A countershaft carrying two V-belt pulleys is shown below. Pulley A receives power from a motor through a belt with the belt tensions shown. The power is transmitted through the shaft and delivered to the belt on pulley B. Assume the belt tension on the loose side at B is 15 percent of the tension on the tight side. The shaft is made of 1018 CD steel. a) Determine the tensions in the belt on pulley B, assuming the shaft is running at a constant speed b) Find the magnitudes of the bearing reaction forces, assuming the bearings act as simple supports c) Draw shear force and bending moment diagrams for the shaft. If needed, make multiple diagrams for different planes. d) Determine the maximum bending stress and the torsional shear stress. e) Determine the principal stresses and maximum shear stress. f) Determine the minimum factor of safety for yielding using the maximum shear stress theory. g) Determine the minimum factor of safety for yielding using the distortion energy theory (von Mises). Hint: Appendix Table A-20 N T₁ 250-mm dia. 230 mm T₂ 280 mm 30-mm dia. 300 mm 400-mm dia. 1800 N 270 N Document reading pane SAE and/or UNS AISI No. No. Processing Tensile Strength, MPa (kpsi) Yield Strength, MPa Elongation Reduction (kpsi) in 2 in, % in Area, % Brinell Hardness G10060 1006 HR 300 (43) 170 (24) 30 55 86 CD 330 (48) 280 (41) 20 45 95 G10100 1010 HR 320 (47) 180 (26) 28 50 95 CD 370 (53) 300 (44) 20 40 105 G10150 1015 HR 340 (50) 190 (27.5) 28 50 101 CD 390 (56) 320 (47) 18 40 111 G10180 1018 HR 400 (58) 220 (32) 25 50 116 CD 440 (64) 370 (54) 15 40 126 G10200 1020 HR 380 (55) 210 (30) 25 50 111 CD 470 (68) 390 (57) 15 40 131 G10300 1030 HR 470 (68) 260 (37.5) 20 42 137 CD 520 (76) 440 (64) 12 35 149 G10350 1035 HR 500 (72) 270 (39.5) 18 40 143 CD 550 (80) 460 (67) 12 35 163 G10400 1040 HR 520 (76) 290 (42) 18 40 149 CD 590 (85) 490 (71) 12 35 170 G10450 1045 HR 570 (82) 310 (45) 16 40 163 CD 630 (91) 530 (77) 12 35 179 G10500 1050 HR 620 (90) 340 (49.5) 15 35 179 CD 690 (100) 580 (84) 10 30 197 G10600 1060 HR 680 (98) 370 (54) 12 30 201 G10800 1080 HR 770 (112) 420 (61.5) 10 25 229 G10950 1095 HR 830 (120) 460 (66) 10 10 25 248

A countershaft carrying two V-belt pulleys is shown below. Pulley A receives power from a motor through a belt with the belt tensions shown. The power is transmitted through the shaft and delivered to the belt on pulley B. Assume the belt tension on the loose side at B is 15 percent of the tension on the tight side. The shaft is made of 1018 CD steel. a) Determine the tensions in the belt on pulley B, assuming the shaft is running at a constant speed b) Find the magnitudes of the bearing reaction forces, assuming the bearings act as simple supports c) Draw shear force and bending moment diagrams for the shaft. If needed, make multiple diagrams for different planes. d) Determine the maximum bending stress and the torsional shear stress. e) Determine the principal stresses and maximum shear stress. f) Determine the minimum factor of safety for yielding using the maximum shear stress theory. g) Determine the minimum factor of safety for yielding using the distortion energy theory (von Mises). Hint: Appendix Table A-20 N T₁ 250-mm dia. 230 mm T₂ 280 mm 30-mm dia. 300 mm 400-mm dia. 1800 N 270 N Document reading pane SAE and/or UNS AISI No. No. Processing Tensile Strength, MPa (kpsi) Yield Strength, MPa Elongation Reduction (kpsi) in 2 in, % in Area, % Brinell Hardness G10060 1006 HR 300 (43) 170 (24) 30 55 86 CD 330 (48) 280 (41) 20 45 95 G10100 1010 HR 320 (47) 180 (26) 28 50 95 CD 370 (53) 300 (44) 20 40 105 G10150 1015 HR 340 (50) 190 (27.5) 28 50 101 CD 390 (56) 320 (47) 18 40 111 G10180 1018 HR 400 (58) 220 (32) 25 50 116 CD 440 (64) 370 (54) 15 40 126 G10200 1020 HR 380 (55) 210 (30) 25 50 111 CD 470 (68) 390 (57) 15 40 131 G10300 1030 HR 470 (68) 260 (37.5) 20 42 137 CD 520 (76) 440 (64) 12 35 149 G10350 1035 HR 500 (72) 270 (39.5) 18 40 143 CD 550 (80) 460 (67) 12 35 163 G10400 1040 HR 520 (76) 290 (42) 18 40 149 CD 590 (85) 490 (71) 12 35 170 G10450 1045 HR 570 (82) 310 (45) 16 40 163 CD 630 (91) 530 (77) 12 35 179 G10500 1050 HR 620 (90) 340 (49.5) 15 35 179 CD 690 (100) 580 (84) 10 30 197 G10600 1060 HR 680 (98) 370 (54) 12 30 201 G10800 1080 HR 770 (112) 420 (61.5) 10 25 229 G10950 1095 HR 830 (120) 460 (66) 10 10 25 248

Mechanics of Materials (MindTap Course List)

9th Edition

ISBN:9781337093347

Author:Barry J. Goodno, James M. Gere

Publisher:Barry J. Goodno, James M. Gere

Chapter11: Columns

Section: Chapter Questions

Problem 11.3.10P: Repeat Problem 11.3-9. Use two C 150 × 12.2 steel shapes and assume that E = 205 GPa and L = 6 m.

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