Shigley's Mechanical Engineering Design (McGraw-Hill Series in Mechanical Engineering)
10th Edition
ISBN: 9780073398204
Author: Richard G Budynas, Keith J Nisbett
Publisher: McGraw-Hill Education
expand_more
expand_more
format_list_bulleted
Concept explainers
Textbook Question
Chapter 4, Problem 53P
Consider the simply supported beam 5 with a center load in Appendix A–9. Determine the deflection equation if the stiffness of the left and right supports are k1 and k2, respectively.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionStudents have asked these similar questions
For the wire form shown, use Castigliano's method to determine the deflec-
tion of point A in the y direction. Consider the effects of bending and torsion
only. Use the straight beam formulation for the bending energy. The wire is
steel with E 200 GPa, v = 0.29, and has a diameter of 5 mm. Before
cation of the 200-N force the wire form is in the xz plane
100 mm.
=
appli-
where the radius R is
A beam with a uniform load has a sliding support at one end and spring support at the other. The spring has a stiffness k = 48EI / L3. Derive the equation of the deflection curve by starting with the third-order differential equation (the shear-force equation). Also, determine the angle of rotation θB at support B.
3. Determine the displacement and slope (i.e. 0) at the load point for the stepped beam
shown in the following figure. Also determine the reaction forces and moments. Each
element has E = 200 GPa. The area moment of inertia are given as I₁ = 1.25 × 105
mm4, and 2 = 4 x 104 mm. Clearly show the elemental stiffness matrices (k) for
each element, assembly of k matrices to get global stiffness matrix (K) and application of
boundary conditions. Then solve the reduced K matrix to get displacements and reactions
3000 N
150 mm
75 mm
125 mm
Chapter 4 Solutions
Shigley's Mechanical Engineering Design (McGraw-Hill Series in Mechanical Engineering)
Ch. 4 - The figure shows a torsion bar OA fixed at O,...Ch. 4 - For Prob. 41, if the simple support at point A...Ch. 4 - A torsion-bar spring consists of a prismatic bar,...Ch. 4 - An engineer is forced by geometric considerations...Ch. 4 - A bar in tension has a circular cross section and...Ch. 4 - Prob. 6PCh. 4 - Prob. 7PCh. 4 - Derive the equations given for beam 2 in Table A9...Ch. 4 - Derive the equations given for beam 5 in Table A9...Ch. 4 - The figure shows a cantilever consisting of steel...
Ch. 4 - A simply supported beam loaded by two forces is...Ch. 4 - Using superposition, find the deflection of the...Ch. 4 - A rectangular steel bar supports the two...Ch. 4 - An aluminum tube with outside diameter of 2 in and...Ch. 4 - The cantilever shown in the figure consists of two...Ch. 4 - Using superposition for the bar shown, determine...Ch. 4 - A simply supported beam has a concentrated moment...Ch. 4 - Prob. 18PCh. 4 - Using the results of Prob. 418, use superposition...Ch. 4 - Prob. 20PCh. 4 - Consider the uniformly loaded simply supported...Ch. 4 - Prob. 22PCh. 4 - Prob. 23PCh. 4 - Prob. 24PCh. 4 - Prob. 25PCh. 4 - Prob. 26PCh. 4 - Prob. 27PCh. 4 - Prob. 28PCh. 4 - 429 to 434 For the steel countershaft specified in...Ch. 4 - Prob. 30PCh. 4 - Prob. 31PCh. 4 - Prob. 32PCh. 4 - For the steel countershaft specified in the table,...Ch. 4 - For the steel countershaft specified in the table,...Ch. 4 - Prob. 35PCh. 4 - Prob. 36PCh. 4 - Prob. 37PCh. 4 - Prob. 38PCh. 4 - Prob. 39PCh. 4 - Prob. 40PCh. 4 - The cantilevered handle in the figure is made from...Ch. 