) Show that the material index for the lightest cantilever beam of length L and square section (not given, i.e., the area is a free variable) that will not deflect by more than 8, In addition, select the best material that meet the constraints and objectives are shown below: Function Self-loaded cantilever beam • Length L specified • Minimize the mass, m • Choice of material Constraints • Maximum deflection, &, specified Objective Free variables F13 8 3EI • Section area A =t? Force f per unit length Free P. Mg.m 7.8 Material E, GPa Mild steel 200 69 2.7 Al 40 1.6 GFRP 189 1.55 CFRP 5635

) Show that the material index for the lightest cantilever beam of length L and square section (not given, i.e., the area is a free variable) that will not deflect by more than 8, In addition, select the best material that meet the constraints and objectives are shown below: Function Self-loaded cantilever beam • Length L specified • Minimize the mass, m • Choice of material Constraints • Maximum deflection, &, specified Objective Free variables F13 8 3EI • Section area A =t? Force f per unit length Free P. Mg.m 7.8 Material E, GPa Mild steel 200 69 2.7 Al 40 1.6 GFRP 189 1.55 CFRP 5635

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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Concept explainers

Slope and Deflection

The slope in a deflected beam is described as an angle in radians made by the tangent of the section with the original axis of the beam. The deflection at any point on the axis of the beam is defined as the lateral displacement of the point before and after loading.

Question

)Show that the material index for the lightest cantilever beam of length L and square section (not
given, i.e., the area is a free variable) that will not deflect by more than 8. In addition, select the best
material that meet the constraints and objectives are shown below:
Function
Self-loaded cantilever beam
• Length L specified
• Minimize the mass, m
Choice of material
Constraints
• Maximum deflection, &,
specified
Objective
Free variables
F13
• Section area A = t2
3EI
Force f per unit length
Free
P. Mg.m³
7.8
Material
E, GPa
200
Mild steel
69
2.7
Al
40
1.6
GFRP
CFRP
189
1.55
076S

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