2. The state of stress at a point in a machine part is given by the following stress tensor. The uniaxial yield stress for a steel material is oyp =950 MPa: 300 []= -400 MPа 300 -800 Calculate (a) the stress invariants I1, I2, I;; (b) the principal stresses by expansion of the characteristic stress determinant. (c) Determine using (i) the Tresca criterion and (ii) the von Mises criterion whether or not yielding occurs at the point with the above stress tensor. (Hint: Determine the principal stresses, o,, o,, and 0,, by solving the cubic Equation: o,-1,0,+I,0,-I, =0). Note: Failure occurs when lhs of the Equation for the Failure Theory being tested is greater than the rhs; FS is not needed for this problem (why?).

2. The state of stress at a point in a machine part is given by the following stress tensor. The uniaxial yield stress for a steel material is oyp =950 MPa: 300 []= -400 MPа 300 -800 Calculate (a) the stress invariants I1, I2, I;; (b) the principal stresses by expansion of the characteristic stress determinant. (c) Determine using (i) the Tresca criterion and (ii) the von Mises criterion whether or not yielding occurs at the point with the above stress tensor. (Hint: Determine the principal stresses, o,, o,, and 0,, by solving the cubic Equation: o,-1,0,+I,0,-I, =0). Note: Failure occurs when lhs of the Equation for the Failure Theory being tested is greater than the rhs; FS is not needed for this problem (why?).

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

See similar textbooks

Related questions

Q: For the three stress states given, find all principal normal stresses using the eigenvalue method.…

A: In eigenvalue approach, the eigenvalue represents the principal normal stresses and eigenvectors…

Q: Q2 The state of stress at a point of an elastic solid is given in the x-yz coordinates by: (a)…

A: (a) Write the given matrix. σ=σxxσxyσxzσyxσyyσyzσzxσzyσzz=901800180240000120 MPa

Q: Torsion From Point A to Point C (point C is where is connect it to the lug nut) Calcuate Bending…

A: Distance between Point A and B = 12 in = 1 ftDistance between point A and C = 3 in = 0.25 ftdiameter…

Q: [20 [o] = 10 0 b. Plot Mohr's circle for this stress state. 10 01 10 005 0 a. Determine the stress…

A: (a) Write the given stress matrix. σ=2010010100005

Q: A very thick structure is subjected to certain traction boundary conditions on its surface. The…

A: “Since you have posted a question with multiple sub-parts, we will provide the solution only to the…

Q: The tank shown in Figure below is fabricated from t = 1/8 in steel plate. The naximum longitudinal…

Q: Given a stress state of a, = -4 MPa, a, = 12 MPa, ty = 7 MPa cew 1) Draw a properly oriented stress…

Q: Rockwell hardness . figure 6.19 Rockwell hardness Tensile strength = 0 MPA Tensile strength = 0 ksi…

A: (a)

Q: Learning Goal: To calculate the shear stress at a point in the web of an l- beam section subjected…

A: To Find : The moment of inertia of the whole cross sectionThe value of QThe shear stress at a point…

Q: The following stress condition is applied to a cubic material. Normal stress in the x direction is…

A: To Find:the stress tensor.the maximum normal stress.the angle with respect to the x-axis at which…

Q: 1. The circular tube shown in Fig. 1 is subjected to a uniform internal pressure P; and external…

A: 1 2

Q: Y Part B - Clockwise Rotation of a Stress Element with Only One Normal Stress The state of stress at…

A: Note:- As per honor code and answering guidelines I can answer 1st question at a time.If you want…

Q: A thin plate is subjected to certain boundary conditions on its thin edges leading to the stress…

Q: 3) Solve the plane stress problem using two-element model to find displacements and stresses. 15 kN…

Concept explainers

Stress transformation

The term stress indicates the measure of internal forces that develop due to an external force's application on an object. When a specific external force is applied to an object, internal stress generates in the material. The value of stress can obtain by taking the ratio of the externally applied force and cross-sectional area of the object. There are different types of stress depending on the type of external force.

Question

2.
The state of stress at a point in a machine part is given by the following stress tensor. The uniaxial yield stress
for a steel material is oyp =950 MPa:
300
[o]= 0
-400
0.
MPa
300
0.
-800
Calculate (a) the stress invariants I1, I2, I;; (b) the principal stresses by expansion of the characteristic stress
determinant. (c) Determine using (i) the Tresca criterion and (ii) the von Mises criterion whether or not yielding
occurs at the point with the above stress tensor.
(Hint: Determine the principal stresses, o,, o,, and o,, by solving the cubic Equation: o–1,0, +I,o,-I, =0).
Note: Failure occurs when lhs of the Equation for the Failure Theory being tested is greater than the rhs; FS is not
needed for this problem (why?).

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 2 steps with 3 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.

Similar questions

The following stress condition is applied to a cubic material.Normal stress in the x direction is 15 Mpa, normal stress in the z direction is -7 Mpa and the shear stress in the x-z plane is 59 Mpa.(a) Write the stress tensor(b) Find the maximum shear stress(c) Determine the angle with respect to the x-axis at which the maximum shear stress is experienced
3. A food product with 73% moisture content in a 10 cm diameter can wants to be frozen. The density of the product is 970 kg / m³, the thermal conductivity is 1.2 W / (m K), and the initial freezing temperature is -2 ° C. After 14 hours in the freezing medium -30 ° C, the product temperature becomes -10 ° C. Estimate the convection heat transfer coefficient of the freezing medium. Assume the can as an infinite cylinder. h = Answer W / (m² K).
The following stress condition is applied to a cubic material. Normal stress in the x direction is 15 Mpa, normal stress in the z direction is -7 Mpa and the shear stress in the x-z plane is 59 Mpa (a) Write the stress tensor (b) Find the maximum normal stress (c) Find the angle with respect to the x-axis at which the maximum normal stress is applied (d) Find the maximum shear stress (e) Determine the angle with respect to the x-axis at which the maximum shear stress is experienced
Given the stress tensor: Find: 3 36 27 0 σ = 27-36 00 0 18 (a) The components of the traction (force per unit area) acting on a plane with unit normal n= 2 21 3 3'3 T (b) The component of the traction in the direction of the normal (c) The angle between the traction and the normal vector (d) The magnitude of the traction vector (e) The net force acting on a cube with corners at (x,y,z)=(±1,±1,±1)
I solved the principal stresses but having a hard time on determing the theta-P (orientation of principla plances), could you help me?
M13.6 Principal stresses from rosette data scenes -200 µE 23 Eb = 200 με Ec 500 µE 30° 30° Ex (LE) a Ey (µE) Yxy (Lurad) The strain rosette shown was used to obtain normal strain data at a point on the free surface of a steel (E = 200 GPa; v = 0.32) plate. Op1 (MPa) Determine the normal strains, the shear strain, and the principal stresses in the x-y plane. Op2 (MPa) Try One 1st 2nd 3rd attempt enter
Calculate the stress state at D (populate the stress tensor)
Calculate the stress state at D (populate the stress tensor)
I have been stuck on this problem for while thar area is 779.1 mm^2 sigma_x is 120.6497159 sigma_y is 0 and tau_xy is 0. Beta is 20 degrees