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# Beam Moment Problem: The stiffness of a beam is directly proportional to the second ISBN: 9781559536547 285

## Solution for problem 13 Chapter 11-4

Calculus: Concepts and Applications | 2nd Edition

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Problem 13

Beam Moment Problem: The stiffness of a beam is directly proportional to the second moment of area of the beams cross section with respect to an axis through the centroid of the cross section. In this problem you will investigate the stiffness of beams with the same cross-sectional area but with different shapes. a. Prove that if a rectangle has base B and height H, then the second moment of areawith respect to an axis through the centroidand parallel to the base is equal to BH3/12.b. Find the stiffness of a 2 in.-by-12 in. beam(Figure 11-4o) if it isi. Turned on edge ii. Lying flatUse k for the proportionality constant.Based on the results, explain why boardsused for floor joists in houses are turned onedge rather than laid flat. Figure 11-4oc. An I-beam is made with the samecross-sectional area as the 2 in.-by-12 in.beam in part b. Find its stiffness ifi. All three parts (two flanges and one web)are 4 in. wideii. The two flanges are 2 in. by 4 in., but theweb is 1 in. by 8 in.d. Does increasing an I-beams depth withoutchanging the cross-sectional area makemuch change in the beams stiffness? Whatphysical limitations keep people frommaking a beam very tall and thus very stiff?

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Exam 4 Study Guide *Study Guide is will be best utilized while following along with the L15 Powerpoint and the L16­18 PowerPoint, or as a quiz after studying the PowerPoints and/or reading chapter 13 of the textbook. Lectures 15­18 Questions 1. What are the 4 functions of the spinal cord 2. Where does the spinal cord begin 3. How many pairs of spinal...

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##### ISBN: 9781559536547

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