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Remark regarding Problem:The relative importance of the strain energies UM in bending and US in shear loading of beams is influenced by the ratio of the length L of the beam to its depth h, by the shape of the cross section, and by the type of loading. The relative magnitudes of UM and US are examined in Problem, for given ratios of L/h and given cross sections. The simple beam in Figure P5.11 is made of steel (E = 200 GPa and G = 77.5 GPa) and has a rectangular cross section. Show that a. the length L must be greater than 17.6h for US < 0.01 UM, b. the length L must be greater than 7.9h for US < 0.05 UM.

Remark regarding Problem:The relative importance of the strain energies UM in bending and US in shear loading of beams is influenced by the ratio of the length L of the beam to its depth h, by the shape of the cross section, and by the type of loading. The relative magnitudes of UM and US are examined in Problem, for given ratios of L/h and given cross sections. The simple beam in Figure P5.11 is made of steel (E = 200 GPa and G = 77.5 GPa) and has a rectangular cross section. Show that a. the length L must be greater than 17.6h for US < 0.01 UM, b. the length L must be greater than 7.9h for US < 0.05 UM.

Structural Analysis
Structural Analysis
6th Edition
ISBN:9781337630931
Author:KASSIMALI, Aslam.
Publisher:KASSIMALI, Aslam.
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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Advanced mechanics of materials 

**Remark regarding Problem:** The relative importance of the strain energies \(UM\) in bending and \(US\) in shear loading of beams is influenced by the ratio of the length \(L\) of the beam to its depth \(h\), by the shape of the cross section, and by the type of loading. The relative magnitudes of \(UM\) and \(US\) are examined in the problem, for given ratios of \(L/h\) and given cross sections. The simple beam in Figure P5.11 is made of steel (\(E = 200 \, \text{GPa}\) and \(G = 77.5 \, \text{GPa}\)) and has a rectangular cross section. Show that: a. The length \(L\) must be greater than \(17.6h\) for \(US < 0.01UM\), b. The length \(L\) must be greater than \(7.9h\) for \(US < 0.05UM\). **Figure Explanation:** - The diagram depicts a simple beam supported at both ends. - The beam is of length \(L\) and is uniformly loaded with a central point load \(P\). - The distance from the center to each support is \(L/2\). - The cross section of the beam is rectangular, with width \(b\) and depth \(h\).
Transcribed Image Text:**Remark regarding Problem:** The relative importance of the strain energies \(UM\) in bending and \(US\) in shear loading of beams is influenced by the ratio of the length \(L\) of the beam to its depth \(h\), by the shape of the cross section, and by the type of loading. The relative magnitudes of \(UM\) and \(US\) are examined in the problem, for given ratios of \(L/h\) and given cross sections. The simple beam in Figure P5.11 is made of steel (\(E = 200 \, \text{GPa}\) and \(G = 77.5 \, \text{GPa}\)) and has a rectangular cross section. Show that: a. The length \(L\) must be greater than \(17.6h\) for \(US < 0.01UM\), b. The length \(L\) must be greater than \(7.9h\) for \(US < 0.05UM\). **Figure Explanation:** - The diagram depicts a simple beam supported at both ends. - The beam is of length \(L\) and is uniformly loaded with a central point load \(P\). - The distance from the center to each support is \(L/2\). - The cross section of the beam is rectangular, with width \(b\) and depth \(h\).
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