Short problems:1.1 Torsional stresses: without doing any calculation, sketch the shear stress distribution for a positive forque Tacting on a hollow circular section.1.2 Stress transformation: without doing any calculation, sketch the positive sign convention for normal and shearstresses on a infinitesimal material volume. Consider a plane state of stress σx, σy and Txy.1.3 Stress transformation: Without doing any calculation, sketch a Mohr's circle in which σ1>0, σ2<0. On the circleidentify the center point, and the radius. Show how the center and radius can be found from σx,y,Txy. Identify ageneric state of stress (σx>0 Txy>0) as point A on the circle, and show graphically the angles 20p1, 20 p2, and 20s.For problem 1.3, see sample below for a Mohr's circle with σ1>0, σ2>0ντιτ-TmaxTxyTmaxesR8ptepi02√σ(+)Osvg = 0x+59, R = √(x-5)² + Txy²

Step 1: to calculate shear stress distribution. Use the equation tau equals T times r divided by J ,…

Answered: Short problems: 1.1 Torsional stresses:…

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 state of plane stress at a point is represented by the element shown in Figure Q1. Construct a Mohr Cirele to determine a) the principal plane and the principle stresses, b) the maximum in-plane shear stress and the associated average normal stress, and c) the state of stress at the point on another element oriented 25° clockwise from the position shown. d) Show the orientation of the element stresses on an appropriate sketch for a), b) and c) 60 MPa 30 MPa 45 MPa Figure Q1
Q.2) A state of stress is specified as shown in Figure (2), By using Mohr's circle determine the normal and shearing stresses and their directions on: a- The principal planes? b- The planes of maximum shearing stress? c- The planes whose normals are at (+50°) and (+140°) with x-axis? show your results on complete sketches of differential elements. 80 MPa 50 MPa YA 40 MPa + 50 MPa, 80 MPa 40 MPa Figure (2)
Question 2 An element in plane stress is subjected to stresses dx = 100 MPa, oy = 34 MPa, and Txy = 28 MPa, as shown in Figure 2. Using Mohr's circle, determine: a) the stresses acting on an element oriented at an angle 0 = 40°, b) the principal stresses, and c) the maximum shear stresses. Show all results on sketches of properly oriented elements. V Oy = Figure 2 34 MPa Txy = 28 MPa Ox= 100 MPa X
The figure shows an element in bi-axial stress and the corresponding Mohr’s circle. Points A and B represents the stresses on the x face and on the y face of the element respectively. A. What is the value of the normal axial stress along x direction? B. What is the value of the normal axial stress along y direction? C. What is the value of the maximum shear stress?
The state of stress at a point with ox, oy, and txy as shown. Analyze the state of stress at the point using the Mohr's circle of stress. Determine the following a) Principal stress, b) Maximum in-plane shear stress and c) Normal stress on the plane defined by x' axis where the angle is 25 degrees. Ne To 0. ox x TEV
2. For the state of stress shown in the figure, determine normal and shearing stresses on the planes whose normal are at +60° and +150° with the x-axis. Show all results using Mohr's Circle diagram. 8 ksi 8 ksi 10 ksi
Determine the magnitude of the shear stress (in units of MPa) when the state of stress is oriented 45 degrees from the element shown (aligned with line AB).
Mohr's circle is shown for a point in a physical object that is subjected to plane stress. Each grid square is 11 MPa in size. (a) Determine the stresses Ox, Oy, and the magnitude of T,xyand show them on a stress element. (b) Determine the principal stresses and the magnitude of the maximum in-plane shear stress acting at the point and show these stresses on an appropriate sketch (e.g., see Figure 12.15 or Figure 12.16).
Question 1 The biaxial stress element of an isotropic and homogenous material is loaded as shown in figure 1 below. Y Oxz =185 MPa Ty = 3D 60 MPа 25° o =180 MPa yz Figure 1 (a) Determine the magnitudes, and senses of the direct and shear stresses which act on the inclined plane as shown in figure 1 using the First Principle method. (b) Using the standard formulae, determine for the element of stressed, homogeneous, isotropic material, shown in figure 1, the following: (i) The magnitudes of principal stresses and their associated planes relative to the x-axis for positive angles. The magnitudes of maximum shear stresses and their associated planes relative to the x-axis for positive angles. Magnitudes of direct and shear stresses acting on the inclined plane. (ii) (ii)
EXAM QUESTION 2 The state of plane stress at a point is represented by the element shown in the figure. (Assume E=210 GPa, v=0.3). Determine a) the principal stresses and the oriented angle associated with the direction of each principal stress using the transformation equations of plane stress; and b) the absolute maximum shear stress at the point according to this stress matrix. 50 MPa 50 MPa 50 MPa
The normal and shear stresses at a point in a structural subjected to a state of plane stress are shown in figure below. Determine using stress transformation equation or Mohr's circle. i) principal stresses and their directions. ii) maximum shearing stress and its direction. iii) stress on a plane making an angle of 30° anticlockwise from plane AD. [Ans: i) o1 = 33 MPa, o2 = -23 MPa, O, = 68°, ii) Tmax = 28 MPa, O, = 22.5°, iii) o = 12.5 MPa, Gy = -2.32 MPa, tay = 27.3 MPa] 25 N/mm? B 20 Nmm 30 15 Nmm?
3. The picture shows a triangular element, area AB is free surface, angle B=30°, request Stress component and the stress unit is MPa. AN* Ox. Txy Txy 40 B

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