Mechanics of Materials, 7th Edition
7th Edition
ISBN: 9780073398235
Author: Ferdinand P. Beer, E. Russell Johnston Jr., John T. DeWolf, David F. Mazurek
Publisher: McGraw-Hill Education
expand_more
expand_more
format_list_bulleted
Concept explainers
Videos
Textbook Question
Chapter 9.4, Problem 85P
Use the method of superposition to solve the following problems and assume that the flexural rigidity El of each beam is constant.
9.85 Beam DE rests on the cantilever beam AC as shown. Knowing that a square rod of side 10 mm is used for each beam, determine the deflection at end C if the 25-N · m couple is applied (a) to end E of the beam DE, (b) to end C of the beam AC. Use E = 200 GPa.
Fig. P9.85
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
For the beam and loading shown, use the double-integration method to determine (a) the equation of the elastic curve for the beam, (b)
the location of the maximum deflection, and (c) the maximum beam deflection. Assume that El is constant for the beam. Let w =
13
kN/m, L = 4.0 m, E = 180 GPa, and I = 130 x 106 mm“.
B
L
Answer:
(b) х %3
m
(c) Vmax
mm
5. The rigid beam rests on two short posts AC and BD as shown. Post AC is made from steel with E =
200 GPa and BD from aluminum with E = 70 GPa. The diameters of posts AC and BD are 25 mm and 40
mm, respectively. Determine the vertical displacement of point F on AB.
100 kN
200 mm
400 mm-
B
F
300 mm
C
D
2. The steel beam ABCD shown is simply supported at A and supported at B and D by steel cables, each
having an effective diameter of 0.5 in. The moment of inertia of the beam is I = 1.2 inª. A force of
5 kips is applied at point C. Determine the deflections of B, C, and D using Superposition method.
A
16 in
E
B
16 in
C
5 kips
16 in
F
D
38 in
Chapter 9 Solutions
Mechanics of Materials, 7th Edition
Ch. 9.2 - In the following problems assume that the flexural...Ch. 9.2 - In the following problems assume that the flexural...Ch. 9.2 - In the following problems assume that the flexural...Ch. 9.2 - 9.1 through 9.4 For the loading shown, determine...Ch. 9.2 - 9.5 and 9.6 For the cantilever beam and loading...Ch. 9.2 - 9.5 and 9.6 For the cantilever beam and loading...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 - Knowing that beam .AB is a W10 33 rolled shape...Ch. 9.2 - Knowing that beam AB is an S200 34 roiled shape...
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
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
- 6.36 Using Castigliano's method on the wire form shown determine the vertical deflection of point A considering bending only. The rigidity of the cross sec- tion is El. R Problem 6.36 Barrow_forwardBeam DE rests on the cantilever beam AC as shown. Knowing that a square rod of side 10 mm is used for each beam, determine the deflection at end C if the 25-N-m couple is applied (a) to end E of the beam DE, (b) to end C of the beam AC. Use E = 200 GPa. 10 mm D E A B 25 N-m 120 mm 180 mm ANS. (a) 5.94 mm ↓. (b) 6.75 mm ↓. 10 mmarrow_forward5. A beam is loaded and supported as shown below. Use singularity functions to determine (a) The deflection at the midpoint of the beam. (b) The slope at C. Y A X -a- B ω a C a Darrow_forward
- Problem 3. (a) Draw the moment diagram for the beam. (b) Observing the direction of load and sign of the moment diagram, and knowledge of the boundary conditions, sketch the elastic curve, that is, the vertical deflection of the axial line thru the centroid of the beam section, (c) Determine the equation of the elastic curve for the beam using the x coordinate. (d) Specify the slope at A and the maximum deflection. El is constant. Mo L Barrow_forwardCurrent Attempt in Progress For the beam and loading shown, use the double-integration method to determine (a) the equation of the elastic curve for segment AB of the beam, (b) the deflection at B, and (c) the slope at A. Assume that El is constant for the beam. Let P = 25 kN, L = 5.5 m, E = 195 GPa, and I = 130 x 106 mm4. P A B Answer: (b) vg = i mm (a) Өд - і rad Save for Later Attempts: 0 of 1 used Submit Answerarrow_forwardA beam ABCD, 6 m long, is simply-supported at the right-hand end D and at a point B 1 m from the left hand end A. It carries a vertical load of 10 kN at A, a second concentrated load of 20 kN at C, 3 m from D, and a uniformly distributed load of 10 kN/m between C and D. Determine the position and magnitude of the maximum deflection if E = 208 GN/m2 and I = 35 x10^-6 m4.arrow_forward
