Traffic and Highway Engineering
5th Edition
ISBN: 9781305156241
Author: Garber, Nicholas J.
Publisher: Cengage Learning
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Chapter 16, Problem 13P
To determine
Difference between supercritical and subcritical flow and the conditions that will occur.
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A gravity retaining wall is shown in the figure below. Calculate the factor of safety with respect to overturning and sliding, given the following data:
Wall dimensions: H = 6 m, x₁ = 0.6 m, x2 = 2 m, x3 = 2m,
x4 0.5 m, x5 = 0.75 m, x6 = 0.8 m, D= 1.5 m
Soil properties: 71 = 14 kN/m³, ₁ = 32°, 72 = 18 kN/m³,
2=22°, c₂ = 40 kN/m²
Y₁
c₁ = 0
H
Φί
x5
x6
Use the Rankine active earth pressure in your calculation. Use Yconcrete = 23.08 kN/m³. Also, use k₁ = k₂ = 2/3 and Pp = 0 in the equation
FS (sliding)
(ΣV) tan(k102) + Bk2c2 + Pp
Pa cos a
(Enter your answers to three significant figures.)
FS (overturning)
FS (sliding)
=
For the cantilever retaining wall shown in the figure below, let the following data be given:
Wall dimensions: H = 8 m, x1 = 0.4 m, x2 = 0.6 m, x3 = 1.5 m,
x4 3.5 m, x5 = 0.96 m, D= 1.75 m, a = 10°
Soil properties: 71 = 14.8 kN/m³, ₁ = 32°, Y₂ = 1
2 = 28°, c = 30 kN/m²
17.6 kN/m³,
The value of Ka is 0.3210. For 2 = 28°: N = 25.80; N₁ = 14.72; N₁ = 16.72.
c=0
H
Χς
Calculate the factor of safety with respect to overturning, sliding, and bearing capacity. Use Yconcrete = 21.58 kN/m³. Also, use k₁ = k₂ = 2/3 and P = 0 in the equation
FS (sliding)
(ΣV) tan(k₁₂) + Bk2C + Pp
Pa cosa
(Enter your answers to three significant figures.)
FS (overturning)
FS (sliding)
FS (bearing)
=
Question 2
The following strains are obtained by a 0-60-120 strain rosette: ε0 = 300 x 10-6, 60 =
200 x 10-6 and 120= 150 x 10-6.
i.
Determine strains Ex, Ey and Yxy
ii.
Determine the strains for 0 = 40°
iii.
Calculate principal strains, maximum shear strain and the orientation of
principal strains
iv.
Determine normal stresses (σx, σy) and shear stress (Txy), if E = 200kPa
and v = 0.25.
(Hint: You may use stress-strain relationship for plane strain,
summarised in matric format as follows:
E
σχ
бу
1-v
v
0
Ex
=
v
1-v
0
Ey
txy. (1+v)(1 − 2v) 0
0
0.5 v
Chapter 16 Solutions
Traffic and Highway Engineering
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- A gravity retaining wall is shown in the figure below. Calculate the factor of safety with respect to overturning and sliding, given the following data: Wall dimensions: H = 6 m, x1 = 0.6 m, x2 = 2 m, x3 = 2m, x4 0.5 m, x5 = 0.75 m, x6 = 0.8 m, D= 1.5 m Soil properties: 71 = 15.5 kN/m³, ₁ = 32°, Y2 = 18 kN/m³, 2=22°, c₂ = 40 kN/m² H x6 X2 TXT X3 Use Coulomb's active earth pressure in your calculation and let ' = 2/3 01. Use Yconcrete = 23.58 kN/m³. Also, use k₁ = k₂ = 2/3 and P = 0 in equation FS (sliding) (ΣV) tan(k₁₂2) + Bk2c + Pp Pa cos a For 1 = 32°, a = 0°, B = 71.57°, Ka = 0.45, 8' = 21.33°. (Enter your answers to three significant figures.) FS (overturning) FS (sliding) =arrow_forwardFor the cantilever retaining wall shown in the figure below, let the following data be given: Wall dimensions: H = 6.5 m, x1 = 0.3 m, x2 = 0.6 m, x3 = 0.8 m, x4 2 m, x5 = 0.8 m, D= 1.5 m, a = 0° Soil properties: 71 = 17.08 kN/m³, ₁ = 36°, Y2 = 19.65 kN/m³, 2 = 15°, c₂ = 30 kN/m² For 2=15°: N = 10.98; N₁ = 3.94; N₁ = 2.65. x2 .. c₁ = 0 Φί H x5 Calculate the factor of safety with respect to overturning, sliding, and bearing capacity. Use Yconcrete = 24.58 kN/m³. Also, use k₁ = k2 = 2/3 and P₂ = 0 in equation (EV) tan(k102) + Bk2c₂ + Pp FS (sliding) Pa cos a (Enter your answers to three significant figures.) FS (overturning) FS (sliding) FS (bearing) = = =arrow_forwardA) # of Disinfection Clearwells: 3 B) Clearwell Operation Style: Parallel (to provide contact time for disinfection using free chlorine (derived from a hypochlorite solution generated onsite). C) The facility's existing system to generate hypochlorite onsite has reached the end of its useful life, and the current operating capacity is insufficient to generate the required mass flow of hypochlorite to accommodate the future capacity of 34.5 MGD. Assume the facility plans to stop generating hypochlorite onsite and will instead purchase a bulk solution of sodium hypochlorite D) Sodium hypochlorite (NaOCI) concentration: 6.25% NaOCI by mass E) Bulk Density: 1,100 kg/m^3 F) Clearwell T10/DT Ratio: (CW1 0.43). (CW2 = 0.51), (CW3 = 0.58) DT is the theoretical mean hydraulic retention time (V/Q) G) pH: 7.0 H) Design Temperature: 15°C 1) 50% of Chlorine is lost in each clearwell J) If the concentration going into the clearwell is C, then you can assume that the concentration leaving the…arrow_forward
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