Bundle: Mechanics Of Materials, Loose-leaf Version, 9th + Mindtap Engineering, 1 Term (6 Months) Printed Access Card
9th Edition
ISBN: 9781337594318
Author: Barry J. Goodno; James M. Gere
Publisher: Cengage Learning
expand_more
expand_more
format_list_bulleted
Concept explainers
Textbook Question
Chapter 9, Problem 9.7.7P
The tapered cantilever beam AB shown in the figure has a thin-walled, hollow circular cross sections of constant thickness t. The diameters at the ends A and B are dAand dB= 2dA, respectively. Thus, the diameter d and moment of inertia / at distance x from the free end are, respectively,
in which IAis the moment of inertia at end A of the beam.
Determine the equation of the deflection curve and the deflection 8 Aat the free end of the beam due to the load P.
Expert Solution & Answer
Trending nowThis is a popular solution!
Chapter 9 Solutions
Bundle: Mechanics Of Materials, Loose-leaf Version, 9th + Mindtap Engineering, 1 Term (6 Months) Printed Access Card
Ch. 9 - The equation of the deflection curve for a...Ch. 9 - The equation of the deflection curve for a simply...Ch. 9 - -3 The deflection curve for a simple beam AB (see...Ch. 9 - The deflection curve for a simple beam AB (sec...Ch. 9 - The deflection curve for a cantilever beam AB (sec...Ch. 9 - The deflection curve for a cantilever beam AB (see...Ch. 9 - A simply supported beam is loaded with a point...Ch. 9 - A I-meter-long, simply supported copper beam (E =...Ch. 9 - A wide-flange beam (W 12 x 35) supports a uniform...Ch. 9 - A uniformly loaded, steel wide-flange beam with...
Ch. 9 - What is the span length L of a uniformly loaded,...Ch. 9 - -6 Calculate the maximum deflection of a uniformly...Ch. 9 - A cantilever beam with a uniform load (see figure)...Ch. 9 - A gold-alloy microbeam attached to a silicon wafer...Ch. 9 - Obtain a formula for the ratio c/maxof the...Ch. 9 - A cantilever beam model is often used to represent...Ch. 9 - B cams AB and CDE are connected using rigid link...Ch. 9 - -12 Derive the equation of the deflection curve...Ch. 9 - -13 Derive the equation of the deflection curve...Ch. 9 - -14 A cantilever beam AB supporting a triangularly...Ch. 9 - A cantilever beam has a length L = 12 ft and a...Ch. 9 - A simple beam with an overhang is subjected to d...Ch. 9 - -17 A cantilever beam AB is acted upon by a...Ch. 9 - -18 The beam shown in the figure has a sliding...Ch. 9 - -19 Derive the equations of the deflect ion curve...Ch. 9 - -20 Derive the equations of the deflection curve...Ch. 9 - -21 Derive the equations of the deflection curve...Ch. 9 - -22 Derive the equations of the deflection curve...Ch. 9 - -23 The beam shown in the figure has a sliding...Ch. 9 - -1 Derive the equation of the deflection curve for...Ch. 9 - -2 A simple beam AB is subjected to a distributed...Ch. 9 - -3 The simple beam AB shown in the figure has...Ch. 9 - -4 A beam with a uniform load has a sliding...Ch. 9 - -5 The distributed load acting on a cantilever...Ch. 9 - -6 A cantilever beam .4B is subjected to a...Ch. 9 - -7 A beam on simple supports is subjected to a...Ch. 9 - Derive the equation of the deflection curve for...Ch. 9 - -9 Derive the equations of the deflection curve...Ch. 9 - -10 Derive the equations of the deflection curve...Ch. 9 - A simply supported beam (E = 1600 ksi) is loaded...Ch. 9 - A simply supported beam (E = 12 GPa) carries a...Ch. 9 - Copper beam AB has circular cross section with a...Ch. 9 - Beam ABC is loaded by a uniform load q and point...Ch. 9 - A cantilever beam of a length L = 2.5 ft has a...Ch. 9 - A cantilever beam carries a trapezoidal...Ch. 9 - -5-7 A cantilever beam AB carries three equalaly...Ch. 9 - A simple beam AB supports five equally spaced...Ch. 9 - The cantilever beam AB shown in the figure has an...Ch. 9 - Beam ACE hangs from two springs, as shown in the...Ch. 9 - What must be the equation y =f(x) of the axis of...Ch. 9 - -12 Determine the angle of rotation Band...Ch. 9 - The cantilever beam ACE shown in the figure has...Ch. 9 - A cantilever beam is subjected to load P at...Ch. 9 - Use the method of superposition to find the angles...Ch. 9 - Repeat Problem 9,5-15 for the anti-symmetric...Ch. 9 - A cantilever beam is subjected to a quadratic...Ch. 9 - A beam ABCD consisting of a simple span BD and an...Ch. 9 - A horizontal load P acts at end C of the bracket...Ch. 9 - A beam ABC having flexural rigidity EI = 75 kN irT...Ch. 9 - Determine the angle of rotation 0Band deflectionCh. 