4 - Prob. 42PCh. 4 - The cantilevered handle in Prob. 384, p. 154, is...Ch. 4 - A flat-bed trailer is to be designed with a...Ch. 4 - The designer of a shaft usually has a slope...Ch. 4 - Prob. 46PCh. 4 - If the diameter of the steel beam shown is 1.25...Ch. 4 - For the beam of Prob. 4-47, plot the magnitude of...Ch. 4 - Prob. 49PCh. 4 - 4-50 and 4-51 The figure shows a rectangular...Ch. 4 - and 451 the ground at one end and supported by a...Ch. 4 - The figure illustrates a stepped torsion-bar...Ch. 4 - Consider the simply supported beam 5 with a center...Ch. 4 - Prob. 54PCh. 4 - Prob. 55PCh. 4 - Solve Prob. 410 using singularity functions. Use...Ch. 4 - Prob. 57PCh. 4 - Prob. 58PCh. 4 - Prob. 59PCh. 4 - Solve Prob. 413 using singularity functions. Since...Ch. 4 - Prob. 61PCh. 4 - Solve Prob. 419 using singularity functions to...Ch. 4 - Using singularity functions, write the deflection...Ch. 4 - Determine the deflection equation for the...Ch. 4 - Use Castiglianos theorem to verify the maximum...Ch. 4 - Use Castiglianos theorem to verify the maximum...Ch. 4 - Solve Prob. 415 using Castiglianos theorem.Ch. 4 - Solve Prob. 452 using Castiglianos theoremCh. 4 - Determine the deflection at midspan for the beam...Ch. 4 - Using Castiglianos theorem, determine the...Ch. 4 - Solve Prob. 441 using Castiglianos theorem. Since...Ch. 4 - Solve Prob. 442 using Castiglianos theorem.Ch. 4 - The cantilevered handle in Prob. 384 is made from...Ch. 4 - Solve Prob. 450 using Castiglianos theorem.Ch. 4 - Solve Prob. 451 using Castiglianos theorem.Ch. 4 - The steel curved bar shown has a rectangular cross...Ch. 4 - Repeat Prob. 476 to find the vertical deflection...Ch. 4 - For the curved steel beam shown. F = 6.7 kips....Ch. 4 - A steel piston ring has a mean diameter of 70 mm....Ch. 4 - For the steel wire form shown, use Castiglianos...Ch. 4 - 4-81 and 4-82 The part shown is formed from a...Ch. 4 - 4-81 and 4-82 The part shown is formed from a...Ch. 4 - Repeat Prob. 481 for the vertical deflection at...Ch. 4 - Repeat Prob. 482 for the vertical deflection at...Ch. 4 - A hook is formed from a 2-mm-diameter steel wire...Ch. 4 - The figure shows a rectangular member OB, made...Ch. 4 - Prob. 87PCh. 4 - For the wire form shown, determine the deflection...Ch. 4 - Prob. 89PCh. 4 - Prob. 90PCh. 4 - Prob. 91PCh. 4 - Prob. 92PCh. 4 - Solve Prob. 492 using Castiglianos method and...Ch. 4 - An aluminum step bar is loaded as shown. (a)...Ch. 4 - The steel shaft shown in the figure is subjected...Ch. 4 - Repeat Prob. 495 with the diameters of section OA...Ch. 4 - The figure shows a 12- by 1-in rectangular steel...Ch. 4 - For the beam shown, determine the support...Ch. 4 - Solve Prob. 498 using Castiglianos theorem and...Ch. 4 - Consider beam 13 in Table A9, but with flexible...Ch. 4 - Prob. 101PCh. 4 - The steel beam ABCD shown is simply supported at C...Ch. 4 - Prob. 103PCh. 4 - A round tubular column has outside and inside...Ch. 4 - For the conditions of Prob. 4104, show that...Ch. 4 - Link 2, shown in the figure, is 25 mm wide, has...Ch. 4 - Link 3, shown schematically in the figure, acts as...Ch. 4 - The hydraulic cylinder shown in the figure has a...Ch. 4 - The figure shows a schematic drawing of a...Ch. 4 - If drawn, a figure for this problem would resemble...Ch. 4 - Design link CD of the hand-operated toggle press...Ch. 4 - Find the maximum values of the spring force and...Ch. 4 - As shown in the figure, the weight W1 strikes W2...Ch. 4 - Part a of the figure shows a weight W mounted...
