Determine the equivalent state of stress on an element at the same point which represents the principal stress, and the maximum in-plane shear stress and the associated average normal stress. Also, for each case, determine the corresponding orientation of the element with respect to the element shown in the figure below. (Figure 1) Figure (< 1 of 1 75 MPa 125 MPa 50 MPa

Determine the equivalent state of stress on an element at the same point which represents the principal stress, and the maximum in-plane shear stress and the associated average normal stress. Also, for each case, determine the corresponding orientation of the element with respect to the element shown in the figure below. (Figure 1) Figure (< 1 of 1 75 MPa 125 MPa 50 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 7.2.8P: An element in plane stress on the fuselage of an airplane (figure part a) is subjected to...

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-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.
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).
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.
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 .
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.
-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
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 xy axes, that is, determine crv, tr(_, and t. Show the results on a sketch of an clement oriented at B = 10
A copper bar with a rectangular cross sectionis held without stress between rigid supports (seefigure). Subsequently, the temperature of the bar israised 50°C.(a) Determine the stresses on all faces of theelements A and B, and show these stresseson sketches of the elements. (Assumeα = 17.5 x 10 6 / °C 2 and E = 120 GPa.)(b) If the shear stress at B is known to be 48 MPaat some inclination θ, find angle θ and showthe stresses on a sketch of a properly orientedelement.
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Consider a point in a structural member thatis subjected to plane stress. Normal and shear stresses acting onhorizontal and vertical planes at the point are shown in the figure below a) Draw Mohr’s circle for this state of stress.(b) Determine the principal stresses and the maximum in-planeshear stress acting at the point, and show these stresses in anappropriate sketch (e.g., see Figure 12.15 or Figure 12.16).(c) Determine the normal and shear stresses on the indicatedplane, and show these stresses in an appropriate sketch.