2.25 At a point in a structural member, the principal stresses are 100, 150, and -200 MPa. If the principal stresses are oriented along the x-, y-, and z-axes, respectively, find the resultant stress across a plane whose normal makes 45° with the z-axis and the projec- tion of the normal on the xy-plane makes 30° with the y-axis is shown in Figure P2.25. Z D A 30°

2.25 At a point in a structural member, the principal stresses are 100, 150, and -200 MPa. If the principal stresses are oriented along the x-, y-, and z-axes, respectively, find the resultant stress across a plane whose normal makes 45° with the z-axis and the projec- tion of the normal on the xy-plane makes 30° with the y-axis is shown in Figure P2.25. Z D A 30°

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 7.2.19P: At a point on the surface of an elliptical exercise machine, the material is in biaxial stress with...

See similar textbooks

Similar questions

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
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.
The principal tensile stress at a point across two mutually perpendicular planes are 100 N/mm2 and 40 N/mm2. The normal, tangential and resultant stresses on a plane inclined at 20° to the axis of the minor principal stress by analytical method is
2.4. The stress at a point is defined by the components Oxr =0 MPa, Oyy= 100 MPa, Oxy = Oyx plane on which the maximum principal stress acts to the x-plane. %3D =-40 MPa. Find the principal stresses o1, 02 and the inclination of the
2. At a point in a brocket, the stresses on two mutually perpendicular planes are 180 MN/m? (tensile) and 70 MN/m2 (Compressive). The shear stress across the planes is 65 MN/m2. Find the following by Mohr's Circle method and compare with Analytical solutions: (i)The Normal stress on a plane making an angle of 50° with the plane of first stress. (ii)Shear stress on the plane (iii) Maximum shear stress (iv) Resultant stress and it's direction. (v) Major and minor principal stresses.
Relative to the x-, y-, and z-axes, the state of stress at a point in a component is found to be proportional to the matrix FIGURE P2.7 40-3 05 -3 2-3) Determine the normal, shear, and resultant stresses that act on a plane whose normal is inclined at 45° to the z-axis and the projection of the normal on the xy- plane makes 50° with the yz-plane (Figure P2.7). Find also the direction of the resultant stress. 40° 45 2 MPa 50⁰
2. The Principal stresses at a point across two perpendicular planes are 90MN/m² (tensile) and 40MN/m² (compressive). The shear stress across these planes is 25 MN/m² (counter clockwise). Find the normal, tangential and the resultant stress & its inclination on a plane making an angle of 35° with the plane of first stress.
A plate in plane stress is subjected to normal stress components σx and σy and shear stress τxy, as shown in Figure Q2. Given the maximum and minimum principal stresses are 645.64 MPa and -495.64 MPa, respectively. (a)Compute the normal stress components σx and σy using Mohr’s circle. Plot the Mohr’s circle for 2 possible cases of normal stresses. (Hint: The σx and σy on the plane stress in Figure Q2 can be either in tension or in compression). (b) Assuming the principal stresses were obtained when the element was oriented in the direction of counterclockwise, identify the corresponding normal stresses σx and σy with your justification. (c) Discuss how does the stress transformation relate to the real-life practice of an engineering discipline.
At a point in a strained material, the intensities of normal stresses on two planes at right angles to each other are 35 N/mm2 and 20 N/ mm2 both tensile. They are accompanied by shear stress of 15 N/ mm2. Find the principal planes and principal stresses. Find also maximum shear stress.
The stresses acting on element A in the web of a train rail are found to be 'X (MPa)' tension in the horizontal x-direction and 'Y (MPa)' compression in the vertical y-direction. Also, shear stresses of magnitude 'S (MPa)' act in the directions shown in the figure. Draw Mohr's circle for the state of stress. Determine the stresses (Ox', Oy' and Txy') acting on an element oriented at an angle 'D' from the horizontal Show these stresses on a sketch of an element oriented at this angle X=45MPA,Y=150MPA,S=52MPA,D=-40 Degree
2. The tires of an agricultural tractor shown below are assumed to be 25 cm wide for the front tires and 40 cm at the rear tires. Ground contact of each tire is 15 cm. Calculate the compressive stress between each tire and the ground surface. Weight = 2,500 kg 15 cm 1.3m Point A 2.2 m 2R 2F
b) For the thin walled pressure vessel subjected to an internal pressure of 150 psi and as shown below, calculate the longitudinal and transverse stresses. Assume length as L ft and 1 in. wall thickness as 8 2 ft E2.5 ft -d Type your answer in the Word format here Page 2 of 2 565 words Search