(a) Explanation Given information: The uniform thickness of the beam is b . The length of the beam is L . The rise of the beam is h 0 . Calculation: Show the free-body diagram of the beam as in Figure 1. Determine the vertical reaction at point B by taking moment at point A . ∑ M A = 0 − P ( L / 2 ) + B y ( L ) = 0 B y = P 2 Determine the vertical reaction at point A by resolving the vertical component of forces. ∑ F y = 0 A y − P + B y = 0 A y − P + P 2 = 0 A y = P 2 Show the free body-diagram of the section AC as in Figure 2. Determine the moment at the section by taking moment about the section. ∑ M = 0 M − P 2 ( x ) = 0 M = P x 2 Determine the section modulus ( S ) of the beam using the relation. S = | M | σ a l l Here, the allowable stress in the beam is σ a l l . Substitute P x 2 for | M | . S = P x 2 σ a l l = P x 2 σ a l l Determine the section modulus ( S ) of the rectangular cross section using the relation. S = 1 6 b h 2 Here, the width of the beam is b and the depth of the beam is h . Substitute P x 2 σ a l l for S (b) To determine The maximum allowable load.

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Author: BEER

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Chapter 5.5, Problem 130P

(a)

To determine

Express h in terms of x, L, and h0 for portion AC.

(b)

To determine

The maximum allowable load.

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Chapter 5.5, Problem 129P

Chapter 5.5, Problem 131P

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Chapter 5 Solutions

EBK MECHANICS OF MATERIALS

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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Express h in terms of x , L , and h 0 for portion AC .

Solution Summary: The author explains the expression for h in terms of x, L, and h_0 for portion AC.

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Express h in terms of x, L, and h0 for portion AC.

The maximum allowable load.

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Chapter 5 Solutions