y ′ ¯ = ( y ¯ − 2 3 a ) cos β − ( x ¯ − 1 6 a ) sin β Substitute 1 2 ( 2 a + y ) for y ¯ , 0 for x ¯ , and 15.8 ° for β . y ′ ¯ = ( 1 2 ( 2 a + y ) − 2 3 a ) cos 15.8 ° − ( 0 − 1 6 a ) sin 15.8 ° = 0.9622 ( a + y 2 − 2 3 a ) + 0.0454 a = 0.3207 a + 0.4811 y + 0.0454 a = 0.3661 a + 0.4811 y Along z ′ axis: x ¯ ′ = ( x ¯ − 1 6 a ) cos β + ( y ¯ − 2 3 a ) sin β Substitute 1 2 ( 2 a + y ) for y ¯ , 0 for x ¯ , and 15.8 ° for β . x ¯ ′ = ( 0 − 1 6 a ) cos 15.8 ° + ( 1 2 ( 2 a + y ) − 2 3 a ) sin 15

7th Edition

ISBN: 9780100257061

Author: BEER

Publisher: YUZU

See similar textbooks

Videos

Question

Chapter 6.6, Problem 81P

To determine

The distribution of the shearing stresses along line D′B′ in the horizontal leg of the angle shape.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 6.6, Problem 80P

Chapter 6.6, Problem 82P

Students have asked these similar questions

Solve for the support reactions at A and B. C 3 kN/m B -1.5 m- -1.5 m 1.5 m- 1.5 m-

4. Solve for the support reactions at A and B. W1 600 lb/ft W2 150 lb/ft A B

In cold isostatic pressing, the mold is most typically made of which one of the following: thermosetting polymer tool steel sheet metal textile rubber

Chapter 6 Solutions

EBK MECHANICS OF MATERIALS

Ch. 6.2 - Three full-size 50 100-mm boards are nailed...Ch. 6.2 - For the built-up beam of Prob. 6.1, determine the...Ch. 6.2 - Three boards, each 2 in. thick, are nailed...Ch. 6.2 - A square box beam is made of two 20 80-mm planks...Ch. 6.2 - The American Standard rolled-steel beam shown has...Ch. 6.2 - The beam shown is fabricated by connecting two...Ch. 6.2 - A column is fabricated by connecting the...Ch. 6.2 - The composite beam shown is fabricated by...Ch. 6.2 - 6.9 through 6.12 For beam and loading shown,...Ch. 6.2 - 6.9 through 6.12 For beam and loading shown,...

