I need detailed help solving this exercise from homework of Mechanics of Materials. I do not really understand, please do it step by step, not that long but clear. Thank you! 7.2-21 An element in plane stress from the frame ofa racing car is oriented at a known angle 0 (see fig-ure). On this inclined element, the normal and shearstresses have the magnitudes and directions shownin the figure.Determine the normal and shear stresses actingon an element whose sides are parallel to the xy axes,that is, determine σ,,,, and 7. Show the results ona sketch of an element oriented at 0 = 0°.ox,Txy'PROBLEM 7.2-2123 MPa15 MPaK90 MPa071 1010=36°no

Answered: 7.2-21 An element in plane stress from…

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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The stresses acting on element A in the web of a train rail are found to be ‘75 (MPa)’tension in the horizontal x-direction and ‘90 (MPa)’ compression in the verticaly-direction. Also, shear stresses of magnitude ‘40(MPa)’ act in the directions shown inthe figure.a) Draw Mohr’s circle for the state of stress.b) Determine the stresses (σx', σy' and τxy') acting on an element oriented at an angle‘D=-10 ˚’ from the horizontal. Show these stresses on a sketch of an elementoriented at this angle Note: If the angle D is positive, then the shear stress is in the direction shown onthe unit element figure; if it is a minus sign, then the shear stress is in theopposite direction shown on the unit element figure.
Q2) B) The steel rod having a diameter of 2Z mm is subjected to an internal moment of 4Y0 Nm as shown in Figure Q2(b). Take: Z =1 Y = 0 i) Determine the stress created at points A, B, and C. ii) Sketch a three-dimensional view of the stress distribution acting over the cross section. Note that moments of inertia for the circular area can be determined by I= (ar' )/ 4. y A B. M = 4Y0 Nm 45° Radius = 0.5(2Z) mm Figure Q2(b)
After being rotated through an angle 0, the stress elements σx and Tx'y' can be calculated by the inclined- plane method by letting the inclined plane be the y' axis. (Figure 2) Balancing the sums of the forces in the primed coordinate system yields two equations: 0x = 0x cos² 0 +σy sin² 0 + Txy (2 sin 0 cos 0) (σy -σx) sin cos 0 + Txy (cos² 0 - sin² 0) Tx'y' = Using the trigonometric identities Figure 6 of 6 Part D - Clockwise Rotation of a Stress Element with No Shear Stress The state of stress at a point in a member is shown on the rectangular stress element in (Figure 6) where the magnitudes of the stresses are |σx | = 29 ksi and |σy| = 26 ksi. Determine the state of stress on an element rotated such that the +x' axis is 20° below the -x axis of the original stress element. Express your answers, separated by commas, to three significant figures. ▸ View Available Hint(s) ΜΕ ΑΣΦ vec - σx =σy =,Tx'y' = 22.6, 19.6, 17.7 Submit Previous Answers στ × Incorrect; Try Again; 5 attempts…
Question-3 An element in pure shear is subjected to stresses - 16 MPa, as shown in the figure. Using Mohr's circle, determine (a) the stresses acting on an element oriented at a counterclockwise angle 0 = 20 from the x axis and (b) the principal stresses. Show all results on sketches of properly oriented elements. 16 MPa
The T-beam is subjected to distributed loading that is applied along its centerline. The state of stress at point B is shown in the element below. Determine: Part1: Using the relevant equations: a) The principal stresses at point B and show the results on an element with the orientation. b) The maximum shear stress at point B and show the results on an element with the orientation. Part2: Using Mohr's circle, draw the circle and determine: a) The principal stresses at point B and show the results on an element with the orientation. b) The maximum shear stress at point B and show the results on an element with the orientation. 12 kN/m 150 mm A A 20 mm 150 mm 50 mm 2 m +1m+ 2 m 20 mm B 195.6 MPa 6.7 MPa
Please answer with complete free diagrams, etc..
8 Expansion is an axial deformation. 9 True 10 False The coordinates of centroid locate the ge ometric center of the cross-section of the material.( True False Torsional stress is also known as bending stress.( True False
Q1: The state of stress at a point in a member is shown on the element in Figure (1). Determine the following: 1) The stress components acting on the inclined plane AB (o, and tx'y'). 2) The principal normal stresses (p1.op2) and max in-plane shear stress (Tmax). Do not calculate the angles of the planes of the principal stresses. Solve the problem using the equations. 8 ksi 2 ksi Figure (1) 60 B 5 ksi
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
: For the given state of stress, determine (a) the maximum principle stress (b) the maximum shearing stress (c) the angles Op and 0, (d) represent all results by Mohr's circle. ( P s (20)(7-5) 69 90 MPa 30 MPa 60 MPa t: -30 Oye.do 0x=90
Problem example Example 7-5: The state of plane stress at a point with respect to the xy- axes is shown in the figure. Using Mohr's circle, determine (a) The principal stresses and principal planes and sketch the results. (b) The maximum shear stress. (c) The state of stress with respect to the x'y'-axes. 20 MPa (+) A 16 MPa 50° X 40 MPa (+) 1. Omax 3. Op 7-42
tate of Stress Caused by Combined Loadings Learning Goal: To use the superposition principle to find the state of stress on a beam under multiple loadings. The beam shown below is subjected to a horizontal force P via the rope wound around the pulley. The state of stress at point A is to be determined. 100 mm 15 mm 20 mm 200 mm 150 mm f 20 mm The dimensions are di - 2.15 m. d₂ = 0.5 m. -0.85 m d-285 mm and r= 150 mm The applied force has magnitude P=4.5 kN Part A-Support Reactions and Internal Loading C₁, C₂=₁ N=, V = ₁ M = Determine the support reactions C, and C, and the internal normal force, shear force, and moment on the cross-section containing point A. Express your answers, separated by commas, to three significant figures. ► View Available Hint(s) Submit Part B- Properties of the Cross-Section A= I= Q = Submit VAX IT VOC JA=.TA= What are the cross-sectional area, moment of inertia with respect to the neutral axis, and first moment of the area with respect to point A for the…

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