An element of a ductile material on the free surface of a component is subjected to the stress system shown in Figure 1. (a) Determine the direct and shear stress on the plane 0 = 35⁰. (b) Calculate the magnitude and direction of the principal stresses, identifying clearly which angle represents the maximum principal stress. (c) Calculate the maximum shear stress. What is its significance in design?

An element of a ductile material on the free surface of a component is subjected to the stress system shown in Figure 1. (a) Determine the direct and shear stress on the plane 0 = 35⁰. (b) Calculate the magnitude and direction of the principal stresses, identifying clearly which angle represents the maximum principal stress. (c) Calculate the maximum shear stress. What is its significance in design?

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: The three principal stresses at a given point are o; = 60 MPa, o2 = -100 MPa, o3 = -10MPA. If the…

A: Given that, σ1 = 60 MPaσ2 = -100 MPaσ3=-10 MPa Yield strength of Material Syt = 250 MPa

Q: 5. The bottom of a frying pan is made from three layers, each of 1 mm thickness. The top and bottom…

A: Step 1: Step 2:

Q: Determine the equivalent state of stress if an element is oriented 60° clockwise from the element…

Q: A circular tube is subjected to torsion by torques T applied at the ends. The bar is 0.75 m long and…

A: The length of the bar is, L=0.75 m The inside diameter of the bar is, d=35 mm The outside diameter…

Q: Determine the equivalent state of stress on an element at the same point oriented 60° clockwise with…

Q: The wood beam in (Figure 1) is subjected to a load of P = 15 kN. Grains of wood in the beam at point…

A: Given data with the suitable variables. P=15 kNβ=25° It is required to determine the normal and…

Q: At a point on a component, the stress has been calculated. The direct stress in the x direction is…

Q: A circular rod of length 18 cm and diameter 5 mm is made of grade 1045 grade steel. a. Calculate the…

Q: (a) the strains in these directions, (b) the changes in dimensions, (c) the volumetric strain and…

Q: An aluminum bar has length L = 5 ft and diameter d = 1.25 in. %D The stress-strain curve for the…

A: Data given- L = 5 ft = 5×12 = 60 in d = 1.25 in E = 10 × 106 psi P = 39 ksi

Q: Describe in words (not equations) the following: (a) Principal stresses (b) Principal centroidal…

A: The principal stresses and the principal centroidal axes of bending.

Q: What is the maximum shear stress RESULTING FROM THE COMBINATION OF THE FOLLOWING stresses: Tesile…

A: Given data: Sx=200 MPaSy=100 MPaSS=50 MPa Need to determine the maximum shear stress.

Q: Besides normal tensile stress, list three other types of material stresses? Are these typically all…

A: Stress: Stress is defined as the internal resistance per unit area of cross-section. There are…

Q: Please solve in detail. Don't use chatgpt,The Free body diagram must be drawn. Thanks -mechanical

A: Step 1

Q: D 3.2-5. Utilice el método gráfico para demostrar que el siguiente modelo no tiene soluciones…

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

An element of a ductile material on the free surface of a
component is subjected to the stress system shown in Figure 1.
(a) Determine the direct and shear stress on the plane 0 = 35⁰.
(b)
Calculate the magnitude and direction of the principal
stresses, identifying clearly which angle represents the
maximum principal stress.
(c) Calculate the maximum shear stress. What is its significance
in design?
100 MN m-²
0
200 MN m-²
80 MN m-²
100 MN m-²
T200
Figure 1: Stresses on element
200 MN m-²
1..
1x
X

Expert Solution

This question has been solved!

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

SEE SOLUTION Check out a sample Q&A here

Step 1: GIVEN VALUES IN PROBLEMS

VIEW

Step 2: DIRECT AND SHEAR STRESS

VIEW

Step 3: MAGNITUDE AND DIRECTION OF PRINCIPAL STRESSES

VIEW

Step 4: MAXIMUM SHEAR STRESS

VIEW

Solution

VIEW

Step by step

Solved in 5 steps with 4 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

A tool steel cylindrical specimen, 6 in. long and 0.25 in. in diameter, is kept rotating like a cantilever beam and must be designed in such a way that rupture never occurs. Assuming that the maximum tensile and compressive stresses are equal, determine the maximum load that can be applied at the end of the life (see figure)
Which of the following is true for an infinitesimal stress element? (T in the options below refers to tau, or shear stress) (a) Txy = Tyz (b) Txy = Tyx (c) Txy = Txz (d) Tx = Ty
For the plane stress state shown: (a) Determine the principal stresses and show them on a properly oriented element. For this part, use the transformation equations only and not Mohr's circle. (b) Repeat part (a) using Mohr's circle. (c) Determine the maximum shear stress and show the complete state of stress on a properly oriented element containing this maximum shear stress. 25 kpsi 15 kpsi 12 kpsi X
The prismatic bar shown below has a solid circular cross section with a 2 in. radius.(a) Calculate the average normal stress at P1 and (b) Calculate the average normal stress at P2.
What’s the answer for this please ?
(c) An element is subject to the stresses shown below in Figure 5 Calculate the centre and radius of the Mohr's stress circle and sketch the circle (1) (ii) Calculate the values of principal stresses and show them on the circle (ii) Determine the direction of the larger principal stress relative to the 75 N/mm. 30 N/mm A 14 Nmm 75 N/mm2 30 N/mm Figure 5
Problem 6. Consider the following stress state: [6 4 01 12 0 ksi 0 a. Determine the corresponding strains if the Young's modulus and Poisson's ratio are equal to 10,000 ksi and 0.25, respectively. [0] = 4 Lo b. Determine the principal stresses. c. Determine the maximum shear stress. d. Determine the angle the axes need to be rotated around the z-axis to obtain the maximum shear Txy stress. e. Can this stress state be a result of a plane stress problem? f. Can this stress state be a result of a plane strain problem?
A rectangular column (blue color) is fixed to a rigid ground (brown color). As shown in the figure, the column is under two external loadings at C. Determine the state of stress at point K of the column and represent the stress components on a stress element.
An element is subject to the stresses shown below in Figure 5 (i) Calculate the centre and radius of the Mohr's stress circle and sketch the circle (ii) Calculate the values of principal stresses and show them on the circle (iii) Determine the direction of the larger principal stress relative to the 75 N/mm?. 30 N/mm? 14 N/mm? 75 N/mm? 75 N/mm? 30 N/mm2 Figure 5
1. A part made of Aluminum 6061-T6 has a yield strength = 400 MPa. For each stress state below, draw all 3 Mohr's circles, find the principal stresses, and calculate the safety factor against yield using both the distortion-energy (von Mises) and maximum shear stress (Tresca) criterions. (If relevant) A clearly labeled diagram (or diagrams) clearly pertaining to your analysis with a coordinate system and relevant labels. Final answer with appropriate units and significant figures. You can use the fprintf() command in MATLAB to format numerical results A 2-3 sentence reflection on your answer. Does it make sense? Why or why not? What are some implications?
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
The state of stress in a machine element is illustrated in the stress element as shown in Figure 4: (a) (b) 250 MPa Figure 4 By calculations ie using equations or formulae find the following: The principal stress. 400 MPa 560 MPa The normal and shear stresses on a plane inclined at 30° CW. L.