5. Solve the following problemUsestress transformation formulas andMohr's circle•to determine the equivalent state of stress of an element atthe same point oriented 60 clockwise with respect to theelement shown. Sketch the results on the element.100 MPa75 MPa150 MPa

Step 1: Step 2: Step 3: Step 4:

Answered: 5. Solve the following problem Use…

Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

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1. The state of plane stress at a point is represented on the element shown in the figure below. Determine the state of stress at this point on another element oriented 27° clockwise from the position shown. 11 ksi 7 ksi
The State of stress at a point is shown with respect to the x-y axis. Determine the equivalent state of stress with respect to the x'-y' axis. Display the results on a sketch of an element aligned with the x'-y' axis. 8KSI 8KSI TOKSI Y' V Y X' 60° X 8KSI 10 KSI 8 KSI
90 MPa 55 MPa 70 MPa 70 MPa 55 MPa -90 MPa 65° The state of stress on an element relative to the xy-axis is presented above. The element is to be reoriented as shown. a) What are the components that describe its original state of stress (x, y, Txy) and what is the angle of rotation (0)? Make sure your signs are correct. b) Using the equations of stress transformation, determine x, y, and Txy and draw these components of stress on the rotated element. c) What are the principal stresses and angles of the principal planes? What is the shear stress associated with this orientation? d) What is the maximum in-plane shear stress and the angle of its associated plane? What are the associated normal stresses in this orientation? e) What is the absolute maximum shear stress and what plane (xy, xz, or yz) does this stress act upon?
Use the stress transformation equations to determine the state of stress for the element shown if it were oriented 60° clockwise. 100 MPa. 75 MPa 150 MPa
The biaxial stress system in an element is shown in the figure. Which of the following will give the normal stress in N/mm² in the plane BD making an angle of 45° with the plane BA? σ¸ = 40 N/mm² G₁ = 60 N/mm 111 = 40 N/mm B a. = 60 N/mm
An element in plane stress is subjected to stresses Ox, sigma y , and I xy (see figure). Using Mohr's circle , determine the stresses acting on an element oriented at an angle from the x axis . Show these stresses on a sketch of an element oriented at the angle Note : The angle positive when counterclockwise and negative when clockwise .) Given : sigma x =33 MPa, sigma y =-9 MPa, tau xy =29 MPa, theta=35^
The state of stress on an element relative to the xy-axis is presented above. The element is to be reoriented as shown. a) What are the components that describe its original state of stress (??, ??, ???) and what is the angle of rotation (?)? Make sure your signs are correct. b) Using the equations of stress transformation, determine ??′, ??′, and ??′?′ and draw these components of stress on the rotated element. c) What are the principal stresses and angles of the principal planes? What is the shear stress associated with this orientation? d) What is the maximum in-plane shear stress and the angle of its associated plane? What are the associated normal stresses in this orientation? e) What is the absolute maximum shear stress and what plane (xy, xz, or yz) does this stress act upon?
Q3) the state of plane stress at a point is represented by the element shown below. Determine state of stress at the point on another element oriented 30° e from the position shown and show these stresses properly on the rotated element. counterClock Wise 50 MPa 80 MPa (a) 25 MPa
T·r T (from torsion) = Tr4 J ="- (Solid rod) F Onormal = A o (from bending) M•y - (Solid rod) The solid rod shown in the figure below has diameter of 1.25 in. If it is subjected to the force of 60 lb, determine the state of stress at point A using the principle of superposition. Neglect the weight of the rod, and the stress due to the I %3D I 4 transverse shear force. 60 lb k-10 in.- 15 in. Front View -20 in. В
The state of strain on an element has components P x = -400(10-6), Py = 0, gxy = 150(10-6). Determine the equivalent state of strain on an element at the same point oriented 30° clockwise with respect to the original element.Sketch the results on this element.
The state of stress in a deformable body is shown in the figure. Consider transformation of the stress from the x-y coordinate system to the X-Y coordinate system. The angle 8, locating the X-axis, is assumed to be positive when measured from the x-axis in counter-clockwise direction. Y G₁ = 40 MPa 0xY Y 0 XY σ.. = 120 MPa = 50 MPa 30⁰ O = 35.6 MPa The absolute magnitude of the shear stress component Oxy (in MPa. round off to one decimal place) in x-y coordinate system is
The principal stresses in N/mm² on a rectangular element are shown in the below figure. The intensity of normal stress o, on the oblique plane BE is 400 N/mm D C 2 100 N/mm E 100 N/mm A 2 2 30 400 N/mm Sn B

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5. Solve the following problem Use stress transformation formulas and Mohr's circle • to determine the equivalent state of stress of an element at the same point oriented 60 clockwise with respect to the element shown. Sketch the results on the element. 100 MPa 75 MPa 150 MPa