[T] The following table provides hypothetical data regarding the level of service for a certain highway.Plot vehicles per hour per lane on the x-axis and highway speed on the y-axis.Compute the average decrease in speed (in miles per hour) per unit increase in congestion (vehicles per hour per lane) as the latter increases from 600 to 1000, from 1000 to 1500, and from 1500 to 2100. Does the decrease in miles per hour depend linearly on the increase in vehicles per hour per lane?Plot minutes per mile (60 times the reciprocal of miles per hour) as a function of vehicles per hour per lane. Is this function linear?Highway SpeedVehicles per Hour per LaneDensity Range (vehicles / mi)> 60< 600 < 1060 - 57600 - 1000 10 - 2057 - 541000 - 150020 - 3054 - 461500 - 190030 - 4546 - 301900 - 210045 - 70< 30Unstable70 - 200

1st point : (600, 60) , 2nd point (1000, 57) , 3rd point (1500, 54 ) , 4th point (1900, 46) , 5th point (2100, 30)1) Average decrease in speed per unit increase in congestion when vehicle per hour per lane increases from 600 to 1000.∆Vavg = Change in speedChange in vehicle per hour per lane = 57 - 601000 - 600= - 0.00752) Average decrease in speed per unit increase in congestion when vehicle per hour per lane increases from 1000 to 1500.∆Vavg = Change in speedChange in vehicle per hour per lane = 54 -571500 - 1000= - 0.0063) Average decrease in speed per unit increase in congestion when vehicle per hour per lane increases from 1500 to 2100.∆Vavg = Change in speedChange in vehicle per hour per lane = 30 -542100 - 1500 =- 0.04As the ∆Vavg have different values , hence it is Non-Linear Variation.Minutes per mile (min/mi)= 60Miles per hour For 60 mi/hr ⇒ min/mi = 6060 = 1 min/miFor 57 mi/hr ⇒ min/mi = 6057 = 1.053 min/miFor 54 mi/hr ⇒ min/mi = 6054 = 1.111min/miFor 46 mi/hr ⇒ min/mi = 6046 = 1.304 min/miFor 30 mi/hr ⇒ min/mi = 6030 = 2 min/mi1st point : (600, 1) , 2nd point : (1000, 1.053) , 3rd point : ( 1500, 1.111) , 4th point : (1900, 1.304) , 5th point: (2100, 2) From the graph above, It is clear that the slope is changing , hence it is Non-Linear Variation.2) Non-Linear Variation3) Non-Linear Variation

Answered: [T] The following table provides…

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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[T] The following table provides hypothetical data regarding the level of service for a certain highway.

Plot vehicles per hour per lane on the x-axis and highway speed on the y-axis.
Compute the average decrease in speed (in miles per hour) per unit increase in congestion (vehicles per hour per lane) as the latter increases from 600 to 1000, from 1000 to 1500, and from 1500 to 2100. Does the decrease in miles per hour depend linearly on the increase in vehicles per hour per lane?
Plot minutes per mile (60 times the reciprocal of miles per hour) as a function of vehicles per hour per lane. Is this function linear?

Highway Speed	Vehicles per Hour per Lane	Density Range (vehicles / mi)
> 60	< 600	< 10
60 - 57	600 - 1000	10 - 20
57 - 54	1000 - 1500	20 - 30
54 - 46	1500 - 1900	30 - 45
46 - 30	1900 - 2100	45 - 70
< 30	Unstable	70 - 200

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