The articular Cartilage is subjected to plane stress with normal stresses ox , o, and shear stress Txy, as shown in the figure. At a counterclockwise angle e = 30° from the x-axis, the normal stress is 3 MPa tension, and at an angle e = 50°, it is 2 MPa compression. Find the principals stresses. Ty 0, =10 MPa

The articular Cartilage is subjected to plane stress with normal stresses ox , o, and shear stress Txy, as shown in the figure. At a counterclockwise angle e = 30° from the x-axis, the normal stress is 3 MPa tension, and at an angle e = 50°, it is 2 MPa compression. Find the principals stresses. Ty 0, =10 MPa

Mechanics of Materials (MindTap Course List)

9th Edition

ISBN:9781337093347

Author:Barry J. Goodno, James M. Gere

Publisher:Barry J. Goodno, James M. Gere

Chapter7: Analysis Of Stress And Strain

Section: Chapter Questions

Problem 7.4.15P: An clement in plane stress is subjected to stresses a,. cry, and (see figure). Using Mohr’s circle,...

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-18 through 7.3-22 An element in plane stress (see figure) is subjected to stresses o, a., and (a) Determine the principal stresses and show them on a sketch of a properly oriented element. (b) Determine the maximum shear stresses and associated normal stresses and show them on a sketch of a properly oriented element. 7.3-18 a=2I50kPa, ay=375kPa.Txy.=-460kPa
3-17 The stresses at a point along a beam supporting a sign (see figure) are sx= 2250 psi, sy,. = 1175 psi, and txy = -820 psi. (a) Find the principal stresses. Show them on a sketch of a properly oriented clement. (b) Find the maximum shear stresses and associated normal stresses. Show them on a sketch of a properly oriented element.
‘7.3-11 The stresses on an element are sx= -300 psi and sy= 600 psi. Find the maximum shear stresses on the element and show them on a sketch of a properly oriented clement.
A prismatic bar is subjected to an axial force that produces a tensile stress ????=65 MPa and a shear stress T??= 23 MPa on a certain inclined plane (see figure). Determine the stresses acting oil all laces of a stress element oriented at ?? = 30°, and show the stresses on a sketch of the element.
A steel hanger bracket ABCD has a solid, circular cross section with a diameter of d = 2 in. The dimension variable is b = 6 in. (see figure). Load P = 1200 lb is applied at D along a line DIh the coordinates of point H arc (8/>, — 5b, 2b), Find normal and shear stresses on a plane stress element on the surface of the bracket at A. Then find the principal stresses and maximum shear stress. Show each stress state on properly rotated elements
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An element in pure shear is subjected to stresses ??xy= 3750 psi, as shown in the figure. Using Mohr’s circle, determine the following: (a) The stresses acting on an clement oriented at a slope of 3 on 4 (sec figure). (b) The principal stresses. Show all results on sketches of properly oriented elements.
-18 through 7.4-25 An clement in plane stress is subjected to stresses ax,ay., and txy. (see figure). Using Mohr’s circle, determine (a) the principal stresses and (b) the maximum shear stresses and associated normal stresses. Show all results on sketches of properly oriented elements. 7.4-18 sx= 2900 kPa, sy= 9100 kPar,txy=-3750kPa
: A hollow, pressurized sphere having a radius r = 4.8 in, and wall thickness t = 0.4 in. is lowered into a lake (see figure). The compressed air in the tank is at a pressure of 24 psi (gage pressure when the tank: is out of the water). At what depth D0will the wall of the tank be subjected to a compressive stress of 90 psi?
A steel pipe is subjected to a quadratic distributed load over its height with the peak intensity q0at the base (see figure). Assume the following pipe properties and dimensions: height L, outside diameter d = 200 mm, and wall thickness f = 10 mm. Allowable stresses for flexure and shear are o~a=125 MPa and Ta= 30 MPa, If L = 2.6 m, Fmd^0ayM (kN/m), assuming that allowable flexure and shear stresses in the pipe are not to be exceeded. If q0= 60 kN/m, find the maximum height Lraajl(m) of the pipe if the allowable flexure and shear stresses in the pipe arc not to be exceeded.
-18 through 7.4-25 An clement in plane stress is subjected to stresses sx,??y, and r. (see figure). Using Mohr’s circle, determine (a) the principal stresses and (b) the maximum shear stresses and associated normal stresses. Show all results on sketches of properly oriented elements. 7.4-19 ??x=800 psi. ??y=-2200 psi, ??xy. =2900 psi
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