(c) Consider a section of a four-lane freeway (two lanes in each direction) as shown below. The freeway typically carries 2571 veh/hr during the morning peak period. An accident occurs at 8:00 AM at Point A, blocking the entire freeway in that direction. Fifteen minutes after the accident, one lane is cleared and traffic begins to flow again past point A. Assuming a triangular fundamental diagram as shown below, use shock wave analysis to answer the following questions: Flow (veh/hour) (1) Where is the end of the queue at 8:15 AM? (2) When (at what time) are the vehicles on the freeway last forced to stop by the queue? (3) What is the maximum size of the queue? (4) What is the maximum distance of the end of the queue from the accident site? *, (k₂) 4000 3000 2000 At Time t = 8:00 AM 1000 (*) H At Time t = 8:15 AM x₂ (k₂) (₂) 정 q= 50 k = 30 veh/mi P x₂ (k₂) uk = 60 mph (₂) 9 1- B H Flow-density relationship (one lane) when k Sk when k, sk Sk k-ke k,-k (k₂) B x₂ (k₂) (30, 1800) qe = 1800 veh/hour x, (k₂) P 7747 x₂ (k₂) k = 150 veh/mi 100 150 200 250 300 Density (veh/mi) (₂) 15 miles 1x₂ (k₂) 15 miles Flow (veh/hour) 4000 3000 2000 1000 x₂ (₂) P H x₂ (k₂) (k₂) x₂ (k₂) A ke = 60 veh/mi 50 100 A u= 60 mph x (₂) F 1x₂ (k₂) B Flow-density relationship (two lanes) (60, 3600) qe = 3600 veh/hour x₂ (k₂) k = 300 veh/mi 150 200 250 Density (veh/mi) 300
(c) Consider a section of a four-lane freeway (two lanes in each direction) as shown below. The freeway typically carries 2571 veh/hr during the morning peak period. An accident occurs at 8:00 AM at Point A, blocking the entire freeway in that direction. Fifteen minutes after the accident, one lane is cleared and traffic begins to flow again past point A. Assuming a triangular fundamental diagram as shown below, use shock wave analysis to answer the following questions: Flow (veh/hour) (1) Where is the end of the queue at 8:15 AM? (2) When (at what time) are the vehicles on the freeway last forced to stop by the queue? (3) What is the maximum size of the queue? (4) What is the maximum distance of the end of the queue from the accident site? *, (k₂) 4000 3000 2000 At Time t = 8:00 AM 1000 (*) H At Time t = 8:15 AM x₂ (k₂) (₂) 정 q= 50 k = 30 veh/mi P x₂ (k₂) uk = 60 mph (₂) 9 1- B H Flow-density relationship (one lane) when k Sk when k, sk Sk k-ke k,-k (k₂) B x₂ (k₂) (30, 1800) qe = 1800 veh/hour x, (k₂) P 7747 x₂ (k₂) k = 150 veh/mi 100 150 200 250 300 Density (veh/mi) (₂) 15 miles 1x₂ (k₂) 15 miles Flow (veh/hour) 4000 3000 2000 1000 x₂ (₂) P H x₂ (k₂) (k₂) x₂ (k₂) A ke = 60 veh/mi 50 100 A u= 60 mph x (₂) F 1x₂ (k₂) B Flow-density relationship (two lanes) (60, 3600) qe = 3600 veh/hour x₂ (k₂) k = 300 veh/mi 150 200 250 Density (veh/mi) 300
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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Question
Transcribed Image Text:(c) Consider a section of a four-lane freeway (two lanes in each direction) as shown below.
The freeway typically carries 2571 veh/hr during the morning peak period. An accident occurs
at 8:00 AM at Point A, blocking the entire freeway in that direction. Fifteen minutes after the
accident, one lane is cleared and traffic begins to flow again past point A. Assuming a
triangular fundamental diagram as shown below, use shock wave analysis to answer the
following questions:
(1) Where is the end of the queue at 8:15 AM?
(2) When (at what time) are the vehicles on the freeway last forced to stop by the queue?
(3) What is the maximum size of the queue?
(4) What is the maximum distance of the end of the queue from the accident site?
At Time t = 8:00 AM
*(k,)
B
A
15 miles
At Time t = 8:15 AM
i, (k,)
*, (k,)
*,(k,)
*, (k,)
, (k,)
A
miles
Flow-density relationship (one lane)
Flow-density relationship (two lanes)
4000
4000
when k <k.
(60, 3600) q. = 3600 veh/hour
k-k.
1-
3000
when k, sk<k,
3000
k;
-k.
2000
(30, 1800) qc = 1800 veh/hour
2000
uf = 60 mph
1000
/u = 60 mph
1000
k, = 150 veh/mi
kc = 60 veh/mi
k, = 300 veh/mi
50
100
150
200
250
300
0.
50
100
150
Density (veh/mi)
200
250
300
Density (veh/mi)
k. = 30 veh/mi
Flow (veh/hour)
Flow (veh/hour)
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Step 1: Determine the given data.
VIEWStep 2: Draw the slope on the triangular diagram.
VIEWStep 3: (a) Determine the end of queue.
VIEWStep 4: Draw the slope for the regions mentioned in the figure.
VIEWStep 5: Determine the speed using the slopes.
VIEWStep 6: (b) Determine the time of vehicles stopped.
VIEWStep 7: (c) Determine the maximum size of the queue.
VIEWStep 8: (d) Determine the maximum distance at the end of the queue.
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