9 - -22 A simple beam AB supports a uniform load of...Ch. 9 - The overhanging beam A BCD supports two...Ch. 9 - A thin metal strip of total weight W and length L...Ch. 9 - An overhanging beam ABC with flexural rigidity EI...Ch. 9 - A beam A BCD rests on simple supports at B and C...Ch. 9 - The compound beam ABC shown in the figure has a...Ch. 9 - A compound beam ABC DE (see figure) consists of...Ch. 9 - A steel beam ABC is simply supported at A and held...Ch. 9 - -30. Calculate the deflection at point C of a beam...Ch. 9 - Compound beam ABC is loaded by point load P = 1.5...Ch. 9 - The compound beam shown in the figure consists of...Ch. 9 - -33 Find the horizontal deflection hand vertical...Ch. 9 - The fr a me A BCD shown in the heure is squeezed...Ch. 9 - A framework A BCD is acted on by counterclockwise...Ch. 9 - A framework A BCD is acted on by force P at 2L/3...Ch. 9 - A beam ABCDE has simple supports at B and D and...Ch. 9 - A frame ABC is loaded at point C by a force P...Ch. 9 - The wing of a large commercial jet is represented...Ch. 9 - The wing of a small plane is represented by a...Ch. 9 - Find an expression for required moment MA(in terms...Ch. 9 - Find an expression for required moment MA(in terms...Ch. 9 - Find required distance d (in terms of L) so that...Ch. 9 - A cantilever beam has two triangular loads as...Ch. 9 - -1 A cantilever beam AB is subjected to a uniform...Ch. 9 - The load on a cantilever beam AB has a triangular...Ch. 9 - A cantilever beam AB is subjected to a...Ch. 9 - Determine the angle of rotation BBand the...Ch. 9 - -5 Calen1ate the deflections S 3a ndCh. 9 - A cantileverbeam^Cßsupportstwo concentrated loads...Ch. 9 - Obtain formulas for the angle of rotation 0Aat...Ch. 9 - A simple beam AB supports two concentrated loads P...Ch. 9 - A simple beam AB is subjected to a load in the...Ch. 9 - -10 The simple beam AB shown in the figure...Ch. 9 - A simple beam AB is subjected to couples M0and 2A0...Ch. 9 - The cantilever beam ACB shown in the figure has...Ch. 9 - The cantilever beam ACB shown in the figure...Ch. 9 - Beam ACB hangs from two springs, as shown in the...Ch. 9 - -4 A simple beam ABCD has moment of inertia I near...Ch. 9 - A beam ABC has a rigid segment from A to B and a...Ch. 9 - A simple beam ABC has a moment of inertia 1,5 from...Ch. 9 - The tapered cantilever beam AB shown in the figure...Ch. 9 - The tapered cantilever beam AB shown in the figure...Ch. 9 - A tapered cantilever beam A B supports a...Ch. 9 - A tapered cantilever beam AB supports a...Ch. 9 - Repeat Problem 97-10, but now use the tapered...Ch. 9 - A simple beam ACE is constructed with square cross...Ch. 9 - A uniformly loaded simple beam AB (see figure) of...Ch. 9 - A simple beam AB of length L supports a...Ch. 9 - A propped cantilever beam AB of length L and with...Ch. 9 - A simple beam AB of length L is subjected to loads...Ch. 9 - A beam ABC with simple supports at A and B and an...Ch. 9 - A simple beam ACB supporting a uniform load q over...Ch. 9 - The frame shown in the figure consists of a beam...Ch. 9 - A simple beam AB of length L is loaded at the...Ch. 9 - The simple beam shown in the figure supports a...Ch. 9 - An overhanging beam ABC supports a concentrated...Ch. 9 - The cantilever beam shown in the figure supports a...Ch. 9 - A simple beam ACB supports a uniform load of...Ch. 9 - A cantilever beam ACB supports two concentrated...Ch. 9 - The cantilever beam A CB shown in the hgure is...Ch. 9 - The frame A BC support s a concentrated load P at...Ch. 9 - A simple beam ABC DE supports a uniform load of...Ch. 9 - An overhanging beam ABC is subjected to a couple...Ch. 