CEE 3804: Computer Applications in Civil Engineering
Spring 2011
Assignment 7: Simulink and Modeling Systems
Solution
Instructor: Trani
Problem 1
Your task is design an emergency exit ramp for a runaway truck. Figure 1 illustrates the situation.
Figure 1. Emergency Exit Ramp.
The truck has a mass of 40,000 kg. and enters the ramp at a speed of 42 m/s (~80 mph) while on a 5% grade. The ramp is
constructed in two segments: a) curved section with a radius of 1000 meters and b) straight section with a grade of 15%.
neglecting the aerodynamic drag acting on the truck, a freebody diagram showing the forces acting on the truck are shown in
Figure 2.
Figure 2. Free Body Diagram of Truck.
CEE 3804
Trani
Page 1 of 9
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Define a common set notation to solve the problem. When the truck is going downhill, the gravity force helps accelerate the
truck. When is going uphill the gravity force helps slow down the motion. The fundamental equation of motion to describe the
deceleration of the truck on the exit ramp is:
m
dV
dt
=
−
mg
cos(
δ
)
μ
+
mg
sin(
δ
)
Here we adopt the nomenclature that when angle
δ
is positive (i,e., downhill) the term
mg
sin(
δ
)
will be positive and thus
opposite to the friction term. In this case, the gravity helps accelerate the truck. When going uphill
δ
is negative and the term
mg
sin(
δ
)
is negative helping decelerate the truck.
Task 1
Model the curved section of the road as either a series of line segments or by deriving an equation that relates the local grade of
the curve as a function of the path length along the curve.
This is the end of the preview.
Sign up
to
access the rest of the document.
 Spring '07
 AATrani
 matlab, Orders of magnitude, path length, Trani, Matlab Script ___________

Click to edit the document details