EBK MECHANICS OF MATERIALS
EBK MECHANICS OF MATERIALS
7th Edition
ISBN: 8220100257063
Author: BEER
Publisher: YUZU
bartleby

Concept explainers

bartleby

Videos

Textbook Question
Book Icon
Chapter 9.4, Problem 90P

Use the method of superposition to solve the following problems and assume that the flexural rigidity El of each beam is constant.

9.90 Before the load P was applied, a gap, δ0 = 0.5 mm, existed between the cantilever beam AC and the support at B. Knowing that E = 200 GPa, determine the magnitude of P for which the deflection at C is 1 mm.

Chapter 9.4, Problem 90P, Use the method of superposition to solve the following problems and assume that the flexural

Fig. P9.90

Expert Solution & Answer
Check Mark
To determine

Find the magnitude of load P for the given condition using superposition method.

Answer to Problem 90P

The magnitude of load P in the beam is P=5.63kN()_.

Explanation of Solution

Given information:

The gap at the point B is δ0=0.5mm.

The modulus of elasticity of the material is E=200GPa.

The size of the square cross section is a=60mm.

The deflection at point C is δC=1mm.

Calculation:

Find the moment of inertia of the square cross section (I) using the relation.

I=a412

Here, the size of the square cross section is a.

Substitute 60 mm for a.

I=60412=1.08×106mm4×(1m1,000mm)4=1.08×106m4

Consider the portion AB of the beam.

The load P at point C will be converted into a load and moment at point B.

Show the free-body diagram of the superimposed beam AB as in Figure 1.

EBK MECHANICS OF MATERIALS, Chapter 9.4, Problem 90P , additional homework tip  1

Loading I:

The downward load P is acting at point B of the beam.

Refer to Case 1 in Appendix D “Beam Deflections and Slopes” in the textbook.

Write the deflection equation for concentrated load acting in a cantilever beam as follows;

y=PL33EI

Find the deflection at point B due to load P at point B as follows;

(yB)I=PL33EI

Loading II:

The upward reaction By is acting at point B of the beam.

Refer to Case 1 in Appendix D “Beam Deflections and Slopes” in the textbook.

Write the deflection equation for concentrated load acting in a cantilever beam as follows;

y=PL33EI

Find the deflection at point B due to reaction at point B as follows;

(yB)II=ByL33EI

Loading III:

The clockwise moment is acting at point B of the beam.

Refer to Case 3 in Appendix D “Beam Deflections and Slopes” in the textbook.

Write the deflection equation for moment in a cantilever beam as follows;

y=ML22EI

Find the deflection at point B due to the moment at point B as follows;

(yB)III=PaL22EI

Find the resultant deflection at point B as follows.

yB=(yB)I+(yB)II+(yB)III

Substitute δ0 for yB, PL33EI for (yB)I, ByL33EI for (yB)II, and PaL22EI for (yB)III.

δ0=PL33EIByL33EI+PaL22EI=1EI(PL33ByL33+PaL22)

Substitute 0.5 mm for δ0, 0.5 m for L, 0.2 m for a, 200 GPa for E, and 1.08×106m4 for I.

0.5mm×1m103mm=1200GPa×109Pa1GPa×1.08×106(P(0.5)33By(0.5)33+P(0.2)(0.5)22)0.5103=1200×109×1.08×106(0.041667P0.041667By+0.025P)108=0.06667P0.041667By (1)

Consider the beam ABC.

Show the free-body diagram of the superimposed beam ABC as in Figure 2.

EBK MECHANICS OF MATERIALS, Chapter 9.4, Problem 90P , additional homework tip  2

Loading IV:

The downward load P is acting at point C of the beam.

Refer to Case 1 in Appendix D “Beam Deflections and Slopes” in the textbook.

Write the deflection equation for concentrated load acting in a cantilever beam as follows;

y=PL33EI

Find the deflection at point C due to load P at point C as follows;

(yC)IV=P(L+a)33EI

Loading V:

The upward reaction By is acting at point B of the beam.

Refer to Case 1 in Appendix D “Beam Deflections and Slopes” in the textbook.

Write the slope and deflection equation for concentrated load acting in a cantilever beam as follows;

θ=PL22EIy=PL33EI

Find the deflection at point B due to reaction at point B as follows;

(yB)V=ByL33EI

Find the slope at point B due to reaction at point B as follows;

(θB)V=ByL22EI

The portion BC remains straight.

Find the deflection at point C due to reaction at point B as follows;

(yC)V=(yB)V+a(θB)V

Substitute ByL33EI for (yB)V and ByL22EI for (θB)V.

(yC)V=ByL33EIaByL22EI

Find the resultant deflection at point C as follows.

yC=(yC)IV+(yC)V

Substitute δC for yC, P(L+a)33EI for (yC)IV , and (ByL33EIaByL22EI) for (yC)V.

