For a point under a plane state of stress, the stresses on the vertical andhorizontal planes are shown in the figure below.100 MPa48°80 MPa60 MPaUsing only the stress transformation EQUATIONS, determine the following:a) The normal stresses on the plane oriented along plane a-b.o, =b) The shear stress on the plane oriented along plane a-bTy'=c) The locations of the principal planes (express your answers as angles made by theprincipal planes with respect to the horizontal)Op2=d) The principal stressesOp1=Op2=e) The maximum in-plane shear stressTmaxip=Show the results of both stresses in plane a-b and principal planes on a sketch of theplane on which these stresses act.

Answered: Image /qna-images/answer/84ad65c8-097e-4fa3-b5a6-e59884920fb2.jpg

For a point under a plane state of stress, the stresses on the vertical and horizontal planes are shown in the figure below. 100 MPa 48° 80 MPa 60 MPa Using only the stress transformation EQUATIONS, determine the following: a) The normal stresses on the plane oriented along plane a-b. a,'= b) The shear stress on the plane oriented along plane a-b c) The locations of the principal planes (express your answers as angles made by the principal planes with respect to the horizontal) Op2= d) The principal stresses Opi= Op2= e) The maximum in-plane shear stress Tmaxip= Show the results of both stresses in plane a-b and principal planes on a sketch of the plane on which these stresses act.

For a point under a plane state of stress, the stresses on the vertical and horizontal planes are shown in the figure below. 100 MPa 48° 80 MPa 60 MPa Using only the stress transformation EQUATIONS, determine the following: a) The normal stresses on the plane oriented along plane a-b. a,'= b) The shear stress on the plane oriented along plane a-b c) The locations of the principal planes (express your answers as angles made by the principal planes with respect to the horizontal) Op2= d) The principal stresses Opi= Op2= e) The maximum in-plane shear stress Tmaxip= Show the results of both stresses in plane a-b and principal planes on a sketch of the plane on which these stresses act.

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 7.4.2P: .4-2 An element in uniaxial stress is subjected to tensile stresses sx= 57 MPa. as shown in the...

See similar textbooks

Similar questions

-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
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.
-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.
-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
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
The stresses acting on an element are x= 750 psi, y= 600 psi, and xy = 400 psi. Determine the principal stresses and show them on a sketch of a properly oriented element.
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.
.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 .
A thin square plate in biaxial stress is subjected to stresses ?? and ??., as shown in part a of the figure. The width of the plate is h = 12.0 in. Measurements show that the normal strains in the x and v directions are s = 427 × 10-6 and s = 113 × l0-6, respectively. With reference to part b of the figure. which shows a Iwo-dimensional view of the plate. determine the following quantities. (a) The increase .d in the length of diagonal Oil. (b) The change . in the angle between diagonal Oti and the x axis, (c) The shear strain y associated with diagonals Oil and cf(that is. find the decrease in angle ced).
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.
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 ??.