advertisement

Chapter 1 Problems Solutions d1 PROBLEM 1.1 d2 125 kN B C A Two solid cylindrical rods AB and BC are welded together at B and loaded as shown. Knowing that d1 30 mm and d 2 50 mm, find the average normal stress at the midsection of (a) rod AB, (b) rod BC. 60 kN 125 kN 0.9 m 1.2 m SOLUTION (a) Rod AB: Force: P 60 103 N tension Area: A Normal stress: (b) AB 4 d12 4 (30 103 ) 2 706.86 106 m 2 P 60 103 84.882 106 Pa A 706.86 106 AB 84.9 MPa Rod BC: Force: P 60 103 (2)(125 103 ) 190 103 N Area: A Normal stress: BC 4 d 22 4 (50 103 )2 1.96350 103 m 2 P 190 103 96.766 106 Pa A 1.96350 103 BC 96.8 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. 3 PROBLEM 1.7 0.4 m C 0.25 m 0.2 m B Each of the four vertical links has an 8 36-mm uniform rectangular cross section and each of the four pins has a 16-mm diameter. Determine the maximum value of the average normal stress in the links connecting (a) points B and D, (b) points C and E. E 20 kN D A SOLUTION Use bar ABC as a free body. M C 0 : (0.040) FBD (0.025 0.040)(20 103 ) 0 FBD 32.5 103 N Link BD is in tension. 3 M B 0 : (0.040) FCE (0.025)(20 10 ) 0 FCE 12.5 103 N Link CE is in compression. Net area of one link for tension (0.008)(0.036 0.016) 160 106 m 2 For two parallel links, (a) BD A net 320 106 m 2 FBD 32.5 103 101.563 106 6 Anet 320 10 BD 101.6 MPa Area for one link in compression (0.008)(0.036) 288 106 m 2 For two parallel links, (b) CE A 576 106 m 2 FCE 12.5 103 21.701 106 6 A 576 10 CE 21.7 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. 9 4 kips 6 C in. u B 1 308 Link BD consists of a single bar 1 in. wide and 1 in. thick. Knowing that each pin has a 83 -in. 2 diameter, determine the maximum value of the average normal stress in link BD if (a) = 0, (b) = 90. . 2 in A PROBLEM 1.10 D SOLUTION Use bar ABC as a free body. (a) 0. M A 0: (18 sin 30)(4) (12 cos30) FBD 0 FBD 3.4641 kips (tension) Area for tension loading: Stress: (b) 3 1 A (b d )t 1 0.31250 in 2 8 2 F 3.4641 kips BD A 0.31250 in 2 11.09 ksi 90. M A 0: (18 cos30)(4) (12 cos 30) FBD 0 FBD 6 kips i.e. compression. Area for compression loading: Stress: 1 A bt (1) 0.5 in 2 2 F 6 kips BD A 0.5 in 2 12.00 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. 12 PROBLEM 1.21 P 5 40 kN 120 mm b A 40-kN axial load is applied to a short wooden post that is supported by a concrete footing resting on undisturbed soil. Determine (a) the maximum bearing stress on the concrete footing, (b) the size of the footing for which the average bearing stress in the soil is 145 kPa. 100 mm b SOLUTION (a) Bearing stress on concrete footing. P 40 kN 40 103 N A (100)(120) 12 103 mm 2 12 103 m 2 (b) P 40 103 3.3333 106 Pa A 12 103 Footing area. P 40 103 N P A 3.33 MPa 145 kPa 45 103 Pa A P 40 103 0.27586 m 2 3 145 10 Since the area is square, A b 2 b A 0.27586 0.525 m b 525 mm 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. 23 PROBLEM 1.45 Three 34 -in.-diameter steel bolts are to be used to attach the steel plate shown to a wooden beam. Knowing that the plate will support a load P = 24 kips and that the ultimate shearing stress for the steel used is 52 ksi, determine the factor of safety for this design. P SOLUTION For each bolt, A 4 d2 3 2 2 0.44179 in 44 PU A U (0.44179)(52) 22.973 kips For the three bolts, PU (3)(22.973) 68.919 kips Factor of safety: F. S . PU 68.919 24 P F. S . 2.87 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. 51 PROBLEM 1.46 Three steel bolts are to be used to attach the steel plate shown to a wooden beam. Knowing that the plate will support a load P = 28 kips, that the ultimate shearing stress for the steel used is 52 ksi, and that a factor of safety of 3.25 is desired, determine the required diameter of the bolts. P SOLUTION For each bolt, Required: P 24 8 kips 3 PU ( F. S.) P (3.25)(8.0) 26.0 kips U d PU P 4P U 2 U2 A d d 4 4 PU U (4)(26.0) 0.79789 in. (52) d 0.798 in. 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. 52