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
- A horizontal load P acts at end C of the bracket ABC shown in the figure. Determine the deflection 6Cof point C. Determine the maximum upward deflection 8 of member AB. Note: Assume that the flexural rigidity EI is constant throughout the frame. Also, disregard the effects of axial deformations and consider only the effects of bending due to the load P.arrow_forwardThe cantilever beam ACB shown in the figure has moments of inertia /, and I{in parts AC and CB, respectively. Using the method of superposition, determine the deflection 8Bat the free end due to the load P. Determine the ratio r of the deflection 8Bto the deflection S:at the free end of a prismatic cantilever with moment of inertia /] carrying the same load. Plot a graph of the deflection ratio r versus the ratio 12 //L of the moments of inertia. (Let /, II- vary from I to 5.)arrow_forwardRepeat Problem 97-10, but now use the tapered propped cantilever tube A B with sliding support at B (see figure) that supports a concentrated load P at the sliding end. Find the equation of the deflection curve and the deflection 8Bat the sliding end of the beam due to the load P.arrow_forward
- -33 Find the horizontal deflection hand vertical deflection vat the free end C of the frame ABC shown in the figure. (The flexural rigidity EI is constant throughout the frame.) Note: Disregard the effects of axial deformations and consider only the effects of bending due to the load P.arrow_forwardPlot the load-deflection diagram for a pinned-end column with eccentric axial loads (see figure) if the eccentricity e of the load is 5 mm and the column has a length L = 3.6 m, moment of inertia L = 9,0 × 106 mm4, and modulus of elasticity E = 210 GPa. Note: Plot the axial load as ordinate and the deflection at the midpoint as abscissa.arrow_forward-22 A simple beam AB supports a uniform load of intensity q acting over the middle region of the span (see figure). Determine the angle of rotation A at the left-hand support and the deflection max at the midpoint.arrow_forward
- A heavy object of weight W is dropped onto the midpoint of a simple beam AB from a height h (see figure). Obtain a formula for the maximum bending stress ^ma* due to tne filing weight in terms of h, st, and 5st, where it is the maximum bending stress and Sstis the deflection at the midpoint when the weight W acts on the beam as a statically applied load. Plot a graph of the ratio o"max/ö"it (that is, the ratio of the dynamic stress to the static stress) versus the ratio iifS^r(Let h/S^ vary from 0 to 10.)arrow_forward-3 The deflection curve for a simple beam AB (see figure) is given by v=q0x360LEI(7L410L2x2+3x4) Describe the load acting on the beam.arrow_forwardThe wing of a large commercial jet is represented by a simplified prismatic cantilever beam model with uniform load \v and concentrated loads P at the two engine locations (see figure). Find expressions for the tip deflection and rotation at D in terms of \\\ P, L, and EL.arrow_forward
- The compound beam ABC shown in the figure has a sliding support at A and a fixed support at C. The beam consists of two members joined by a pin connection (i.e., moment release) at B. Find the deflectionarrow_forwardThe column shown in the figure is fixed at the base and free at the upper end. A compressive load P acts at the top of the column with an eccentricity e from the axis of the column. Beginning with the differential equation of the deflection curve, derive formulas for the maximum deflection S of the column and the maximum bending moment Mmaxin the column.arrow_forwardA beam ABC has a rigid segment from A to B and a flexible segment with moment of inertia / from B to C(see figure). A concentrated load P acts at point B. Determine the angle of rotation SAof the rigidsegment, the deflection 8Bat point ß, and the maximum deflection 8.arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
- Mechanics of Materials (MindTap Course List)Mechanical EngineeringISBN:9781337093347Author:Barry J. Goodno, James M. GerePublisher:Cengage Learning
Mechanics of Materials (MindTap Course List)
Mechanical Engineering
ISBN:9781337093347
Author:Barry J. Goodno, James M. Gere
Publisher:Cengage Learning
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