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 4, Problem 4.43SP
Calculate the reactions at each support for the beam shown. Neglect the weight of the beam.
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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 4 Solutions
Applied Statics and Strength of Materials (6th Edition)
Ch. 4 - and 4.2 Sketch free-body diagram for the members...Ch. 4 - Sketch free-body diagram for the members shown.Ch. 4 - A steel cylinder having a mass of 120 kgis...Ch. 4 - A 50-lb block is supported by a pin support and a...Ch. 4 - A cylinder weighing 200 lb is supported on an...Ch. 4 - A weight W is supported by a flexible cable and an...Ch. 4 - The ladder shown is supported by a smooth...Ch. 4 - What horizontal force F applied at the center of...Ch. 4 - Calculate the force in cable AB and the angle (...Ch. 4 - Calculate the horizontal force F that should be...
Ch. 4 - Calculate the reactions of the two smooth inclined...Ch. 4 - Calculate the force in each cable for the...Ch. 4 - Three members of a truss intersect at joint B as...Ch. 4 - Four concurrent forces in equilibrium act at point...Ch. 4 - The beam shown carries vertical concentrated...Ch. 4 - Find the reactions at A and B for the beam shown....Ch. 4 - A simply supported beam spans 10 m. The beam...Ch. 4 - The beam shown carries vertical loads. Calculate...Ch. 4 - Calculate the reaction at each support for the...Ch. 4 - Calculate the reactions at A and B for the beam...Ch. 4 - Calculate the reactions at A and B for the beam...Ch. 4 - A 12-ft simple beam is supported at each end. It...Ch. 4 - The beam shown carries vertical loads as...Ch. 4 - Determine the reactions for the beam shown. The...Ch. 4 - Calculate the reaction at each support for the...Ch. 4 - Calculate the wall reactions for the cantilever...Ch. 4 - Determine the reactions at supports A and B of the...Ch. 4 - A mass M of 300 kg is supported by a boom, as...Ch. 4 - Rework Problem 4.28 assuming that point D has been...Ch. 4 - Calculate the force in the tie rod BC and the...Ch. 4 - The davit shown is used in pairs for...Ch. 4 - For the following computer problems, any...Ch. 4 - For the following computer problems, any...Ch. 4 - For the following computer problems, any...Ch. 4 - For the structure shown, draw free-body diagram...Ch. 4 - A 1200-lb load is supported by a cable that runs...Ch. 4 - For the pin-connected frame shown, sketch a...Ch. 4 - For the concurrent force system shown, calculate...Ch. 4 - A strut having a mass of 40 kg/m is supported by a...Ch. 4 - Calculate the reaction at each support for the...Ch. 4 - Calculate the reaction at each support for the...Ch. 4 - A beam supports a nonuniformly distributed load as...Ch. 4 - Calculate the reactions at each support for the...Ch. 4 - Compute reactions at each support for the beam...Ch. 4 - A rod of uniform cross section weighs 4 lb/ft and...Ch. 4 - A 12-ft-long weightiness member supports two...Ch. 4 - A uniform rod AB, having a weight of 5.00 lb and a...Ch. 4 - The plastic barrel tent anchor of Problem 2.11...Ch. 4 - Compute the reactions at A and B for the bracket...Ch. 4 - The truss shown is supported by a pin at A and a...Ch. 4 - Find the reactions at supports A and B for the...Ch. 4 - Find the reactions at supports A and B for the...Ch. 4 - Determine the reactions at A and B for the truss...Ch. 4 - A 40-ft ladder weighing 130 lb is pin-connected to...Ch. 4 - The frame shown is pin-connected at point A and...Ch. 4 - Prob. 4.56SPCh. 4 - A horizontal beam is pin-connected to a wall at...Ch. 4 - Calculate the force in the cable for the structure...Ch. 4 - The Thenard shutter dam shown was originally...Ch. 4 - An inclined railway can be used to lift heavy...Ch. 4 - Two cylinders are supported in a box, as shown....
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