A thin beam with a solid rectangular cross-section is loaded as shown in Figure Q7 below. W W L/3 L/3 L/3 Figure Q7 Consider the following statemonts and solect which combination correctly describes the bending moment diagram for this boam, along its length using the sign conventions provided in lectures. i ltis symmetrical. ii. It has a value of zero at the mid-point. i it has a negative valuo for the entire length of the beam. iv. It is described by a quadratic (2nd order) function. O a li and i. are both correct. Obili. and iv. are both correct. Oci. and i. are both correct. O d.i. and iv. are both correct. Oeili and iv. are both correct. Of. None of the provided answers are correct. OBi, and i. are both correct.

A thin beam with a solid rectangular cross-section is loaded as shown in Figure Q7 below. W W L/3 L/3 L/3 Figure Q7 Consider the following statemonts and solect which combination correctly describes the bending moment diagram for this boam, along its length using the sign conventions provided in lectures. i ltis symmetrical. ii. It has a value of zero at the mid-point. i it has a negative valuo for the entire length of the beam. iv. It is described by a quadratic (2nd order) function. O a li and i. are both correct. Obili. and iv. are both correct. Oci. and i. are both correct. O d.i. and iv. are both correct. Oeili and iv. are both correct. Of. None of the provided answers are correct. OBi, and i. are both correct.

Mechanics of Materials (MindTap Course List)

9th Edition

ISBN:9781337093347

Author:Barry J. Goodno, James M. Gere

Publisher:Barry J. Goodno, James M. Gere

Chapter9: Deflections Of Beams

Section: Chapter Questions

Problem 9.7.7P: The tapered cantilever beam AB shown in the figure has a thin-walled, hollow circular cross sections...

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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.
.2 A ligmio.irc ii supported by two vorlical beams consistins: of thin-walled, tapered circular lubes (see ligure part at. for purposes of this analysis, each beam may be represented as a cantilever AB of length L = 8.0 m subjected to a lateral load P = 2.4 kN at the free end. The tubes have a constant thickness ; = 10.0 mm and average diameters dA = 90 mm and dB = 270 mm at ends A and B, re s pec lively. Because the thickness is small compared to the diameters, the moment of inerlia at any cross section may be obtained from the formula / = jrrf3;/8 (see Case 22, Appendix E); therefore, the section modulus mav be obtained from the formula S = trdhlA. (a) At what dislance A from the free end docs the maximum bending stress occur? What is the magnitude trllul of the maximum bending stress? What is the ratio of the maximum stress to the largest stress (b) Repeat part (a) if concentrated load P is applied upward at A and downward uniform load q {-x) = 2PIL is applied over the entire beam as shown in the figure part b What is the ratio of the maximum stress to the stress at the location of maximum moment?
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