3 A y 0.090

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1 ROBLM in. 5 8 in. diameter A standard tension test is used to determine the properties of an experimental plastic. The test specimen is a 5 -in.-diameter rod and it is subjected to an 800-lb tensile 8 force. Knowing that an elongation of 0.45 in. and a decrease in diameter of 0.05 in. are observed in a 5-in. gage length, determine the modulus of elasticity, the modulus of rigidity, and oisson s ratio for the material. ' 5 A d in lb 800 y psi A y 0.45 y L 5.0 x 0.05 x d 0.5 y psi y x v y psi (1 v) ()( ) psi v psi RORITARY MATRIAL. Copyright 015 McGraw-Hill ducation. This is proprietary material solely for authorized instructor use. 1

2 y ROBLM.8 z in. z D A C 4 in. B x x A fabric used in air-inflated structures is subjected to a biaxial loading that results in normal stresses x 18 ksi and z 4 ksi. Knowing that the properties of the fabric can be approximated as psi and v 0.4, determine the change in length of (a) side AB, (b) side BC, (c) diagonal AC. (a) (b) 18 ksi 0 4 ksi x y z 1 1 x ( x y z) 18,000 (0.4)(4,000) z ( x y z) (0.4)(18,000) 4, AB ( AB) (4in.)( ) in. x ( BC) (in.)( ) in. BC z Label sides of right triangle ABC as a, b, c. Then c a b Obtain differentials by calculus. cdc ada bdb a b dc da db c c 0.001in in. But a 4in. bin. c 4 5in. (c) da in. db in. AB 4 AC dc (0.0018) ( ) 5 5 BC in. RORITARY MATRIAL. Copyright 015 McGraw-Hill ducation. This is proprietary material solely for authorized instructor use. 19

3 ROBLM.70 The block shown is made of a magnesium alloy, for which 45 Ga and v 0.5. Knowing that x 180 Ma, determine (a) the magnitude of y for which the change in the height of the block will be zero, (b) the corresponding change in the area of the face ABCD, (c) the corresponding change in the volume of the block. (a) y y z 1 y ( x v y vz ) v (0.5)( ) (b) A0 LxL y x 10 a.0 Ma 1 v (0.5)( 410 ) z ( z vx v y) ( x y) x v y x ( x v y vz) z A L (1 ) L (1 ) L L (1 ) x x z z x z x z x z A A A L L ( ) LL( ) 0 x z x z x z x z x z y A (100 mm)(5 mm)( ) (c) V0 L L L x y z V L (1 ) L (1 ) L (1 ) x x y y z z LLL(1 ) x y z x y z x y y z z x x y z V V V L L L ( small terms) 0 x y z x y z V (100)(40)(5)( ) A 4.05 mm V 1.0 mm RORITARY MATRIAL. Copyright 015 McGraw-Hill ducation. This is proprietary material solely for authorized instructor use. 171

4 . in. ROBLM.75 The plastic block shown is bonded to a rigid support and to a vertical plate to which a 55-kip load is applied. Knowing that for the plastic used G 150 ksi, determine the deflection of the plate. 4.8 in. in. A (.)(4.8) 15. in lb psi A 15. G psi G h in. h ()( ) in in. RORITARY MATRIAL. Copyright 015 McGraw-Hill ducation. This is proprietary material solely for authorized instructor use. 177

5 ROBLM.79 An elastomeric bearing (G 10 psi) is used to support a bridge girder as shown to provide flexibility during earthquakes. The beam must not displace more than in. when a 5-kip lateral load is applied as shown. 8 Knowing that the maximum allowable shearing stress is 0 psi, determine (a) the smallest allowable dimension b, (b) the smallest required thickness a. a 8 in. b Shearing force: 5 kips 5000 lb Shearing stress: 0 psi 5000, or A 8.in A 0 and A (8in.)( b ) (a) A 8. b in. b 10.4in rad 10 (b) 0.75 in. But, or a a a 0.81in. RORITARY MATRIAL. Copyright 015 McGraw-Hill ducation. This is proprietary material solely for authorized instructor use. 181

6 ROBLM mm A 100 mm A vibration isolation unit consists of two blocks of hard rubber bonded to a plate AB and to rigid supports as shown. Knowing that a force of magnitude 5 kn causes a deflection 1.5 mm of plate AB, determine the modulus of rigidity of the rubber used. B 0 mm 0 mm 1 1 (5 10 N) N F F ( N) a A (0.15 m)(0.1 m) m h 0.0 m h G a 0.05 G 1.7 Ma RORITARY MATRIAL. Copyright 015 McGraw-Hill ducation. This is proprietary material solely for authorized instructor use. 18