HhVbThe internal shear force V at a certain section of a beam is 60 kN.m. If the beam has a cross-section shown in the figure where h=243 mm, a=112mm, b=182 mm, c=10,8 mm and t=14,7 mm,Determine the location of the centroid of the cross-section in the y-axis from the bottom (mm).

Given: h= 243 mm a= 112 mm b= 182 mm c= 10.8 mm t= 14.7 mm To determine: The location of the…

Answered: Determine the location of the centroid…

Engineering

Mechanical Engineering

Determine the location of the centroid of the cross-section in the y-axis from the bottom (mm).

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 6.10.1P: Determine the shape factor f for a cross section in the shape of a double trapezoid having the...

See similar textbooks

Similar questions

Find expressions for shear force V and moment M at v = L/2 of beam AB in structure (a). Express V and M in terms of peak load intensity q0and beam length variable L. Repeat for structure (b) but find Fand M at m id-span of member BC.
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.
.10 A built-up bourn supporting a condominium balcony is made up of a structural T (one half of a W 200 x 31.3) for the top flange and web and two angles (2 L 2 / b / 6.4. long legal back-lo-backl lot the bottom flange and web. as shown. The beam is subjected to a bending moment .1/ having its vector at an angle ft lo the z axis (see figure). Determine the or ion ta I ion of the neutral axis and calculate the maximum tensile stress ir, and maximum compressive stress tr. in ".he beam. .Assume that 9 = 30°andM = 15 kN · m. Use the numerical properties: c =4.111mm, c2 =4.169 mm, of = 134 mm, I, = 76 mm, A = 4144 mm 3 =3.88 X 106 mm 4, and = 34.18 X 10 mm 4.
A cylindrical brick chimney of height H weighs w = 825 lb/ft of height (see figure). The inner and outer diameters are d1= 3 ft and d2= 4 ft, respectively. The wind pressure against the side of the chimney is p = 10 lb/ft2 of projected area. Determine the maximum height H if there is to be no tension in the brickwork.
A beam supporting a uniform load of intensity q throughout its length rests on pistons at points A, C and B (sec figure). The cylinders are filled with oil and are connected by a tube so that the oil pressure on each piston is the same. The pistons at A and B have diameter d1and the piston at C has diameter D2. (a) Determine the ratio of d2to d1so that the largest bending moment in the beam is as small as possible. Under these optimum conditions, what is the largest bending moment Mmaxin the beam? What is the difference in elevation between point C and the end supports?
The beam ABC shown in the figure is simply supported at A and B and has an overhang from B to C. The loads consist of a horizontal force P1= 4,0 kN acting at the end of a vertical arm and a vertical force P2= 8.0 kN acting at the end of the overhang, Determine the shear force Fand bending moment M at a cross section located 3,0 m from the left-hand support. Note: Disregard the widths of the beam and vertical arm and use centerline dimensions when making calculations, Find the value of load A that results in V = 0 at a cross section located 2.0 m from the left-hand support. If P2= 8.0 kN, find the value of load P1that results in M = 0 at a cross section located 2,0 m from the left-hand support.
A small dam of a height h = 6 ft is constructed of vertical wood beams AB, as shown in the figure. The wood beams, which have a thickness I = 2.5 in., are simply supported by horizontal steel beams at A and Ä Construct a graph showing the maximum bending stress tram in the wood beams versus the depth d of the water above the lower support at B. Plot the stress0mas(psi) as the ordinate and the depth d(ft) as the abscissa. Note: The weight density y of water equals 62.4 lb/ft3.
A cantilever beam AB having rectangular cross sections with varying width bxand varying height hxis subjected to a uniform load of intensity q (sec figure). If the width varies linearly with x according to the equation hx= bBxiL^ how should the height hxvary as a function of v in order to have a fully stressed beam? (Express hxin terms of the height hBat the fixed end of the beam.)
The cross section of a bimetallic strip is shown in the figure. Assuming that the moduli of elasticity for metals A and B are EA=168 GPa and EB= 90 GPa, respectively, determine the smaller of the two section moduli for the beam. (Recall that section modulus is equal to bending moment divided by maximum bending stress.) In which material does the maximum stress occur?
Determine the shape factor f for a cross section in the shape of a double trapezoid having the dimensions shown in the figure. Also, check your result for the special cases of a rhombus (b1= 0) and a rectangle (b1= b2).
A beam made up all woun equal leg angles is subjected to a bending moment M having its vector .u an angle (i) lo lire axis (see figure paria). (a) For the position shown in lire figure, determine lire orienlalion of lire neulral axis and calculate lire maximum tensile s'av-s ir, and maximum compressive stress (b) The two angles are now inverted and attached back-lo-back lo lorn, a lintel beam that supports two courses of brick facade i see figure part b). Find the new orientation of the neutral axis and calculate the maximum tensile slress r. a::d maximum compressive s'avsrr . in I he beam using 6 = 30° and M = 30 kip-in.
The horizontal beam ABC of an oil-wellpump has the cross section shown in the figure. If thevertical pumping force acting at end C is 9 kips andif the distance from the line of action of that force topoint B is 16 ft, what is the maximum bending stressin the beam due to the pumping force?