An element is subject to the following normal and shear strains: €x = -350 x 10-6 €y = 200 x 10-6 Yxy = 300 X 10-6 If the element were oriented at an angle of 15° counterclockwise: a) Determine the normal and shear strains Ex', ', and Yx'y'. b) The principal strains and the orientation upon which they act. c) The maximum in-plane shear strain and the orientation upon which they act.

An element is subject to the following normal and shear strains: €x = -350 x 10-6 €y = 200 x 10-6 Yxy = 300 X 10-6 If the element were oriented at an angle of 15° counterclockwise: a) Determine the normal and shear strains Ex', ', and Yx'y'. b) The principal strains and the orientation upon which they act. c) The maximum in-plane shear strain and the orientation upon which they act.

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: Why is there no normal stress due to bending moment Mz at the Z-axis? The answer my professor gave…

A: Normal stresses due to bending are induced when the bending moment acts perpendicular to the member…

Q: The strain components Ex, Ey, and Yxy are given for a point in a body subjected to plane strain.…

Q: normal stresses of 0 and 10 MPa (T)

A: Given:A rod element is oriented orthogonally to the horizontal and verticalσx=0 MPaσy=10 MPaτxy= 6…

Q: Material is subjected to a general state of plane stress. Express the strain energy density in terms…

A: Consider the figure shown below. The expression for the normal strain along the x axis is given by,…

Q: A stat of stress is specified in figure by using Mohr's circle determine the normal and shearing…

A: Given:Required:Normal and shear stress on principal planes and on plane having maximum shear stress.

Q: PROBLEM 10-n GIVEN: THE STATE OF STRAIN AT THE POINT ON THE PIN LEAF HAS COMPONENTS OF = 200(106), y…

A: εx=200×10-6 εy=180×10-6 γxy=-300×10-6 θ=-30o counter clock wise

Q: 1: he in-plane principal stresses and ar stress along with their orientations and mal stress for an…

A: Radius of the circleR=(σx-σy2)2+τxy2R=(116+282)2+642R=77.25 MPA

Q: What is meant by strain transformation? Describe two procedures for obtaining stress form Mohr’s…

A: Strain transformation equations are given as : This is similar to stress transformation equations,…

Q: The initially square element of a material is deformed as shown. Determine the shear strain of the…

A: To find shear strain of element To find normal strain along AC,BD

Q: Please give correct answer

A: Given data : σX=100 MPaσY=80 MPaζXY=-30 MPa

Q: The state of strain at a point is; ϵx = - R x 10-6 , ϵy = R/2 x 10-6 and γxy = 1.4R x 10-6 .…

A: The principal strain is the largest and smallest normal strain that happens at a particular point on…

Q: The 2D stress at a point is given by the matrix 50 15 Oxx Oxy МРа 15 10 Oxy Oyy The maximum shear…

A: To get maximum shear stress, first we have to calculate major and minor principal stress. Then…

Q: The strain components Ex, Ey, and Yxy are given for a point in a body subjected to plane strain.…

A: Given :- εx=0εy=370 μεγxy=260 μrad To find:- εp1, εp2, γmax , γabsolute max and θp

Q: Rev Part C-Orientation of the element subjected to maximum shear stress on its sides Determine the…

Q: 7. For the state of stress shown, determine the principal stresses and the principal directions.…

Q: Transform the state of stress shown by rotating its orientation 50 degrees counterclockwise. What…

A: Shear stress and normal stress are given anaylitically we can find unknown

Q: The principal stresses in N/mm² on a rectangular element are shown in the below figure. The…

A: Given, σ1 = 400 N/mm2σ2 =-100N/mm2θ = 30°

Q: The state of strain at the point on the leaf of the caster assembly has components of Ex =…

Q: 7.2-2 Solve the preceding problem for an element in plane stress subjected to stresses o, = 100 MPa,…

Q: If the given element is oriented at an angle of 25° with the x-axis, calculate the stresses acting…

A: Given: σx=110 MPaσy=90 MPaτxy=25 MPaθ=30°

Q: In a pure shear condition, the maximum value of shear stress is observed to be 20 ME element shown,…

Q: A rigid bar ABCD is supported by two bars as shown in Figure below. There is no strain in the…

A: Determine: a. The normal strain in bar (2). b. The normal strain in bar (2) if there is a 1 mm gap…

Q: The state of stress at a point is the result of two loadings as shown in figure. When acting alone,…

