4 The state of stress on an element at a point is described by the Figure shown. Stress magnitudes: 0x = 120 MPa, oy = 200 MPa, Txy = 80 MPa (a) Neatly sketch the Mohr's Circle, identifying the locations of the two principal stresses and the two maximum in-plane shear stresses. (b) Determine the magnitudes of the stresses using the circle. (c) Determine the orientation of the stresses using the circle. (d) Sketch the results Txy

4 The state of stress on an element at a point is described by the Figure shown. Stress magnitudes: 0x = 120 MPa, oy = 200 MPa, Txy = 80 MPa (a) Neatly sketch the Mohr's Circle, identifying the locations of the two principal stresses and the two maximum in-plane shear stresses. (b) Determine the magnitudes of the stresses using the circle. (c) Determine the orientation of the stresses using the circle. (d) Sketch the results Txy

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 7.4.21P: -18 through 7.4-25 An clement in plane stress is subjected to stresses a,, ay., and axy. (see...

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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.
-18 through 7.4-25 An clement in plane stress is subjected to stresses a,, ay., and axy. (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.
-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
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.
.4-2 An element in uniaxial stress is subjected to tensile stresses sx= 57 MPa. as shown in the figure. Using Mohr’s circle, determine the following. (a) The stresses acting on an clement oriented at an angle 0 = 33° from the x axis (minus means clockwise). (b) The maximum shear stresses and associated normal stresses. Show all results on sketches of properly oriented elements.
An clement m plane stress from the frame of a racing car is oriented at a known angle 8 (sec figure). On this inclined clement, the normal and shear stresses have the magnitudes and directions shown in the figure. Determine the normal and shear stresses acting on an clement whose sides are parallel to the \y axes, that is, determine crv, tr(_, and t, Show the results on a sketch of an clement oriented at B .
Solve the preceding problem for an element in plane stress on the bottom surface of a fuel tanker (figure part a); stresses are sx= 105 MPa, sy. = 75 MPa, and ??xy= 25 MPa. Determine the stresses acting on an element oriented at an angle ?? = 40° from the x axis, where the angle is positive when counterclockwise. Show these stresses on a sketch of an element oriented at the angle ??.
-27 A square plate with side dimension of 2 in. is subjected to compressive stress a and tensile stress The stresses on element A oriented at angle ?? x1=45° aresy1= 75 psi. tx1y1= 275 psi. . Find the state of stress on the element lilt is rotated clockwise to align the x3 axis with the horizontal x axis.
Through 7.4-25 An clement in plane stress is subjected to stresses x,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. 7.422x=29.5,y=29.5MPa,xy=27MPa
-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
The normal and shear stresses acting on element A are 6500 psi, 17,300 psi, and 2900 psi (see the figure b for Problem 7.2-5). Determine the maximum shear stresses and associated normal stresses and show them on a sketch of a properly oriented element.
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