3.8 Relative to the Cartesian axes Ox,x,x3 a stress field is given by thematrix(4-x} )x,(3–x; )x,(a) Show that the equilibrium equations are satisfied everywhere forzero body forces.(b) Determine the stress vector at the point P(2,-1,6) of the planewhose equation is 3x, +6x, +2x, = 12.

Answered: Image /qna-images/answer/5e4c7696-5534-402f-812a-78224731e8f7.jpg

Answered: Relative to the Cartesian axes Ox,x,x3…

Relative to the Cartesian axes Ox,x,x3 a stress field is given by the matrix (1–x; )x, + x -(4– x²)x, -(- 12%,) 0. (3-x} )x,

Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

See similar textbooks

Related questions

Q: The state of stress at a point in a member is shown in A 0x' = 60° σ y B on the element. Assume ox…

Q: A stress element i's shown in Figure, ueing Mohr's circle. Find the principal stresses and the…

Q: 40MPA 30 40MPA 100MPA

Q: 3= The state of strains at a point are defined as follows. Find X and Y such that the normal and…

Q: • If a point is subjected to the state of stress, determine the principal stresses and the maximum…

Q: Q.2) A state of stress is specified as shown in Figure (2), By using Mo determine the normal and…

A: Radius of the circleR=(σx-σy2)2+τxy2R=(40+802)2+502R=78.1…

Q: The uniform wire is bent into the shape shown and held by the frictionless pin at O. Determine the…

A: It is given that,

Q: As shown in the figure, the simply supported beam is only subject to the action of dead weight, the…

Q: rs circle is shown for a point in a physical object that is subjected to plane stress. Each grid…

Q: 3. The tensile member shown, 60 mm x 90 mm in cross section is subjected to a load P=300 kN. The…

A: Solution Given Data: P= 300 KN Cross-section area A=(60mm×90mm) Angle with horizontal axis= 140

Q: Q4) ( ): A state of stress is specified as shown in Figure (4), By using Mohr's circle determine the…

A: .

Q: Determine whether the following stress functions satisfy the conditions of compatibility for a…

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

Q: Displacement components at a point in a solid u(x, y, t) = 2y²x + 2t v(x, y, t) = 8y³x³ + 5t? w(x,…

Q: An axial bar is shown below. E = 200 × 10⁹ Pa, A = 0.42 × 10-3 m². The bar can be divided into two…

Q: Determine the equivalent state of stress on an element at the same point oriented 0 = 40° clockwise…

Q: A rigid beam is supported by bar DE. If the vertical displacement of point D is to be less than 0.1…

A: Vertical displacement of point D (∆D) = 0.1 in. Determine the minimum cross sectional area of bar DE…

Q: For the given state of stress of element A, strictly using Mohr's Circle perform the following:…

Q: Find the normal stress and shear stress in the shaded plane using the MOHR circle for the element in

A: Given that:

Q: 3= The state of strains at a point are defined as follows. Find X and Y such that the normal and…

Q: Principle stresses of 100 kPa (tension) act on two mutually perpendicular faces of a rectangular two…

A: Principle stress=100 kPa

Q: 4. Complete the following a. Draw Mohr's circle for the element given and label the axes b.…

A: Answer Since we are not allowed to provide handwritten solution we have used Autocad to draw the…

Q: 2. A bar of elliptical cross-section defined by the boundary -1 = 0 is loaded by a shear force F, =…

A: Bar of elliptical cross section defined by the boundary x2a2+y2b2-1=0 Calculate shear stress…

Q: : For the state of stress ox = 2, txy = -3, Gy = -1 Compute the eigenvector associated with the…

A: INTRODUCTION: For the 2D Stress system, the matrix represent of normal and shear stress is…

Q: A state of strains is defined by; €, = 250 x 106, €, = -350 x 106 and y»y = 400 x 10°. Analyze the…

Q: 3. The plane stress is shown on the element. Use Mohr's circle. 1) Determine the principal stresses…

A: Finding out principal planes and stresses.