δC=P(L+a)33EIByL33EIaByL22EI=1EI(P(L+a)33ByL33aByL22)

Substitute 1 mm for δC, 0.5 m for L, 0.2 m for a, 200 GPa for E, and 1.08×106m4 for I.

1mm×1m103mm=1200GPa×109Pa1GPa×1.08×106(P(0.5+0.2)33By(0.5)33(0.2)By(0.5)22)216=0.11433P0.041667By0.025By216=0.11433P0.06667By (2)

Solve the Equation (1) and (2).

By=6.42×103NP=5.63×103N×1kN103N=5.63kN()

Therefore, the magnitude of load P in the beam is P=5.63kN()_.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!
Students have asked these similar questions
First monthly exam Gas dynamics Third stage Q1/Water at 15° C flow through a 300 mm diameter riveted steel pipe, E-3 mm with a head loss of 6 m in 300 m length. Determine the flow rate in pipe. Use moody chart. Q2/ Assume a car's exhaust system can be approximated as 14 ft long and 0.125 ft-diameter cast-iron pipe ( = 0.00085 ft) with the equivalent of (6) regular 90° flanged elbows (KL = 0.3) and a muffler. The muffler acts as a resistor with a loss coefficient of KL= 8.5. Determine the pressure at the beginning of the exhaust system (pl) if the flowrate is 0.10 cfs, and the exhaust has the same properties as air.(p = 1.74 × 10-3 slug/ft³, u= 4.7 x 10-7 lb.s/ft²) Use moody chart (1) MIDAS Kel=0.3 Q3/Liquid ammonia at -20°C is flowing through a 30 m long section of a 5 mm diameter copper tube(e = 1.5 × 10-6 m) at a rate of 0.15 kg/s. Determine the pressure drop and the head losses. .μ= 2.36 × 10-4 kg/m.s)p = 665.1 kg/m³
2/Y Y+1 2Cp Q1/ Show that Cda Az x P1 mactual Cdf Af R/T₁ 2pf(P1-P2-zxgxpf) Q2/ A simple jet carburetor has to supply 5 Kg of air per minute. The air is at a pressure of 1.013 bar and a temperature of 27 °C. Calculate the throat diameter of the choke for air flow velocity of 90 m/sec. Take velocity coefficient to be 0.8. Assume isentropic flow and the flow to be compressible. Quiz/ Determine the air-fuel ratio supplied at 5000 m altitude by a carburetor which is adjusted to give an air-fuel ratio of 14:1 at sea level where air temperature is 27 °C and pressure is 1.013 bar. The temperature of air decreases with altitude as given by the expression The air pressure decreases with altitude as per relation h = 19200 log10 (1.013), where P is in bar. State any assumptions made. t = ts P 0.0065h
36 2) Use the method of MEMBERS to determine the true magnitude and direction of the forces in members1 and 2 of the frame shown below in Fig 3.2. 300lbs/ft member-1 member-2 30° Fig 3.2. https://brightspace.cuny.edu/d21/le/content/433117/viewContent/29873977/View

