Consider the shaft shown (Figure 1) that has a diameter d = 5.3 cm . The length of each segment is L = 2.2 m and the loads P = 1.5 kN are applied horizontally and vertically as shown. The bearings do not exert a moment on the shaft. Use the following process to calculate the maximum bending stress on a section through the shaft at C. Part A Moment due to the horizontal load Since the section is circular, use the y and z-axes as the principal axes. What is the magnitude of the moment about the z-axis at point C due to effects of the the horizontal load? Express your answer with appropriate units to three signficant figures. View Available Hint(s) |M₂| = Submit μA Value Part B - Moment due to the vertical load Submit O What is the magnitude of the moment about the y-axis at point C due to the effects of the vertical load? Express your answer with appropriate units to three significant figures. ► View Available Hint(s) Units μA |M₂| = Value ? Units ?

Consider the shaft shown (Figure 1) that has a diameter d = 5.3 cm . The length of each segment is L = 2.2 m and the loads P = 1.5 kN are applied horizontally and vertically as shown. The bearings do not exert a moment on the shaft. Use the following process to calculate the maximum bending stress on a section through the shaft at C. Part A Moment due to the horizontal load Since the section is circular, use the y and z-axes as the principal axes. What is the magnitude of the moment about the z-axis at point C due to effects of the the horizontal load? Express your answer with appropriate units to three signficant figures. View Available Hint(s) |M₂| = Submit μA Value Part B - Moment due to the vertical load Submit O What is the magnitude of the moment about the y-axis at point C due to the effects of the vertical load? Express your answer with appropriate units to three significant figures. ► View Available Hint(s) Units μA |M₂| = Value ? Units ?

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 6.5.13P: A cold-formed steel section is made by folding a steel plate to form a structural section such as...

See similar textbooks

Similar questions

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.
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 etand maximum compressive stress te if the section is an L 152 × 152 × 127 section and M = 2.5 kN · m. See Table F-4(b) of Appendix F for the dimensions and properties of the angle section.
The cross section of a sign post of constant thickness is shown in the figure. Derive the formula for the distance e from the cent crime of the wall of the post to the shear center S: where I2. = moment of inertia about the z axis. Also, compare this formula with that given in Problem 6.9-11 for the special case of ß = 0 here and a = h/2 in both formulas.
A built-Lip I-section steel beam with channels attached to the flanges (sec Figure part a) is simply supported at the ends. Two equal and oppositely directed bending moments I/2, act at the ends of the beam, so the beam is in pure bending. The moments act in plane mm. which is oriented at an angle a to (a) Determine the orientation of the neutral axis and calculate the maximum (ensile stress on till due to the moments Ma. (b) Repeat pan (a) if (he channels now have their flanges pointing away from the beam flange, as shown in the figure part b. Data for the beam are S 6 x 12.5 section with C 4 x 5.4 sections attached to the Hanges, .V/2— 45 kip-in., and a = 40°. See Tables F-2(a) and F-3(a) of Appendix F l or the dimensions and properlies of the S and shapes.
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.
A cold-formed steel section is made by folding a steel plate to form a structural section such as that shown in the figure. This beam is subjected to bending moment M = 2 kip-in, at angle 0 = 10º to the z axis. Find the centroid and the orientation of the neutral axis. Find flexural normal stresses at points A and B (see figure). Use the flexure formula based on principal axes and then confirm your solution using the general flexure formula. Hint: the plate is thin so use centerline dimensions.
A beam having a cross section in the form of a channel (sec figure) is subjected to a bending moment acting about the z axis. Calculate the thickness t of the channel in order that the bending stresses at the top and bottom of the beam will be in the ratio 7:3, respectively.
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?
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.
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.
Determine the maximum tensile stress (7, (due to pure bending about a horizontal axis through C by positive bending moments (B) for beams having cross sections as follows (see figure). A semicircle of diameter d. An isosceles trapezoid with bases (b) = b and f2 = 4W3 and altitude h. A circular sector with a = ît/3 and r = d/2.
A thin-walled rectangular tube has uniform thickness t and dimensions a x b to the median line of the cross section (see figure). How does the shear stress in the tube vary with the ratio = a/b if the total length Lmof the median line of the cross section and the torque T remain constant? From your results, show that the shear stress is smallest when the tube is square (ß = 1).