The most common stress-strain relationship encountered in engineering is the equation for a linear elastic material, which is defined by Ο σ = Εε 6= OT τ = Εδ 08: = Eε Ο σ = Εδ O o = Ey
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- a L₁ C 3 of 6 > Determine the orientation of the planes maximum and minimum normal stress, ₂1 and ₂2. respectively. Use the value for 8,2 that is negative. Then use this value to determine the value of 8,1. Express your answers to four significant figures separated by a comma. ► View Available Hint(s) VAΣo↓ vec ? 8p1, 8p2= Submit Part B - In-plane principal stresses Determine the in-plane principal stresses for the element (as oriented in Part A), and calculate 01 and 2 such that they correspond with 81 and 8,2. Express your answers to four significant figures separated by a comma. ► View Available Hint(s) IVE ΑΣΦ vec ? 5 O1) The state of plane stress at a point is shown on the element in Figure. Determine the maximum in-plane shear stress at this point. B 50 MPa ox Ox= -80 MPa = +50 MPa Oy Txy = -25 MPa 80 MPa 80 MPa A 25 MPa Ľ 50 MPaThe state of stress at a certain point in a stressed body is as shown in the figure. Normal stress in x-direction is 80 MPa (Tensile) and in y-direction is 40 MPa (Compressive). The radius of the Mohr's circle for this state of stress will be O, = 40 MPa O, = 80 MPa + Ox = 80 MPa Oy = 40 MPa (а) 60 MPа (b) 40 MPa (c) 20 MPa (d) 10 MPa
- The major and minor principal strains in a 2D stressed element are 70μ and -25µ respectively. If the normal strain at a plane is given as 15µ, then what will be the normal strain on a plane perpendicular to it? A B d C D 40μ 30μ 25μ 20μox The state of stress at a given point in a material component is = 120 MPa; Oy = - 80 MPa and t = 60 MPa The loading on the component is increased so that stresses are increased to values which are k times the given values. Determine the maximum value of k if the material can withstand maximum normal and shear stresses of 300 MPa and 200 MPa respectively. 1 11The 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
- A steel section having a cross section of 20 mm x 30 mm is subjected to an axial force of 240 kN. The steel section has produces a strain of 0.002. If it has a value of Poisson's ratio of 0.30. Which of the following gives the bulk modulus of the steel section. a. 133333 MPa b. 166667 MPa c. 111111 MPa d. 144444 MPaThe thin bar is subjected to an increase in temperature along its axis. Determine the end B of the bar due to the increase in temperature y; b) the average normal strain in the bar.The normal strain is 70X10^(-2) z^1/3, where z is expressed in meters. L = 300 mm.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 0, locating the X-axis is assumed to be positive when measured from the x-axis in counter-clockwise direction y = 120 MPa 40 MPa Oxy 50 MPa %3D 30% Oyy = 35.6 MPa The absolute magnitude of the shear stress component o,xy (in MPa, round off to one decimal nlace) in x-y coordinate system is
- 2. For the state of stress shown, determine the range of value of for which the normal is equal to or less than 100 MPa and 50 MPa. stress x' + 90 MPa 60 MPa =Problems: Stress (ksi) 53.2 1. Determine the ductility (u) of the material based on the stress- strain diagram (problem S5.1). 43.6 37.1 0.0013 0.0063 0.163 0.247 Strain (in/in)Q 2: The state of stress at a point is characterized by the components: Ox Txy Txz [12 3 Tyx Oy Tyz = 4 [Tzx Tzy Oz 0 10. Find the values of the principal stresses and their directions?