Rigid bar ABC is supported by two identical solid bronze [σY = 331 MPa; E = 105 GPa; α = 22.0 × 10−6/°C] rods and a single solid steel [σY = 250 MPa; E = 200 GPa; α = 11.7×10−6/°C] rod. Bronze rods (1) each have diameters of d1 = 28 mm and lengths of L1 = 3.9 m. Steel rod (2) has a length of L2 = 5.2 m. (a) Calculate the diameter d2 required for steel rod (2) so that the deflection of joint B is zero for any change in temperature.
Rigid bar ABC is supported by two identical solid bronze [σY = 331 MPa; E = 105 GPa; α = 22.0 × 10−6/°C] rods and a single solid steel [σY = 250 MPa; E = 200 GPa; α = 11.7×10−6/°C] rod. Bronze rods (1) each have diameters of d1 = 28 mm and lengths of L1 = 3.9 m. Steel rod (2) has a length of L2 = 5.2 m.
(a) Calculate the diameter d2 required for steel rod (2) so that the deflection of joint B is zero for any change in temperature.
(b) Using the value of d2 determined in part (a), determine the maximum temperature decrease that is allowable for this assembly if a factor of safety of 2.0 is specified for the normal stress in each rod. Since the temperature is decreasing, the answer should be negative.
![Rigid
bar ABC is supported by two identical solid bronze [oy = 331 MPa; E = 105 GPa; a = 22.0 x 10-6/°C] rods and a single solid steel
[oy= 250 MPa; E = 200 GPa; a = 11.7x10-6/°C] rod. Bronze rods (1) each have diameters of d₁ = 28 mm and lengths of L₁ = 3.9 m.
Steel rod (2) has a length of L₂ = 5.2 m.
(a) Calculate the diameter d2 required for steel rod (2) so that the deflection of joint B is zero for any change in temperature.
(b) Using the value of d2 determined in part (a), determine the maximum temperature decrease that is allowable for this assembly if a
factor of safety of 2.0 is specified for the normal stress in each rod. Since the temperature is decreasing, the answer should be negative.
(1)
(1)
L
Answer:
(a) d₂ = i
(b) ΔT = \ i
a
2
B
a
L2
mm
°℃](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0340ab0c-e54f-482a-bc54-4a3b868cdaba%2Fc3bf9665-0e42-417b-90dd-95d97dc9c23e%2Fylnca3_processed.png&w=3840&q=75)
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