PEARSON ETEXT ENGINEERING MECH & STATS
15th Edition
ISBN: 9780137514724
Author: HIBBELER
Publisher: PEARSON
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Chapter 18, Problem 7RP
To determine
The velocity of the collar when the rod becomes horizontal.
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2. Express the following complex numbers in rectangular form.
(a) z₁ = 2еjл/6
(b) Z2=-3e-jπ/4
(c) Z3 =
√√√3e-j³/4
(d) z4 = − j³
A prismatic beam is built into a structure. You can consider the boundary conditions at A and B to be
fixed supports. The beam was originally designed to withstand a triangular distributed load, however,
the loading condition has been revised and can be approximated by a cosine function as shown in the
figure below. You have been tasked with analysing the structure. As the beam is prismatic, you can
assume that the bending rigidity (El) is constant.
wwo cos
2L
x
A
B
Figure 3: Built in beam with a varying distributed load
In order to do this, you will:
a. Solve the reaction forces and moments at point A and B.
Hint: you may find it convenient to use the principal of superposition.
(2%)
b. Plot the shear force and bending moment diagrams and identify the maximum shear force
and bending moment.
(2%)
c. Develop an expression for the vertical deflection. Clearly state your expression in terms of x.
(1%)
Question 1: Beam Analysis
Two beams (ABC and CD) are connected using a pin immediately to the left of Point C. The pin acts
as a moment release, i.e. no moments are transferred through this pinned connection. Shear forces
can be transferred through the pinned connection. Beam ABC has a pinned support at point A and a
roller support at Point C. Beam CD has a roller support at Point D. A concentrated load, P, is applied
to the mid span of beam CD, and acts at an angle as shown below. Two concentrated moments, MB
and Mc act in the directions shown at Point B and Point C respectively. The magnitude of these
moments is PL.
Moment Release
A
B
с
°
MB = PL
Mc=
= PL
-L/2-
-L/2-
→
P
D
Figure 1: Two beam arrangement for question 1.
To analyse this structure, you will:
a) Construct the free body diagrams for the structure shown above. When constructing your
FBD's you must make section cuts at point B and C. You can represent the structure as three
separate beams. Following this, construct the…
Chapter 18 Solutions
PEARSON ETEXT ENGINEERING MECH & STATS
Ch. 18 - The 80-kg wheel has a radius of gyration about its...Ch. 18 - The uniform 50-lb slender rod is subjected to a...Ch. 18 - The uniform 50-kg slender rod is at rest m the...Ch. 18 - The 50-kg wheel is subjected to a force of 50 N....Ch. 18 - If the uniform 30-kg slender rod starts from rest...Ch. 18 - The 20-kg wheel has a radius of gyration about its...Ch. 18 - At a given instant the body of mass m has an...Ch. 18 - A force of P = 20 N is applied to the cable, which...Ch. 18 - A force of P = 20 N is applied to the cable, which...Ch. 18 - The double pulley consists of two parts that are...
Ch. 18 - The double pulley cons1sts of two parts that are...Ch. 18 - Prob. 9PCh. 18 - The 10-kg uniform slender rod is suspended at rest...Ch. 18 - Prob. 14PCh. 18 - The pendulum consists of a 10-kg uniform disk and...Ch. 18 - The center O of the thin ring of mass m is given...Ch. 18 - Prob. 18PCh. 18 - Prob. 19PCh. 18 - Prob. 22PCh. 18 - Prob. 23PCh. 18 - Prob. 27PCh. 18 - The 10-kg rod AB is pin connected at A and...Ch. 18 - Motor M exerts a constant force of P = 750 Non the...Ch. 18 - The two 2-kg gears A and B are attached to the...Ch. 18 - F187. If the 30-kg disk is released from rest when...Ch. 18 - The 50-kg reel has a radius of gyration about its...Ch. 18 - The 60-kg rod OA is released from rest when = 0....Ch. 18 - Prob. 10FPCh. 18 - The 30-kg rod is released from rest when = 45....Ch. 18 - Prob. 12FPCh. 18 - Prob. 36PCh. 18 - Prob. 37PCh. 18 - The 40-kg wheel has a radius of gyration about its...Ch. 18 - The assembly consists of two 10-kg bars which are...Ch. 18 - The assembly consists of two 10-kg bars which are...Ch. 18 - Prob. 51PCh. 18 - Prob. 52PCh. 18 - If the 250-lb block is released from rest when the...Ch. 18 - The slender 15-kg bar is initially at rest and...Ch. 18 - The 50-lb wheel has a radius of gyration about its...Ch. 18 - The system consists of 60-lb and 20-lb blocks A...Ch. 18 - The pendulum of the Charpy impact machine has a...Ch. 18 - Prob. 2RPCh. 18 - The drum has a mass of 50 kg and a radius of...Ch. 18 - The spool has a mass of 60 Kg and a radius of...Ch. 18 - Prob. 5RPCh. 18 - At the Instant shown, the 50-lb bar rotates...Ch. 18 - Prob. 7RPCh. 18 - Prob. 8RP
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