Statics and Mechanics of Materials (5th Edition)
5th Edition
ISBN: 9780134382593
Author: Russell C. Hibbeler
Publisher: PEARSON
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Chapter 16.5, Problem 72P
To determine
Find the greater force (P) applied to the center of the top member.
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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 16 Solutions
Statics and Mechanics of Materials (5th Edition)
Ch. 16.2 - In each ease, determine the internal bending...Ch. 16.2 - Prob. 1FPCh. 16.2 - Determine the slope and deflection of end A of the...Ch. 16.2 - Prob. 3FPCh. 16.2 - Prob. 4FPCh. 16.2 - Determine the maximum deflection of the simply...Ch. 16.2 - Prob. 6FPCh. 16.2 - An L2 steel strap having a thickness of 0.125 in....Ch. 16.2 - The L2 steel blade of the band saw wraps around...Ch. 16.2 - A picture is taken of a man performing a pole...
Ch. 16.2 - Determine the equation of the elastic curve for...Ch. 16.2 - Determine the deflection of end C of the...Ch. 16.2 - Prob. 6PCh. 16.2 - The A-36 steel beam has a depth of 10 in. and is...Ch. 16.2 - Prob. 8PCh. 16.2 - Determine the equations of the elastic curve for...Ch. 16.2 - Determine the equations of the elastic curve using...Ch. 16.2 - Determine the equations of the elastic curve using...Ch. 16.2 - Prob. 12PCh. 16.2 - Determine the maximum deflection of the beam and...Ch. 16.2 - The simply supported shaft has a moment of inertia...Ch. 16.2 - A torque wrench is used to tighten the nut on a...Ch. 16.2 - The pipe can be assumed roller supported at its...Ch. 16.2 - Determine the equations of the elastic curve for...Ch. 16.2 - The bar is supported by a roller constraint at B,...Ch. 16.2 - The bar is supported by a roller constraint at B,...Ch. 16.2 - Determine the equations of the elastic curve using...Ch. 16.2 - Prob. 21PCh. 16.2 - Determine the elastic curve for the cantilevered...Ch. 16.2 - Prob. 23PCh. 16.2 - Prob. 24PCh. 16.2 - The floor beam of the airplane is subjected to the...Ch. 16.2 - Determine the maximum deflection of the simply...Ch. 16.2 - The beam is made of a material having a specific...Ch. 16.2 - Determine the slope at end B and the maximum...Ch. 16.2 - Prob. 29PCh. 16.2 - Determine the equations of the elastic curve using...Ch. 16.3 - The shaft is supported at A by a journal bearing...Ch. 16.3 - The shaft supports the two pulley loads shown....Ch. 16.3 - Prob. 33PCh. 16.3 - Prob. 34PCh. 16.3 - The beam is subjected to the load shown. Determine...Ch. 16.3 - Prob. 36PCh. 16.3 - Determine the equation of the elastic curve and...Ch. 16.3 - Prob. 38PCh. 16.3 - Prob. 39PCh. 16.3 - Determine the slope at A and the deflection of end...Ch. 16.3 - Determine the maximum deflection in region AB of...Ch. 16.3 - Prob. 42PCh. 16.3 - Prob. 43PCh. 16.3 - Prob. 44PCh. 16.4 - The W10 15 cantilevered beam is made of A-36...Ch. 16.4 - The W10 15 cantilevered beam is made of A-36...Ch. 16.4 - The W14 43 simply supported beam is made of A992...Ch. 16.4 - The W14 43 simply supported beam is made of A992...Ch. 16.4 - The W14 43 simply supported beam is made of A-36...Ch. 16.4 - The W14 43 simply supported beam is made of A-36...Ch. 16.4 - The W8 48 cantilevered beam is made of A-36 steel...Ch. 16.4 - The beam supports the loading shown. Code...Ch. 16.4 - Prob. 53PCh. 16.4 - The W8 48 cantilevered beam is made of A-36 steel...Ch. 16.4 - Prob. 55PCh. 16.4 - Prob. 56PCh. 16.4 - Prob. 57PCh. 16.4 - The assembly consists of a cantilevered beam CB...Ch. 16.4 - Prob. 59PCh. 16.4 - Prob. 60PCh. 16.5 - Determine the reactions at the fixed support A and...Ch. 16.5 - Prob. 8FPCh. 16.5 - Determine the reactions at the fixed support A and...Ch. 16.5 - Prob. 10FPCh. 16.5 - Prob. 11FPCh. 16.5 - Prob. 12FPCh. 16.5 - Prob. 61PCh. 16.5 - Determine the reactions at the supports, then draw...Ch. 16.5 - Determine the reactions at the supports, then draw...Ch. 16.5 - Prob. 64PCh. 16.5 - The beam is used to support the 20-kip load....Ch. 16.5 - Prob. 66PCh. 16.5 - Determine the reactions at the supports A and B....Ch. 16.5 - Before the uniform distributed load is applied to...Ch. 16.5 - Prob. 69PCh. 16.5 - Prob. 70PCh. 16.5 - The beam is supported by the bolted supports at...Ch. 16.5 - Prob. 72PCh. 16.5 - Prob. 73PCh. 16 - Prob. 1RPCh. 16 - Draw the bending-moment diagram for the shaft and...Ch. 16 - Prob. 3RPCh. 16 - Determine the equations of the elastic curve for...Ch. 16 - Determine the maximum deflection between the...Ch. 16 - Prob. 6RPCh. 16 - The framework consists of two A-36 steel...Ch. 16 - Prob. 8RPCh. 16 - Using the method of superposition, determine the...
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