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 = 24 mm and lengths of L1 = 4.5 m. Steel rod (2) has a length of L2 = 6 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 1.6 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 = 24 mm and lengths of L₁ = 4.5 m.Steel rod (2) has a length of L₂ = 6 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 afactor of safety of 1.6 is specified for the normal stress in each rod. Since the temperature is decreasing, the answer should be negative.(1)(1)L₁Answer:(a) d₂ =i(b) ΔT = liaBaL2mm°℃

The given data is: For two identical solid bronze, σY=331 MPa E=105 GPa α=22.0×10−6/°C For a single…

Answered: Rigid bar ABC is supported by two…

Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

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Rigid bar ABC is supported by two identical solid bronze [σ_Y = 331 MPa; E = 105 GPa; α = 22.0 × 10⁻⁶/°C] rods and a single solid steel [σ_Y = 250 MPa; E = 200 GPa; α = 11.7×10⁻⁶/°C] rod. Bronze rods (1) each have diameters of d₁ = 24 mm and lengths of L₁ = 4.5 m. Steel rod (2) has a length of L₂ = 6 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 1.6 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 = 24 mm and lengths of L₁ = 4.5 m.
Steel rod (2) has a length of L₂ = 6 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 1.6 is specified for the normal stress in each rod. Since the temperature is decreasing, the answer should be negative.
(1)
(1)
L₁
Answer:
(a) d₂ =
i
(b) ΔT = li
a
B
a
L2
mm
°℃

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