Chapter 9 Solutions

EBK MECHANICS OF MATERIALS

Ch. 9.2 - For the beam and loading shown, (a) express the...Ch. 9.2 - (a) Determine the location and magnitude of the...Ch. 9.2 - For the beam and loading shown, determine the...Ch. 9.2 - Knowing that beam AE is a W360 101 rolled shape...Ch. 9.2 - For the beam and loading shown, knowing that a = 2...Ch. 9.2 - Knowing that beam AE is an S200 27.4 rolled shape...Ch. 9.2 - For the beam and loading shown, determine (a) the...Ch. 9.2 - For the beam and loading shown, determine (a) the...Ch. 9.2 - 9.19 through 9.22 For the beam and loading shown,...Ch. 9.2 - 9.19 through 9.22 For the beam and loading shown,...Ch. 9.2 - 9.19 through 9.22 For the beam and loading shown,...Ch. 9.2 - 9.19 through 9.22 For the beam and loading shown,...Ch. 9.2 - For the beam shown, determine the reaction at the...Ch. 9.2 - For the beam shown, determine the reaction at the...Ch. 9.2 - 9.25 through 9.28 Determine the reaction at the...Ch. 9.2 - 9.25 through 9.28 Determine the reaction at the...Ch. 9.2 - Prob. 27PCh. 9.2 - 9.25 through 9.28 Determine the reaction at the...Ch. 9.2 - 9.29 and 9.30 Determine the reaction at the roller...Ch. 9.2 - 9.29 and 9.30 Determine the reaction at the roller...Ch. 9.2 - 9.37 and 9.32 Determine the reaction at the roller...Ch. 9.2 - 9.31 and 9.32 Determine the reaction at the roller...Ch. 9.2 - Prob. 33PCh. 9.2 - 9.33 and 9.34 determine the reaction at A and draw...Ch. 9.3 - 9.35 and 9.36 For the beam and loading shown,...Ch. 9.3 - 9.35 and 9.36 For the beam and loading shown,...Ch. 9.3 - 9.37 and 9.38 For the beam and loading shown,...Ch. 9.3 - 9.37 and 9.38 For the beam and loading shown,...Ch. 9.3 - 9.39 and 9.40 For the beam and loading shown,...Ch. 9.3 - 9.39 and 9.40 For the beam and loading shown,...Ch. 9.3 - 9.41 and 9.42 For the beam and loading shown,...Ch. 9.3 - 9.41 and 9.42 For the beam and loading shown (a)...Ch. 9.3 - For the beam and loading shown, determine (a) the...Ch. 9.3 - For the beam and loading shown, determine (a) the...Ch. 9.3 - For the timber beam and loading shown, determine...Ch. 9.3 - For the beam and loading shown, determine (a) the...Ch. 9.3 - For the beam and loading shown, determine (a) the...Ch. 9.3 - For the beam and loading shown, determine (a) the...Ch. 9.3 - 9.49 and 9.50 For the beam and loading shown,...Ch. 9.3 - 9.49 and 9.50 For the beam and loading shown,...Ch. 9.3 - 9.51 and 9.52 For the beam and loading shown,...Ch. 9.3 - 9.49 and 9.50 For the beam and loading shown,...Ch. 9.3 - For the beam and loading shown, determine (a) the...Ch. 9.3 - For the beam shown, and knowing that P = 40 kN,...Ch. 9.3 - 9.55 and 9.56 For the beam and loading shown, (a)...Ch. 9.3 - 9.55 and 9.56 For the beam and loading shown, (a)...Ch. 9.3 - For the beam and loading shown, determine (a) the...Ch. 9.3 - For the beam and loading shown, determine (a) the...Ch. 9.3 - Prob. 59PCh. 9.3 - 9.59 through 9.62 For the beam and loading...Ch. 9.3 - Prob. 61PCh. 9.3 - 9.59 through 9.62 For the beam and loading...Ch. 9.3 - The rigid bars BF and DH are welded to the...Ch. 9.3 - The rigid bar DEF is welded at point D to the...Ch. 9.4 - Use the method of superposition to solve the...Ch. 9.4 - Use the method of superposition to solve the...Ch. 9.4 - Use the method of superposition to solve the...Ch. 9.4 - Use the method of superposition to solve the...Ch. 9.4 - Use the method of superposition to solve the...Ch. 9.4 - Use the method of superposition to solve the...Ch. 9.4 - Use the method of superposition to solve the...Ch. 9.4 - Use the method of superposition to solve the...Ch. 9.4 - Use the method of superposition to solve the...Ch. 9.4 - Use the method of superposition to solve the...Ch. 9.4 - Use the method of superposition to solve the...Ch. 9.4 - Use the method of superposition to solve the...Ch. 9.4 - Use the method of superposition to solve the...Ch. 9.4 - Use the method of superposition to solve the...Ch. 9.4 - Use the method of superposition to solve the...Ch. 9.4 - Use the method of superposition to solve the...Ch. 9.4 - Use the method of superposition to solve the...Ch. 9.4 - Use the method of superposition to solve the...Ch. 9.4 - Use the method of superposition to solve the...Ch. 9.4 - Prob. 84PCh. 9.4 - Use the method of superposition to solve the...Ch. 9.4 - Use the method of superposition to solve the...Ch. 9.4 - Use the method of superposition to solve the...Ch. 9.4 - Use the