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122_Mechanics Homework Mechanics of Materials Solution

122_Mechanics Homework Mechanics of Materials Solution - i...

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Unformatted text preview: i 7“} T l 1 4—] PROBLEM 2.81 PROBLEM 2.82 2.81 An elastomeric bearing (G = 0.9 MP3) is used to support a bridge girder as shown to provide flexibility during earthquakes. The beam must not displace more than 10 mm when a 22 kN lateral load is applied as shown. Determine (a) the smallest allowable dimension b, (b) the smallest required thickness 0 if the maximum allowable shearing stress is 420 kPa. SOLUTION 5'0 eart'nfl $0.122 P 7: 22,403 N Sheam‘nm Shes; 't '- 42!) HOS Pa :3. ‘ ‘=_E a"os «- -3 1' Z A to A a: 3% niszSI $10 In :- 52.38! "[0:5 Mom-L A '= (200mm)(b) b ___L: 52.38'K103 - 200 30° 3 .. Y‘ ‘ I“ ‘ ”20”“) - seawwo 3 - _ v on? ”to6 O. 4%.: Ion” = 2,.q ham ”r seer? ”0‘5 2.82 For the elastomeric bearing in Prob. 2.8] with b = 220 mm and a = 30 mm, determine the shearing modulus G and the shear stress rfor a maximum lateral load P = 19 kN and a maximum displacement 6= 12 mm. SOLUTION Shearing $0“? P 3 l9 x103 N Area A ‘-' (200 MM)(220 mn‘l 3 14'4““): Mint = Ll‘l HO“ In" _ 3 THE: £1‘%3 -= HSLSHIO‘Pfi. ‘ikl = 43’ kpfi. Shearing S'i'raivx Y“ % =—m = O.’-§OO 30 Mb. Shea-n.» 5 Monoupus N 3 Gus;- = ”fi‘fi"’° = Losowo‘ Pa. = l.08o MP0. ‘1 ...
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