6a In Figure Q6, a simply supported 3.50 m long beam (L) has a concentrated point load (F)of 150 kN acting at the mid-point of the beam. The beam has a solid and homogeneousL-shaped cross-section with the following dimensions:h = 125 mm, t = 15 mm and w = 90 mm%3D%3DLoadFABSupportFigure Q6 а)Determine the centroid coordinates (X , ỹ) for the beam section shown in Figure Q6.Give your answer relative to the origin (0) in millimetres (mm) and to twodecimal places.

( x , y ) = ( 24.375 mm , 41.875 mm )

Answered: Determine the centroid coordinates (X ,…

Determine the centroid coordinates (X , ỹ) for the beam section shown in Figure Q6. a) Give your answer relative to the origin (0) in millimetres (mm) and to two decimal places.

Mechanics of Materials (MindTap Course List)

9th Edition

ISBN:9781337093347

Author:Barry J. Goodno, James M. Gere

Publisher:Barry J. Goodno, James M. Gere

Chapter10: Statically Indeterminate Beams

Section: Chapter Questions

Problem 10.3.6P: A cantilever beam of a length L and loaded by a uniform load of intensity q has a fixed support at A...

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 cantilever beam of a length L and loaded by a uniform load of intensity q has a fixed support at A and spring support at B with rotational stiffness kR. A rotation B at B results in a reaction moment MB=kRxB. Find rotation B and displacement Bat end B. Use the second-order differential equation of the deflection curve to solve for displacements at end B.
A square wood platform is 8 ft × 8 ft in area and rests on masonry walls (see figure). The deck of the platform is constructed of 2-in. nominal thickness tongue-and-groove planks (actual thickness 1.5 in.; sec Appendix CL) supported on two S-ft long beams. The beams have 4 in. × (i in. nominal dimensions (actual dimensions 3.5 in. × 5.5 in.). The planks arc designed to support a uniformly distributed load n ( lb/ft" i acting over the entire top surface of the platform. I be allowable bending stress for the planks is 2400 psi and the allowable shear stress is 100 psi. W ben analyzing the planks, disregard their weights and assume that their reactions are uniformly distributed over the top surfaces of the supporting beams. (a) Determine the allowable platform load Mr. (lb/ft2) based upon the bending stress in the planks. (b) Determine the allowable platform load if-. (lb/ft-) based upon the shear stress in the planks. (c) Which of the preceding values becomes the allowable load alolow on the platform? Hints: Use care in constructing the loading diagram for the planks, noting especially that the reactions are distributed loads instead of concentrated loads. Also, note that the maximum shear forces occur at the inside faces of the supporting beams.
A seesaw weighing 3 lb/ft of length is occupied by two children, each weighing 90 lb (see figure). The center of gravity of each child is 8 ft from the fulcrum. The board is 19 ft long, 8 in. wide, and 1.5 in. thick. What is the maximum bending stress in the board?
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.
Figure 1a shows a simply supported beam, AB of length L = 5.6 m, with a uniform distributed load of w = 4.5 kN/m. The shear force diagram is shown below the beam and the cross-section in Figure 1b. The cross section has a constant thickness t = 8.7 mm, the width of the flange is b = 217.5 mm and height of the web is d = 211.41 mm. 1. Determine the position of the neutral axis. 2. Determine the moment of inertia about the neutral axis 3. Determine the maximum shear stress acting on the cross-section
A cantilever beam (with a clamp at x=0 and free at x=L, where L is the length of the beam) is modelled using two flexural elements. A moment, M, is applied at the free end. Which of the following describes the vector of external forces? Note that no other external forces are applied, and the degrees of freedom are defined in the usual order. f = [0 0 0 0 M 0]T f = [0 0 M 0]T f = [0 0 0 0 0 M]T f = [0 0 0 M]T f = [M 0 0 0]T f = [0 M 0 0]T
A simply supported beam of a total length ll is shown in Figure Q5, where point A is supported by a pin connection and point C is supported by a roller support. The concentrated load is P=mgP=mg at the location of l1l1. Note that l1/l=l1/l= 0.65. Determine the shear-force and bending-moment distributions produced in the beam by the concentrated load PP.
3. A 3-meter-long beam is used to support a heavy object. The object has a uniform distributed load of 6 kN/m on the entire beam. The Young’s modulus and moment of inertia of the beam are 200 GPa and 5×105 mm4, respectively. The beam is supported at three positions as shown below. (a) Label the element and node numbers (either on the figure or with a new simple sketch). (b) Determine the slopes at the three support positions of the beam.
The formwork plan with column dimensions 30/60 and 60/30 and beam dimensions 30/60 in the figure below is seen. According to this; a-) To which point is the center of stiffness of the current system close? Why? b-) If the S2 column size is changed to 30/120 in the current system, which two points does the center of stiffness is expected between Why? c-) If the S1 and S2 column sizes are changed to 30/150 in the current system, which two between points? Why?
A cantilever beam with a length of 5 meters and a circular cross-section of diameter 200 mm carriestwo concentrated loads of P1 = 10 kN and P2 = 100 kN at its free end as shown in Figure Q2. Bothloads act through the centroid of the beams cross-section.(i) Determine the maximum bending moment acting on the beam (ii) Develop for the beam, the expressions for the maximum tensile and compressive stressesthrough its depth (iii) Draw a schematic of the maximum stresse distribution through the depth of the beam and fromit and using equations, determine the distance of the neutral axis from the top and bottomsurfaces of the beam
(VI.) In the following figure, a uniform beam of length 6.00 meters is supported by a horizontal cable and a hinge at angle 60.0 degrees, the weight of the beam and the box are 4.00x10^2 and 1.00x10^3 N respectively. Find out a) the tension in the cable, b) the forces the hinge exerts on the beam.