STRUCTURAL ANALYSIS W/MOD MAST
10th Edition
ISBN: 9780134863375
Author: HIBBELER
Publisher: PEARSON
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Chapter 4, Problem 4.41P
To determine
Shear and moment diagram of each member of frame.
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derive the expressions for V and M, and draw the shear forceandbendingmomentdiagrams.Neglecttheweightofthebeam.
a.
Draw trajectories of approximately 8 to 11 vehicles moving on a one way 1-lane road with
different time-varying speeds.
b. Consider a time-space window in the time-space diagram of part (a). See below. Denote
the number of vehicles passing BD, DC, AC, and AB respectively as n1, N2, N3, and n4. Write
an equation relating n₁, N2, N3, and n4 to each other. What is the physical intuition of this
equation? Please elaborate.
X 4
X.
n4
n3
с
n2
X1
D
B
n1
t
c. Using density (k) definition at time instances t₁ and t₂ and flow (q) definition at locations
X1 and X2, rewrite equation of interest in part (b) to demonstrate
KAB-KCD 9BD-9AC
+
t₂-t1
x2-x1
= 0.
d. What will be the equation in part (c), in case of x2 → x1 and t₂
→ t₁.
Consider a city center where the traffic conditions are described by a Macroscopic
Fundamental Diagram (MFD) of network outflow (g- rate of trips finished) vs. accumulation (n-
number of cars) with a trapezoidal shape, as shown in the figure below. The values of the
parameters are:
•
•
maximum trip completion rate gmax=100 [veh/min]
critical accumulations ncr1=1000 [veh] and ncr2=1500 [veh]
jam accumulation njam=4000 [veh].
gmax
ncr1
ncr2
njam
There are two types of demands in the morning peak hour (7-8am): trips generated from
outside the city center with rate q1=80 [veh/min], and trips generated from within the city
center with rate q2=50 [veh/min]. In addition, a perimeter traffic control, u, is available that
only restricts vehicles entering the city from outside.
If at 7am there are already no=500 [veh] in the city center:
a. Write the dynamic equations (mass conservation equation) in a continuous form for the
center of the city.
b. Convert the continuous dynamic into the discrete…
Chapter 4 Solutions
STRUCTURAL ANALYSIS W/MOD MAST
Ch. 4 - Prob. 4.1PCh. 4 - Prob. 4.2PCh. 4 - Prob. 4.3PCh. 4 - Prob. 4.4PCh. 4 - Prob. 4.5PCh. 4 - Prob. 4.6PCh. 4 - Prob. 4.7PCh. 4 - Prob. 4.8PCh. 4 - Prob. 4.9PCh. 4 - Prob. 4.10P
Ch. 4 - Prob. 4.11PCh. 4 - Prob. 4.12PCh. 4 - Prob. 4.13PCh. 4 - Prob. 4.14PCh. 4 - Prob. 4.15PCh. 4 - Prob. 4.16PCh. 4 - Prob. 4.17PCh. 4 - Prob. 4.18PCh. 4 - Prob. 4.19PCh. 4 - Prob. 4.20PCh. 4 - Prob. 4.21PCh. 4 - Prob. 4.22PCh. 4 - Prob. 4.23PCh. 4 - Prob. 4.24PCh. 4 - Prob. 4.25PCh. 4 - Prob. 4.26PCh. 4 - Prob. 4.27PCh. 4 - Prob. 4.28PCh. 4 - Prob. 4.29PCh. 4 - Prob. 4.30PCh. 4 - Prob. 4.31PCh. 4 - Prob. 4.32PCh. 4 - Prob. 4.33PCh. 4 - Prob. 4.34PCh. 4 - Prob. 4.35PCh. 4 - Prob. 4.36PCh. 4 - Prob. 4.37PCh. 4 - Prob. 4.38PCh. 4 - Prob. 4.39PCh. 4 - Prob. 4.40PCh. 4 - Prob. 4.41PCh. 4 - Prob. 4.42PCh. 4 - Prob. 4.43PCh. 4 - Prob. 4.44PCh. 4 - Prob. 4.45PCh. 4 - Prob. 4.46PCh. 4 - Prob. 4.47PCh. 4 - Prob. 4.48PCh. 4 - Prob. 4.49PCh. 4 - Prob. 4.50PCh. 4 - Prob. 4.51PCh. 4 - Prob. 4.52PCh. 4 - Prob. 4.53PCh. 4 - Prob. 4.54PCh. 4 - Prob. 4.55PCh. 4 - Prob. 4.56PCh. 4 - Prob. 4.57PCh. 4 - Prob. 4.58PCh. 4 - Prob. 4.59PCh. 4 - Prob. 4.1PPCh. 4 - Prob. 4.2PP
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