A simply supported beam of length 4 m, is subjected to an Uniformly distributed load of 22 kN/m for entire span. has a hollow rectangular cross section of outer width 45 mm and outer depth of 90 mm with the wall thickness of 3mm. Find (i) The maximum bending moment, (ii)Bending stress induced, (iii) Radius of curvature, (iv) Flexural rigidity. Take E as 150 GPa. The maximum bending moment (in Nm) = Maximum Bending stress induced (in MPa) = Radius of curvature (in m) = Flexural Rigidity of the beam (in Nm2) :

A simply supported beam of length 4 m, is subjected to an Uniformly distributed load of 22 kN/m for entire span. has a hollow rectangular cross section of outer width 45 mm and outer depth of 90 mm with the wall thickness of 3mm. Find (i) The maximum bending moment, (ii)Bending stress induced, (iii) Radius of curvature, (iv) Flexural rigidity. Take E as 150 GPa. The maximum bending moment (in Nm) = Maximum Bending stress induced (in MPa) = Radius of curvature (in m) = Flexural Rigidity of the beam (in Nm2) :

Mechanics of Materials (MindTap Course List)

9th Edition

ISBN:9781337093347

Author:Barry J. Goodno, James M. Gere

Publisher:Barry J. Goodno, James M. Gere

Chapter5: Stresses In Beams (basic Topics)

Section: Chapter Questions

Problem 5.13.4P: A rectangular beam with semicircular notches, as shown in part b of the figure, has dimensions h =...

See similar textbooks

Similar questions

.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?
A rectangular beam with semicircular notches, as shown in part b of the figure, has dimensions h = 0,88 in. and h1 = 0.80 in. The maximum allowable bending stress in the metal beam is emax = 60 ksi, and the bending moment is M = 600 lb-in. Determine the minimum permissible width bminof the beam.
A two-axle carriage that is part of an over head traveling crane in a testing laboratory moves slowly across a simple beam AB (sec figure). The load transmitted to the beam from the front axle is 2200 lb and from the rear axle is 3800 lb. The weight of the beam itself may be disregarded. Determine the minimum required section modulus S for the beam if the allowable bending stress is 17,0 ksi, the length of the beam is 18 ft, and the wheelbase of the carriage is 5 ft. Select the most economical I-beam (S shape) from Table F-2(a), Appendix F.
The cross section of a rectangular beam having a width b and height h is shown in part a of the figure. For reasons unknown to the beam designer, it is planned to add structural projections of width b/9 and height d/9 the top and bottom of the beam (see part b of the figure). For what values of d is the bending-moment capacity of the beam increased? For what values is it decreased?
A simple beam with a W 10 x 30 wide-flange cross section supports a uniform load of intensity q = 3.0 kips/ft on a span of length L = 12 ft (sec figure). The dimensions of the cross section are q = 10.5 in., b = 5.81 in., t1= 0.510 in., and fw = 0.300 in. Calculate the maximum shear stress tjuly on cross section A—A located at distance d = 2.5 ft from the end of the beam. Calculate the shear stress rat point Bon the cross section. Point B is located at a distance a = 1.5 in. from the edge of the lower flange.
The hollow box beam shown in the figure is subjected to a bending moment M of such magnitude that the flanges yield but the webs remain linearly elastic. (a) Calculate the magnitude of the moment M if the dimensions of the cross section are A = 15 in., A] = 12.75 in., h = 9 in., and ey =7.5 in. Also, the yield stress is eY = 33 ksi. (b) What percent of the moment M is produced by the elastic core?
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.
A frame ABCD is constructed of steel wide-flange members (W8 x 21; E = 30 x ID6 psi) and subjected to triangularly distributed loads of maximum intensity q0acting along the vertical members (see figure). The distance between supports is L = 20 ft and the height of the frame is h = 4 ft. The members are rigidly connected at B and C. Calculate the intensity of load q0 required to produce a maximum bending moment of 80 kip-in. in the horizontal member BC. If the load q0 is reduced to one-half of the value calculated in part (a), what is the maximum bending moment in member BC? What is the ratio of this moment to the moment of 80 kip-in. in part (a)?
A simple beam A B of a span length L = 24 ft is subjected to two wheel loads acting at a distance d = 5 ft apart (see figure). Each wheel transmits a load P = 3.0 kips, and the carriage may occupy any position on the beam. Determine the maximum bending stress Gmaxdue to the wheel loads if the beam is an I-beam having section modulus S = 16.2 in3. If d = 5 ft. Find the required span length L to reduce the maximum stress in part (a) to 18 ksi. If L = 24 ft, Find the required wheel spacing s to reduce the maximum stress in part (a) to 18 ksi.
A sandwich beam having steel faces enclosing a plastic core is subjected to a bending moment M = 5 kN · m. The thickness of each steel face is 1 = 3 mm with modulus of elasticity E = 200 GPa, The height of the plastic core is hp= 140 mm, and its modulus of elasticity is Ep= 800 MPa. The overall dimensions of the beam are h = 146 mm and h = 175 mm. Using the transformed-section method, determine the maximum tensile and compressive stresses in the faces and the core.
Two identical, simply supported beams AB and CD are placed so that they cross each other at their midpoints (sec figure). Before the uniform load is applied, the beams just touch each other at the crossing point. Determine the maximum bending moments (mab)max* and (MCD)max beams AB and CD, respectively, due to the uniform load if the intensity of the load is q = 6.4 kN/m and the length of each beam is L = 4 m.
The cross section of a sand wie h beam consisting of aluminum alloy faces and a foam core is shown in the figure. The width b of the beam is 8.0 in, the thickness I of the faces is 0.25 in., and the height hcof the core is 5.5 in. (total height h = 6.0 in). The moduli of elasticity are 10.5 × 106 psi for the aluminum faces and 12.000 psi for the foam core. A bending moment M = 40 kip-in. acts about the z axis. Determine the maximum stresses in the faces and the core using (a) the general theory for composite beams and (b) the approximate theory for sandwich beams.