(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
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
Related questions
Question
100%
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
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 2 images
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.Recommended textbooks for you
Elements Of Electromagnetics
Mechanical Engineering
ISBN:
9780190698614
Author:
Sadiku, Matthew N. O.
Publisher:
Oxford University Press
Mechanics of Materials (10th Edition)
Mechanical Engineering
ISBN:
9780134319650
Author:
Russell C. Hibbeler
Publisher:
PEARSON
Thermodynamics: An Engineering Approach
Mechanical Engineering
ISBN:
9781259822674
Author:
Yunus A. Cengel Dr., Michael A. Boles
Publisher:
McGraw-Hill Education
Elements Of Electromagnetics
Mechanical Engineering
ISBN:
9780190698614
Author:
Sadiku, Matthew N. O.
Publisher:
Oxford University Press
Mechanics of Materials (10th Edition)
Mechanical Engineering
ISBN:
9780134319650
Author:
Russell C. Hibbeler
Publisher:
PEARSON
Thermodynamics: An Engineering Approach
Mechanical Engineering
ISBN:
9781259822674
Author:
Yunus A. Cengel Dr., Michael A. Boles
Publisher:
McGraw-Hill Education
Control Systems Engineering
Mechanical Engineering
ISBN:
9781118170519
Author:
Norman S. Nise
Publisher:
WILEY
Mechanics of Materials (MindTap Course List)
Mechanical Engineering
ISBN:
9781337093347
Author:
Barry J. Goodno, James M. Gere
Publisher:
Cengage Learning
Engineering Mechanics: Statics
Mechanical Engineering
ISBN:
9781118807330
Author:
James L. Meriam, L. G. Kraige, J. N. Bolton
Publisher:
WILEY