Q: a) Find the deformation b) Find the deformation volume of the unit cube of area of OABC X3,x3 B A…

Q: 5. The state of stress at a point in a member is shown on the element. Determine the stress…

Q: 2. Using Mohr's Circle, determine the stresses on the element below if it were rotated by 0,. Do the…

A: Given as in above figure: - σx=+45 MPaσy=-60 MPaτ=30 MPa

Q: ected to the stresses σxx = 2,900[kP a], σyy = 9,100[kP a] and τxy = −3,750[kP a]. Using Mohr's…

A: σx=2900kpaσy=9100kpaτxy=-3750kpaRadius of the circleR=(σx-σy2)2+τxy2R=(2900-91002)2+-37502R=4865kPA

Q: In a triaxial stress system, the six components of the stress at a point are: 0 = 6 MPa Try = 1 MPa…

A: Given data : This is a problem of Solid mehanics.

Q: The state of stress at a point is shown on the element. Enter your answers numerically separated by…

A: Consider the figure.

Q: 3= The state of strains at a point are defined as follows. Find X and Y such that the normal and…

Q: t y n

Q: e of stress if an element is oriented 50° counterclockwise to the element. Show the result on the…

Q: Determine the principal stress, the maximum in-plane shear stress, and average normal stress.…

A: Solutions are given below

Q: 80 50 50 80

A: Note: Hi! Thank you for the question, As per the honour code, we are allowed to answer three…

Q: Question 1 Find the state of of stress for the element in Figure Q1 inclined by 30° counter…

A: Given data Tensile load Compressive load Shear stress Angle of plane

Q: stresses acting on an oriented element An Angle Θ from the x-axis, show those stresses on an element…

Q: 500 400 300 200 100 -400 B00 -200100 400 500 -500 100 200 300 -100 -200 -300 -400 -500

A: Given : Stress state of a 2D element is as shown below Required: To determine following a) Maximum…

Q: 3= The state of strains at a point are defined as follows. Find X and Y such that the normal and…

A: This question is related to the Strength of Material.

Concept explainers

Planar Stresses

Question

3.8 Relative to the Cartesian axes Ox,x,x3 a stress field is given by the
matrix
(4-x} )x,
(3–x; )x,
(a) Show that the equilibrium equations are satisfied everywhere for
zero body forces.
(b) Determine the stress vector at the point P(2,-1,6) of the plane
whose equation is 3x, +6x, +2x, = 12.

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

Step 6

Trending now

This is a popular solution!

Step by step

Solved in 6 steps with 6 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, civil-engineering and related others by exploring similar questions and additional content below.

Similar questions

Young modulus and stress have same dimension. a.True b.false
Consider the stress state shown in Fig a) Find the "max shear stress" (t max) and the "average normal stress" (o avg). Indicate these points on the circle Mohr and show the summary on a square element b) Find the Cartesian constraints if the element is rotated 30degree Counterclockwise (CCW) and show the summary on a square element Note: for part (d) you can use the equations or the circle, it's your choice (using equations is faster)“ yt 40 MPа 30 MPa 20 MPa
A beam having the cross section shown is subjected to a vertical shear V. Determine (a) the horizontal line along which the shearing stress is maximum, (b) the constant k in the following expression for the maximum shearing stress.τmax=k*V/Awhere A is the cross-sectional area of the beam
16 Yield point is the boundary in the stress-s train diagram where stress loses its prop ortionality with strain.( 17 True 18 False Strain is the ratio deformation over origin al length.( True False The value of stress can be unitless. True False
Mohr’s circle is shown for a point in a physical object that is subjected to plane stress. Each grid square is 8 MPa in size.(a) Determine the stresses σx, σy, and the magnitude of τxy and show them on a stress element.(b) Determine the stresses σn, σt, and the magnitude of τnt and show them on a stress element that is properly rotated with respect to the x-y element. The sketch must include the magnitude of the angle between the x and n axes and an indication of the rotation direction (i.e., either clockwise or counterclockwise).
Q1) A stat of stress is specified in Figure. By using Mohr's circle determine the normal and shearing stresses on the principal plane, and sketch the results. 18 MPa 60 MPa 15 MPA
Flexure stress *Please answer in complete solution and draw the shear and moment diagram, Solve the Area moment of inertia*
Two dimensional stress tensor at a point is given by a matrix *][* [100 30 30 20 The maximum shear stress is MPa MPa.
n=8
The given stresses are 0x = 48 MPa, 0x =- 32 MPa, and Txy = 20 MPa. The rotation angle 0 = 30°.Use the stress transformation equations to determine the stresses on an element that is rotated bythe given angle 0 and show the calculated stresses on the rotated element.