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A floor system in a small building consists of wood planks supported by 2-in. (nominal width) joists spaced at distance s and measured from center to center (see figure). The span length L of each joist is 12 ft, the spacing s of the joists is 16 in., and the allowable bending stress in the wood is 1250 psi. The uniform floor load is 120 lb/ft", which includes an allowance for the weight of the floor system itself. Calculate the required section modulus S for the joists, and then select a suitable joist size (surfaced lumber) from Appendix G, assuming that each joist may be represented as a simple beam carrying a uniform load. What is the maximum floor load that can be applied to your final beam selection in part (a)?

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Mechanics of Materials (MindTap Co...

9th Edition
Barry J. Goodno + 1 other
Publisher: Cengage Learning
ISBN: 9781337093347

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BuyFindarrow_forward

Mechanics of Materials (MindTap Co...

9th Edition
Barry J. Goodno + 1 other
Publisher: Cengage Learning
ISBN: 9781337093347
Chapter 5, Problem 5.6.9P
Textbook Problem
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A floor system in a small building consists of wood planks supported by 2-in. (nominal width) joists spaced at distance s and measured from center to center (see figure). The span length L of each joist is 12 ft, the spacing s of the joists is 16 in., and the allowable bending stress in the wood is 1250 psi. The uniform floor load is 120 lb/ft", which includes an allowance for the weight of the floor system itself.

  1. Calculate the required section modulus S for the joists, and then select a suitable joist size (surfaced lumber) from Appendix G, assuming that each joist may be represented as a simple beam carrying a uniform load.

  • What is the maximum floor load that can be applied to your final beam selection in part (a)?
  •   Chapter 5, Problem 5.6.9P, A floor system in a small building consists of wood planks supported by 2-in. (nominal width) joists

    (a)

    To determine

    The required section modulus S .

    Explanation of Solution

    Given information:

    The span length of each joist is 12ft , the spacing of the joists is 16in , the permissible bending stress is 1250psi , the total floor load is 120lb/ft2 .

    The following figure gives the free body diagram of the beam:

      

    Figure-(1)

    Write the expression for the uniformly distributed load.

      q=FLL2×s.....(I)

    Here, the uniformly distributed load is q , the total floor load is FL , the span length is L , the spacing between the joists is s .

    Write the expression for the maximum bending moment.

      Mmax=qL28.....(II)

    Here, the maximum bending moment is Mmax .

    Write the expression for the section modulus.

      S=Mmaxσallow.....(I)

    Here, the permissible stress is σallow .

    Calculation:

    Substitute 120lb/ft2 for FL , 12in for L and 16in for s in Equation (II)

      q=(120lb 122 in2)×(16in)=13

    (b)

    To determine

    The maximum floor load applied on the section modulus.

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    Chapter 5 Solutions

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