CCHHAAPPTTEERR 11PROPRIETARY 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. 3 d1d2125 kN125 kN60 kNCAB0.9 m 1.2 mPROBLEM 1.1 Two solid cylindrical rods AB and BC are welded together at B and loaded as shown. Knowing that 130 mmd and 250 mm,d find the average normal stress at the midsection of (a) rod AB, (b) rod BC. SOLUTION (a) Rod AB: Force: 360 10 N tensionP Area: 232 621(30 10 ) 706.86 10 m44Ad Normal stress: 36660 1084.882 10 Pa706.86 10ABPA 84.9 MPaAB (b) Rod BC: Force: 33360 10 (2)(125 10 ) 190 10 NP Area: 232 322(50 10 ) 1.96350 10 m44Ad Normal stress: 363190 1096.766 10 Pa1.96350 10BCPA 96.8 MPaBC 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. 4 d1d2125 kN125 kN60 kNCAB0.9 m 1.2 mPROBLEM 1.2 Two solid cylindrical rods AB and BC are welded together at B and loaded as shown. Knowing that the average normal stress must not exceed 150 MPa in either rod, determine the smallest allowable values of the diameters d1 and d2. SOLUTION (a) Rod AB: Force: 360 10 NP Stress: 6150 10 PaAB Area: 214Ad 2132621644 (4)(60 10 )509.30 10 m(150 10 )ABABABABPPAAPdPd 3122.568 10 md 122.6 mmd (b) Rod BC: Force: 33360 10 (2)(125 10 ) 190 10 NP Stress: 6150 10 PaBC Area: 224Ad 2232322644(4)(19010)1.61277 10 m(150 10) BCBCPPAdPd 3240.159 10 md 240.2 mmd 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. 5 0.75 in.1.25 in.12 kipsPBC25 in.30 in.A PROBLEM 1.3 Two solid cylindrical rods AB and BC are welded together at B and loaded as shown. Knowing that P = 10 kips, find the average normal stress at the midsection of (a) rod AB, (b) rod BC. SOLUTION (a) Rod AB: 22 2112 10 22 kips(1.25) 1.22718 in442217.927 ksi1.22718ABPAdPA 17.93 ksiAB (b) Rod BC: 22 2210 kips(0.75) 0.44179 in441022.635 ksi0.44179ABPAdPA 22.6 ksiAB 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. 6 0.75 in.1.25 in.12 kipsPBC25 in.30 in.A PROBLEM 1.4 Two solid cylindrical rods AB and BC are welded together at B and loaded as shown. Determine the magnitude of the force P for which the tensile stresses in rods AB and BC are equal. SOLUTION (a) Rod AB: 222212 kips(1.25 in.)441.22718 in12 kips1.22718 inABPPdAAP (b) Rod BC: 2222(0.75 in.)440.44179 in0.44179 inBCPPAdAP 2212 kips1.22718 in 0.44179 in5.3015 0.78539AB BCPPP 6.75 kipsP 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. 7 1200 N1200 NCAB PROBLEM 1.5 A strain gage located at C on the surface of bone AB indicates that the average normal stress in the bone is 3.80 MPa when the bone is subjected to two 1200-N forces as shown. Assuming the cross section of the bone at C to be annular and knowing that its outer diameter is 25 mm, determine the inner diameter of the bone’s cross section at C. SOLUTION PPAA Geometry: 2212()4Add 22 221 123226623244(4)(1200)(25 10 )(3.80 10 )222.92 10 m14.93 10 m APdd ddd 214.93 mmd 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. 8 100 m15 mm10 mm b a B C A PROBLEM 1.6 Two brass rods AB and BC, each of uniform diameter, will be brazed together at B to form a nonuniform rod of total length 100 m, which will be suspended from a support at A as shown. Knowing that the density of brass is 8470 kg/m3, determine (a) the length of rod AB for which the maximum normal stress in ABC is minimum, (b) the corresponding value of the maximum normal stress. SOLUTION Areas: 22 6222 62(15 mm) 176.715 mm 176.715 10 m4(10 mm) 78.54 mm 78.54 10 m4ABBCAA From geometry, b 100 a Weights: 66(8470)(9.81)(176.715 10 ) 14.683(8470)(9.81)(78.54 10 )(100 ) 652.59 6.526AB AB ABBCBCBCWgA a aWgA a a Normal stresses: At A, 63652.59 8.1573.6930 10 46.160 10 AABBCAAABPWW aPaA (1) At B, 63652.59 6.5268.3090 10 83.090 10 BBCBBBCPWaPaA (2) (a) Length of rod AB. The maximum stress in ABC is minimum when AB or 634.6160 10 129.25 10 0 a 35.71 ma 35.7 mABa (b) Maximum normal stress. 636363.6930 10 (46.160 10 )(35.71)8.3090 10 (83.090 10 )(35.71)5.34 10 Pa ABAB 5.34 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
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