9 - An overhanging beam ABC rests on a simple support...Ch. 9 - A symmetric beam A BCD with overhangs at both ends...Ch. 9 - A heavy object of weight W is dropped onto the...Ch. 9 - An object of weight Wis dropped onto the midpoint...Ch. 9 - A cantilever beam AB of length L = 6 It is...Ch. 9 - A weight W = 20 kN falls through a height h = 1,0...Ch. 9 - A weight W = 4000 lb falls through a height h =...Ch. 9 - An overhanging beam ABC with a rectangular cross...Ch. 9 - A heavy flywheel rotates at an angular speed m...Ch. 9 - A simple beam AB of length L and height /;...Ch. 9 - A cantilever beam JA of length Land height/; (see...Ch. 9 - An overhanging beam ABC of height h has a sliding...Ch. 9 - A simple beam AB of length L and height h (see...Ch. 9 - Beam AB has an elastic support kR at A, pin...
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
- The tapered cantilever beam AB shown in the figure has a solid circular cross section. The diameters at the ends A and B are dAand dB= 2dA, respectively. Thus, the diameter d and moment of inertia / at distance v from the free end are, respectively, in which IAis the moment of inertia at end A of the beam. Determine the equation of the deflection curve and the deflection SAat the free end of the beam due to the load P.arrow_forwardA tapered cantilever beam A B supports a concentrated load P at the free end (see figure). The cross sections of the beam are rectangular with constant width A, depth d Aat support A, and depth ds= ^dJ2 at the support. Thus, the depth d and moment of inertia / at distance x from the free end are, respectively, in which / 4 is the moment of inertia at end A of the beam. Determine the equation of the deflection curve and the deflection S 4at the free end of the beam due to the load P.arrow_forward-1 through 5.10-6 A wide-flange beam (see figure) is subjected to a shear force V. Using the dimensions of the cross section, calculate the moment of inertia and then determine the following quantities: The maximum shear stress tinixin the web. The minimum shear stress rmin in the web. The average shear stress raver (obtained by dividing the shear force by the area of the web) and the ratio i^/t^ The shear force carried in the web and the ratio K b/K. Note: Disregard the fillets at the junctions of the web and flanges and determine all quantities, including the moment of inertia, by considering the cross section to consist of three rectangles. 5.10-2 Dimensions of cross section: b = 180 mm, v = 12 mm, h = 420 mm, i = 380 mm, and V = 125 kN.arrow_forward
- The beam AB shown in the figure is simply supported at A and B and supported on a spring of stiffness k at its midpoint C. The beam has flexural rigidity EI and length IL. What should be the stiffness k of the spring in order that the maximum bending moment in the beam (due to the uniform load) will have the smallest possible value?arrow_forwardA beam with a channel section is subjected to a bending moment M having its vector at an angle 0 to the 2 axis (see figure). Determine the orientation of the neutral axis and calculate the maximum tensile stress et and maximum compressive stress ecin the beam. Use the following data: C 8 × 11.5 section, M = 20 kip-in., tan0=l/3. See Table F-3(a) of Appendix F for the dimensions and properties of the channel section.arrow_forward-1 through 5.10-6 A wide-flange beam (see figure) is subjected to a shear force V. Using the dimensions of the cross section, calculate the moment of inertia and then determine the following quantities: The maximum shear stress tinixin the web. The minimum shear stress rmin in the web. The average shear stress raver (obtained by dividing the shear force by the area of the web) and the ratio i^/t^ The shear force carried in the web and the ratio V^tV. Noie: Disregard the fillets at the junctions of the web and flanges and determine all quantities, including the moment of inertia, by considering the cross section to consist of three rectangles. 5.10-3 Wide-flange shape, W 8 x 28 (see Table F-L Appendix F); V = 10 karrow_forward
