If the stress distribution in the rectangular plate shown in the figure can be given by the Airy stress function P = pr³y+ qry³, where p, q are constants, then, (a) Verify whether the given stress function satisfies the compatibility conditions for plane stress problem. (b) Determine the stresses oz, Oy and Try. (c) Sketch the boundary stresses on the plate. (d) Find the resultant normal and shearing boundary forces along the right and bottom edges of the plate. y a

If the stress distribution in the rectangular plate shown in the figure can be given by the Airy stress function P = pr³y+ qry³, where p, q are constants, then, (a) Verify whether the given stress function satisfies the compatibility conditions for plane stress problem. (b) Determine the stresses oz, Oy and Try. (c) Sketch the boundary stresses on the plate. (d) Find the resultant normal and shearing boundary forces along the right and bottom edges of the plate. y a

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: A composite shaft consists of 3 cylinders that are made from aluminum, copper and steel. Multiple…

A: To findDetermine the normal stress in section AB, Determine the normal stress in section BC,…

Q: A circular plate with simply supported edges subjected to a uniform pressure of P=1,450 KPa, as…

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: 3 m 30° 30°

A: The uniform temperature rise in bar 1 is .The modulus of elasticity is .The area given is .The…

Q: Consider a point in a structural member that is subjected to plane stress. Normal and shear stress…

Q: A large thin rectangular plate is subjected to certain traction boundary conditions on its thin…

A: Given : φ(x,y)=Ax4+Bx2y2+Cy2

Q: A 0.625" OD x 0.035" Wall x 0.561" ID Copper Round Tube is being used in a pressure system that is…

Q: occur in the n-n plane of the figure. Present a diagram showing such stresses on the n-n plane.…

Q: A closed ended, thick-walled cylinder, manufactured from silicon material is designed to contain…

A: Given data, Outer radius of the cylinder, ro = 0.3 m Inner radius of the cylinder, ri = 0.1 m…

Q: A typical aluminum-alloy scuba diving tank is shown in the figure. The outside diameter of the tank…

Q: A 150 min x a mnm x 20 mm stecl plate is subjected a pull of 150 kN along its central axis as show…

Q: The hollow drill pipe for an oil well (see figure)is 6.2 in. in outer diameter and 0.75 in. in…

A: Given Outer diameter = 6.2 in Thickness = 0.75 in Weight = 62 kips Torque = 185 kip-in To find…

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: A differential stress element as shown in Figure Q1 is subjected to a plane strain.(given E = 73 Gpa…

A: Since we only answer upto 3 subparts, we will answer the first 3. Please resubmit the question and…

Q: 3. As in the figure, a ship can move both with the wind and with a diesel engine. your ship The mast…

Q: (1) A steel cylinder (Oyp = 260 MPa) of inner radius a and outer radius 3a is subjected to an in %3D…

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: In a thin plate, the state of stress prevails according to the figure. Calculate the principal…

Q: 2- Determine the nodal displacements and the element stresses for the thin plate with a uniform…

A: Find outDetermine the nodal displacement and the element stresses for the thin plate.GivenYoung's…

Q: A point On a free surface of a machine point (E = 214Gpa, G= 83Gpa) the stress state is shown on the…

A: GIVEN :- E = 214Gpa G= 83Gpa σy=15 MPaσx=-30 Mpaζxy=25 MPa

Q: A state of stress is specified in the figure shown below. Determine the Normal stress ox (mPa) on…

Q: 2. Consider the Flamant solution - a line load on the edge of a half space. The valid stress…

A: according to a given question

Q: A roadway sign weighs 5 kN and is supported by a structural pipe that has an outside diameter of 295…

Q: A steel rail for railroad track is 10 m long. Determine the stress in the rail if it was completely…

Q: A structural member is subjected to a plane stress loading condition. The state of stress at a point…

Q: The carrier plate in the figure is attached to the column with the help of 3 bolts. A vertical force…

Q: If the principal stresses in a plane stress problem, are o1 = 100 MPa, o2 = 40 MPa, the magnitude of…

Q: For the pressure vessel in which the loading condition is seen in the figure determine the maximum…

A: Note: the stress values are calculated for the point “a” on the top of the cylindrical pressure…

Q: A typical aluminum-allóy scuba diving tank is shown in thế ngure. The outside diameter óf the tank…

A: Solution:

Q: To draw the internal normal force diagram, it is important to determine the internal normal force at…

A: Find internal force at point A Given data:- P1=4.5 kips P2=8 kips

Q: In a plane stress condition, the components of stress at point are ox = 20 MPa, ơy = 80 MPa and txy…

A: Given, Stress in x-direction = σx = 20 MPa Stress in y-direction = σy = 80 MPa Sheat stress in…

Q: square plate is subjected to uniform pressure as shown in Figure.1. The 2D loading stresses are…

A: E=200 GPa,μ=0.3Strain in x-direction,εx=∆LLεx=1Eσx-μσyεx=120080-0.3×40εx=0.34×10-3

Q: 3) Objects 1 and 2 are positioned as shown in the figure. Object 1 is a rigid support. For object 2,…

A: Consider a body having length L,cross-sectional area A and Young's Modulus E is heated by ΔT°C.…

Q: Solve the previous problem again for the case where the mass of the rear door is Mt = 27 kg and the…

A: Given data: Mass of crate, mC = 68 kg. Mass of rear door, mT = 27 kg. Crosssection area of cable, A…

Q: The articular Cartilage is subjected to plane stress with normal stresses &x ,Oy and shear stress…

Q: Calculate the principal normal stresses and their directions, the maximum shear stresses and the…

Question

If the stress distribution in the rectangular plate shown in the figure can be given by the Airy
stress function P = pr³y+qxy°, where p, q are constants, then,
(a) Verify whether the given stress function satisfies the compatibility conditions for plane
stress problem.
(b) Determine the stresses oz, Oy and Try.
(c) Sketch the boundary stresses on the plate.
(d) Find the resultant normal and shearing boundary forces along the right and bottom edges
of the plate.
y
a

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

Step 2

Step 3

Step 4

Step 5

Trending now

This is a popular solution!

