A horizontal beam of length 4 m and mass 9.0 kg has a mass of 3.0 kg and width 0.8 m sitting at the end of the beam (see the following figure). What is the torque due to gravity (in N - m) on the beam-block system about the support at the wall? (Enter the magnitude.) Wall support 0.8 m, 3.0 kg 4 m, 9.0 kg N-m

A horizontal beam of length 4 m and mass 9.0 kg has a mass of 3.0 kg and width 0.8 m sitting at the end of the beam (see the following figure). What is the torque due to gravity (in N - m) on the beam-block system about the support at the wall? (Enter the magnitude.) Wall support 0.8 m, 3.0 kg 4 m, 9.0 kg N-m

Mechanics of Materials (MindTap Course List)

9th Edition

ISBN:9781337093347

Author:Barry J. Goodno, James M. Gere

Publisher:Barry J. Goodno, James M. Gere

Chapter5: Stresses In Beams (basic Topics)

Section: Chapter Questions

Problem 5.12.11P: A cylindrical brick chimney of height H weighs w = 825 lb/ft of height (see figure). The inner and...

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A non prism elk- bar ABC made up of segments AB(length £,, cross-sectional area .Inland BC (length i-,, cross-sectional area A2) is fixed at end A and free al end C (see figure). The modulus of elasticity of the bar is E. A small gap of d intension s exists between the end of the bar and an elastic spring of length Lj and spring constant k3. If bar ABC only (not tin? spring} is subjected to temperature increase A3", determine the following. (a) Write an expression for reaction forces R^ and RDif the elongation of /I BC exceeds gap length s. (b) Find expressions for the displacements of points B and C if the elongation of ABC exceeds gap length s.
.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?
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 fiberglass pipe is lifted by a sling, as shown in the figure. The outerdiameter of the pipe is 6,0 in., its thickness is 0.25 in,, and its weightdensity is 0,053 1b/in3 the length of the pipe is L = 36 ft and the distancebetween lifting points is s = 11 ft.a. Determine the maximum bending stress in the pipe due to its ownweight,b. Find the spacing s between lift points which minimizes thebending stress. What is the minimum bebding stress?c. What spacing s leads to maximum bending stress? What is thatstress?
N for Newton, m for meter, mm for millimeter, N/(mm^2) for Stress, mm^2 or m^2 for Area, mm^4 for Moment of inertia and Nm for bending moment. Use brackets if the power is MINUS for Example: 0.00125 N =1.25*10^(-3)N. A simply supported beam AB = 11 m has a hollow rectangular cross-section with 14 cm as width, 29 cm as depth and inner thickness as 1 cm is subjected to a point load of 6 N & 8 N acting at C and D respectively and a uniformly distributed load (UDL) of 8 N/m starts from mid-span and ends at the right support of the beam. Determine the maximum bending stress and the bending stress at 1 cm from the top. Take AC = 1 m & CD = 2 m. Solution: i) Reaction force at B = ii) Reaction Force at A = iii) The distance from B at which the shear Force value changes from "-" to "+" = iv) Maximum Bending Moment (Please write the Maximum bending moment valve in "Nm") = v) Moment of Inertia, I = vi) Maximum bending stress = vii) Bending stress at 1 cm from…
N for Newton, m for meter, mm for millimeter, N/(mm^2) for Stress, mm^2 or m^2 for Area, mm^4 for Moment of inertia and Nm for bending moment. Use brackets if the power is MINUS for Example: 0.00125 N =1.25*10^(-3)N. A simply supported beam AB = 11 m has a hollow rectangular cross-section with 14 cm as width, 29 cm as depth and inner thickness as 1 cm is subjected to a point load of 6 N & 8 N acting at C and D respectively and a uniformly distributed load (UDL) of 8 N/m starts from mid-span and ends at the right support of the beam. Determine the maximum bending stress and the bending stress at 1 cm from the top. Take AC = 1 m & CD = 2 m. Solution: i) Reaction force at B = ii) Reaction Force at A = iii) The distance from B at which the shear Force value changes from "-" to "+" = Answer and unit for part 3 iv) Maximum Bending Moment (Please write the Maximum bending moment valve in "Nm") = v) Moment of Inertia, I = vi) Maximum bending stress = vii)…