Ch. 6.2 - 6.9 through 6.12 For beam and loading shown,...Ch. 6.2 - 6.9 through 6.12 For beam and loading shown,...Ch. 6.2 - 6.13 and 6.14 For a beam having the cross section...Ch. 6.2 - 6.13 and 6.14 For a beam having the cross section...Ch. 6.2 - For a timber beam having the cross section shown,...Ch. 6.2 - Two steel plates of 12 220-mm rectangular cross...Ch. 6.2 - Two W8 31 rolled sections may be welded at A and...Ch. 6.2 - For the beam and. loading shown, determine the...Ch. 6.2 - Fig. P6.19 6.19 A timber beam AB of length L and...Ch. 6.2 - A timber beam AB of Length L and rectangular cross...Ch. 6.2 - 6.21 and 6.22 For the beam and loading shown,...Ch. 6.2 - 6.21 and 6.22 For the beam and loading shown,...Ch. 6.2 - 6.23 and 6.24 For the beam and loading shown,...Ch. 6.2 - 6.23 and 6.24 For the beam and loading shown,...Ch. 6.2 - 6.25 through 6.28 A beam having the cross section...Ch. 6.2 - 6.25 through 6.28 A beam having the cross section...Ch. 6.2 - Prob. 27P Ch. 6.2 - 6.25 through 6.28 A beam having the cross section...Ch. 6.5 - The built-up timber beam shown is subjected to a...Ch. 6.5 - The built-up beam shown is made by gluing together...Ch. 6.5 - The built-up beam was made by gluing together...Ch. 6.5 - Several wooden planks are glued together to form...Ch. 6.5 - The built-up wooden beam shown is subjected to a...Ch. 6.5 - Knowing that a W360 122 rolled-steel beam is...Ch. 6.5 - 6.35 and 6.36 An extruded aluminum beam has the...Ch. 6.5 - 6.35 and 6.36 An extruded aluminum beam has the...Ch. 6.5 - Knowing that a given vertical shear V causes a...Ch. 6.5 - The vertical shear is 1200 lb in a beam having the...Ch. 6.5 - The vertical shear is 1200 lb in a beam having the...Ch. 6.5 - 6.40 and 6.47 The extruded aluminum beam has a...Ch. 6.5 - Prob. 41P Ch. 6.5 - Prob. 42P Ch. 6.5 - Three planks are connected as shown by bolts of...Ch. 6.5 - A beam consists of three planks connected as shown...Ch. 6.5 - A beam consists of five planks of 1.5 6-in. cross...Ch. 6.5 - Four L102 102 9.5 steel angle shapes and a 12 ...Ch. 6.5 - A plate of 14-in. thickness is corrugated as shown...Ch. 6.5 - Prob. 48P Ch. 6.5 - An extruded beam has the cross section shown and a...Ch. 6.5 - Prob. 50P Ch. 6.5 - The design of a beam calls for connecting two...Ch. 6.5 - The cross section of an extruded beam is a hollow...Ch. 6.5 - Prob. 53P Ch. 6.5 - Prob. 54P Ch. 6.5 - Prob. 55P Ch. 6.5 - 6.56 and 6.57 A composite beam is made by...Ch. 6.5 - 6.56 and 6.57 A composite beam is made by...Ch. 6.5 - Prob. 58P Ch. 6.5 - Prob. 59P Ch. 6.5 - Prob. 60P Ch. 6.6 - 6.61 through 6.64 Determine the location of the...Ch. 6.6 - 6.61 through 6.64 Determine the location of the...Ch. 6.6 - 6.61 through 6.64 Determine the location of the...Ch. 6.6 - Prob. 64P Ch. 6.6 - 6.65 through 6.68 An extruded beam has the cross...Ch. 6.6 - 6.65 through 6.68 An extruded beam has the cross...Ch. 6.6 - 6.65 through 6.68 An extruded beam has the cross...Ch. 6.6 - 6.65 through 6.68 An extruded beam has the cross...Ch. 6.6 - 6.69 through 6.74 Determine the location of the...Ch. 6.6 - Prob. 70P Ch. 6.6 - Prob. 71P Ch. 6.6 - Prob. 72P Ch. 6.6 - Prob. 73P Ch. 6.6 - Prob. 74P Ch. 6.6 - Prob. 75P Ch. 6.6 - 6.75 and 6.76 A thin-walled beam has the cross...Ch. 6.6 - 6.77 and 6.78 A thin-walled beam of uniform...Ch. 6.6 - Prob. 78P Ch. 6.6 - Prob. 79P Ch. 6.6 - Prob. 80P Ch. 6.6 - Prob. 81P Ch. 6.6 - Prob. 82P Ch. 6.6 - Prob. 83P Ch. 6.6 - Prob. 84P Ch. 6.6 - Prob. 85P Ch. 6.6 - Solve Prob. 6.85, assuming that the thickness of...Ch. 6.6 - Prob. 87P Ch. 6.6 - Prob. 88P Ch. 6 - Three boards are nailed together to form the beam...Ch. 6 - For the beam and loading shown, consider section...Ch. 6 - For the wide-flange beam with the loading shown,...Ch. 6 - For the beam and loading shown, consider section...Ch. 6 - The built-up timber beam is subjected to a 1500-lb...Ch. 6 - Knowing that a given vertical shear V causes a...Ch. 6 - Three planks are connected as shown by bolts of...Ch. 6 - Three 1 18-in. steel plates are bolted to four L6...Ch. 6 - The composite beam shown is made by welding C200 ...Ch. 6 - Prob. 98RP Ch. 6 - A thin-walled beam of uniform thickness has the...Ch. 6 - Determine the location of the shear center O of a...

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.

Similar questions

SEE MORE QUESTIONS

Recommended textbooks for you

Elements Of Electromagnetics
Mechanical Engineering
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Oxford University Press
Mechanics of Materials (10th Edition)
Mechanical Engineering
ISBN:9780134319650
Author:Russell C. Hibbeler
Publisher:PEARSON
Thermodynamics: An Engineering Approach
Mechanical Engineering
ISBN:9781259822674
Author:Yunus A. Cengel Dr., Michael A. Boles
Publisher:McGraw-Hill Education
Control Systems Engineering
Mechanical Engineering
ISBN:9781118170519
Author:Norman S. Nise
Publisher:WILEY
Mechanics of Materials (MindTap Course List)
Mechanical Engineering
ISBN:9781337093347
Author:Barry J. Goodno, James M. Gere
Publisher:Cengage Learning
Engineering Mechanics: Statics
Mechanical Engineering
ISBN:9781118807330
Author:James L. Meriam, L. G. Kraige, J. N. Bolton
Publisher:WILEY