The steel rails of a railroad track (Es = 200 GPa, αs = 11.7 × 10–6/°C)...
The steel rails of a railroad track (Es = 200 GPa, αs = 11.7 × 10–6/°C) were laid at a temperature of 6°C. Determine the normal stress in the rails when the temperature reaches 48°C, assuming that the rails (a) are welded to form a continuous track, (b) are 10 m long with 3-mm gaps between them.
Homework Answers
(a) Calculate the normal stress
developed in continuous steel railroad track, due to change in temperature using the equation
…… (1)
Here, 
is the young’s modulus of steel. 
is the coefficient of thermal expansion for steel. 
is the change in temperature.
Calculate 
using the equation,
Here 
are the initial and final temperatures
Substitute 
for 
and 
for 
Substitute 200 GPa for
, 
for 
in equation (1)
Therefore, normal stress developed in the continuous track is 
(b) Calculate the change in length
in the railroad tracks due to change in temperature using the equation,
Here, L is the length of the rod.
Substitute 10 m for L
Since there is a gap between the railroad tracks is less than
, the change in length will be restricted. Calculate the original change in length 
using the equation,
Here, 
is the gap between the railroad tracks.
Substitute, 3 mm for 
Calculate strain
using the equation
Calculate the normal stress developed in railroad track with restricted elongation using the equation
Therefore, the normal stress developed in railroad track, 3m long and with 3 mm restricted elongation is 
Add Answer to:
The steel rails of a railroad track (Es = 200 GPa, αs = 11.7 × 10–6/°C)...
During the construction of the LRT railroad track, hot rolled structural steel A36 of 10-m-long rails...
During the construction of the LRT railroad track, hot rolled structural steel A36 of 10-m-long rails were used. The steel rails were laid on the track with a 5-mm gaps between the rails during the night when the temperature of the steel was 20°C. Determine the normal stress in the steel rails when the temperature of the steel is 40°C. E = 200 GPa and a = 11.7 x 10-6 m/(m °C)
Given a steel railroad track which was installed at 30 F. Let E = 29 x...
Given a steel railroad track which was installed at 30 F. Let E
= 29 x 10^6 psi and α = 6.5 x 10^-6 / F
If the temperature reaches 125 F,
a) Find the normal stress in the rails which are welded together
to form a continuous track.
b) Find the normal stress in the rails assuming the rails are 39
ft. long with 1/4" gap between them
3a fr オ Given: A steel railroad track which was installed...
A railroad track la made of individual rails of steel each 29 feet in length. By...
A railroad track la made of individual rails of steel each 29 feet in length. By what length would one rail change from a cold winter day when the temperature is -10 degree Cto a hot summer day at 30 degree C? (1 m. 3.281 ).(1km = 1000m) (5280 ft = 1 mile) (1 mile = 1.609 km) TABLE 14.1. Coefficients of linear expansion for selected materials Material a (K 'or C-1) Quartz (fused) 0.04 x 10 Invar (nickel- iron...
Full solution thank The 12-m-long A-36 steel rails on a train track are laid with a...
Full solution thank
The 12-m-long A-36 steel rails on a train track are laid with a small gap between them to allow for thermal expansion. The CROSS-sectional area of each railis 3100 mm . (Figure 1) - Part A Determine the required gap & so that the rails just touch one another when the temperature is increased from Ti -30°C to 30°C Express your answer to three significant figures and include the appropriate units. :MAO ? Value Units Fiqure 1...
The 40-ft long A-36 steel rails on a train track are laid with a small gap...
The 40-ft long A-36 steel rails on a train track are laid with a small gap between them to allow for thermal expansion. Determine the total required gap, 2*6, so that the rails just touch one another when the temperature is increased from T1 -20°F to T2 90 °F. If the rails were installed at -20 °F with this gap, what would be the axial force in the rails if the temperature were to rise to T3 = 110 °F....
The concrete post (Ec = 3.6 × 106 psi and αc = 5.5 × 10-6/°F) is...
The concrete post (Ec = 3.6 × 106
psi and αc = 5.5 × 10-6/°F) is
reinforced with six steel bars, each of 78-in.78-in. diameter
(Es = 29 × 106 psi and
αs = 6.5 × 10-6/°F). Determine the
normal stresses induced in the steel and in the concrete by a
temperature rise of 75°F.
The normal stress in the steel is _____ ksi.
The normal stress in the concrete is _____psi
6 ft 10 in. 10 in.
A 1.2 m concrete column is reinforced by four steel bars, each 20 mm in diameter, as indicated. It is known that for ste...
A
1.2 m concrete column is reinforced by four steel bars, each 20 mm
in diameter, as indicated. It is known that for steel E = 200 GPa
and α = 11.7 (10-6) / ° C and for concrete E = 25 GPa and α = 9.9
(10-6) / ° C brass tube 300 mm in length, 30 mm outside diameter
and 3 mm wall thickness, is fixed in a hand-operated lathe which is
adjusted in such a way as...
2) The rigid bar CDE is attached to a pin support at E and rests on...
