Tensile Strength and Solution

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problem 261
A steel rod with a cross-sectional area of 0.25 in2 is stretched between two fixed points. The tensile load at 70°F is 1200 lb. What will be the stress at 0°F? At what temperature will the stress be zero? Assume α = 6.5 × 10-6 in/(in·°F) and E = 29 × 106 psi.  

Solution 261
For the stress at 0°C:

 answer
 
For the temperature that causes zero stress:
 

 answer
problem 262
A steel rod is stretched between two rigid walls and carries a tensile load of 5000 N at 20°C. If the allowable stress is not to exceed 130 MPa at -20°C, what is the minimum diameter of the rod? Assume α = 11.7 µm/(m·°C) and E = 200 GPa.  

Solution 262

 

 

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Problem 263
Steel railroad reels 10 m long are laid with a clearance of 3 mm at a temperature of 15°C. At what temperature will the rails just touch? What stress would be induced in the rails at that temperature if there were no initial clearance? Assume α = 11.7µm/(m·°C) and E = 200 GPa.  

Solution 263 
Temperature at which :

 answer
 
Required stress:

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Problem 264
A steel rod 3 feet long with a cross-sectional area of 0.25 in.2 is stretched between two fixed points. The tensile force is 1200 lb at 40°F. Using E = 29 × 106 psi and α= 6.5 × 10-6 in./(in.·°F), calculate (a) the temperature at which the stress in the bar will be 10 ksi; and (b) the temperature at which the stress will be zero.  

Solution 264

(a) Without temperature change:
  

A drop of temperature is needed to increase the stress to 10 ksi. See figure above.

Required temperature: (temperature must drop from 40°F)
 answer
 
(b) From the figure below:
  

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th a cross sectional area of 320 mm2 is placed between two rigid walls as shown in Fig. P-265. At a temperature of -20°C, the gap Δ = 25 mm. Find the temperature at which the compressive stress in the bar will be 35 MPa. Use α = 18.0 × 10-6 m/(m·°C) and E = 80 GPa.  

Problem 265

 answer
 
Problem 266
Calculate the increase in stress for each segment of the compound bar shown in Fig. P-266 if the temperature increases by 100°F. Assume that the supports are unyielding and that the bar is suitably braced against buckling.

 Problem 266

 

 

where 

 

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 answer
 
Problem 267
At a temperature of 80°C, a steel tire 12 mm thick and 90 mm wide that is to be shrunk onto a locomotive driving wheel 2 m in diameter just fits over the wheel, which is at a temperature of 25°C. Determine the contact pressure between the tire and wheel after the assembly cools to 25°C. Neglect the deformation of the wheel caused by the pressure of the tire. Assume α = 11.7 μm/(m·°C) and E = 200 GPa.  

Solution 267

 

 answer
Problem 268
The rigid bar ABC in Fig. P-268 is pinned at B and attached to the two vertical rods. Initially, the bar is horizontal and the vertical rods are stress-free. Determine the stress in the aluminum rod if the temperature of the steel rod is decreased by 40°C. Neglect the weight of bar ABC.  

 Solution 268
Contraction of steel rod, assuming complete freedom:

The steel rod cannot freely contract because of the resistance of aluminum rod. The movement of A (referred to as δA), therefore, is less than 0.4212 mm. In terms of aluminum, this movement is (by ratio and proportion):  

 

 Equation (1)
 

 Equation (2)
 
Equations (1) and (2)

 

 answer
 
Problem 269
As shown in Fig. P-269, there is a gap between the aluminum bar and the rigid slab that is supported by two copper bars. At 10°C, Δ = 0.18 mm. Neglecting the mass of the slab, calculate the stress in each rod when the temperature in the assembly is increased to 95°C. For each copper bar, A = 500 mm2, E = 120 GPa, and α = 16.8 µm/(m·°C). For the aluminum bar, A = 400 mm2, E = 70 GPa, and α = 23.1µm/(m·°C).  

Solution 269
Assuming complete freedom:

 
From the figure:

 

 answer
 answer
 
Problem 270
A bronze sleeve is slipped over a steel bolt and held in place by a nut...
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