3. Two forces are applied on the beam shown below. (a) Determine the normal and shear stresses at point B on the shown cross-section. (b) Show the state of stress at the point B on a volume element. 400 lb 1 in. 2 in. 500 lb 2 in 10 in. 1.5 in. 1.5 in. Show your steps and highlight the following answers on your solution sheets: Iz = A = Q = Normal stresses expression: Shear stresses expression: OB (i. e.,ox) = %3D TB-y(i. e. , Txy) =

3. Two forces are applied on the beam shown below. (a) Determine the normal and shear stresses at point B on the shown cross-section. (b) Show the state of stress at the point B on a volume element. 400 lb 1 in. 2 in. 500 lb 2 in 10 in. 1.5 in. 1.5 in. Show your steps and highlight the following answers on your solution sheets: Iz = A = Q = Normal stresses expression: Shear stresses expression: OB (i. e.,ox) = %3D TB-y(i. e. , Txy) =

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 7.3.1P: The stresses acting on an element are x= 750 psi, y= 600 psi, and xy = 400 psi. Determine the...

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Two forces are applied on the beam shown below. (a) Determine the normal and shear stresses at point B on the shown cross-section. (b) Show the state of stress at the point B on a volume element. 400 lb B 1 in. 2 in. 500 Ib 2 in 10 in. 1.5 in. 1.5 in. Show your steps and highlight the following answers please I =
Problem 1: A state of plane stress at a point on the surface of a structure consists of the following stress components: Ox = 25 ksi, oy = 12 ksi, and Txy = 10 ksi. Note that the stress components act in the directions shown on the element below. Ox Txy 12 ksi 5 25 ksi 10 ksi (a) Draw a complete Mohr's circle for this stress state. Clearly label the X and Y faces, the center C, and the radius R. (b) Using Mohr's circle, determine the principal stresses, the maximum in-plane shear stress, and the normal stress that acts on the maximum shear stress plane. Label all of these quantities on the circle. (c) Calculate the orientation of the principal planes and the planes of maximum shear stress. Label all of these quantities on the circle. (d) Show all stresses from part (b) on properly oriented stress element(s). Be sure to include all stress components acting on the elements(s).
Problem 2: A state of plane stress at a point on the surface of a structure consists of the following stress components: Ox = 18 ksi, oy = 24 ksi, and Txy = 15 ksi. Note that the stress components act in the directions shown on the element below. Ox Txy 24 ksi бу 18 ksi 15 ksi (a) Draw a complete Mohr's circle for this stress state. Clearly label the X and Y faces, the center C, and the radius R. (b) Using Mohr's circle, determine the stress components Ox, Oy, and Txy on an element rotated 25° counter-clockwise from the original element shown. Label all of these quantities on the circle. (c) Show all stresses from part (b) on a properly oriented stress element. Be sure to include all stress components acting on the element.
Problem 3: For the plane stress state listed below, draw a Mohr's circle diagram properly labeled. Keep in mind that the principal stress is that stress state where the shear stress is zero. That means it is the stress state along the normal stress line in Mohr's space. So, use your Mohr's circle to find the principal normal and shear stresses, and determine the angle from the x axis to o1. 0x = 16 kpsi, oy = 9 kpsi, Ty = 5 kpsi ccw
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.
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
Problem 2: For the plane stress state listed below, draw a Mohr's circle diagram properly labeled. Keep in mind that the principal stress is that stress state where the shear stress is zero. That means it is the stress state along the normal stress line in Mohr's space. So, use your Mohr's circle to find the principal normal and shear stresses, and determine the angle from the x axis to o1. 0x = 20 kpsi, oy =-10 kpsi, Txy = 8 kpsi cw
(a) Construct Mohr's circle for an element in a uniaxial state of stress (b) Use this Mohr's circle to derive the equation for the normal stress On and shear stress En on the n-face. The equations should depend on Ox and θ (c) Use the Mohr's circle to determine the planes on which the maximum shear stress acts. Sketch a properly oriented maximum-shear-stress element and indicate the normal and shear stresses acting on its faces. Ơn nt o, Note: for (b), the angle θ is between 0 and 90° and is positive
Mohr's circle is shown for a point in a physical object that is subjected to plane stress, Each grid square is 13 MPa in size. (a) Determine the stresses o, 0, and the magnitude of t, and show them on a stress element. (b) Determine the stresses a o, and the magnitude of Ta and show them on a stress element that is properly rotated with respect to the xy element. The sketch must include the magnitude of the angle between the x andnaxes and an indication of the rotation direction (ie, either clockwise or counterclockwise). Answer: (a) d. MPa dy. 110.0720 MPa Ty 1100720 MPa (b) C- s8.3065 MPa 16230865 MPa Tat- 110.3086 MPa
For the stresses given with the cube below: 1. Compute the center, radius (R), principal normal stresses (0₁ and 03), max shear stress (Tmax) and draw the Mohr's Circle. 2. Compute the normal and shear stresses when the cube is rotated 20° clockwise from the horizontal plane and draw them on the cube. 3. The yield point stress (σyp) is 6 kPa. Determine if the material will fail under stresses shown using Tresca's Hexagon. вкра акра 6 экра 8 кра экра 4кра
The normal and shear stresses acting on one plane passing through a point in a soil mass are 120 psi compression and 25 psi, respectively. On an orthogonal plane, the respective stresses are 40 psi compression and 25 psi. (a) Draw the Mohr’s circle for this stress condition. (b) What are the principal stresses? (c) Determine the angle between the plane on which the 120 psi stress acts and the major principal plane. (d) What is the maximum shear stress acting at the point?
Consider the 2-D state of stress shown below. Using the provided scales graph the Mohr's Circle for the 2-D state of stress with “full" details II-Obtain the Principal Stresses, the Maximum Shear Stress, and complete the table below III- Draw the Planes of Principal and Maximum Shear Stresses in the space provided below Provide "full" details and Use 3 Sig. Fig. in this problem Oy = 15 Ksi Tcw > S y Ox =10 Ksi Тух 5 Ksi 10 5 -20 -15 -10 5 10 15 20 5 10 Tccw > S' O Avg. TMax. 01 02 Op1