Mechanics of Materials, SI Edition
9th Edition
ISBN: 9781337093354
Author: Barry J. Goodno, James M. Gere
Publisher: Cengage Learning
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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.
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Chapter 9 Solutions
Mechanics of Materials, SI Edition
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 distrib uted...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 verti cal...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...
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