Consider a point in a structural member that is subjected to plane stress. Normal and shear stress magnitudes acting on horizontal and vertical planes at the point are S,- 2750 psi, S, - 1100 psi, and Sy 1950 psi. Assume ß-53 (a) Draw Mohr's circle for this state of stress. (b) Determine the principal stresses and the maximum in-plane shear stress acting at the point. Show these stresses on an appropriate sketch (e.g., see Fig. 12.15 or Fig. 12.16). (c) Determine the normal and shear stresses on the indicated plane and show these stresses on a sketch. (d) Determine the absolute maximum shear stress at the point. Sxy

Consider a point in a structural member that is subjected to plane stress. Normal and shear stress magnitudes acting on horizontal and vertical planes at the point are S,- 2750 psi, S, - 1100 psi, and Sy 1950 psi. Assume ß-53 (a) Draw Mohr's circle for this state of stress. (b) Determine the principal stresses and the maximum in-plane shear stress acting at the point. Show these stresses on an appropriate sketch (e.g., see Fig. 12.15 or Fig. 12.16). (c) Determine the normal and shear stresses on the indicated plane and show these stresses on a sketch. (d) Determine the absolute maximum shear stress at the point. Sxy

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 7.2.26P: -26 A rectangular plate of dimensions 125 mm × 75 mm is subjected to tensile stress sy= 67 kPa and...

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-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
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Determine the equivalent state of stress which represents the principal stresses, and the maximum in-plane shear stress and the associated average normal stress. For each case, determine the corresponding orientation of the element with respect to the element shown in the figure below. (Figure 1) Determine the orientation of principal planes of stress. Express your answers in degrees to three significant figures separated by a comma.
Consider a point in a structural member that is subjected to plane stress. Normal and shear stress magnitudes acting on horizontal and vertical planes at the point are Sx = 12 ksi, Sy = 17 ksi, and Sxy = 18 ksi.(a) Draw Mohr’s circle for this state of stress.(b) Determine the principal stresses (σp1>σp2σp1>σp2) and the maximum in-plane shear stress τmaxτmax acting at the point.(c) Find the smallest rotation angle θpθp (counterclockwise is positive, clockwise is negative) that will rotate to principal directions. Then show these stresses in an appropriate sketch (e.g., see Figure 12.15 or Figure 12.16)
Considering the original state of stress as shown in figure below and recalling the already developed equations for normal and shear stress at an angle Ɵ c.c.w from x-axis, mathematically prove that the planes of maximum in-plane shear stress are inclined at 45o to the principal planes.
The principal stresses at a point across two mutually perpendicular planes are 70 MN/m2 tension and 55 MN/m2 tension respectively. The shear stress across these planes is 25 MN/m2 (Counter clockwise). Determine the magnitude of the normal, tangential, the resultant stress, and inclination of resultant stress on a plane inclined at 25o to the plane of greater principal stress. And also verify the answer by drawing the Mohr’s circle.
Consider a point in a structural member that is subjected to plane stress. Normal and shear stress magnitudes acting on horizontal and vertical planes at the point are Sx = 150 MPa, Sy = 21 MPa, and Sxy = 85 MPa. Assume β = 56°.(a) Draw Mohr’s circle for this state of stress.(b) Determine the principal stresses and the maximum in-plane shear stress acting at the point. Show these stresses on an appropriate sketch (e.g., see Fig. 12.15 or Fig. 12.16).(c) Determine the normal stresses and the magnitude of the shear stress on the indicated plane and show these stresses on a sketch.(d) Determine the absolute maximum shear stress at the point. Answer:(a) Draw Mohr's Circle for this state of stress.(b) σp1 = MPa σp2 = MPa τmax in-plane = MPa(c) σn = MPa τnt = MPa(d) τabs max = MPa
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