Problem 4: The state of stress at a particular point in a structure is given below. 10 20 0 ¹-[20 = 20 -10√2 MPa 0 -10√2 10/27/1 [o] (a) Write the characteristic equation (cubic equation) that would be used to determine the principal stresses. (b) Without solving the characteristic equation, verify that one of the principal stresses is Op = 30 MPa. Find its corresponding principal direction (i.e., find its direction cosines). (c) Determine the other principal stresses and their corresponding principal directions. (d) Determine the maximum shear stress.

Question 1 The cube in Figure Ql made of 200 mm sides of a certain material is subjected to a volumetric stress of 50 N/mm?. Determine the change in its volume if the Bulk modulus of the material is 100x10° N/mm?. 200 mm Figure Q1: Cube subjected to volumetric stress

Learning Goal: A material is homogenous and isotropic when it has a modulus of elasticity that does not vary with direction and it has uniform properties throughout. When a point in a material is subjected to only normal stresses in three dimensions, but they are not necessarily equal, the state is called triaxial stress. When the response of the material is linear elastic, the strains along the three axes can be calculated using a generalized form of Hooke's law. Each strain depends on all three stresses because of the Poisson effect. €1 Figure 1 [0₂ - V (O₂ +0₂)] a 1 of 1 A cube is subjected to stresses with magnitudes a = 16 MPa, b = 26 MPa, and c = 5 MPa (Figure 1). What is the strain in the y-direction? Let E = 200 GPa and v= 0.26. Express your answer to three significant figures. ► View Available Hint(s) Submit VE ΑΣΦ Part B - Change in volume f change in volume = vec The cube from Part A originally has side length 3.2 cm . What is the change in volume of the cube under the given…

q1 b In 2D XY-plane-stress analysis, how many stress components you need to calculate.Please write/show their names in XY plane on a plane element.

SECTION B- STRUCTURES-DR LARISA MALYSHEVA QB1 DIRECT STRESS Two round solid bars of different materials are connected (in parallel) and have a common tensile force, P, of 190 kN is applied,ras shown in Figure QB1. For each bar, determine the: a) b) Stress. Strain and Strain in the diameter. Use the following information. Clearly show all your derivations. The original length of each bar = 1.7m. %3D Steel Bar: 32mm Dia. Poisson's Ratio = 0.31 18mm Dia. Young's Modulus = 210 GPa %3D Steel Aluminium Bar Bar Common Connection Aluminium Bar: P = 190 kN Poisson's Ratio = 0.34 Young's Modulus = 68 GPa Fig QB1