For points not on a surace of the beam, we can use Omax /c = -o/y Part A - Moment Required to Produce a Given Stress to rewrite the flexure formula in the more general form The cross-section of a wooden, built-up beam is shown below. The dimensions are L = 220 mm and w = 40 mm My (Figure 1) Determine the magnitude of the moment M that must be applied to the beam to create a compressive stress of op = 30 MPa at point D. Also calculate the maximum stress developed in the beam. The moment M is applied in the vertical plane about the geometric center of the Figure < 1 of 3 beam. Express your answers, separated by a comma, to three significant figures. > View Available Hint(s) 'D vec ? kN-m, MPa M =, Omax =

For points not on a surace of the beam, we can use Omax /c = -o/y Part A - Moment Required to Produce a Given Stress to rewrite the flexure formula in the more general form The cross-section of a wooden, built-up beam is shown below. The dimensions are L = 220 mm and w = 40 mm My (Figure 1) Determine the magnitude of the moment M that must be applied to the beam to create a compressive stress of op = 30 MPa at point D. Also calculate the maximum stress developed in the beam. The moment M is applied in the vertical plane about the geometric center of the Figure < 1 of 3 beam. Express your answers, separated by a comma, to three significant figures. > View Available Hint(s) 'D vec ? kN-m, MPa M =, Omax =

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 6.5.7P: The cross section of a steel beam is constructed of a W 18 × 71 wide-flange section with a 6 in. ×...

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The cross section of a composite beam made of aluminum and steel is shown in the figure. The moduli of elasticity are TA= 75 GPa and Es= 200 GPa. Under the action of a bending moment that produces a maximum stress of 50 M Pa in the aluminum, what is the maximum stress xs in the steel? If the height of the beam remains at 120 mm and allowable stresses in steel and aluminum are defined as 94 M Pa and 40 M Pa, respectively, what heights h and h. arc required for aluminum and steel, respectively, so that both steel and aluminum reach their allowable stress values under the maximum moment?
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?
A wood beam reinforced by an aluminum channel section is shown in the figure. The beam has a cross section of dimensions 150 mm x 250 mm, and the channel has a uniform thickness of 6.5 mm. If the allowable stresses in the wood and aluminum are 8 M Pa and 38 M Pa, respectively, and if their moduli of elasticity are in the ratio 1 to 6, what is the maximum allowable bending moment for the beam?
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 beam having a cross section in the form of an un symmetric wide-flange shape (sec figure) is subjected to a negative bending moment acting about the 2 axis. Determine the width b of the top flange in order that the stresses at the top and bottom of the beam will be in the ratio 4:3, respectively.
A cantilever beam(Z, = 6 ft) with a rectangular cross section (/> = 3.5 in., h = 12 in.) supports an upward load P = 35 kips at its free end. (a) Find the state of stress ((7T, o^., and r in ksi) on a plane-stress element at L/2 that is i/ = 8 in. up from the bottom of the beam. Find the principal normal stresses and maximum shear stress. Show these stresses on sketches of properly oriented elements. (b) Repeat part (a) if an axial compressive centroidal load N = 40 kips is added at B
An aluminum pole for a street light weighs 4600 N and supports an arm that weighs 660 N (see figure). The center of gravity of the arm is 1.2 m from the axis of the pole, A wind force of 300 N also acts in the (y) direction at 9 m above the base. The outside diameter of the pole (at its base) is 225 mm, and its thickness is 18 mm. Determine the maximum tensile and compressive stresses o, and e1., respectively, in the pole (at its base) due to the weights and the wind force.
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.)
Solve the preceding problem for a box beam with dimensions h = 0.5 m, h = 0.18 m, and t = 22 mm. The yield stress of the steel is 210 MPa.
An angle section with equal legs is subjected to a bending moment M having its vector directed along the 1—1 axis, as shown in the figure. Determine the orientation of the neutral axis and calculate the maximum tensile stress e1 and maximum compressive stress et if the angle is an L 6 × 6 × 3/4 section and M = 20 kip-in. See Table F-4(a) of Appendix F for the dimensions and properties of the angle section.
A wood beam AB on simple supports with span length equal to 10 ft is subjected to a uniform load of intensity 125 lb/ft acting along the entire length of the beam, a concentrated load of magnitude 7500 lb acting at a point 3 ft from the right-hand support, and a moment at A of 18,500 ft-lb (sec figure). The allowable stresses in bending and shear, respectively, are 2250 psi and 160 psi. From the table in Appendix G, select the lightest beam that will support the loads (disregard the weight of the beam). Taking into account the weight of the beam (weight density = 35 lb/ft3), verify that the selected beam is satisfactory, or if it is not, select a new beam.
The cross section of a steel beam is shown in the figure. This beam is subjected to a bending moment M having its vector at an angle 8 to the - axis. Determine the orientation of the neutral axis and calculate the maximum tensile stress tiand maximum compressive stress tcin the beam. Assume that e = 22.5° and M = 4.5 kN · m. Use cross-sectional properties Ix=93.14 × 106 mm4, Iy= 152.7 X 10e mm4, and 9 = 27.3º.