Statics and Mechanics of Materials (5th Edition)
5th Edition
ISBN: 9780134382593
Author: Russell C. Hibbeler
Publisher: PEARSON
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Textbook Question
Chapter 2.4, Problem 7FP
Resolve each force into its x and y components.
Prob. F2–7
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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 2 Solutions
Statics and Mechanics of Materials (5th Edition)
Ch. 2.3 - In each case, construct the parallelogram law to...Ch. 2.3 - In each case, show how to resolve the force F into...Ch. 2.3 - Determine the magnitude of the resultant force...Ch. 2.3 - Determine the magnitude of the resultant force....Ch. 2.3 - Determine the magnitude of the resultant force and...Ch. 2.3 - Resolve the 30-lb force into components along the...Ch. 2.3 - Resolve the force into components acting along...Ch. 2.3 - Prob. 6FPCh. 2.3 - If = 60 and F = 450 N, determine the magnitude of...Ch. 2.3 - If the magnitude of the resultant force is to be...
Ch. 2.3 - Determine the magnitude of the resultant force FR...Ch. 2.3 - Determine the magnitudes of the two components of...Ch. 2.3 - Solve Prob. 24 with F = 350 lb. 24. Determine the...Ch. 2.3 - Determine the magnitude of the resultant force FR...Ch. 2.3 - Resolve the force F1 into components acting along...Ch. 2.3 - Resolve the force F2 into components acting along...Ch. 2.3 - If the resultant force acting on the support is to...Ch. 2.3 - Determine the magnitude of the resultant force and...Ch. 2.3 - If = 60, determine the magnitude of the resultant...Ch. 2.3 - Determine the angle for connecting member A to...Ch. 2.3 - The force acting on the gear tooth is F = 20 lb....Ch. 2.3 - The component of force F acting along line aa is...Ch. 2.3 - Force F acts on the frame such that its component...Ch. 2.3 - Force F acts on the frame such that its component...Ch. 2.3 - If F1 = 30 lb and F2 = 40 lb, determine the angles...Ch. 2.3 - Determine the magnitude and direction of FA so...Ch. 2.3 - Determine the magnitude of the resultant force...Ch. 2.3 - Prob. 20PCh. 2.3 - If the resultant force of the two tugboats is 3...Ch. 2.3 - If FB = 3 kN and = 45, determine the magnitude of...Ch. 2.3 - If the resultant force of the two tugboats is...Ch. 2.4 - Resolve each force into its x and y components....Ch. 2.4 - F28. Determine the magnitude and direction of the...Ch. 2.4 - Prob. 9FPCh. 2.4 - Prob. 10FPCh. 2.4 - Prob. 11FPCh. 2.4 - Determine the magnitude of the resultant force and...Ch. 2.4 - Determine the magnitude of the resultant force and...Ch. 2.4 - Prob. 25PCh. 2.4 - Prob. 26PCh. 2.4 - Determine the magnitude of the resultant force and...Ch. 2.4 - Prob. 28PCh. 2.4 - Determine the magnitude of the resultant force...Ch. 2.4 - Prob. 30PCh. 2.4 - Prob. 31PCh. 2.4 - Prob. 32PCh. 2.4 - Determine the magnitude of the resultant force and...Ch. 2.4 - Prob. 34PCh. 2.4 - Prob. 35PCh. 2.4 - Determine the magnitude of the resultant force and...Ch. 2.4 - Determine the magnitude and direction of the...Ch. 2.6 - Sketch the following forces on the x, y, z...Ch. 2.6 - In each case, establish F as a Cartesian vector,...Ch. 2.6 - Show how to resolve each force into its x, y, z...Ch. 2.6 - Determine the coordinate direction angles of the...Ch. 2.6 - Prob. 14FPCh. 2.6 - Prob. 15FPCh. 2.6 - Prob. 16FPCh. 2.6 - Prob. 17FPCh. 2.6 - Determine the resultant force acting on the hook....Ch. 2.6 - The force F has a magnitude of 80 lb. Determine...Ch. 2.6 - The bolt is subjected to the force F, which has...Ch. 2.6 - Determine the magnitude and coordinate direction...Ch. 2.6 - Prob. 41PCh. 2.6 - Prob. 42PCh. 2.6 - Express each force in Cartesian vector form and...Ch. 2.6 - Prob. 44PCh. 2.6 - Determine