Answer:
a) the maximum stress that can be applied without plastic deformation is 398.72 N/mm²
b) length of the specimen is 66.97 mm
Explanation:
Given the data in the question;
a) Determine the maximum stress that can be applied without plastic deformation
when know that; maximum stress σ[tex]_{max}[/tex] = F / A
where F is the force in the rod ( 39872 N )
A is the cross-sectional area of the rod ( 100 mm² )
so we substitute;
σ[tex]_{max}[/tex] = 39872 N / 100 mm²
σ[tex]_{max}[/tex] = 398.72 N/mm²
Therefore, the maximum stress that can be applied without plastic deformation is 398.72 N/mm²
b)
strain in the members can be calculated using the expression
ε = σ / E
where σ is the stress in the rod
E is the module of elasticity ( 110 GPa = 110000 N/mm² )
(Sl-L) / L = σ/E
where Sl-L is the change in length of the member
L is the original length of the specimen
so we substitute
(67.21 - L) / L = 398.72 / 110000
110000( 67.21 - L) = 398.72L
7393100 - 110000L = 398.72L
7393100 = 398.72L+ 110000L
7393100 = 110398.72L
L = 7393100 / 110398.72
L = 66.97 mm
Therefore; length of the specimen is 66.97 mm
