BeerMOM ISM_C02-P001-P64BeerMOM ISM_C02-P065-P135CCHHAAPPTTEERR 22PROPRIETARY MATERIAL. Copyright © 2015 McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part. 93 PROBLEM 2.1 A nylon thread is subjected to a 8.5-N tension force. Knowing that 3.3 GPaE and that the length of the thread increases by 1.1%, determine (a) the diameter of the thread, (b) the stress in the thread. SOLUTION (a) Strain: 1.10.011100L  Stress: 96(3.3 10 )(0.011) 36.3 10 Pa   E PA Area: 9268.5234.16 10 m36.3 10  PA Diameter: 964(4)(234.1610)546 10 m Ad 0.546 mmd  (b) Stress: 36.3 MPa PROPRIETARY MATERIAL. Copyright © 2015 McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part. 94 PROBLEM 2.2 A 4.8-ft-long steel wire of 14-in.-diameter is subjected to a 750-lb tensile load. Knowing that E = 29 × 106 psi, determine (a) the elongation of the wire, (b) the corresponding normal stress. SOLUTION (a) Deformation: 2;4PLdAAE Area: 222(0.25 in.)4.9087 10 in4A 22 6(750 lb)(4.8 ft 12 in./ft)(4.9087 10 in )(29 10 psi) 23.0347 10 in. 0.0303 in. (b) Stress: PA Area: 22(750lb)(4.9087 10 in ) 41.52790 10 psi 15.28 ksi PROPRIETARY MATERIAL. Copyright © 2015 McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part. 95 PROBLEM 2.3 An 18-m-long steel wire of 5-mm diameter is to be used in the manufacture of a prestressed concrete beam. It is observed that the wire stretches 45 mm when a tensile force P is applied. Knowing that 200 GPa,E determine (a) the magnitude of the force P, (b) the corresponding normal stress in the wire. SOLUTION (a) ,orPLAEPAEL with 22 6211(0.005) 19.6350 10 m44  Ad 62 9 2(0.045 m)(19.6350 10 m )(200 10 N/m )9817.5 N18 mP 9.82 kNP (b) 6629817.5 N500 10 Pa19.6350 10 m  PA 500 MPa PROPRIETARY MATERIAL. Copyright © 2015 McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part. 96 PROBLEM 2.4 Two gage marks are placed exactly 250 mm apart on a 12-mm-diameter aluminum rod with E = 73 GPa and an ultimate strength of 140 MPa. Knowing that the distance between the gage marks is 250.28 mm after a load is applied, determine (a) the stress in the rod, (b) the factor of safety. SOLUTION (a) 0LL 250.28 mm 250 mm 0.28 mm 0L 0.28 mm250 mm 41.11643 10  E 94(73 10 Pa) (1.11643 10 )  78.1760 10 Pa 81.8 MPa (b) F.S.u 140 MPa81.760 MPa 1.71233 F.S. 1.712 PROPRIETARY MATERIAL. Copyright © 2015 McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part. 97 PROBLEM 2.5 An aluminum pipe must not stretch more than 0.05 in. when it is subjected to a tensile load. Knowing that 610.1 10E psi and that the maximum allowable normal stress is 14 ksi, determine (a) the maximum allowable length of the pipe, (b) the required area of the pipe if the tensile load is 127.5 kips. SOLUTION (a) PLAE Thus, 63(10.1 10 ) (0.0 5)14 10EA ELP 36.1 in.L  (b) PA Thus, 33127.5 1014 10PA 29.11 inA PROPRIETARY MATERIAL. Copyright © 2015 McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part. 98 PROBLEM 2.6 A control rod made of yellow brass must not stretch more than 3 mm when the tension in the wire is 4 kN. Knowing that E = 105 GPa and that the maximum allowable normal stress is 180 MPa, determine (a) the smallest diameter rod that should be used, (b) the corresponding maximum length of the rod. SOLUTION (a) 2;4PdAA Substituting, we have 2363444(4 10 N)(180 10 Pa)5.3192 10 mPPdddd 5.32 mmd   (b) ;EL Substituting, we have EELL 936(105 10 Pa)(3 10 m)(180 1 0 Pa)L 1.750 mL  PROPRIETARY MATERIAL. Copyright © 2015 McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part. 99 PROBLEM 2.7 A steel control rod is 5.5 ft long and must not stretch more than 0.04 in. when a 2-kip tensile load is applied to it. Knowing that 629 10 psi,E  determine (a) the smallest diameter rod that should be used, (b) the corresponding normal stress caused by the load. SOLUTION (a) 6(2000 lb) (5.5 12 in.)0.04 in.(29 10 psi):PLAE A 2210.113793 in4Ad 0.38063 in.d 0.381 in.d (b) 22000 lb17575.8 psi0.113793 inPA  17.58 ksi PROPRIETARY MATERIAL. Copyright © 2015 McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part. 100 PROBLEM 2.8 A cast-iron tube is used to support a