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412_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

# 412_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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Unformatted text preview: 05Ch05.qxd 9/24/08 406 4:59 AM Page 406 CHAPTER 5 Stresses in Beams (Basic Topics) MAX. STRESSES IN SPAN AB sC st st MmaxAB (12) c1 I MmaxAB (12) c2 I 7810 psi ; sc MAX. STRESSES IN SPAN BC MB (12) c2 I 13885 psi sc 2352 psi sc MB (12) c1 I st max. tensile stress ; max. compressive stress st 4182 psi A Problem 5.5-20 A frame ABC travels horizontally with an acceleration a0 (see figure). Obtain a formula for the maximum stress smax in the vertical arm AB, which had length L, thickness t , and mass density r. t a0 = acceleration L C B Solution 5.5-20 Accelerating frame L length of vertical arm t thickness of vertical arm r mass density a0 acceleration Let b width of arm perpendicular to the plane of the figure Let q inertia force per unit distance along vertical arm TYPICAL UNITS FOR USE VERTICAL ARM t IN THE PRECEDING EQUATION q S rbta0 bt2 6 Mmax smax Mmax S m/s2 a0 meters (m) N/m2 (pascals) USCS units: r slug/ft3 L rbta0L2 2 3rL2a0 t N # s2/m4 meters (m) L smax qL2 2 kg/m3 SI units: r 2 smax ; ft a0 ft/s 2 t lb-s2/ft4 ft lb/ft (Divide by 144 to obtain psi) ...
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