A: For the two loadings act simultaneouslythen resultant (absolute) share stress at that point with…

Q: The state of strain at the point has components of € = 300 (10-6), y = -260 (10-6), and Yay = 460…

Q: The state plane stress at a point is represented by the stress element below. Determine the stresses…

A: Radius of the circleR=(σx-σy2)2+τxy2R=(90+602)2+202R=77.62…

Q: A differential element on the bracket as shown in Figure Q1 is subjected to plane strain that has…

Concept explainers

Design of structures using FEA

An arrangement, in which various members are interconnected with their constrained relative motion, the whole arrangement is then known as a structure. The degree of freedom of such a structure is zero. In such a structure, the load can act throughout the length of the structure or at the joints.

Question

An element is subject to the following normal and shear strains:
Ex = -350 × 10-6
€y = 200 x 10-6
Yxy = 300 X 10-6
If the element were oriented at an angle of 15° counterclockwise:
a) Determine the normal and shear strains €¸', €', and Yx'y'.
b) The principal strains and the orientation upon which they act.
c) The maximum in-plane shear strain and the orientation upon which they act.

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: (a) Determination of normal strain

VIEW

Step 2: (b) Determination of principal strain

VIEW

Step 3: (c) Determination of maximum shear strain

VIEW

Step 4: orientation

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, civil-engineering and related others by exploring similar questions and additional content below.

Similar questions

10-2. The state of strain at the point on the pin leaf has components of € = 200(106), y = 180(106), and Y xy = -300(10-6). Use the strain transformation equations and determine the equivalent in-plane strains on an element oriented at an angle of 0 = 30° counterclockwise from the original position. Sketch the deformed element due to these strains within the x-y plane. X Prob. 10-2/3
9. The initially square element of a material is deformed as shown. Determine the shear strain of the element and the normal strains of the diagonals AC and BD. Undeformed Deformed A B D 2.0 mm 2.015 mm C 1.995 mm
The initially square element of a material is deformed as shown. Determine the shear strain of the element in radian and the normal strains in mm/mm of the diagonals AC and BD. B Undeformed Deformed C 1.997 mm D 2.003 mm 2.015 mm
4
PROBLEM 10-1 GIVEN: THE STATE OF STRAIN AT THE POINT ON THE PIN LEAF HAS COMPONENTS OF = 200(106), e,= 180(10), AND Yay = -300(10).; REQUIRED: USE THE MOHR'S CIRCLE AND DETERMINE THE EQUIVALENT IN-PLANE STRAINS ON AN ELEMENT ORIENTED AT AN ANGLE OF 8 - 30° COUNTER CLOCKWISE FROM THE ORIGINAL POSITION. SKETCH THE DEFORMED ELEMENT DUE TO THESE STRAINS WITHIN THE X-Y PLANE.
Solve using Mohr’s circle
M #1 3 ksi M # 2 6 ksi 9 ksi E FOR THE ELEMENT SHOWN, DETERMINE THE MAXIMUM NORMAL STRESS AND SHOW IT ON A PROPERLY ORIENTED ELEMENT, AND DETERMINE THE MAXIMUM SHEAR STRESS AND SHOW IT ON A PROPERLY ORIENTED ELEMENT.
The state of plane strain on the element is P x = -300(10-6), P y = 0, and gxy = 150(10-6). Determine the equivalent state of strain which represents (a) theprincipal strains, and (b) the maximum in-plane shear strain and the associated average normal strain. Specify the orientation of the corresponding elements for these states of strain with respect to the original element.
Principal stress: 01,2 Ox+0y tan20, = Txy 2 (Ox-0y)/2 2 maximum in-plane shear stress: Tmax *) : + Txy? tan20s -(0x-0y)/2 Ox+0y σανg Txy 2 The state of plane stress at a point is represented on the element shown in the figure below. (a) Determine the principal stresses acting on this point, and the corresponding orientation (angle). (b) Determine the maximum in-plane shear stress, and the corresponding orientation (angle). Also determine the associated average normal stress. Show your work. 57 MPa 28 MPa 42 MPa
0.01 in. - Undeformed Deformed 0.10 in. 0.004 in. FIG. P2.39 0.12 in.
Solve the required values using Mohr's Circle
X=75MPa Y=90MPa S=40MPa D=-10 Note: If the angle D is positive, then the shear stress is in the direction shown on the unit element figure; if it is a minus sign, then the shear stress is in theopposite direction shown on the unit element figure.