Explanation Given information: The width of the rectangular cross sectional prismatic beam is b = 2 in . . The depth of the rectangular cross sectional prismatic beam is h = 10 in . . The size of the rectangular cross sectional built-up beam is a = 2 in . . Calculation: Show the free-body diagram of the prismatic beam as in Figure 1. Determine the moment at point B by taking moment at point B . ∑ M B = 0 P ( 6.25 ) − M B = 0 | M B | = 6.25 P Show the free body diagram of the built-up beam as in Figure 2. Determine the moment at point C by taking moment at point C . ∑ M C = 0 P ( 6.25 − l 1 ) + M C = 0 | M C | = P ( 6.25 − l 1 ) Determine the moment at point D by taking moment at point D . ∑ M D = 0 P ( 6.25 − l 2 ) + M D = 0 | M D | = P ( 6.25 − l 2 ) Determine the section modulus ( S B ) of the region BD as follows; S B = 1 6 b h 2 Here, the width of the beam is b and the depth of the beam is h . All five pieces are in contact. So, b = 2 in . ; h = 10 in . . Substitute 2 in. for b and 10 in. for h . S B = 1 6 × 2 × 10 2 = 33.333 in . 3 Determine the section modulus ( S D ) of the region CD as follows; S C = 1 6 b h 2 Three pieces are in contact. So, b = 2 in . ; h = 6 in . . Substitute 2 in. for b and 6 in. for h . S D = 1 6 × 2 × 6 2 = 12 in . 3 Determine the section modulus ( S C ) of the region AC as follows; S C = 1 6 b h 2 Three pieces are in contact. So, b = 2 in . ; h = 2 in . . Substitute 2 in. for b and 2 in. for h . S C = 1 6 × 2 × 2 2 = 1

7th Edition

ISBN: 9780073398235

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

Publisher: McGraw-Hill Education

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Chapter 5.5, Problem 132P

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The respective lengths of the two inner and outer pieces of timber (l1 and l2).

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Chapter 5.5, Problem 131P

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Chapter 5 Solutions

Mechanics of Materials, 7th Edition

Ch. 5.1 - 5.1 through 5.6 For the beam and loading shown,...Ch. 5.1 - 5.1 through 5.6 For the beam and loading shown,...Ch. 5.1 - 5.1 through 5.6 For the beam and loading shown,...Ch. 5.1 - 5.1 through 5.6 For the beam and loading shown,...Ch. 5.1 - 5.1 through 5.6 For the beam and loading shown,...Ch. 5.1 - 5.1 through 5.6 For the beam and loading shown,...Ch. 5.1 - 5.7 and 5.8 Draw the shear and bending-moment...Ch. 5.1 - 5.7 and 5.8 Draw the shear and bending-moment...Ch. 5.1 - 5.9 and 5.10 Draw the shear and bending-moment...Ch. 5.1 - 5.9 and 5.10 Draw the shear and bending-moment...

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The respective lengths of the two inner and outer pieces of timber ( l 1 and l 2 ) .

Solution Summary: The author shows the free-body diagram of the rectangular cross sectional prismatic beam as in Figure 1. Determine the moment at point B by taking moment

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The respective lengths of the two inner and outer pieces of timber (l1 and l2).

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Chapter 5 Solutions