Applied Statics and Strength of Materials (6th Edition)
6th Edition
ISBN: 9780133840544
Author: George F. Limbrunner, Craig D'Allaird, Leonard Spiegel
Publisher: PEARSON
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Chapter 5, Problem 5.25SP
Calculate the forces in all members of the trusses shown, using the method of joints.
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100
As a spring is heated, its spring constant decreases. Suppose the spring is heated and then cooled so that the
spring constant at time t is k(t) = t sin + N/m. If the mass-spring system has mass m = 2 kg and a
damping constant b = 1 N-sec/m with initial conditions x(0) = 6 m and x'(0) = -5 m/sec and it is
subjected to the harmonic external force f (t) = 100 cos 3t N. Find at least the first four nonzero terms in
a power series expansion about t = 0, i.e. Maclaurin series expansion, for the displacement:
• Analytically (hand calculations)
Creating Simulink Model
Plot solutions for first two, three and four non-zero terms as well as the Simulink solution on the same graph
for the first 15 sec. The graph must be fully formatted by code.
Two springs and two masses are attached in a straight vertical line as shown in Figure Q3. The system is set
in motion by holding the mass m₂ at its equilibrium position and pushing the mass m₁ downwards of its
equilibrium position a distance 2 m and then releasing both masses. if m₁ = m² = 1 kg, k₁ = 3 N/m and
k₂ = 2 N/m.
(y₁ = 0)
www
k₁ = 3
Jm₁ = 1
k2=2
www
(Net change in
spring length
=32-31)
(y₂ = 0)
m₂ = 1
32
32
System in
static
equilibrium
System in
motion
Figure Q3 - Coupled mass-spring system
Determine the equations of motion y₁ (t) and y₂(t) for the two masses m₁ and m₂ respectively:
Analytically (hand calculations)
Using MATLAB Numerical Functions (ode45)
Creating Simulink Model
Produce an animation of the system for all solutions for the first minute.
Two large tanks, each holding 100 L of liquid, are interconnected by pipes, with the liquid flowing from tank
A into tank B at a rate of 3 L/min and from B into A at a rate of 1 L/min (see Figure Q1). The liquid inside each
tank is kept well stirred. A brine solution with a concentration of 0.2 kg/L of salt flows into tank A at a rate of
6 L/min. The diluted solution flows out of the system from tank A at 4 L/min and from tank B at 2 L/min. If,
initially, tank A contains pure water and tank B contains 20 kg of salt.
A
6 L/min
0.2 kg/L
x(t)
100 L
4 L/min
x(0) = 0 kg
3 L/min
1 L/min
B
y(t)
100 L
y(0) = 20 kg
2 L/min
Figure Q1 - Mixing problem for interconnected tanks
Determine the mass of salt in each tank at time t≥ 0:
Analytically (hand calculations)
Using MATLAB Numerical Functions (ode45)
Creating Simulink Model
Plot all solutions on the same graph for the first 15 min. The graph must be fully formatted by code.
Chapter 5 Solutions
Applied Statics and Strength of Materials (6th Edition)
Ch. 5 - through 5.7 Calculate the forces in all members of...Ch. 5 - Calculate the forces in all members of the trusses...Ch. 5 - Calculate the forces in all members of the trusses...Ch. 5 - Calculate the forces in all members of the trusses...Ch. 5 - Calculate the forces in all members of the trusses...Ch. 5 - Calculate the forces in all members of the trusses...Ch. 5 - Calculate the forces in all members of the trusses...Ch. 5 - Determine the forces in members CD, DH, and HI for...Ch. 5 - Determine the forces in members BC, BE, and FE for...Ch. 5 - Determine the forces in members BC, CH, and CG in...
Ch. 5 - For the Howe roof truss shown, determine the...Ch. 5 - Determine the forces in members DE, CE, and BC in...Ch. 5 - Calculate the forces in members BC, BG, and FG for...Ch. 5 - Determine the forces in members CD, BD, BE, and CB...Ch. 5 - A pin-connected A-frame supports a load, as shown....Ch. 5 - Determine the pin reactions at pins A, B, and C in...Ch. 5 - Calculate the pin reactions at each of the pins in...Ch. 5 - A bracket is pin connected at points A, B, and D...Ch. 5 - A pin-connected frame is loaded, as shown....Ch. 5 - The cylinder shown has a mass of 500 kg. Determine...Ch. 5 - A simple frame is pin connected at points A, B,...Ch. 5 - Using the method of sections, determine the forces...Ch. 5 - Using the method of sections, determine the forces...Ch. 5 - through 5.31 Calculate the forces in all members...Ch. 5 - Calculate the forces in all members of the trusses...Ch. 5 - Calculate the forces in all members of the trusses...Ch. 5 - Calculate the forces in all members of the trusses...Ch. 5 - Calculate the forces in all members of the trusses...Ch. 5 - Calculate the forces in all members of the trusses...Ch. 5 - Calculate the forces in all members of the trusses...Ch. 5 - Calculate the forces in all members of the trusses...Ch. 5 - For Problems 5.32 through 5.38, calculate the...Ch. 5 - For Problem 5.32 through 5.38, Calculate the...Ch. 5 - For Problems 5.32 through 5.38, calculate the...Ch. 5 - For Problems 5.32 through 5.38, calculate the...Ch. 5 - For Problem 5.32 through 5.38 , Calculate the...Ch. 5 - For Problems 5.32 through 5.38, calculate the...Ch. 5 - For Problems 5.32 through 5.38, calculate the...Ch. 5 - A pin-connected crane framework is loaded and...Ch. 5 - Calculate the pin reactions at pins A, B, and D in...Ch. 5 - Determine the pin reactions at pins A, B, and C in...Ch. 5 - The wall bracket shown is pin-connected at points...Ch. 5 - Calculate the pin reactions at each of the pins in...Ch. 5 - The A-frame shown is pin-connected at A,B,C, and...Ch. 5 - The tongs shown are used to grip an object. For an...Ch. 5 - A toggle joint is a mechanism by which a...Ch. 5 - In the toggle joint of Problem 5.46 , assume that...Ch. 5 -
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