HW6_Solutions

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California State University, Long Beach *

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373

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Mechanical Engineering

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Apr 3, 2024

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3/28/23, 9:53 PM Assignment Print View https://ezto.mheducation.com/api/caa/activity/C15Print?jwt=eyJhbGciOiJSUzI1NiJ9.eyJlbnZpcm9ubWVudCI6InByb2QiLCJpc3MiOiJlenQiLCJwcmlud… 2/11 1. Award: 0 out of 10.00 points Three wooden beams and two steel plates are securely bolted together to form the composite member shown. Using the data given in the table, determine the largest permissible bending moment when the member is bent about a horizontal axis. Take x = 9 in. The largest permissible bending moment when the member is bent about a horizontal axis is 357.8 kip·in. References Numeric Response Difficulty: Medium Three wooden beams and two steel plates are securely bolted together to form the composite member shown. Using the data given in the table, determine the largest permissible bending moment when the member is bent about a horizontal axis. Take x = 9 in.
3/28/23, 9:53 PM Assignment Print View https://ezto.mheducation.com/api/caa/activity/C15Print?jwt=eyJhbGciOiJSUzI1NiJ9.eyJlbnZpcm9ubWVudCI6InByb2QiLCJpc3MiOiJlenQiLCJwcmlud… 3/11 The largest permissible bending moment when the member is bent about a horizontal axis is 271.3966 ± 5% kip·in. Explanation: Use wood as the reference material. For wood, For steel, Designate steel as 1 and wood as 2. For the transformed section, For wood, For steel,
3/28/23, 9:53 PM Assignment Print View https://ezto.mheducation.com/api/caa/activity/C15Print?jwt=eyJhbGciOiJSUzI1NiJ9.eyJlbnZpcm9ubWVudCI6InByb2QiLCJpc3MiOiJlenQiLCJwcmlud… 4/11 Choose the smaller value.
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3/28/23, 9:53 PM Assignment Print View https://ezto.mheducation.com/api/caa/activity/C15Print?jwt=eyJhbGciOiJSUzI1NiJ9.eyJlbnZpcm9ubWVudCI6InByb2QiLCJpc3MiOiJlenQiLCJwcmlud… 5/11 2. Award: 0 out of 10.00 points A copper strip ( E c = 105 GPa) and an aluminum strip ( E a = 75 GPa) are bonded together to form the composite beam shown. Knowing that the beam is bent about a horizontal axis by a couple of moment M = 35 N·m, determine the maximum stress in the aluminum strip and in the copper strip. The maximum compressive stress in the aluminum strip is n/r MPa (include a negative sign). The maximum tensile stress in the copper strip is n/r MPa. References Numeric Response Difficulty: Medium A copper strip ( E c = 105 GPa) and an aluminum strip ( E a = 75 GPa) are bonded together to form the composite beam shown. Knowing that the beam is bent about a horizontal axis by a couple of moment M = 35 N·m, determine the maximum stress in the aluminum strip and in the copper strip. The maximum compressive stress in the aluminum strip is -56 ± 5% MPa (include a negative sign). The maximum tensile stress in the copper strip is 66.4 ± 5% MPa. Explanation:
3/28/23, 9:53 PM Assignment Print View https://ezto.mheducation.com/api/caa/activity/C15Print?jwt=eyJhbGciOiJSUzI1NiJ9.eyJlbnZpcm9ubWVudCI6InByb2QiLCJpc3MiOiJlenQiLCJwcmlud… 6/11 Use aluminum as the reference material. n = 1.0 for aluminum. n = E c / E a = 105 GPa/75 GPa = 1.4 for copper. For the transformed section, A nA 1 144 mm 2 144 mm 2 9 mm 1296 mm 3 2 144 mm 2 201.6 mm 2 3 mm 604.8 mm 3 Σ 345.6 mm 2 1900.8 mm 3 is taken from the bottom section. The neutral axis lies 5.50 mm above the bottom. Aluminum: Copper:
3/28/23, 9:53 PM Assignment Print View https://ezto.mheducation.com/api/caa/activity/C15Print?jwt=eyJhbGciOiJSUzI1NiJ9.eyJlbnZpcm9ubWVudCI6InByb2QiLCJpc3MiOiJlenQiLCJwcmlud… 7/11 A steel bar ( E s = 210 GPa) and an aluminum bar ( E a = 70 GPa) are bonded together to form the composite bar shown. References Section Break Difficulty: Medium
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3/28/23, 9:53 PM Assignment Print View https://ezto.mheducation.com/api/caa/activity/C15Print?jwt=eyJhbGciOiJSUzI1NiJ9.eyJlbnZpcm9ubWVudCI6InByb2QiLCJpc3MiOiJlenQiLCJwcmlud… 8/11 3. Award: 0 out of 10.00 points Determine the maximum stress in aluminum when the bar is bent about a horizontal axis, with M = 64 N m. The maximum stress in aluminum is n/r MPa. References Numeric Response Difficulty: Medium Determine the maximum stress in aluminum when the bar is bent about a horizontal axis, with M = 64 N m. The maximum stress in aluminum is 55.3277 ± 5% MPa. Explanation: Use aluminum as the reference material. For aluminum, For steel, For the transformed section, 1 and 2 are areas of aluminum and 3 is the area of steel. A , mm 2 nA , mm 2 1 192 192 4 768 2 128 128 12 1536 3 64 192 12 2304 512 4608 The neutral axis lies 9 mm above the bottom.
3/28/23, 9:53 PM Assignment Print View https://ezto.mheducation.com/api/caa/activity/C15Print?jwt=eyJhbGciOiJSUzI1NiJ9.eyJlbnZpcm9ubWVudCI6InByb2QiLCJpc3MiOiJlenQiLCJwcmlud… 9/11 For aluminum,
3/28/23, 9:53 PM Assignment Print View https://ezto.mheducation.com/api/caa/activity/C15Print?jwt=eyJhbGciOiJSUzI1NiJ9.eyJlbnZpcm9ubWVudCI6InByb2QiLCJpc3MiOiJlenQiLCJwcmlu… 10/11 4. Award: 0 out of 10.00 points Determine the maximum stress in steel when the bar is bent about a horizontal axis, with M = 64 N m. The maximum stress in steel is − n/r MPa. References Numeric Response Difficulty: Medium Determine the maximum stress in steel when the bar is bent about a horizontal axis, with M = 64 N m. The maximum stress in steel is − 129.0979 ± 5% MPa. Explanation: Use aluminum as the reference material. For aluminum, For steel, For the transformed section, 1 and 2 are areas of aluminum and 3 is the area of steel. A, mm 2 nA, mm 2 1 192 192 4 768 2 128 128 12 1536 3 64 192 12 2304 512 4608 The neutral axis lies 9 mm above the bottom.
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3/28/23, 9:53 PM Assignment Print View https://ezto.mheducation.com/api/caa/activity/C15Print?jwt=eyJhbGciOiJSUzI1NiJ9.eyJlbnZpcm9ubWVudCI6InByb2QiLCJpc3MiOiJlenQiLCJwcmlu… 11/11 For steel,