Respuesta :
Answer:
A) Change in length of pipe = -2.4265 x 10^(-3)m
B) Change in pipe outer diameter = 9.6096 x 10^(-2)mm
C) change in thickness = 4.004 x 10^(-3)mm
Explanation:
Load = 640KN or 640,000N
E = 73 GPa or 73 x 10^(9)Pa
and v = 0.33
A) Inner Diameter of rod(di) = do - 2t
= 0.24m - (2x0.01) = 0.24 - 0.02 = 0.22m
So, area of cross section = (π/4)[(do)^2 - (di)^2] = (π/4)[(0.24)^2 - (0.22)^2] = 7.226 x 10^(-3) m^2
Now change in pipe length;
ΔL = - PL/EA
= -[640,000 x 2] /[(73 x 10^(9)) x (7.226 x 10^(-3)] =
- [1280000]/[527.498 x 10^(6)] =
-2.4265 x 10^(-3)m
B)let's first calculate the strain in longitudinal direction;
ε = (δL) /L = [-2.4265 x 10^(-3)]/2
= - 1.2133 x 10^(-3)
For change in diameter;
Δdo = do(εLAT)
εLAT = - v(ε)
So v = 0.33 from the question, thus
εLAT = -(0.33 x - 1.2133 x 10^(-3)) = 4.004 x 10^(-4)
Thus; Δdo = 240 x 4.004 x 10^(-4) =
9.6096 x 10^(-2)mm
C) for change in thickness;
Δt = t(εLAT) = 10 x 4.004 x 10^(-4) = 4.004 x 10^(-3)mm