the magnitude and coordinate direction...Ch. 2.6 - Determine the magnitude and coordinate direction...Ch. 2.6 - Prob. 47PCh. 2.6 - Determine the magnitude and coordinate direction...Ch. 2.6 - Prob. 49PCh. 2.6 - Prob. 50PCh. 2.6 - Prob. 51PCh. 2.6 - Determine the magnitude and coordinate direction...Ch. 2.6 - Prob. 53PCh. 2.6 - Prob. 54PCh. 2.6 - Determine the magnitude and coordinate direction...Ch. 2.8 - In each case, establish a position vector from...Ch. 2.8 - In each case, express F as a Cartesian vector. (a)...Ch. 2.8 - Prob. 19FPCh. 2.8 - Determine the length of the rod and the position...Ch. 2.8 - Prob. 21FPCh. 2.8 - Express the force as a Cartesian vector. Prob....Ch. 2.8 - Prob. 23FPCh. 2.8 - Prob. 24FPCh. 2.8 - Determine the length of the connecting rod AB by...Ch. 2.8 - Express force F as a Cartesian vector; then...Ch. 2.8 - Express each force as a Cartesian vector, and then...Ch. 2.8 - If F = {350i 250j 450k} N and cable AB is 9 m...Ch. 2.8 - The 8-m-long cable is anchored to the ground at A....Ch. 2.8 - The 8-m-long cable is anchored to the ground at A....Ch. 2.8 - Express each of the forces in Cartesian vector...Ch. 2.8 - If FB = 560 N and FC = 700 N, determine the...Ch. 2.8 - If FB = 700 N, and FC = 560 N, determine the...Ch. 2.8 - The plate is suspended using the three cables...Ch. 2.8 - Prob. 66PCh. 2.8 - Determine the magnitude and coordinate direction...Ch. 2.8 - Prob. 68PCh. 2.8 - The load at A creates a force of 60 lb in wire AB....Ch. 2.8 - Determine the magnitude and coordinate direction...Ch. 2.9 - In each case, set up the dot product to find the...Ch. 2.9 - In each case, set up the dot product to find the...Ch. 2.9 - Determine the angle between the force and the...Ch. 2.9 - Determine the angle between the force and the...Ch. 2.9 - Determine the angle between the force and the...Ch. 2.9 - Determine the projected component of the force...Ch. 2.9 - Find the magnitude of the projected component of...Ch. 2.9 - Determine the components of the force acting...Ch. 2.9 - Prob. 31FPCh. 2.9 - Prob. 71PCh. 2.9 - Determine the magnitudes of the components of F =...Ch. 2.9 - Determine the angle between BA and BC. Probs. 273Ch. 2.9 - Determine the magnitude of the projected component...Ch. 2.9 - Prob. 75PCh. 2.9 - Determine the magnitude of the projection of the...Ch. 2.9 - Determine the angle between the pole and the wire...Ch. 2.9 - Determine the magnitude of the projection of the...Ch. 2.9 - Determine the magnitude of the projected component...Ch. 2.9 - Prob. 80PCh. 2.9 - Determine the angle between the two cables. Prob....Ch. 2.9 - Determine the projected component of the force...Ch. 2.9 - Determine the angles and between the flag pole...Ch. 2.9 - Determine the magnitudes of the components of F...Ch. 2.9 - Prob. 85PCh. 2.9 - Determine the angle between the pipe segments BA...Ch. 2.9 - If the force F = 100 N lies in the plane DBEC,...Ch. 2.9 - Determine the magnitudes of the components of the...Ch. 2.9 - Determine the magnitudes of the projected...Ch. 2.9 - Determine the magnitude of the projected component...Ch. 2.9 - Two cables exert forces on the pipe. Determine the...Ch. 2.9 - Determine the angle between the two forces. Prob....Ch. 2 - Determine the magnitude of the resultant force FR...Ch. 2 - Resolve the force into components along the u and...Ch. 2 - Determine the magnitude of the resultant force...Ch. 2 - The cable exerts a force of 250 lb on the crane...Ch. 2 - The cable attached to the tractor at B exerts a...Ch. 2 - Express F1 and F2 as Cartesian vectors. Prob. R26Ch. 2 - Determine the angle between the edges of the...Ch. 2 - Determine the projection of the force F along the...
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