2) The rigid bar CDE is attached to a pin support at E and rests on the 30-mm diameter brass cylinder BD. A 22-mm-diameter steel rod AC passes through a hole in the bar and is secured by a nut which is snugly fitted when the temperature of the entire assembly is 20°C. The temperature of the brass cylinder is then raised to 50°C while the steel rod remains at 20°C. Assuming that no stresses were present before the temperature...
Question 6 A 25x25x25-cm block of steel (E-200 GPa, v 0.3) is loaded with a uniformly...
Question 6 A 25x25x25-cm block of steel (E-200 GPa, v 0.3) is loaded with a uniformly distributed pressure of 200 MPa on the four faces having outward normals in the x- and y-directions. Rigid constraints limit the displacements of the cube in the z-direction to 5x10 cm. Determine the normal stress o that develops as the pressure is applied
2) The rigid bar CDE is attached to a pin support at E and rests on...
2) The rigid bar CDE is attached to a pin support at E and rests on the 30-mm diameter brass cylinder BD. A 22-mm-diameter steel rod AC passes through a hole in the bar and is secured by a nut which is snugly fitted when the temperature of the entire assembly is 20°C. The temperature of the brass cylinder is then raised to 50°C while the steel rod remains at 20°C. Assuming that no stresses were present before the temperature...
During the construction of the LRT railroad track, hot rolled structural steel A36 of 10-m-long rails were used. The steel rails were laid on the track with a 5-mm gaps between the rails during the night when the temperature of the steel was 20°C. Determine the normal stress in the steel rails when the temperature of the steel is 40°C. E = 200 GPa and a = 11.7 x 10-6 m/(m °C)
Given a steel railroad track which was installed at 30 F. Let E
= 29 x 10^6 psi and α = 6.5 x 10^-6 / F
If the temperature reaches 125 F,
a) Find the normal stress in the rails which are welded together
to form a continuous track.
b) Find the normal stress in the rails assuming the rails are 39
ft. long with 1/4" gap between them
3a fr オ Given: A steel railroad track which was installed...
A railroad track la made of individual rails of steel each 29 feet in length. By what length would one rail change from a cold winter day when the temperature is -10 degree Cto a hot summer day at 30 degree C? (1 m. 3.281 ).(1km = 1000m) (5280 ft = 1 mile) (1 mile = 1.609 km) TABLE 14.1. Coefficients of linear expansion for selected materials Material a (K 'or C-1) Quartz (fused) 0.04 x 10 Invar (nickel- iron...
Full solution thank
The 12-m-long A-36 steel rails on a train track are laid with a small gap between them to allow for thermal expansion. The CROSS-sectional area of each railis 3100 mm . (Figure 1) - Part A Determine the required gap & so that the rails just touch one another when the temperature is increased from Ti -30°C to 30°C Express your answer to three significant figures and include the appropriate units. :MAO ? Value Units Fiqure 1...
The 40-ft long A-36 steel rails on a train track are laid with a small gap between them to allow for thermal expansion. Determine the total required gap, 2*6, so that the rails just touch one another when the temperature is increased from T1 -20°F to T2 90 °F. If the rails were installed at -20 °F with this gap, what would be the axial force in the rails if the temperature were to rise to T3 = 110 °F....
The concrete post (Ec = 3.6 × 106
psi and αc = 5.5 × 10-6/°F) is
reinforced with six steel bars, each of 78-in.78-in. diameter
(Es = 29 × 106 psi and
αs = 6.5 × 10-6/°F). Determine the
normal stresses induced in the steel and in the concrete by a
temperature rise of 75°F.
The normal stress in the steel is _____ ksi.
The normal stress in the concrete is _____psi
6 ft 10 in. 10 in.
A
1.2 m concrete column is reinforced by four steel bars, each 20 mm
in diameter, as indicated. It is known that for steel E = 200 GPa
and α = 11.7 (10-6) / ° C and for concrete E = 25 GPa and α = 9.9
(10-6) / ° C brass tube 300 mm in length, 30 mm outside diameter
and 3 mm wall thickness, is fixed in a hand-operated lathe which is
adjusted in such a way as...
2) The rigid bar CDE is attached to a pin support at E and rests on the 30-mm diameter brass cylinder BD. A 22-mm-diameter steel rod AC passes through a hole in the bar and is secured by a nut which is snugly fitted when the temperature of the entire assembly is 20°C. The temperature of the brass cylinder is then raised to 50°C while the steel rod remains at 20°C. Assuming that no stresses were present before the temperature...
Question 6 A 25x25x25-cm block of steel (E-200 GPa, v 0.3) is loaded with a uniformly distributed pressure of 200 MPa on the four faces having outward normals in the x- and y-directions. Rigid constraints limit the displacements of the cube in the z-direction to 5x10 cm. Determine the normal stress o that develops as the pressure is applied
2) The rigid bar CDE is attached to a pin support at E and rests on the 30-mm diameter brass cylinder BD. A 22-mm-diameter steel rod AC passes through a hole in the bar and is secured by a nut which is snugly fitted when the temperature of the entire assembly is 20°C. The temperature of the brass cylinder is then raised to 50°C while the steel rod remains at 20°C. Assuming that no stresses were present before the temperature...
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