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(b) Show that the lightest cantilever beam of length (b) L and square section (area free) that will not deflect by more than 8 under an end load F is that made of the material with the largest value of ME/2/p (neglect self-weight). Plot each index on the given (E-p) chart indicating the search area for materials with the highest values of each. HINT: Start each of the problem by listing the function, the objective and the constraints. You will need the equations for the deflection of a cantilever beam with a square cross-section t x t. You can either derive the equations or use the equations provided in Appendix B, Section B3. 1000 100 oung s modulusEGPa 9 10 1 10-² Loungs modulus density 10-4 Longitudinal wave speed 10 ms 3x10 Foams, 10 ms " 10-33x102 10² Rigid polymer foams ms Al alloys Composites CFRP Technical ceramics Glase Bamboo Mg alloys GFRP Wood Flexible polymer foams Natural PMMA- materials PA Cork grain PS Wood grain Leat EVA Isoprene Buty rubber Polyester Concrete PP RET Diamond Al2O3 Steels SIC Ti alloys SigNa PE PEEK Epoxies PC PTFE Polymers Silicone elastomers Polyuret ane. Neoprene Zinc alloys Nontechnical ceramics Ni alloys Elastomers WC O-W alloys Cu alloys - Metals Lead alloys F, d Guidelines for minimum mass design MFA +

(b) Show that the lightest cantilever beam of length (b) L and square section (area free) that will not deflect by more than 8 under an end load F is that made of the material with the largest value of ME/2/p (neglect self-weight). Plot each index on the given (E-p) chart indicating the search area for materials with the highest values of each. HINT: Start each of the problem by listing the function, the objective and the constraints. You will need the equations for the deflection of a cantilever beam with a square cross-section t x t. You can either derive the equations or use the equations provided in Appendix B, Section B3. 1000 100 oung s modulusEGPa 9 10 1 10-² Loungs modulus density 10-4 Longitudinal wave speed 10 ms 3x10 Foams, 10 ms " 10-33x102 10² Rigid polymer foams ms Al alloys Composites CFRP Technical ceramics Glase Bamboo Mg alloys GFRP Wood Flexible polymer foams Natural PMMA- materials PA Cork grain PS Wood grain Leat EVA Isoprene Buty rubber Polyester Concrete PP RET Diamond Al2O3 Steels SIC Ti alloys SigNa PE PEEK Epoxies PC PTFE Polymers Silicone elastomers Polyuret ane. Neoprene Zinc alloys Nontechnical ceramics Ni alloys Elastomers WC O-W alloys Cu alloys - Metals Lead alloys F, d Guidelines for minimum mass design MFA +

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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M=E/p². (b) Show that the lightest cantilever beam of length L and square section (area free) that will not deflect by more than 8 under an end load F is that made of the material with the largest value of M = Ep (neglect self-weight). loungs modulusE GPa Plot each index on the given (E- p) chart indicating the search area for materials with the highest values of each. 1000 HINT: Start each of the problem by listing the function, the objective and the constraints. You will need the equations for the deflection of a cantilever beam with a square cross-section t x t. You can either derive the equations or use the equations provided in Appendix B, Section B3. 100 10 1 10-1 10-2 Loungs modulus density 10-4 Longitudinal wave speed 10 ms 3x10² Foams. 10 ms- 10-3 3x10² Rigid polymer foams 10 ms Technical ceramics Al alloys Composites CFRP Glass Bamboo Mg alloys GFRP Wood Flexible polymer foams Natural PMMA- materials PA grain Cork PS Wood grain Leat e EVA Isoprene Buty rubber B4C. Polyester PP RET Diamond Al2O3 Steels SIC Ti alloys SigNa Concrete PE (b) 12 -PEEK Epoxies PC PTFE Polymers Silicone elastomers Polyuretane. Neoprene L Ni alloys Zinc alloys Nontechnical ceramics Elastomers WC O-W alloys Cu alloys. - Metals Lead alloys F, d Guidelines for minimum mass design MFA Free
Transcribed Image Text:M=E/p². (b) Show that the lightest cantilever beam of length L and square section (area free) that will not deflect by more than 8 under an end load F is that made of the material with the largest value of M = Ep (neglect self-weight). loungs modulusE GPa Plot each index on the given (E- p) chart indicating the search area for materials with the highest values of each. 1000 HINT: Start each of the problem by listing the function, the objective and the constraints. You will need the equations for the deflection of a cantilever beam with a square cross-section t x t. You can either derive the equations or use the equations provided in Appendix B, Section B3. 100 10 1 10-1 10-2 Loungs modulus density 10-4 Longitudinal wave speed 10 ms 3x10² Foams. 10 ms- 10-3 3x10² Rigid polymer foams 10 ms Technical ceramics Al alloys Composites CFRP Glass Bamboo Mg alloys GFRP Wood Flexible polymer foams Natural PMMA- materials PA grain Cork PS Wood grain Leat e EVA Isoprene Buty rubber B4C. Polyester PP RET Diamond Al2O3 Steels SIC Ti alloys SigNa Concrete PE (b) 12 -PEEK Epoxies PC PTFE Polymers Silicone elastomers Polyuretane. Neoprene L Ni alloys Zinc alloys Nontechnical ceramics Elastomers WC O-W alloys Cu alloys. - Metals Lead alloys F, d Guidelines for minimum mass design MFA Free
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