(a)
Interpretation:
The length and the diameter of the given bar should be determined
A 500-lb load is applied on the bar, after this length and the diameter of the bar are to be determined where the Poisson's ratio is 0.30.
Concept Introduction:
Following formulas will be used for the calculation of new length and the diameter of titanium bar-
Stress formula-
Poisson's ratio-
P= applied force
L= initial length
A= area
E= modulus of elasticity
δl= Change in length
P= applied force
A = area
(b)
Interpretation:
The applied load should be determined for the given copper bar.
Concept Introduction:
Applied load is calculated by using the following formulas-
Relation between rigidity modulus, modulus of elasticity and Poisson's ratio is-
Where,
G = modulus of rigidity
E = modulus of elasticity
Hooke's law for shear stress (t) and strain (τ) is −
Shear stress is −
Shear strain is-
Where,
τ = shear stress
γ = shear strain
G = proportional constant, modulus of rigidity
τ = shear stress
F= applied force
A= area
τ = shear strain
ΔA= deformed area or change in area
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Chapter 6 Solutions
Essentials of Materials Science and Engineering, SI Edition
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