The dimensions of a rectangular beam are limited to b = 300 mm and effective depth, d = 700 mm. Using f’c = 28 MPa, long bar fy = 415 MPa, calculate the required amount of tensile reinforcement so that a tensile strain of 0.005 is attained under a sustained ultimate bending moment of 1,200 kN.m. Compression bars centroid is 70 mm from beam edge. 4,387 3,839 6,180 5.353

The dimensions of a rectangular beam are limited to b = 300 mm and effective depth, d = 700 mm. Using f’c = 28 MPa, long bar fy = 415 MPa, calculate the required amount of tensile reinforcement so that a tensile strain of 0.005 is attained under a sustained ultimate bending moment of 1,200 kN.m. Compression bars centroid is 70 mm from beam edge. 4,387 3,839 6,180 5.353

Mechanics of Materials (MindTap Course List)

9th Edition

ISBN:9781337093347

Author:Barry J. Goodno, James M. Gere

Publisher:Barry J. Goodno, James M. Gere

Chapter6: Stresses In Beams (advanced Topics)

Section: Chapter Questions

Problem 6.2.15P: -15 A composite beam is constructed froma wood beam (3 in. x 6 in.) and a steel plate (3 in, wide)....

See similar textbooks

Similar questions

A square tube section has side dimension of 20 in. arid thickness of 0.5 in. If the section is used for a 10-ft-long beam subjected to 1250 kip-in, torque at both ends, calculate the maximum shear stress and the angle of twist between the ends. Use G = 11,600 ksi.
The Z-section of Example D-7 is subjected to M = 5 kN · m, as shown. Determine the orientation of the neutral axis and calculate the maximum tensile stress c1and maximum compressive stress ocin the beam. Use the following numerical data: height; = 200 mm, width ft = 90 mm, constant thickness a = 15 mm, and B = 19.2e. Use = 32.6 × 106 mm4 and I2= 2.4 × 10e mm4 from Example D-7
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.
A beam of wide-flange shape, W 8 x 28, has the cross section shown in the figure. The dimensions are b = 6.54 in., h = 8.06 in., fw = 0.285 in., and tf = 0.465 in.. The loads on the beam produce a shear force V = 7.5 kips at the cross section under consideration. Use center line dimensions to calculate the maximum shear stress raiaxin the web of the beam. Use the more exact analysis of Section 5,10 in Chapter 5 to calculate the maximum shear stress in the web of the beam and compare it with the stress obtained in part .
-15 A composite beam is constructed froma wood beam (3 in. x 6 in.) and a steel plate (3 in, wide). The wood and the steel are securely fastened to act as a single beam. The beam is subjected to a positive bending moment M. = 75 kip-in. Calculate the required thickness of the steel plate based on the following limit states: Allowable compressive stress in the wood = 2 ksi Allowable tensile stress in the wood = 2 ksi Allowable tensile stress in the steel plate = 16 ksi Assume that Ew= 1,500 ksi and es= 30,000 ksi.
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 C 200 x 17.1 channel section has an angle with equal legs attached as shown; the angle serves as a lintel beam. The combined steel section is subjected to a bending moment M having its vector directed along the z axis, as shown in the figure. The cent roi d C of the combined section is located at distances xtand ycfrom the centroid (C1) of the channel alone. Principal axes yl and yvare also shown in the figure and properties Ix1,Iy1and 0pare given. Find the orientation of the neutral axis and calculate the maximum tensile stress exand maximum compressive stress if the angle is an L 76 x 76 x 6.4 section and M = 3.5 kN - m. Use the following properties for principal axes for the combined section:/^, = 18.49 X 106 nrai4,/;| = 1.602 X 106 mm4, ep= 7.448*(CW),_r£ = 10.70 mm,andvf= 24.07 mm.
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.
A cantilever beam of length L = 2 m supports a load P = 8,0 kN (sec figure). The beam is made of wood with cross-sectional dimensions 120 mm x 200 mm. Calculate the shear stresses due to the load/"at points located 25 mm, 50 mm, 75 mm, and 100 mm from the top surface of the beam. From these results, plot a graph showing the distribution of shear stresses from top to bottom of the beam.
A steel plate (called a cover ploie) having cross-sectional dimensions 6,0 in. × 0.5 in. is welded along the full length of the bottom flange of a W 12 × 50 wide-flange beam (sec figure, which shows the beam cross section). What is the percent increase in the smaller section modulus (as compared to the wide-flange beam alone)?
The cross section of a steel beam is constructed of a W 18 × 71 wide-flange section with a 6 in. × 1/2 in, cover plate welded to the top flange and a C 10 × 30 channel section welded to the bottom flange. This beam is subjected to a bending moment M having its vector at an angle tc to the - axis (see figure). Determine the orientation of the neutral axis and calculate the maximum tensile stress oxand maximum compressive stress tcin the beam. Assume that S = 30e and M = 75 kip-in. Note: The cross-sectional properties of this beam were computed in Examples D-2 and D-5.
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?