N for Newton, m for meter, mm for millimeter, N/(mm^2) for Stress, mm^2 or m^2 for Area, mm^4 for Moment of inertia and Nm for bending moment. Use brackets if the power is MINUS for Example: 0.00125 N =1.25*10^(-3)N. A beam has a bending moment of 3 kN-m applied to a section with a hollow circular cross-section of external diameter 3.4 cm and internal diameter 2.4 cm . The modulus of elasticity for the material is 210 x 109 N/m2. Calculate the radius of curvature and maximum bending stress. Also, calculate the stress at the point at 0.6 cm from the neutral axis Solution: (i) The moment of inertia = ii) The radius of curvature is (iii) The maximum bending stress is iv) The bending stress at the point 0.6 cm from the neutral axis is
3) The force, FT = 1 kN, and moment, MT = 0.5 kN-m, at the tip are caused by a wing tip vortexand a winglet, not shown. L = 12 m and the spar has an elastic modulus of E = 70 GPa and aPoisson’s ratio of n = 0.33. The mass of the wing is 4000 kg, and the weight of the engine is 107kN. Use 9.8 m/s 2 for the acceleration due to gravity.Consider the cross-section shown (you can look these up). Pay attention to the coordinate systemgiven in the drawing.d) where is the centroid?e) what is the area?f) Calculate the shear modulus
3) The force, FT = 1 kN, and moment, MT = 0.5 kN-m, at the tip are caused by a wing tip vortexand a winglet, not shown. L = 12 m and the spar has an elastic modulus of E = 70 GPa and aPoisson’s ratio of n = 0.33. The mass of the wing is 4000 kg, and the weight of the engine is 107kN. Use 9.8 m/s 2 for the acceleration due to gravity.Consider the cross-section shown (you can look these up). Pay attention to the coordinate systemgiven in the drawing.g) Compute each of these moments of inertia with the values b = 0.4 m, d =0.5 m , t =0.1 m.
3) The force, FT = 1 kN, and moment, MT = 0.5 kN-m, at the tip are caused by a wing tip vortexand a winglet, not shown. L = 12 m and the spar has an elastic modulus of E = 70 GPa and aPoisson’s ratio of n = 0.33. The mass of the wing is 4000 kg, and the weight of the engine is 107kN. Use 9.8 m/s 2 for the acceleration due to gravity.Consider the cross-section shown (you can look these up). Pay attention to the coordinate systemgiven in the drawing.a) what is the moment of inertia about y-axis in terms of the symbolic dimensions shown?b) what is the moment of inertia about z-axis in terms of the symbolic dimensions shown?c) what is the polar moment of inertia in terms of the symbolic dimensions shown (i.e.about the x-axis)?d) where is the centroid?e) what is the area?f) Calculate the shear modulusg) Compute each of these moments of inertia with the values b = 0.4 m, d =0.5 m , t =0.1 m.
nonuniform beam 4.50 m long and weighing 1.40 kNmakes an angle of 25.0° below the horizontal. It is held in position bya frictionless pivot at its upper right end and by a cable 3.00 m fartherdown the beam and perpendicular to it . The center ofgravity of the beam is 2.00 m down the beam from the pivot. Lightingequipment exerts a 5.00 kN downward force on the lower left end ofthe beam. Find the tension T in the cable and the horizontal and verticalcomponents of the force exerted on the beam by the pivot. Start bysketching a free-body diagram of the beam.
A shaft having length equal to 10 m and diameter equal to (50+ 01) mm is simply supported at both ends. The shatt carries four masses (150 + 01) kg, (200 + 01) kg, (250 +01) kg and (300 + 01) kg. These masses are located at a distance of 1.5m, 2.5 m, 5.5 mand 7.5 m from the left hand side support, respectively. The modulus of elasticity, E, for the material of the shaft is 200 GN/m? and mass density for the shaft material is 7500 kg/m?3. Determine critical speed of the shaft in revolutions per minute for the following two cases: 1. Effect of the mass of the shaft is neglected. 2. Effect of the mass of the shaft is considered. What is the usefulness of the answers determined in this problem?