- -1 through 5.10-6 A wide-flange beam (see figure) is subjected to a shear force V. Using the dimensions of the cross section, calculate the moment of inertia and then determine the following quantities: The maximum shear stress tinixin the web. The minimum shear stress rmin in the web. The average shear stress raver (obtained by dividing the shear force by the area of the web) and the ratio i^/t^ The shear force carried in the web and the ratio V^tV. Note: Disregard the fillets at the junctions of the web and flanges and determine all quantities, including the moment of inertia, by considering the cross section to consist of three rectangles. 5.10-4 Dimensions of cross section: b = 220 mm, f = 12 mm, h = 600 mm, hx= 570 mm, and V = 200 kN.arrow_forward-1 through 5.10-6 A wide-flange beam (see figure) is subjected to a shear force V. Using the dimensions of the cross section, calculate the moment of inertia and then determine the following quantities: The maximum shear stress tinixin the web. The minimum shear stress rmin in the web. The average shear stress raver (obtained by dividing the shear force by the area of the web) and the ratio i^/t^. The shear force i^/t^ carried in the web and the ratio V^tV. Note: Disregard the fillets at the junctions of the web and flanges and determine all quantities, including the moment of inertia, by considering the cross section to consist of three rectangles. 5.10-6 Dimensions of cross section: b = 120 mm, a = 7 mm, h = 350 mm, hx= 330 mm, and K=60kN.arrow_forwardA tapered cantilever beam A B of length L has square cross sections and supports a concentrated load P at the free end (sec figure part a). The width and height of the beam vary linearly from kAat the free end to hBat the fixed end. Determine the distance.y from the free end A to the cross section of maximum bending stress if hE= 3h4, What is the magnitude ffœai of the maximum bending stress? What is the ratio of the maximum stress to the largest stress B at the support? Repeat part (a) if load P is now applied as a uniform load of intensity q = P/L over the entire beam, A is restrained by a roller support, and B is a sliding support (see figure part b).arrow_forward
- A simple beam ACE is constructed with square cross sections and a double taper (see figure). The depth of the beam at the supports is dAand at the midpoint is dc= 2d 4. Each half of the beam has length L. Thus, the depth and moment of inertia / at distance x from the left-hand end are, respectively, in which IAis the moment of inertia at end A of the beam. (These equations are valid for .x between 0 and L, that is, for the left-hand half of the beam.) Obtain equations for the slope and deflection of the left-hand half of the beam due to the uniform load. From the equations in part (a), obtain formulas for the angle of rotation 94at support A and the deflection Scat the midpoint.arrow_forward-1 through 5.10-6 A wide-flange beam (see figure) is subjected to a shear force V. Using the dimensions of the cross section, calculate the moment of inertia and then determine the following quantities: The maximum shear stress tinixin the web. The minimum shear stress rmin in the web. The average shear stress t (obtained by dividing the shear force by the area of the web) and the ratio tmax/taver. The shear force Vweb/V carried in the web and the Vweb/V. Note: Disregard the fillets at the junctions of the web and flanges and determine all quantities, including the moment of inertia, by considering the cross section to consist of three rectangles. 5.10-1 Dimensions of cross section: b = 6 in,, ï = 0.5 in., h = 12 in,, A, = 10.5 in., and V = 30 k.arrow_forward-22 Derive the equations of the deflection curve for a simple beam AB with a distributed load of peak intensity q0acting over the left-hand half of the span (see figure). Also, determine the deflection cat the midpoint of the beam. Use the second-order differential equation of the deflection curve.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