method of superposition to solve the...Ch. 9.4 - Use the method of superposition to solve the...Ch. 9.4 - Use the method of superposition to solve the...Ch. 9.4 - Use the method of superposition to solve the...Ch. 9.4 - Use the method of superposition to solve the...Ch. 9.4 - Use the method of superposition to solve the...Ch. 9.4 - Use the method of superposition to solve the...Ch. 9.5 - 9.95 through 9.98 For the uniform cantilever beam...Ch. 9.5 - Prob. 96PCh. 9.5 - 9.95 through 9.98 For the uniform cantilever beam...Ch. 9.5 - 9.95 through 9.98 For the uniform cantilever beam...Ch. 9.5 - 9.99 and 9.100 For the uniform cantilever beam and...Ch. 9.5 - 9.99 and 9.100 For the uniform cantilever beam and...Ch. 9.5 - For the cantilever beam and loading shown,...Ch. 9.5 - Prob. 102PCh. 9.5 - Prob. 103PCh. 9.5 - Prob. 104PCh. 9.5 - Prob. 105PCh. 9.5 - For the cantilever beam and loading shown,...Ch. 9.5 - Two cover plates are welded to the rolled-steel...Ch. 9.5 - Two cover plates are welded to the rolled-steel...Ch. 9.5 - 9.109 through 9.114 For the prismatic beam and...Ch. 9.5 - Prob. 110PCh. 9.5 - Prob. 111PCh. 9.5 - Prob. 112PCh. 9.5 - Prob. 113PCh. 9.5 - Prob. 114PCh. 9.5 - Prob. 115PCh. 9.5 - 9.115 and 9.116 For the beam and loading shown,...Ch. 9.5 - Prob. 117PCh. 9.5 - 9.118 and 9.119 For the beam and loading shown,...Ch. 9.5 - Prob. 119PCh. 9.5 - Prob. 120PCh. 9.5 - Prob. 121PCh. 9.5 - Prob. 122PCh. 9.5 - Prob. 123PCh. 9.5 - Prob. 124PCh. 9.6 - 9.125 through 9.128 For the prismatic beam and...Ch. 9.6 - Prob. 126PCh. 9.6 - Prob. 127PCh. 9.6 - Prob. 128PCh. 9.6 - 9.129 and 9.130 For the beam and loading shown,...Ch. 9.6 - Prob. 130PCh. 9.6 - For the timber beam and loading shown, determine...Ch. 9.6 - Prob. 132PCh. 9.6 - For the beam and loading shown, determine (a) the...Ch. 9.6 - Prob. 134PCh. 9.6 - Prob. 135PCh. 9.6 - Knowing that the beam AD is made of a solid steel...Ch. 9.6 - Prob. 137PCh. 9.6 - For the beam and loading shown, determine (a) the...Ch. 9.6 - Prob. 139PCh. 9.6 - For the beam and loading shown, determine the...Ch. 9.6 - Prob. 141PCh. 9.6 - Prob. 142PCh. 9.6 - Prob. 143PCh. 9.6 - Prob. 144PCh. 9.6 - Prob. 145PCh. 9.6 - For the beam and loading shown, determine (a) the...Ch. 9.6 - Prob. 147PCh. 9.6 - Prob. 148PCh. 9.6 - Prob. 149PCh. 9.6 - Prob. 150PCh. 9.6 - 9.151 and 9.152 For the beam and loading shown,...Ch. 9.6 - Prob. 152PCh. 9.6 - Prob. 153PCh. 9.6 - Prob. 154PCh. 9.6 - Prob. 155PCh. 9.6 - Fig. P9.155 and P9.156 9.156 For the beam and...Ch. 9 - For the loading shown, determine (a) the equation...Ch. 9 - Prob. 158RPCh. 9 - For the beam and loading shown, determine (a) the...Ch. 9 - Determine the reaction at A and draw the bending...Ch. 9 - For the beam and loading shown, determine (a) the...Ch. 9 - For the beam and loading shown, determine (a) the...Ch. 9 - Beam CE rests on beam AB as shown. Knowing that a...Ch. 9 - The cantilever beam BC is attached to the steel...Ch. 9 - For the cantilever beam and loading shown,...Ch. 9 - Knowing that P = 4 kips, determine (a) the slope...Ch. 9 - For the beam and loading shown, determine (a) the...Ch. 9 - Determine the reaction at the roller support and...
Knowledge Booster
Background pattern image
Mechanical Engineering
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.
Similar questions
SEE MORE QUESTIONS
Recommended textbooks for you
Text book image
Elements Of Electromagnetics
Mechanical Engineering
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Oxford University Press
Text book image
Mechanics of Materials (10th Edition)
Mechanical Engineering
ISBN:9780134319650
Author:Russell C. Hibbeler
Publisher:PEARSON
Text book image
Thermodynamics: An Engineering Approach
Mechanical Engineering
ISBN:9781259822674
Author:Yunus A. Cengel Dr., Michael A. Boles
Publisher:McGraw-Hill Education
Text book image
Control Systems Engineering
Mechanical Engineering
ISBN:9781118170519
Author:Norman S. Nise
Publisher:WILEY
Text book image
Mechanics of Materials (MindTap Course List)
Mechanical Engineering
ISBN:9781337093347
Author:Barry J. Goodno, James M. Gere
Publisher:Cengage Learning
Text book image
Engineering Mechanics: Statics
Mechanical Engineering
ISBN:9781118807330
Author:James L. Meriam, L. G. Kraige, J. N. Bolton
Publisher:WILEY
Solids: Lesson 53 - Slope and Deflection of Beams Intro; Author: Jeff Hanson;https://www.youtube.com/watch?v=I7lTq68JRmY;License: Standard YouTube License, CC-BY