8.7 At a point in a material under stress, there is a compressive stress of 200 MN/m and a shear stress of 300 MN/m2 acting on the same plane. Determine the principal stresses and the directions of the planes on which they act. [216 MN/m2 at 54.2° to 200 MN/m2 plane;- 416 MN/m2 at 144.2°] 8.8 At a certain point in a material, the following stresses act: a tensile stress of 150 MN/m2, a compressive stress of 105 MN/m2 at right angles to the tensile stress and a shear stress clockwise in effect of 30 MN/m2. Calculate the principal stresses and the directions of the principal planes. [153.5,- 108.5 MN/m²; at 6.7° and 96.7° counterclockwise to 150 MN/m plane]

8.7 At a point in a material under stress, there is a compressive stress of 200 MN/m and a shear stress of 300 MN/m2 acting on the same plane. Determine the principal stresses and the directions of the planes on which they act. [216 MN/m2 at 54.2° to 200 MN/m2 plane;- 416 MN/m2 at 144.2°] 8.8 At a certain point in a material, the following stresses act: a tensile stress of 150 MN/m2, a compressive stress of 105 MN/m2 at right angles to the tensile stress and a shear stress clockwise in effect of 30 MN/m2. Calculate the principal stresses and the directions of the principal planes. [153.5,- 108.5 MN/m²; at 6.7° and 96.7° counterclockwise to 150 MN/m plane]

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 7.2.21P: An clement m plane stress from the frame of a racing car is oriented at a known angle 8 (sec...

See similar textbooks

Similar questions

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.
At a point in a piece of elastic material there are three mutually perpendicular planes on which the stresses are as follows : tensile stress 50 N/mm2, shear stress 40 N/mm2 on plane, compressive stress 35 N/mm2 and complementary shear stress 40 N/mm2 on the second plane, no stress on the third plane. Find (a) the principal stresses and the positions of the plane on which they act (b) the position of the planes on which there is no normal stress.
1. A material is subjected to equal bi-axial tensile stresses of 60 MPa along the x- and y-axes. There is no additional stress. Determine the shear stress on the (1 1 1) plane toward the [1 0 -1] direction.
At a point in a stressed body, the cartesian components of stress are sigma xx = 60 MPa, sigma yy= -40 MPa, sigma zz = 20 MPa, tau xy = -40 MPa, tau yz = 20 MPa, and tau zx= 30 MPa. Determine: (a) 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
3. Listed below is a combination of stresses acting at a point and referred to axes x and y in an elastic material. Using Mohr’s circle of stress determine the principal stresses at the point and their directions for each combination. 1}sigmax -60 n/mm2 , sigmay -36n/mm2 ,TAUxy=5n/mm2 2}}sigmax 30 n/mm2 , sigmay -50n/mm2, TAUxy= 30n/mm2
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 = 26.9 ksi, Sy = 6.8 ksi, and Sxy= 19.0 ksi. (a) Determine the principal stresses and the maximum in-plane shear stress acting at the point. (b) On a piece of paper, show these stresses on an appropriate sketch (e.g., see Figure 12.15 or Figure 12.16). For the sketch, calculate 0p, the angle between the x axis and the principal stress orientation. Also, calculate avg, the normal stress on planes of maximum in- plane shear stress. (c) Compute the absolute maximum shear stress at the point. Answers: (a) Opl = Op2 = Tmax = (b) 0,= Oavg = (c) Tabs max Sxy = i i Mi i i ksi ksi ksi 0 ksi ksi
3. An axial pull of 35000 N is acting on a bar consisting of three lengths as shown below. If the Young's Modulus is 2.1 x 105 N/mm2. Determine (i) Stresses in each section, and; (ii) Total extension of the bar. Section 3 Section 2 Section 1 35000 N 35000 N 2 cm DIA 3 cm DIA 5 cm DIA k-20 cm- 25 cm -22 cm-
A point on a thin plate is subjected to two successive states of stress. The stresses have magnitude σx | = 31.5 MPa, |σy' | = 45.5 MPa, and |Tx'y' | = 20.5 MPa. 0x , Oy, Txy || = Determine the resulting state of stress on the element on the right. The rotation angles on the left-hand side of the figure are in relation to the orientation of the element on the right. Express your answers, separated by commas, to three significant figures. View Available Hint(s) 1977| ΑΣΦ | 11 VE 60° vec 220% ? Txy MPa, MPa, MPa ·0x
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
2- The state of stresses at a point are defined as follows. Find the normal and shear stress vector components (O₂. ) on a plane tangent to a cylinder of diameter D and coaxial with x-axis (Z-axis) at point (B.y.B). Also, determine the octahedral shear stress. Stu. Nom. D B Y 30 45 60 5.0 2.0 1.5 Ju = 45 20 50 MPa 60 50 10
Mohr's Circle At a point, the normal and shear stresses acting on one plane are 8000 psf compression and 2000 psf, respectively. On a perpendicular plane, the normal and shear stress combination is 2000 psf compression and 2000 psf. (a) Draw the Mohr's circle. (b) Determine the value of the principal stresses. (c) Find the angle between the plane on which the 8000 psf compressive stress acts and the major principal plane. (d) What is the maximum shear stress acting at the point? kindly answer the following with a complete solution so that i can understand how to solve it. thank you
A certain point in the mechanical part has shearing and normal stresses measured in MN/m^2 as shown in the figure below. Use Mohr's stress circle to determine: (a) the magnitude of the principal stresses and the inclinations of the principal planes (b) the maximum shear stress and the inclinations of the planes on which it acts (c) the magnitude of the normal stress on a plane inclined at 30° counterclockwise to the plane on which the 90 MN/m^2 stress acts and draw the corresponding stress clements.