Step by step

Solved in 5 steps with 1 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

principal stress is 10 kPa, then the normal stress stress, is shown in the figure below. If the minimum The state of stress at a point, for a body in place o (in kPa) is = 50 kPa 0,= 100 kPa %3D X,
: A rigid platform weighing 53.5 kN is supported by three equally spaced rods. The arrangement is shown in the figure. Determine the stress in the rod if the rise in temperature of these rods 55.5 °C. Bronze L= 0.9 m Steel L = 0.6 m Os As Ob Ab Steel OsAsL= 0.6 m P = 53.5 kN
A torque and two forces seen in the figure are applied. the diameter is 65mm. Determine the principal stresses And the maximum shear stress at K.
nc./Johan H σy 7.2-1 The stresses on the bottom surface of a fuel tanker (figure part a) are known to be o = 7750 psi, = 1175 psi, and 7 xy = 940 psi (figure part b). Determine the stresses acting on an element oriented at an angle = 55° from the x axis, where the angle is positive when counterclockwise. Show these stresses on a sketch of an element oriented at the angle 0. (a) PROBLEM 7.2-1 (b) 1175 psi Ţ 940 psi 7750 psi 7.2-5 The stresses acting on element A on the web of a train rail (see figure part a) are found to be 6500 psi tension in the horizontal direction and 18,500 psi com- pression in the vertical direction (see figure part b). Also, shear stresses with a magnitude of 3800 psi act in the directions shown. Determine the stresses acting on an element ori- ented at a counterclockwise angle of 30° from the horizontal. Show these stresses on a sketch of an ele- ment oriented at this angle. Cross Section (a) PROBLEM 7.2-5 B A Side View A (b) 18,500 psi 76500 psi 3800 psi
The state of stress at a point in a structure is shown in the following figure.Determine:(a) The forces acting on an element oriented at an angle in the directioncounterclockwise angle = 40 ° from the x-axis (Show results in a sketch ofcorrectly oriented)(b) Find the maximum shear stress with its average stress (Show theresults in a correctly oriented sketch).
pru 7 Oy enüz žvaplanmadı Ot .00 üzerinden aretlenmiş Txy Soruyu aretle Ka Tnt Ox On (a) (b) On the surface of a structural member, stresses are given as ox=61 MPa, oy=32,7 MPa and Txy=-28,1 as shown in figure (a). Determine the maximum principal stress (MPa). Note: If the stress is compressive, use - sign. Yanıt:
In the figure, both ends of the rectangular plate are under the effect of a force p = 150kN. What is the value of the shear stress occurring in the NN 'plane which makes an angle Q = 30 ° as shown in the figure? cross-sectional area is 100mm ^ 2.
Calcuate Torsion and Bending From Point A to Point B and Point A to Point C. Draw a FBD from point A to point B and another for point A to C indicating what stresses are been calculate. Use the stress tensor and stress cube to Indicate what forces are acting at point A. Force apply at point B is 70lb Distacen from Point A to B is 12 in or 1 feet long Distacen from Point A to C is 3 in Handle diameter 0.625 in
Q.1) For the element of material is in biaxial stress with ox and oy and shear stress ty, as shown in the figure. At a counterclockwise angle 0 = 32° from the x axis, the normal stress (0 ) is 29 MPa in tension, and at an angle 0 = 46°, it is 17 MPa in compression. If the stress ox equals 105 MPa in tension, what are the stresses o,y and Ty? oz= 105 MPa
A structural member is subjected to the plane stress condition. The state of stress at a point of the member is shown in the figure. 45 MP (1) Draw the Mohr's circle for this 2D state of stress. (2) Determine the principal stresses, the maximum in-plane shear stresses and associated normal stresses acting at this point, (3) Represent these critical stresses on new stress elements, and indicate the angles of rotation of the new stress elements with respect to the original stress elements. 25 MP
The principal plane stresses and associated strains in a plane at a point are s1 = 36 ksi, s2 = 16 ksi, P1 = 1.02(10-3), P2 = 0.180(10-3). Determine the modulus of elasticity and Poisson’s ratio
4-Find the stresses in each direction, also find the change in volume of the block of dimension 110 mm x 50 mm x 31 mm, subjected to 3 mutually perpendicular loads. The load along length, breadth and depth directions are 22 kN (tensile), 30 kN (compressive), 22 kN (compressive) respectively. Take E as 100 GPa, Poisson’s ratio as 0.3 The stress along length direction (Unit in MN/m2)= _____________ The compressive stress along width direction (Unit in MN/m2)= _____________ The compressive stress along depth direction (Unit in MN/m2)= _____________ The change in volume of the block is (unit in mm3) = ______________