8.5 The material of Problem 8.4 is subjected to an additional shearing stress of 10 MN/m. Determine the principal stresses acting on the material and the maximum shear stress. [46, - 61, 53.5 MN/m2] 8.6 At a certain section in a material under stress, direct stresses of 45 MN/m² tensile and 75 MN/m? tensile act on perpendicular planes together with a shear stress r acting on these planes. If the maximum stress in the material is limited to 150 MN/m² tensile, determine the value of r. [88.7 MN/m]

8.5 The material of Problem 8.4 is subjected to an additional shearing stress of 10 MN/m. Determine the principal stresses acting on the material and the maximum shear stress. [46, - 61, 53.5 MN/m2] 8.6 At a certain section in a material under stress, direct stresses of 45 MN/m² tensile and 75 MN/m? tensile act on perpendicular planes together with a shear stress r acting on these planes. If the maximum stress in the material is limited to 150 MN/m² tensile, determine the value of r. [88.7 MN/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

Chapter7: Analysis Of Stress And Strain

Section: Chapter Questions

Problem 7.3.18P: -18 through 7.3-22 An element in plane stress (see figure) is subjected to stresses o, a., and (a)...

See similar textbooks

Similar questions

An element in plane stress on the fuselage of an airplane (figure part a) is subjected to compressive stresses with a magnitude of 42 MPa in the horizontal direction and tensile stresses with a magnitude of 9.5 MPa in the vertical direction (sec figure part b). Also, shear stresses with a magnitude of 15.5 MPa act in the directions shown. Determine the stresses acting on an element oriented at a clockwise angle of 40g from the horizontal. Show these stresses on a sketch of an element oriented at this angle.
-26 A rectangular plate of dimensions 125 mm × 75 mm is subjected to tensile stress sy= 67 kPa and compressive stress a. If it is known that the normal stress along the diagonal t—t is ??t= -6.57 kPa, find stress ??y on element A. a
At a point on the surface of an elliptical exercise machine, the material is in biaxial stress with t = 1400 psi and trv = —900 psi, as shown in the figure part a. The figure part b shows an inclined plane aa cut through the same point in the material but oriented at an angle ft Determine the value of the angle 6 between zero and 90° such that no normal stress acts on plane aa. Sketch a stress clement having plane aa as one of its sides and show all stresses acting on the clement
A brass plate with a modulus of elastici ty E = 16 X 106 psi and Poisson’s ratio a = 0.34 is loaded in biaxial stress by normal stresses r and cry. (sec figure). A strain gage is bonded to the plate at an angle 4 = 350 If the stress o is 10,700 psi and the strain means used by the gageise = 390 X 106.whatisthcmax- imum in-plane shear stress (Tr, ),. and shear strain (>‘ ).? What is the maximum shear strain (y ) in the x-: plane? What is the maximum shear strain (y ).. in the y-r plane?
The polyethylene liner of a settling pond is subjected to stresses ax= 350 psi. a = 112 psi. and = -120 psi, as shown by the plalte-stress element in the figure part a. Determine the normal and shear stresses acting on a seam oriented at an angle 01300 to the element, as shown in the figure part b. Show these stresses on a sketch of an element having its sides parallel and perpendicular to the seam.
During a test of an airplane wing, the strain gage readings from a 45° rosette (see figure) are as follows: gage A, 520 × l0-6; gage B. 360 × l0-6; and gage C,-80 × 10-6. Determine the principal strains and maximum shear strains, and show them on sketches of properly oriented elements.
-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
Q-2 In an elastic material under load, two planes AB and BC are perpendicular to each other. The stresses on these planes are as follows: 1. on AB, 30 MN/m² compression stress and 60 MN/m² counterclockwise shear. 2. on BC, 60 MN/m² clockwise shear. Find (a) the principal stresses and directions of the principal planes. (b) the normal and tangential stresses on a plane inclined at 75" counterclockwise to the BC plane. Confirm your answer by means of Mohr's stress circle diagram.
Consider the plane stress element shown in representing the state of stress at a material point. If the magnitudes of the stresses are such that ox 210 Pa, oy = 110 Pa, and = - Txy = 70 Pa, calculate the magnitudes of principal stresses oj and 02, and the maximum shear stress, Tmax, generated at %3D this material point. (a) Record here the the positive of the two principle stresses. (b) Record here the the negative of the two principle stresses. (c) Record here the the maximum shear stress. Tyz Oy
2. At a point in a brocket, the stresses on two mutually perpendicular planes are 180 MN/m? (tensile) and 70 MN/m2 (Compressive). The shear stress across the planes is 65 MN/m2. Find the following by Mohr's Circle method and compare with Analytical solutions: (i)The Normal stress on a plane making an angle of 50° with the plane of first stress. (ii)Shear stress on the plane (iii) Maximum shear stress (iv) Resultant stress and it's direction. (v) Major and minor principal stresses.
At a point in a stressed body, the cartesian components of stress are Oxx = 60 MPa, Guy = -40 MPa, Ozz = 20 MPa, Txy = -40 MPa, Tyz = 20 MPa, and Txz = 30 MPa. Determine: (a) The principle stresses and their direction cosines. (b) The normal and shear stresses on a plane whose outer normal has the following direction cosines: cos (n,x) = 0.429; cos (n, y) = 0.514; cos (n, z) = 0.743
Q5: At a point in a strained material the stresses acting on planes at right angles to each other are o, 30, MN/m² tensile, together with associated shear stresses which assumed clockwise in effect on oy plane. If the maximum principal stress is limited to 1002 MN/m² tensile, and xy-60 MN/m², calculate: (a) the magnitude of the o, and oy; (b) the values of the maximum and minimum principal stresses; (c) the directions of the principal planes; (d) the maximum shear stress.