- 6.2 Derive the expression for the maximum deflection of a simply supported beam of negligible weight carrying a point load at its mid-span position. The distance between the supports is L, the second moment of area of the cross-section is I and the modulus of elasticity of the beam material is E. The maximum deflection of such a simply supported beam of length 3 m is 4.3 mm when carrying a load of 200 kN at its mid-span position. What would be the deflection at the free end of a cantilever of the same material, length and cross-section if it carries a load of 100 kN at a point 1.3 m from the free end? [13.4 mm]arrow_forwardA 7/8-in.-diameter rod BC is attached to the lever AB and to the fixed support at C. Lever AB has a uniform cross section 38 in. thick and 1 in. deep. For the loading shown, determine the deflection of point A. Use E=29 *106 psi and G=11.2 *106 psi.arrow_forwardProblem 2. (a) Draw the moment diagram for the beam. (b) Observing the direction of load and sign of the moment diagram, and knowledge of the boundary conditions, sketch the elastic curve, that is, the vertical deflection of the axial line thru the centroid of the beam section, (c) Using integration, determine the equation of the elastic curve for the beam using the x coordinate that is valid for 0 < x < L/2. (d) Specify the slope at A and the beam's maximum deflection. El is constant. For parts (a) and (b), model only one-half of the beam, from x=0 to x=L/2, and use the symmetry dv boundary condition, slope = 0, at the vertical line of symmetry at x=L/2. dx X NA Barrow_forward
- Question 1: Determine the piecewise exact displacement solution (in units of m) for the shown 6 m long cantilever Euler-Bernoulli beam. The beam has a Young's modulus and moment of inertia of 20,000 MPa and 0.003 m*, respectively and is subjected to a uniformly distributed load of 45 kN/m and a downward concentrated load of 100 kN located at a distance of 4 m from the fixed support. 4m 6 m 45 kN/m KNarrow_forwardFor the beam shown: 1) Determine the reactions in terms of P. Modulus - E Area Moment of Inertia - I Заarrow_forwardPROBLEM 4.The beam AB consisting of a cast iron plate of uniform thickness, b, and length, L, is to support the distributed load w(x) shown a) Knowing that the beam is to be of constant strength (fully stressed beam), express h in terms of x, L and ho. b) Determine the smallest value of ho if L=800 mm, b=25 mm, wo=300 kN/m and oall=200 MPa. w-=WoCos(ITX/2L) A ho Barrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Elements Of ElectromagneticsMechanical EngineeringISBN:9780190698614Author:Sadiku, Matthew N. O.Publisher:Oxford University Press
Mechanics of Materials (10th Edition)Mechanical EngineeringISBN:9780134319650Author:Russell C. HibbelerPublisher:PEARSON
Thermodynamics: An Engineering ApproachMechanical EngineeringISBN:9781259822674Author:Yunus A. Cengel Dr., Michael A. BolesPublisher:McGraw-Hill Education
Control Systems EngineeringMechanical EngineeringISBN:9781118170519Author:Norman S. NisePublisher:WILEY
Mechanics of Materials (MindTap Course List)Mechanical EngineeringISBN:9781337093347Author:Barry J. Goodno, James M. GerePublisher:Cengage Learning
Engineering Mechanics: StaticsMechanical EngineeringISBN:9781118807330Author:James L. Meriam, L. G. Kraige, J. N. BoltonPublisher:WILEY
Elements Of Electromagnetics
Mechanical Engineering
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Oxford University Press
Mechanics of Materials (10th Edition)
Mechanical Engineering
ISBN:9780134319650
Author:Russell C. Hibbeler
Publisher:PEARSON
Thermodynamics: An Engineering Approach
Mechanical Engineering
ISBN:9781259822674
Author:Yunus A. Cengel Dr., Michael A. Boles
Publisher:McGraw-Hill Education
Control Systems Engineering
Mechanical Engineering
ISBN:9781118170519
Author:Norman S. Nise
Publisher:WILEY
Mechanics of Materials (MindTap Course List)
Mechanical Engineering
ISBN:9781337093347
Author:Barry J. Goodno, James M. Gere
Publisher:Cengage Learning
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