at the top to 90 kPa at the bottom. As an additional support, it is anchored at depth y = 2 m. with maximum tension equal to 25 kN. Calculate: (a) Maximum positive bending moment per linear meter; (b) maximum negative bending moment per linear meter; (c) maximum shear force per linear meter. Soil surface 25 kN H Anchor

at the top to 90 kPa at the bottom. As an additional support, it is anchored at depth y = 2 m. with maximum tension equal to 25 kN. Calculate: (a) Maximum positive bending moment per linear meter; (b) maximum negative bending moment per linear meter; (c) maximum shear force per linear meter. Soil surface 25 kN H Anchor

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 5.13.4P: A rectangular beam with semicircular notches, as shown in part b of the figure, has dimensions h =...

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A rectangular beam with semicircular notches, as shown in part b of the figure, has dimensions h = 120 mm and h1= 100 mm. The maximum allowable bending stress in the plastic beam is emix = 6 M Pa, and the bending moment is M = 150 N · m. Determine the minimum permissible width bminof the beam.
A timber dam is made of planking backed by vertical piles. The piles are built-in at the section A where they enter the ground and they are supported by horizontal struts whose center lines are 10 m above A. The piles are spaced 1 m apart between centers and the depth of water against the dam is 10 m. Assuming that the thrust in the strut is two-sevenths the total water pressure resisted by each pile, sketch the form of the bending moment and shearing force diagrams for a pile. Determine the magnitude of the bending moment at A and the position of the section which is free from bending moment. (Cambridge). i. 238 kN-m; 0.75 m from A. ii. 238 kN-m; 0.75 m from B.
A beam is subjected to equal bending moments of Mz = 44 kip·ft. The cross-sectional dimensions are b1 = 6.5 in., d1 = 1.5 in., b2 = 0.90 in., d2 = 6.2 in., b3 = 2.6 in., and d3 = 1.8 in. Determine:(a) the centroid location (measured with respect to the bottom of the cross-section), the moment of inertia about the z axis, and the controlling section modulus about the z axis.(b) the bending stress at point H. Tensile stress is positive, while compressive stress is negative.(c) the bending stress at point K. Tensile stress is positive, while compressive stress is negative.(d) the maximum bending stress produced in the cross section. Tensile stress is positive, while compressive stress is negative.
A beam is subjected to equal bending moments of Mz = 57 kip·ft. The cross-sectional dimensions are b1 = 8.3 in., d1 = 1.4 in., b2 = 0.90 in., d2 = 6.2 in., b3 = 2.4 in., and d3 = 1.7 in. Determine: (a) the centroid location (measured with respect to the bottom of the cross-section), the moment of inertia about the z axis, and the controlling section modulus about the z axis. (b) the bending stress at point H. Tensile stress is positive, while compressive stress is negative. (c) the bending stress at point K. Tensile stress is positive, while compressive stress is negative. (d) the maximum bending stress produced in the cross section. Tensile stress is positive, while compressive stress is negative.
Consider a 6−m6−m long horizontal beam supported by a pin at one end and a roller at the other end. If a 30kN⋅m30kN⋅m bending moment is applied at the roller end of the beam, what is the internal bending moment at a distance of 2m2m from the pin?
determine the diagram of the shear forces and bending moments in the beam shown below. Data P = 20kN, M = 60kNm, q = 10kN / m, a = 5m, b = 2m, c = 3, alpha = 60.
The beam cross section shown below has been proposed for a short pedestrian bridge. The cross section will consist of two pipes that are welded to a rectangular web plate. Dimensions of the cross section are: h = 430 mm tw = 16 mm d = 110 mm t = 4.8 mm Additionally: • The area of each pipe is A = 1586 mm2. • The moment of inertia of the entire beam cross section about the z centroidal axis is IZ = 194710000 mm4. If the beam will be subjected to a shear force of V = 170 kN, determine the shear stress at point K, located at yK = 70 mm below the z centroidal axis.
Draw the shear and moment diagram of the overhanging beam shown below. For this part, please show the necessary solutions using the LONG METHOD, not the AREA MOMENT METHOD
1. Determine the maximum positive bending moment in the beam in kN-m. 2. Determine the maximum shear in kN. 3. Determine the location of Neutral Axis, in mm, from the top of the section. 4. Determine the location of the centroid, in mm, from the left of the section. 5. Determine the moment of inertia of the section in x106 mm4 . 6. Determine the moment capacity of the section, kN-m, if fbcap≤300 MPa. 7. Determine the maximum flexural stress experienced by the beam in MPa. 8. Determine the maximum shearing stress in MPa at Neutral Axis. 9. Determine the spacing of rivets in mm. 10. Determine the maximum flexural stress at 1 m from the support at D to E in MPa.
A beam having a tee-shaped cross section is subjected to equal 13 kN-m bending moments, as shown. Assume bf = 95 mm, tf = 25 mm, d = 165 mm, tw = 40 mm. The cross-sectional dimensions of the beam are also shown. Determine(a) the centroid location (measured upward from the bottom), the moment of inertia about the z axis, and the controlling section modulus about the z axis.(b) the bending stress at point H (positive if tensile and negative if compressive).(c) the maximum bending stress (positive if tensile and negative if compressive) produced in the cross section.
A beam is subjected to equal 19.1 kip-ft bending moments. Assume ty = t2 = ty= 1 in., d = 10 in, by= 4 in., and b2 = 7 in. The cross- sectional dimensions of the beam are illustrated. Determine; (a) the distance y to the centroid (measured from the bottom), the moment of inertia & about the z axis, and the controlling section modulus S, about the z axis. (b) the bending stress O, at point H (positive if tension, negative if compression). (c) the bending stress y at point K (positive if tension, negative if compression). (d) the maximum bending stress, Omax produced in the cross section (positive if tension, negative if compression).
Consider that the section is transmitting a positive bending moment about the z axis,Mz, where Mz=10 kip*in if the dimensions of the section are given in ips units, or Mz=1.13kN*m if the dimensions are in SI units. Determine the resulting stresses at the top and bottom surfaces and at every abrupt change in the cross section. Find the second moment of area, the location of the neutral axis, and the distances from the neutral axis to the top and bottom surfaces.