Using the figure and the included equations, determine the following:a. The signal phasing plan that will yield the minimum cylce length (assuming 95% capacity utilization (Xc) and three timing stages). (Hint: First determine N-S phasing possibilities and E-W phasing possibilities, and then consider possible combinations). Use the attached equation for Cmin.b. "Optimal" cycle length. Use the attached equation for Copt.c. Effective green times for each phase (for balanced v/c ratios), for minimum cycle. Use the attached equation for gi.d. Displayed yellow and all-red times for each phase. Use the attached equations for Y and AR.e. Required pedestrian green times. Use the attached equations for Gp. whereX₂whereCmin = minimum necessary cycle length in seconds (typically rounded up to thenearest 5-second increment in practice),total lost time for cycle in seconds,critical v/c ratio for the intersection,LXXL =X =(v/s)a= flow ratio for critical lane group i, andn = number of critical lane groups.Copt=Σ(;)where1.5XL +51.0-i=1Coptcycle length to minimize delay in seconds, andother terms are as defined previously.*-0.6g; = effective green time for timing stage i,(v/s) a = flow ratio for critical lane group i,C = cycle length in seconds, andX₁ = v/c ratio for lane group i.whereY=1, +whereV2a + 2gGY = yellow time (usually rounded up to the nearest 0.5 seconds),t₁ = driver perception/reaction time, usually taken as 1.0 second,V = speed of approaching traffic in ft/s,a = deceleration rate for the vehicle, usually taken as 10.0 ft/s²,g = acceleration due to gravity [32.2 ft/s²], andG= percent grade divided by 100.AR=W+1VAR = all-red time (usually rounded up to the nearest 0.5 seconds),w = width of the cross street in ft,/= length of the vehicle, usually taken as 20 ft, andV = speed of approaching traffic in ft/s.= 3.2+ ++(0.27N) for Wg ≤10ftG₁ =32+ = - + (27)+2.7-WEfor WE > 10 ftwhereG₂ = minimum pedestrian green time in seconds,3.2 = pedestrian start-up time in seconds,L = crosswalk length in ft,Sp walking speed of pedestrians, usually taken as 3.5 ft/s,Nped number of pedestrians crossing during an interval, andWE = effective crosswalk width in ft. 45 mph12'5035 mph12'525402703011'17520011'253505057512'25N••12'Assume the following:Sthru/rt = 1800 veh/hSshared 1650 veh/hSleft = 700 veh/htsi/phase: 2 sectel/phase = 2 secVehicle length: 20 ftLevel gradeWE = 8 ftped/phase = 15

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Answered: Using the figure and the included…

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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Using the figure and the included equations, determine the following:

a. The signal phasing plan that will yield the minimum cylce length (assuming 95% capacity utilization (X_c) and three timing stages). (Hint: First determine N-S phasing possibilities and E-W phasing possibilities, and then consider possible combinations). Use the attached equation for C_min.

b. "Optimal" cycle length. Use the attached equation for C_opt.

c. Effective green times for each phase (for balanced v/c ratios), for minimum cycle. Use the attached equation for g_i.

d. Displayed yellow and all-red times for each phase. Use the attached equations for Y and AR.

e. Required pedestrian green times. Use the attached equations for Gp.

where
X₂
where
Cmin = minimum necessary cycle length in seconds (typically rounded up to the
nearest 5-second increment in practice),
total lost time for cycle in seconds,
critical v/c ratio for the intersection,
LXX
L =
X =
(v/s)a= flow ratio for critical lane group i, and
n = number of critical lane groups.
Copt=
Σ(;)
where
1.5XL +5
1.0-
i=1
Coptcycle length to minimize delay in seconds, and
other terms are as defined previously.
*-0.6
g; = effective green time for timing stage i,
(v/s) a = flow ratio for critical lane group i,
C = cycle length in seconds, and
X₁ = v/c ratio for lane group i.
where
Y=1, +
where
V
2a + 2gG
Y = yellow time (usually rounded up to the nearest 0.5 seconds),
t₁ = driver perception/reaction time, usually taken as 1.0 second,
V = speed of approaching traffic in ft/s,
a = deceleration rate for the vehicle, usually taken as 10.0 ft/s²,
g = acceleration due to gravity [32.2 ft/s²], and
G= percent grade divided by 100.
AR=W+1
V
AR = all-red time (usually rounded up to the nearest 0.5 seconds),
w = width of the cross street in ft,
/= length of the vehicle, usually taken as 20 ft, and
V = speed of approaching traffic in ft/s.
= 3.2+ ++(0.27N) for Wg ≤10ft
G₁ =32+ = - + (27)
+2.7-
WE
for WE > 10 ft
where
G₂ = minimum pedestrian green time in seconds,
3.2 = pedestrian start-up time in seconds,
L = crosswalk length in ft,
Sp walking speed of pedestrians, usually taken as 3.5 ft/s,
Nped number of pedestrians crossing during an interval, and
WE = effective crosswalk width in ft.

45 mph
12'
50
35 mph
12'
525
40
270
30
11'
175
200
11'
25
350
50
575
12'
25
N
•
•
12'
Assume the following:
Sthru/rt = 1800 veh/h
Sshared 1650 veh/h
Sleft = 700 veh/h
tsi/phase: 2 sec
tel/phase = 2 sec
Vehicle length: 20 ft
Level grade
WE = 8 ft
ped/phase = 15

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